make style

revert make file
fix style
2021-09-13 10:51:52 -07:00 · 2021-09-13 18:42:10 +03:00 · 2021-09-13 18:41:43 +03:00 · 2021-09-13 11:39:22 +03:00 · 2021-09-13 11:34:44 +03:00 · 2021-09-03 11:59:51 +03:00
285 changed files with 22575 additions and 7174 deletions
@@ -47,26 +47,36 @@ jobs:
    strategy:
      matrix:
        os: [ubuntu-18.04, macos-10.15]
-        target: [debug, optim]
-        mpi: [sequential, parallel]
+        target: [dbg, opt]
+        mpi: [seq, par]
        build-system: [make]
-        # 'include' allows us to
-        # - add a variable without creating a new matrix dimension.
-        # - add a new combination ('build-system: cmake' case here)
+        hypre-target: [int32]
+        # 'include' allows us to:
+        # - Add a variable to all jobs without creating a new matrix dimension.
+        #   Codecov is defined that way.
+        # - Add a new combination.
+        #   'build-system: cmake' and 'hypre-target: int64'
        #
        # note: we will gather coverage info for any non-debug run except the
        # CMake build.
        include:
-          - target: debug
+          - target: dbg
            codecov: NO
-          - target: optim
+          - target: opt
            codecov: YES
          - os: ubuntu-18.04
-            target: optim
+            target: opt
            codecov: NO
-            mpi: parallel
+            mpi: par
            build-system: cmake
-    name: ${{ matrix.os }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.build-system }}
+            hypre-target: int32
+          - os: ubuntu-18.04
+            target: opt
+            codecov: NO
+            mpi: par
+            build-system: make
+            hypre-target: int64
+    name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}

    runs-on: ${{ matrix.os }}

@@ -92,7 +102,7 @@ jobs:
    # TODO: It would be nice to have only one step, e.g. with a dedicated
    # action, but I (@adrienbernede) don't see how at the moment.
    - name: get MPI (Linux)
-      if: matrix.mpi == 'parallel' && matrix.os == 'ubuntu-18.04'
+      if: matrix.mpi == 'par' && matrix.os == 'ubuntu-18.04'
      run: |
        sudo apt-get install mpich libmpich-dev
        export MAKE_CXX_FLAG="MPICXX=mpic++"
@@ -103,11 +113,11 @@ jobs:
        sudo apt-get install lcov

    - name: Set up Homebrew
-      if: ( matrix.mpi == 'parallel' || matrix.codecov == 'YES' ) && matrix.os == 'macos-10.15'
+      if: ( matrix.mpi == 'par' || matrix.codecov == 'YES' ) && matrix.os == 'macos-10.15'
      uses: Homebrew/actions/setup-homebrew@c4aafe8c4620bf08883dd4679c374f11e73329d3

    - name: get MPI (MacOS)
-      if: matrix.mpi == 'parallel' && matrix.os == 'macos-10.15'
+      if: matrix.mpi == 'par' && matrix.os == 'macos-10.15'
      run: |
        export HOMEBREW_NO_INSTALL_CLEANUP=1
        brew install openmpi
@@ -123,39 +133,40 @@ jobs:
    # Install will only run on cache miss.
    - name: cache hypre
      id: hypre-cache
-      if: matrix.mpi == 'parallel'
+      if: matrix.mpi == 'par'
      uses: actions/cache@v2
      with:
        path: ${{ env.HYPRE_TOP_DIR }}
-        key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-v2
+        key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-${{ matrix.hypre-target }}-v2.0

    - name: get hypre
-      if: matrix.mpi == 'parallel' && steps.hypre-cache.outputs.cache-hit != 'true'
-      uses: mfem/github-actions/build-hypre@v1.0
+      if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true'
+      uses: mfem/github-actions/build-hypre@v2.0
      with:
-        hypre-archive: ${{ env.HYPRE_ARCHIVE }}
-        hypre-dir: ${{ env.HYPRE_TOP_DIR }}
+        archive: ${{ env.HYPRE_ARCHIVE }}
+        dir: ${{ env.HYPRE_TOP_DIR }}
+        target: ${{ matrix.hypre-target }}

    # Get Metis through cache, or build it.
    # Install will only run on cache miss.
    - name: cache metis
      id: metis-cache
-      if: matrix.mpi == 'parallel'
+      if: matrix.mpi == 'par'
      uses: actions/cache@v2
      with:
        path: ${{ env.METIS_TOP_DIR }}
-        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2
+        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.0

    - name: install metis
-      if: matrix.mpi == 'parallel' && steps.metis-cache.outputs.cache-hit != 'true'
-      uses: mfem/github-actions/build-metis@v1.0
+      if: matrix.mpi == 'par' && steps.metis-cache.outputs.cache-hit != 'true'
+      uses: mfem/github-actions/build-metis@v2.0
      with:
-        metis-archive: ${{ env.METIS_ARCHIVE }}
-        metis-dir: ${{ env.METIS_TOP_DIR }}
+        archive: ${{ env.METIS_ARCHIVE }}
+        dir: ${{ env.METIS_TOP_DIR }}

    # MFEM build and test
    - name: build
-      uses: mfem/github-actions/build-mfem@v1.0
+      uses: mfem/github-actions/build-mfem@v2.0
      with:
        os: ${{ matrix.os }}
        target: ${{ matrix.target }}
@@ -168,17 +179,17 @@ jobs:

    # Run checks (and only checks) on debug targets
    - name: checks
-      if: matrix.build-system == 'make' && matrix.target == 'debug'
+      if: matrix.build-system == 'make' && matrix.target == 'dbg'
      run: |
        cd ${{ env.MFEM_TOP_DIR }}  && make check

    - name: unit tests
-      if: matrix.build-system == 'make' && matrix.target == 'optim'
+      if: matrix.build-system == 'make' && matrix.target == 'opt'
      run: |
        cd ${{ env.MFEM_TOP_DIR }} && make unittest

    - name: tests
-      if: matrix.build-system == 'make' && matrix.target == 'optim'
+      if: matrix.build-system == 'make' && matrix.target == 'opt'
      run: |
        cd ${{ env.MFEM_TOP_DIR }} && make test

@@ -190,8 +201,8 @@ jobs:
    # Code coverage (process and upload reports)
    - name: codecov
      if: matrix.codecov == 'YES'
-      uses: mfem/github-actions/upload-coverage@v1.0
+      uses: mfem/github-actions/upload-coverage@v2.0
      with:
-        name: ${{ matrix.os }}-${{ matrix.mpi }}
+        name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}
        project_dir: ${{ env.MFEM_TOP_DIR }}
        directories: "fem general linalg mesh"
@@ -53,32 +53,33 @@ jobs:
      uses: actions/cache@v2
      with:
        path: ${{ env.HYPRE_TOP_DIR }}
-        key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-v2
+        key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-v2.0

    - name: Get Hypre
      if: steps.hypre-cache.outputs.cache-hit != 'true'
-      uses: mfem/github-actions/build-hypre@master
+      uses: mfem/github-actions/build-hypre@v2.0
      with:
-        hypre-archive: ${{ env.HYPRE_ARCHIVE }}
-        hypre-dir: ${{ env.HYPRE_TOP_DIR }}
+        archive: ${{ env.HYPRE_ARCHIVE }}
+        dir: ${{ env.HYPRE_TOP_DIR }}
+        target: int32

    - name: Cache Metis Install
      id: metis-cache
      uses: actions/cache@v2
      with:
        path: ${{ env.METIS_TOP_DIR }}
-        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2
+        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.0

    - name: Install Metis
      if: steps.metis-cache.outputs.cache-hit != 'true'
-      uses: mfem/github-actions/build-metis@master
+      uses: mfem/github-actions/build-metis@v2.0
      with:
-        metis-archive: ${{ env.METIS_ARCHIVE }}
-        metis-dir: ${{ env.METIS_TOP_DIR }}
+        archive: ${{ env.METIS_ARCHIVE }}
+        dir: ${{ env.METIS_TOP_DIR }}

    # MFEM build and test
    - name: build-mfem
-      uses: mfem/github-actions/build-mfem@master
+      uses: mfem/github-actions/build-mfem@v2.0
      with:
        os: ${{ runner.os }}
        target: optim
@@ -16,10 +16,6 @@ permissions:

 on:
  push:
-    branches:
-      - master
-      - next
-  pull_request:

 jobs:
  file-headers-check:
@@ -32,49 +28,24 @@ jobs:
        access_token: ${{ github.token }}
    - name: checkout mfem
      uses: actions/checkout@v2
-      with:
-        path: mfem

    - name: copyright check
      id: copyright
      run: |
-        cd mfem
-        if git grep -l "^\(#\|//\).*\(\-2020\|\ 2010,\)" > matches.txt
-        then
-          echo "Please update the following files to Copyright (c) 2010-2021:"
-          cat matches.txt
-          exit 1
-        else
-          echo "No outdated copyright found."
-        fi
+        ./config/githooks/pre-push --copyright
+
      continue-on-error: true

    - name: license check
      id: license
      run: |
-        cd mfem
-        if git grep -li "^\(#\|//\).*GNU\ Lesser\ General\ Public\ License" > matches.txt
-        then
-          echo "Please update the following files to the BSD-3 license:"
-          cat matches.txt
-          exit 1
-        else
-          echo "No GNU GPL license found."
-        fi
+        ./config/githooks/pre-push --license
      continue-on-error: true

    - name: release check
      id: release
      run: |
-        cd mfem
-        if git grep -l "^\(#\|//\).*LLNL\-CODE\-443211" > matches.txt
-        then
-          echo "Please update the following files to LLNL-CODE-806117:"
-          cat matches.txt
-          exit 1
-        else
-          echo "No outdated release number found."
-        fi
+        ./config/githooks/pre-push --release
      continue-on-error: true

    - name: wrap-up
@@ -104,8 +75,7 @@ jobs:

    - name: style check
      run: |
-        cd tests/scripts
-        ./runtest code-style
+        ./config/githooks/pre-push --style

  documentation:
    runs-on: ubuntu-18.04
@@ -137,5 +107,4 @@ jobs:
      run: |
        git fetch origin master:master
        git checkout -b gh-actions-branch-history
-        cd tests/scripts
-        ./runtest branch-history
+        ./config/githooks/pre-push --history
@@ -26,6 +26,7 @@ CMakeFiles/
 config/_config.hpp
 config/config.mk
 config/sample-runs-build.log
+config/user.mk
 doc/CodeDocumentation.conf
 doc/CodeDocumentation.html
 doc/CodeDocumentation
@@ -248,6 +249,10 @@ miniapps/performance/sol.*

 miniapps/shifted/distance
 miniapps/shifted/ParaViewDistance
+miniapps/shifted/diffusion
+miniapps/shifted/diffusion.mesh
+miniapps/shifted/diffusion.gf
+miniapps/shifted/ParaViewDiffusion

 miniapps/tools/display-basis
 miniapps/tools/load-dc
@@ -292,6 +297,7 @@ tests/unit/psedov_tests_*
 tests/unit/tmop_pa_tests_*
 tests/unit/ptmop_pa_tests_*
 tests/unit/ceed_tests
+tests/unit/debug_device_tests

 # Test script output
 tests/scripts/*.err
@@ -40,43 +40,67 @@
 # Directory used to place artifacts.

 variables:
-  BUILD_ROOT: ${CI_BUILDS_DIR}/${CI_PROJECT_NAME}_${CI_COMMIT_REF_SLUG}_${CI_PIPELINE_ID}
+  BUILD_ROOT: ${CI_BUILDS_DIR}/MFEM/${CI_PROJECT_NAME}_${CI_COMMIT_REF_SLUG}_${CI_PIPELINE_ID}
+  AUTOTEST_ROOT: ${CI_BUILDS_DIR}/MFEM
  REBASELINE: "NO"
+  AUTOTEST: "NO"
  ALLOC_NAME: ${CI_PROJECT_NAME}_ci_${CI_PIPELINE_ID}
  TPLS_REPO: ssh://git@mybitbucket.llnl.gov:7999/mfem/tpls.git
  TESTS_REPO: ssh://git@mybitbucket.llnl.gov:7999/mfem/tests.git
+  AUTOTEST_REPO: ssh://git@mybitbucket.llnl.gov:7999/mfem/autotest.git
+  MFEM_DATA_REPO: https://github.com/mfem/data.git
  ARTIFACTS_DIR: artifacts
+  SLURM_OVERLAP: 1

-# The pipeline is divided into stages. Usually, these are also synchronization
-# points, however, we use "needs" keyword to express the DAG of jobs for more
-# efficiency.
-# - We use setup phase to download content outside of mfem directory.
+# The pipeline is divided into stages. Usually, jobs in a given stage wait for
+# the preceding stages to complete before to start. However, we sometimes use
+# the "needs" keyword and express the DAG of jobs for more efficiency.
+# - We use setup and setup_baseline phases to download content outside of mfem
+#   directory.
 # - Allocate/Release is where quartz resources are allocated/released once for all.
 # - Build and Test is where we build and MFEM for multiple toolchains.
 # - Baseline_checks gathers baseline-type test suites execution
 # - Baseline_publish, only available on master, allows to update baseline
 #   results
 stages:
+  - setup
  - q_allocate_resources
  - q_build_and_test
  - q_release_resources
  - l_build_and_test
  - c_build_and_test
-  - setup
+  - setup_baseline
  - baseline_check
+  - baseline_to_autotest
  - baseline_publish

-# The setup job in setup stage don't rely on MFEM git repo. It prepares a
-# pipeline-wide working directory downloading/updating external repos.
-# TODO: updating tests and tpls is not necessary anymore since pipelines are
-# now using unique directories so repo are never shared with another pipeline.
-# This is not memory efficient (we keep a lot of data), hence this reminder.
-# Setup
+# setup clones the mfem/data repo in ${BUILD_ROOT}. The build_and_test script
+# then symlinks the repo to the parent directory of the MFEM source directory.
+# Unit tests that depend on the mfem/data repo will then detect that this
+# directory is present and be enabled.
 setup:
  tags:
    - shell
    - quartz
  stage: setup
+  variables:
+    GIT_STRATEGY: none
+  script:
+    - mkdir -p ${BUILD_ROOT} && cd ${BUILD_ROOT}
+    - if [ ! -d data ]; then git clone ${MFEM_DATA_REPO}; fi
+
+# The setup_baseline job in setup stage_baseline doesn't rely on MFEM git repo.
+# It prepares a pipeline-wide working directory downloading/updating external
+# repos. TODO: updating tests and tpls is not necessary anymore since pipelines
+# are now using unique directories so repo are never shared with another
+# pipeline. This is not memory efficient (we keep a lot of data), hence this
+# reminder.
+# Note: This job can start immediately.
+setup_baseline:
+  tags:
+    - shell
+    - quartz
+  stage: setup_baseline
  variables:
    GIT_STRATEGY: none
  script:
@@ -85,6 +109,9 @@ setup:
    - if [ ! -d "tests" ]; then git clone ${TESTS_REPO}; fi
    - cd tpls && git pull && cd ..
    - cd tests && git pull && cd ..
+    - cd ${AUTOTEST_ROOT}
+    - if [ ! -d "autotest" ]; then git clone ${AUTOTEST_REPO}; fi
+    - cd autotest && git pull && cd ..
  needs: []

 .build_toss_3_x86_64_ib_script:
@@ -99,10 +126,10 @@ setup:
  script:
    - srun -p mi60 -t 15 -N 1 tests/gitlab/build_and_test

-# Lassen uses a different job scheduler (spectrum lsf) that does not
-# allow pre-allocation the same way slurm does.
-# We use pdebug queue on lassen to speed-up the allocation.
-# However this would not be scalable to multiple builds.
+# Lassen uses a different job scheduler (spectrum lsf) that does not allow
+# pre-allocation the same way slurm does.  We use pdebug queue on lassen to
+# speed-up the allocation.  However this would not be scalable to multiple
+# builds.
 .build_blueos_3_ppc64le_ib_script:
  script:
    - lalloc 1 -W 30 -q pdebug tests/gitlab/build_and_test
@@ -111,16 +138,10 @@ setup:
 # differentiates between the two tests.
 .baseline_script: &baseline_script |
  # locals
-  _glob_out=${BASELINE_TEST}.out
  _glob_err=${BASELINE_TEST}.err
  _base_diff=${BASELINE_TEST}-${SYS_TYPE}.diff
  _base_patch=${BASELINE_TEST}-${SYS_TYPE}.patch
  _base_out=${BASELINE_TEST}-${SYS_TYPE}.out
-
-  _out=${BASELINE_TEST}-${SYS_TYPE}.out
-  _ref=../${BASELINE_TEST}-${SYS_TYPE}.saved
-  _out_txt=${BASELINE_TEST}.txt
-  _diff=${BASELINE_TEST}-diff.txt
  # prepare
  cd ${BUILD_ROOT}
  ln -snf ${CI_PROJECT_DIR} mfem
@@ -135,7 +156,7 @@ setup:
    echo "ERROR during ${BASELINE_TEST} execution";
    echo "Here is the ${_glob_err} file content";
    cat ${_glob_err}
-    cp ${_glob_err} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_glob_err}.txt
+    cp ${_glob_err} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_glob_err}
    exit 1;
  elif [[ ! -f ${_base_patch} && ! -f ${_base_out} ]]
  then
@@ -145,18 +166,20 @@ setup:
  elif [[ -f ${_base_patch} ]]
  then
    echo "${BASELINE_TEST}: Differences found, patch generated"
-    cp ${_base_patch} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_base_patch}.txt
+    cp ${_base_patch} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_base_patch}
  elif [[ -f ${_base_out} ]]
  then
    echo "${BASELINE_TEST}: Differences found, replacement file generated"
-    cp ${_base_out} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_base_out}.txt
+    cp ${_base_out} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_base_out}
  fi
  # _base_diff won't even exist if there is no difference.
  if [[ -f ${_base_diff} ]]
  then
    echo "${BASELINE_TEST}: Relevant differences (filtered diff) ..."
    cat ${_base_diff}
-    cp ${_base_diff} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_base_diff}.txt
+    cp ${_base_diff} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/${_base_diff}
+    # We create a .err file, because that's how we signal that there was a diff.
+    cp ${_base_diff} ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/gitlab-${BASELINE_TEST}-${SYS_TYPE}.err
  fi
  if [[ ! -s ${_base_diff} ]]
  then
@@ -195,7 +218,7 @@ setup:
      - ${ARTIFACTS_DIR}
  allow_failure: true

-# This job can only be manually triggers on a pipeline for master branch, or if
+# This job can only be manually triggered on a pipeline for master branch, or if
 # the pipeline was triggered with REBASELINE="YES"
 .rebaseline_mfem:
  stage: baseline_publish
@@ -208,19 +231,18 @@ setup:
    - export DIFF_FILE=${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/baseline-${SYS_TYPE}.diff
    - cd ${BUILD_ROOT}/tests
    - |
-      if [[ ! -f "${DIFF_FILE}.txt" ]]
+      if [[ ! -f "${DIFF_FILE}" ]]
      then
          echo "Nothing to be done: no relevant change in baseline"
          exit 0
-      elif [[ -f "${PATCH_FILE}.txt" ]]
+      elif [[ -f "${PATCH_FILE}" ]]
      then
-          mv ${PATCH_FILE}.txt ${PATCH_FILE}
          patch "./baseline-${SYS_TYPE}.saved" < "${PATCH_FILE}"
-      elif [[ -f "${FULL_FILE}.txt" ]]
+      elif [[ -f "${FULL_FILE}t" ]]
      then
-          cp "${FULL_FILE}.txt" "./baseline-${SYS_TYPE}.saved"
+          cp "${FULL_FILE}" "./baseline-${SYS_TYPE}.saved"
      else
-          echo "File missing: expected ${PATCH_FILE}.txt or ${FULL_FILE}.txt"
+          echo "File missing: expected ${PATCH_FILE} or ${FULL_FILE}"
          exit 1
      fi
    - git add baseline-${SYS_TYPE}.saved
@@ -22,12 +22,13 @@

 # Spack helped builds
 # Generic lassen build job, extending build script
+# Note: Lassen jobs can start as soon as the setup job is complete.
 .build_and_test_on_lassen:
  extends: [.build_blueos_3_ppc64le_ib_script, .on_lassen]
  stage: l_build_and_test
-  needs: []
+  needs: [setup]

 opt_mpi_cuda_xl_16_1_1_8:
  variables:
-    SPEC: "%xl@16.1.1.8 +mpi +cuda cuda_arch=sm_70"
+    SPEC: "%xl@16.1.1.8 +mpi +cuda cuda_arch=70"
  extends: .build_and_test_on_lassen
@@ -16,12 +16,39 @@
    - shell
    - quartz
  rules:
-    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_QUARTZ == "OFF"' #run except if ...
+    # Don't run quartz jobs if...
+    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_QUARTZ == "OFF"'
      when: never
+    # Don't run autotest update if...
+    - if: '$CI_JOB_NAME =~ /update_autotest/ && $AUTOTEST != "YES"'
+      when: never
+    # Don't run autotest update if...
+    - if: '$CI_JOB_NAME =~ /q_report/ && $AUTOTEST != "YES"'
+      when: never
+    # Report success on success status
+    - if: '$CI_JOB_NAME =~ /q_report_success/ && $AUTOTEST == "YES"'
+      when: on_success
+    # Report failure on failure status
+    - if: '$CI_JOB_NAME =~ /q_report_failure/ && $AUTOTEST == "YES"'
+      when: on_failure
+    # Always release resources
    - if: '$CI_JOB_NAME =~ /release_resources/'
      when: always
+    # Default is to run if previous stage succeeded
    - when: on_success

+# This is a yaml anchor, it can be used to avoid duplication like here.
+# The code below will simply be pasted wherever the anchor is placed.
+.safe_create_rundir: &safe_create_rundir |
+  if ! mkdir ${rundir}; then
+    n=1
+    while ! mkdir ${rundir}_${n}
+    do
+      n=$((n+1))
+    done
+    rundir=${rundir}_${n}
+  fi
+
 # Allocate
 q_allocate_resources:
  variables:
@@ -42,6 +69,40 @@ q_release_resources:
    - export JOBID=$(squeue -h --name=${ALLOC_NAME} --format=%A)
    - ([[ -n "${JOBID}" ]] && scancel ${JOBID})

+# Release
+q_report_success:
+  variables:
+    GIT_STRATEGY: none
+  extends: .on_quartz
+  stage: q_release_resources
+  script:
+    - echo "Can only run if all the quartz jobs passed"
+    - cd ${AUTOTEST_ROOT}/autotest && git pull
+    - rundir="gitlab/$(date +%Y-%m-%d)-github-${CI_COMMIT_REF_SLUG}"
+    - *safe_create_rundir
+    - echo "The Quartz jobs were successful" > ${rundir}/gitlab.out
+    - echo "See the pipeline here -> $CI_PIPELINE_URL" >> ${rundir}/gitlab.err
+    - git add ${rundir}
+    - git commit -am "Gitlab CI log for baseline on quartz with intel ($(date +%Y-%m-%d))"
+    - git push origin master
+
+q_report_failure:
+  variables:
+    GIT_STRATEGY: none
+  extends: .on_quartz
+  stage: q_release_resources
+  script:
+    - echo "Runs if there was at least one failure on quartz"
+    - cd ${AUTOTEST_ROOT}/autotest && git pull
+    - rundir="gitlab/$(date +%Y-%m-%d)-github-${CI_COMMIT_REF_SLUG}"
+    - *safe_create_rundir
+    - echo "There was an error while running CI on Quartz" > ${rundir}/gitlab.err
+    - echo "See the pipeline here -> $CI_PIPELINE_URL" >> ${rundir}/gitlab.err
+    - cp ${rundir}/gitlab.err ${rundir}/autotest-email.html
+    - git add ${rundir}
+    - git commit -am "Gitlab CI log for baseline on quartz with intel ($(date +%Y-%m-%d))"
+    - git push origin master
+
 # Spack helped builds
 # Generic quartz build job, extending build script
 .build_and_test_on_quartz:
@@ -89,10 +150,34 @@ opt_par_gcc_6_1_0_pumi:
    SPEC: "%gcc@6.1.0 +pumi"
  extends: .build_and_test_on_quartz

-# Baseline
+# Baseline jobs form an independent set of jobs. We use `needs:[]` to specify
+# that "setup-baseline" can start immediately. Then, we have to use needs for
+# each one of the baseline jobs, otherwise they will wait for the rest of the
+# pipeline.
+
 baselinecheck_mfem_intel_quartz:
  extends: [.baselinecheck_mfem, .on_quartz]
-  needs: [setup]
+  needs: [setup_baseline]
+
+update_autotest:
+  extends: [.on_quartz]
+  needs: [baselinecheck_mfem_intel_quartz]
+  stage: baseline_to_autotest
+  script:
+    - cd ${AUTOTEST_ROOT}/autotest && git pull
+    - rundir="quartz/$(date +%Y-%m-%d)-github-${CI_COMMIT_REF_SLUG}"
+    - *safe_create_rundir
+    - cp ${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/* ${rundir}
+    # We create an autotest-email.html file, because that's how we signal that there was a diff (temporary).
+    - |
+      if [[ -f ${rundir}/*.err ]]
+      then
+        echo "See the pipeline here -> $CI_PIPELINE_URL" >> ${rundir}/*.err
+        cp ${rundir}/*.err ${rundir}/autotest-email.html
+      fi
+    - git add ${rundir}
+    - git commit -am "Gitlab CI log for baseline on quartz with intel ($(date +%Y-%m-%d))"
+    - git push origin master

 baselinepublish_mfem_quartz:
  extends: [.on_quartz, .rebaseline_mfem]
@@ -1,469 +0,0 @@
-# Copyright (c) 2010-2021, 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.
-
-language: cpp
-
-os: linux
-dist: bionic
-
-stages:
-  - checks
-  - tests
-  - optional
-
-env:
-  global:
-    - HYPRE_ARCHIVE=v2.19.0.tar.gz
-      HYPRE_URL=https://github.com/hypre-space/hypre/archive/$HYPRE_ARCHIVE
-      HYPRE_TOP_DIR=hypre-2.19.0
-
-jobs:
-  include:
-
-    # ========================
-    #         Checks
-    # ========================
-    # - code-style
-    # - documentation
-    # - gitignore
-
-    - stage: checks
-      os: linux
-      dist: xenial
-      name: "code-style"
-      addons:
-        apt:
-          packages:
-            - astyle=2.05.1-0ubuntu1
-      script:
-        - cd ${TRAVIS_BUILD_DIR}
-        - cd tests/scripts
-        - ./runtest code-style
-
-    - stage: checks
-      os: linux
-      name: "documentation"
-      addons:
-        apt:
-          packages:
-            - doxygen
-            - graphviz
-      script:
-        - cd ${TRAVIS_BUILD_DIR}
-        - cd tests/scripts
-        - ./runtest documentation
-
-    - stage: checks
-      os: linux
-      name: "gitignore"
-      addons:
-        apt:
-          packages:
-            - mpich
-            - libmpich-dev
-      env: MPI=YES
-      before_script:
-        - cd ${TRAVIS_BUILD_DIR}
-        - mpicxx -v
-        - make config MFEM_USE_MPI=YES MFEM_MPI_NP=2
-        - make all -j3
-        - make test-noclean
-      script:
-        - cd tests/scripts
-        - ./runtest gitignore
-      cache:
-        ccache: true
-        directories:
-          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
-          - $TRAVIS_BUILD_DIR/../metis-4.0
-      before_cache:
-        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
-          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
-          rm -f Lib/*.{c,o}
-
-    # ========================
-    #  Optional Checks/Tests
-    # ========================
-    # - branch-history
-
-    - stage: optional
-      name: "branch-history"
-      if: branch != next
-      # need full git history for the binary/big files check
-      git:
-        depth: false
-      script:
-        - cd ${TRAVIS_BUILD_DIR}
-        # update master
-        - git fetch origin master:master
-        # checkout a branch (otherwise Travis works in detached head)
-        - git checkout -b travis_tests
-        - cd tests/scripts
-        - ./runtest branch-history
-
-    # ========================
-    #       Linux tests
-    # ========================
-    # - serial + debug
-    # - serial
-    # - parallel + debug
-    # - parallel
-
-    - stage: tests
-      os: linux
-      compiler: gcc
-      name: "Linux: Serial + Debug"
-      env: DEBUG=YES
-           MPI=NO
-           CODECOV=NO
-           MFEM_TEST_TARGET=check
-      cache:
-        ccache: true
-
-    - os: linux
-      compiler: gcc
-      name: "Linux: Serial"
-      env: DEBUG=NO
-           MPI=NO
-           CODECOV=NO
-           MFEM_TEST_TARGET=test
-      cache:
-        ccache: true
-
-    - os: linux
-      compiler: gcc
-      name: "Linux: Parallel + Debug"
-      addons:
-        apt:
-          # sources:
-            # - ubuntu-toolchain-r-test
-          packages:
-            # GCC 4.9
-            # - g++-4.9
-            # MPICH
-            - mpich
-            - libmpich-dev
-            # OpenMPI
-            # - openmpi-bin
-            # - libopenmpi-dev
-      env: DEBUG=YES
-           MPI=YES
-           CODECOV=NO
-           MFEM_TEST_TARGET=check
-           NPROCS=2
-      cache:
-        ccache: true
-        directories:
-          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
-          - $TRAVIS_BUILD_DIR/../metis-4.0
-      before_cache:
-        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
-          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
-          rm -f Lib/*.{c,o}
-
-    - os: linux
-      compiler: gcc
-      name: "Linux: Parallel"
-      addons:
-        apt:
-          # sources:
-            # - ubuntu-toolchain-r-test
-          packages:
-            # GCC 4.9
-            # - g++-4.9
-            # MPICH
-            - mpich
-            - libmpich-dev
-            # OpenMPI
-            # - openmpi-bin
-            # - libopenmpi-dev
-      env: DEBUG=NO
-           MPI=YES
-           CODECOV=YES
-           MFEM_TEST_TARGET=test
-           NPROCS=2
-      cache:
-        ccache: true
-        directories:
-          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
-          - $TRAVIS_BUILD_DIR/../metis-4.0
-      before_cache:
-        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
-          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
-          rm -f Lib/*.{c,o}
-
-    - os: linux
-      compiler: gcc
-      name: "Linux: Parallel (cmake)"
-      addons:
-        apt:
-          packages:
-            - mpich
-            - libmpich-dev
-      env: MPI=YES
-           NPROCS=2
-      script:
-        - cd ${TRAVIS_BUILD_DIR}
-        - mkdir ${TRAVIS_BUILD_DIR}/build
-        - cd ${TRAVIS_BUILD_DIR}/build
-        - cmake ..
-             -DMFEM_USE_MPI=ON
-             -DHYPRE_DIR=${TRAVIS_BUILD_DIR}/../$HYPRE_TOP_DIR/src/hypre
-             -DMFEM_MPI_NP=$NPROCS
-        - make -j3 mfem examples
-        - cd ${TRAVIS_BUILD_DIR}/build/tests/unit
-        - make -j3
-        - ctest --output-on-failure
-      cache:
-        ccache: true
-        directories:
-          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
-          - $TRAVIS_BUILD_DIR/../metis-4.0
-      before_cache:
-        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
-          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
-          rm -f Lib/*.{c,o}
-
-    # ========================
-    #      Mac OS X tests
-    # ========================
-    # - serial + debug
-    # - serial
-    # - parallel + debug
-    # - parallel
-
-    - os: osx
-      osx_image: xcode11.2
-      compiler: clang
-      name: "Mac: Serial + Debug"
-      addons:
-        homebrew:
-          packages:
-            - ccache
-      env: DEBUG=YES
-           MPI=NO
-           CODECOV=NO
-           MFEM_TEST_TARGET=check
-      cache:
-        ccache: true
-
-    - os: osx
-      osx_image: xcode11.2
-      compiler: clang
-      name: "Mac: Serial"
-      addons:
-        homebrew:
-          packages:
-            - ccache
-      env: DEBUG=NO
-           MPI=NO
-           CODECOV=NO
-           MFEM_TEST_TARGET=test
-      cache:
-        ccache: true
-
-    - os: osx
-      osx_image: xcode11.2
-      compiler: clang
-      name: "Mac: Parallel + Debug"
-      addons:
-        homebrew:
-          packages:
-            - ccache
-      env: DEBUG=YES
-           MPI=YES
-           CODECOV=NO
-           MFEM_TEST_TARGET=check
-           NPROCS=4
-           TMPDIR=/tmp
-      cache:
-        ccache: true
-        directories:
-          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
-          - $TRAVIS_BUILD_DIR/../metis-4.0
-          - $HOME/local-cached
-      before_cache:
-        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
-          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
-          rm -f Lib/*.{c,o}
-
-    - os: osx
-      osx_image: xcode11.2
-      compiler: clang
-      name: "Mac: Parallel"
-      addons:
-        homebrew:
-          packages:
-            - ccache
-      env: DEBUG=NO
-           MPI=YES
-           CODECOV=YES
-           MFEM_TEST_TARGET=test
-           NPROCS=4
-           TMPDIR=/tmp
-      cache:
-        ccache: true
-        directories:
-          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
-          - $TRAVIS_BUILD_DIR/../metis-4.0
-          - $HOME/local-cached
-      before_cache:
-        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
-          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
-          rm -f Lib/*.{c,o}
-
-before_install:
-   # No addon for brew yet, have to install OSX packages this way.
-   # - if [ $TRAVIS_OS_NAME == "osx" ] && [ $MPI == "YES" ]; then
-   #      brew install open-mpi;
-   #   fi
-
-   # Disable ccache while building dependencies that are cached:
-   - echo "before \$PATH = $PATH";
-     export PATH=${PATH//\/usr\/lib\/ccache:/};
-     echo "after  \$PATH = $PATH"
-
-   # On Mac OS X, build and cache OpenMPI 2.1.6:
-   - if [ $TRAVIS_OS_NAME == "osx" ] && [ $MPI == "YES" ]; then
-        if [ ! -e $HOME/local-cached/bin/mpicc ]; then
-           mkdir -p $HOME/builds && cd $HOME/builds &&
-           wget https://download.open-mpi.org/release/open-mpi/v2.1/openmpi-2.1.6.tar.bz2 &&
-           tar jxf openmpi-2.1.6.tar.bz2 &&
-           mkdir openmpi-build && cd openmpi-build &&
-           ../openmpi-2.1.6/configure --prefix=$HOME/local-cached &&
-           make -j3 all && make install;
-        fi;
-        PATH=$HOME/local-cached/bin:$PATH;
-        cd $TRAVIS_BUILD_DIR;
-     fi
-
-   # Update environment to find g++ 4.9 installation first.
-   # - if [ $TRAVIS_OS_NAME == "linux" ]; then
-   #      mkdir -p latest-gcc-symlinks;
-   #      ln -s /usr/bin/g++-4.9 latest-gcc-symlinks/g++;
-   #      ln -s /usr/bin/gcc-4.9 latest-gcc-symlinks/gcc;
-   #      ln -s /usr/bin/gcov-4.9 latest-gcc-symlinks/gcov;
-   #      export PATH=$PWD/latest-gcc-symlinks:$PATH;
-   #   fi
-
-   # Install tool to upload code coverage reports to coveralls.io
-   - if [ "$CODECOV" == "YES" ]; then
-        export PYTHONUSERBASE=$HOME/local;
-        pip install --user cpp-coveralls;
-        pip install --user pyyaml;
-        PATH=$HOME/local/bin:$PATH;
-     fi
-
-install:
-   # Set MPI compilers, print compiler version
-   - if [ $MPI == "YES" ]; then
-        if [ "$TRAVIS_OS_NAME" == "linux" ]; then
-           export MPICH_CC="$CC";
-           export MPICH_CXX="$CXX";
-        else
-           export OMPI_CC="$CC";
-           export OMPI_CXX="$CXX";
-           mpic++ --showme:version;
-        fi;
-        mpic++ -v;
-     else
-        $CXX -v;
-     fi
-
-   # Back out of the mfem directory to install the libraries
-   - cd ..
-
-   # hypre
-   - if [ $MPI == "YES" ]; then
-        if [ ! -e $HYPRE_TOP_DIR/src/hypre/lib/libHYPRE.a ]; then
-           wget $HYPRE_URL;
-           rm -rf $HYPRE_TOP_DIR;
-           tar xvzf $HYPRE_ARCHIVE;
-           cd $HYPRE_TOP_DIR/src;
-           ./configure --disable-fortran CC=mpicc CXX=mpic++;
-           make -j3;
-           cd ../..;
-        else
-            echo "Reusing cached $HYPRE_TOP_DIR/";
-        fi;
-        ln -s $HYPRE_TOP_DIR hypre;
-     else
-        echo "Serial build, not using hypre";
-     fi
-
-   # METIS, use a mirror because the original source server is not always up.
-   # Original url:
-   #    http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/OLD/metis-4.0.3.tar.gz
-   - if [ $MPI == "YES" ]; then
-        if [ ! -e metis-4.0/libmetis.a ]; then
-           wget https://mfem.github.io/tpls/metis-4.0.3.tar.gz;
-           tar xvzf metis-4.0.3.tar.gz;
-           make -j3 -C metis-4.0.3/Lib CC="$CC" OPTFLAGS="-O2";
-           rm -rf metis-4.0;
-           mv metis-4.0.3 metis-4.0;
-        else
-           echo "Reusing cached metis-4.0/";
-        fi;
-     fi
-
-   # Re-enable ccache on linux; enable ccache on mac os:
-   - if [ $TRAVIS_OS_NAME == "linux" ]; then
-        export PATH="/usr/lib/ccache:$PATH";
-     else
-        if [ $TRAVIS_OS_NAME == "osx" ]; then
-           export PATH="/usr/local/opt/ccache/libexec:$PATH";
-        fi;
-     fi
-
-   - printf "which \$CC  = "; which $CC;
-     printf "which \$CXX = "; which $CXX
-
-script:
-   # Compiler
-   - if [ $MPI == "YES" ]; then
-        export MYCXX=mpic++;
-        export MAKE_CXX_FLAG=MPICXX=$MYCXX;
-     else
-        export MYCXX="$CXX";
-        export MAKE_CXX_FLAG=CXX=$MYCXX;
-     fi
-
-   # Print the compiler version
-   - $MYCXX -v
-
-   # Set some variables
-   - cd $TRAVIS_BUILD_DIR;
-     CPPFLAGS="";
-     SKIP_TEST_DIRS="";
-     if [ "$CODECOV" == "YES" ]; then
-        CPPFLAGS="--coverage -g";
-     fi;
-     if [ "$TRAVIS_OS_NAME" != "linux" ] || [ "$DEBUG" == "YES" ]; then
-        CPPFLAGS+=" -pedantic -Wall -Werror";
-     fi
-
-   # Configure the library
-   - make config MFEM_USE_MPI=$MPI MFEM_DEBUG=$DEBUG $MAKE_CXX_FLAG
-        MFEM_MPI_NP=$NPROCS CPPFLAGS="$CPPFLAGS"
-   # Show the configuration
-   - make info
-   # Build the library
-   - make -j3
-   # Build the examples and the miniapps
-   - make -j3 all
-   # Run tests
-   - make $MFEM_TEST_TARGET SKIP_TEST_DIRS="$SKIP_TEST_DIRS"
-
-after_success:
-   - if [ "$CODECOV" == "YES" ]; then
-        coveralls --include fem --include general --include linalg --include
-           mesh --exclude /usr --gcov-options '\-lp' --root $TRAVIS_BUILD_DIR;
-     fi
@@ -8,40 +8,87 @@
                               https://mfem.org


-Version 4.2.1 (development)
+Version 4.3.1 (development)
 ===========================
- Added initial support for GPU-accelerated versions of PETSc that works with
-  MFEM_USE_CUDA if PETSc has been configured with CUDA support. Examples 1 and 9
-  in the examples/petsc directory have been modified to work with --device cuda.
-  Examples with GAMG (ex1p) and SLEPc (ex11p) are also provided.
+- Added support for hr-adaptivity using TMOP-based error estimator.

- Memory management:
-  * Added method Device::SetMemoryTypes that can be used to change the default
-    host and device MemoryTypes before Device setup.
-  * In class MemoryManager, added methods GetDualMemoryType and
-    SetDualMemoryType; dual MemoryTypes are used to determine the second
-    MemoryType (host or device) when only one MemoryType is specified in methods
-    of class Memory.
-  * Added Memory constructor for setting both the host and device MemoryTypes.
-  * Switched the default behavior of device memory allocations so that they
-    are deferred until the device pointer is needed.
-  * Added a second Umpire device MemoryType, DEVICE_UMPIRE_2, with
-    corresponding allocator that can be set with the method
-    MemoryManager::SetUmpireDevice2AllocatorName.
-  * Added HOST_PINNED MemoryType and a pinned host allocator for CUDA and HIP.
+- Adding lowest order Nedelec and Raviart-Thomas basis functions on wedge
+  shaped elements.

- Added support for Caliper: a library to integrate performance profiling
-  capabilities into applications. See examples/caliper for more details.
+- Added initial support for meshes with pyramidal elements, including several
+  pyramidal meshes in the data/ directory and support for the lowest order H1,
+  Nedelec, Raviart-Thomas, and L2 basis functions on pyramids.

- Added support for explicit vectorization in the high-performance templated
-  code for Fujitsu's A64FX ARM microprocessor architecture.
+- Updated the hypre interface according to changes in hypre-2.22.1. The ADS
+  solver is now fully working on GPUs.

- Added AlgebraicCeedSolver that does matrix-free algebraic p-multigrid for
-  diffusion problems with the Ceed backend.
+- Tetrahedral meshes no longer need to be reordered to support high order
+  Nedelec basis functions. This will allow future support for Nedelec basis
+  functions on wedges and pyramids which are not amenable to reordering. The
+  ReorientTetMesh method of the Mesh and ParMesh classes has been deprecated.

- Introduced new options for the mesh-explorer miniapp to visualize the actual
-  element attributes in parallel meshes while retaining the visualization of
-  the domain decomposition.
+
+Version 4.3, released on July 29, 2021
+======================================
+
+Discretization improvements
+---------------------------
+- Variable order spaces, p- and hp-refinement. This is the initial (serial)
+  support for variable-order FiniteElementCollection and FiniteElementSpace.
+  The new method FiniteElementSpace::SetElementOrder can be called to set an
+  arbitrary order for each mesh element. The conforming interpolation matrix
+  will now automatically constrain p- and hp- interfaces, enabling general
+  hp-refinement in both 2D and 3D, on uniform or mixed NC meshes. Support for
+  parallel variable-order spaces will follow shortly.
+
+- Extended the support for field transfer between high-order and low-order
+  refined finite element spaces to include: dual fields and H1 fields (both
+  primary and dual). These are illustrated in the lor-transfer miniapp.
+
+- Improved libCEED integration, including support for VectorCoefficient,
+  ConvectionIntegrator, and VectorConvectionNLFIntegrator with libCEED backends.
+
+- Extending support for L2 basis functions using MapTypes VALUE and INTEGRAL in
+  linear interpolators and GridFunction "GetValue" methods.
+
+- Changed the interface for the error estimator and implemented the Kelly error
+  indicator for scalar-valued problems, supported in serial and parallel builds.
+
+- Added support for the "BR2" discontinuous Galerkin discretization for
+  diffusion via DGDiffusionBR2Integrator (see Example 14/14p).
+
+- Added convective and skew-symmetric integrators for the nonlinear term in the
+  Navier-Stokes equations.
+
+- Added new classes DenseSymmetricMatrix and SymmetricMatrixCoefficient for
+  efficient evaluation of symmetric matrix coefficients. This replaces the now
+  deprecated EvalSymmetric in MatrixCoefficient. Added DiagonalMatrixCoefficient
+  for clarity, which is a typedef of VectorCoefficient.
+
+- Added support for nonscalar coefficient with VectorDiffusionIntegrator.
+
+Linear and nonlinear solvers
+----------------------------
+- Added support for AMG preconditioners on GPUs based on the hypre library
+  (version 2.22.0 or later). These include BoomerAMG, AMS and ADS and most
+  MFEM examples that use hypre have been ported to support this functionality.
+  The GPU preconditioners require that both hypre and MFEM are built with CUDA
+  support. Hypre builds with CUDA and unified memory are also supported and
+  can be used with `-d cuda:uvm` as a command-line option.
+
+- Added support for AMG preconditioners for non-symmetric systems (e.g.
+  advection-dominated problems) using hypre's approximate ideal restriction
+  (AIR) AMG. Requires hypre version 2.14.0 or newer. Usage is illustrated in
+  example 9/9p.
+
+- Added new functionality for constructing low-order refined discretizations and
+  solvers, see the LORDiscretization and LORSolver classes. A new basis type for
+  H(curl) and H(div) spaces is introduced to give spectral equivalence. This
+  functionality is illustrated in the LOR solvers miniapp in miniapps/solvers.
+
+- Generalized the Multigrid class to support non-geometric multigrid. Previous
+  functionality, based on FiniteElementSpaceHierarchy, is now available in the
+  derived class GeometricMultigrid.

 - Introduced solver interface for linear problems with constraints, a few
  concrete solvers that implement the interface, and a demonstration of their
@@ -52,19 +99,18 @@ Version 4.2.1 (development)
  as described in Barker and Kolev 2020 (https://doi.org/10.1002/nla.2348). See
  Example 3p and linalg/auxiliary.?pp.

- Added a new miniapp block-solvers that compares the performance of various
-  solvers for mixed finite element discretization of the second order scalar
-  elliptic equations. Currently available solvers in the miniapp include a
-  block-diagonal preconditioner that is based on approximate Schur complement
-  (implemented in ex5p), and a newly implemented solver DivFreeSolver, which
-  exploits a multilevel decomposition of the Raviart-Thomas space and its
-  divergence-free subspace. See the miniapps/solvers directory for more details.
+- Improved interface for using the Ginkgo library, including: support for matrix-
+  free operators in Ginkgo solvers, new wrappers for Ginkgo preconditioners, HIP
+  support, and reduction of unnecessary data copies.

- Added a new miniapp for computing (signed) distance functions to a point
-  source or zero level set. See miniapps/shifted/distance.cpp.
+- Added initial support for hypre's mixed integer (mixedint) capability, which
+  uses different data types for local and global indices in order to save memory
+  in large problems. This capability requires that hypre was configured with the
+  --enable-mixedint option. Note that this option is currently tested only in
+  ex1p, ex3p, and ex4p, and may not work in more general settings.

- Added matrix-free GPU-enabled implementations of GradientInterpolator and
-  IdentityInterpolator.
+- Added AlgebraicCeedSolver that does matrix-free algebraic p-multigrid for
+  diffusion problems with the Ceed backend.

 - Added interface to MUMPS direct solver. Its usage is demonstrated in ex25p.
  See http://mumps.enseeiht.fr/ for more details. Supported versions >= 5.1.1.
@@ -72,6 +118,17 @@ Version 4.2.1 (development)
 - Added three ESDIRK time integrators: implicit trapezoid rule, L-stable
  ESDIRK-32, and A-stable ESDIRK-33.

+- Implemented a variable step-size IMEX (VSSIMEX) method for the Navier miniapp.
+
+- Implemented an adaptive linear solver tolerance option for NewtonSolver based
+  on the algorithm of Eisenstat and Walker.
+
+Meshing improvements
+--------------------
+- Added support for reading high-order Lagrange meshes in VTK format. Arbitrary-
+  orders and all element types are supported. See the VTK blog for more info:
+  https://blog.kitware.com/wp-content/uploads/2018/09/Source_Issue_43.pdf.
+
 - Introduced a new non-conforming mesh format that fixes known inconsistencies
  of legacy "MFEM mesh v1.1" NC format and works consistently in both serial and
  parallel. ParMesh::ParPrint can now print non-conforming AMR meshes that can
@@ -80,108 +137,26 @@ Version 4.2.1 (development)
  NC data files are compatible with serial code, e.g., can be viewed with serial
  GLVis. Loading of legacy NC mesh files is still supported.

- Added support for 1D non-conforming meshes (which can be useful for parallel
-  load balancing and derefinement).
-
- Added a "scaled Jacobian" visualization option in the Mesh Explorer miniapp to
-  help identify elements with poor mesh quality.
-
- Added support for the "BR2" discontinuous Galerkin discretization for
-  diffusion via DGDiffusionBR2Integrator (see Example 14/14p).
-
- Generalized the Multigrid class to support non-geometric multigrid. The
-  previous functionality, based on FiniteElementSpaceHierarchy, is now available
-  in the derived class GeometricMultigrid.
-
- Upgraded the Catch unit test framework from version 2.13.0 to version 2.13.2.
-
- The TMOP mesh optimization algorithms were extended to GPU:
-   - QualityMetric #1, #2, #7 and #77 are available in 2D, #302, #303, #315
-     and #321 in 3D
-   - Both AnalyticAdaptTC and DiscreteAdaptTC TargetConstructor are available
-   - Kernels for normalization and limiting have been added
-   - The AdvectorCG now also supports AssemblyLevel::PARTIAL
-
- Added a new command line boolean option (`--all`) to the unit tests to launch
-  *all* non-regression tests.
-
- Added support for different modes of QuadratureInterpolator on GPU.
-  The layout (QVectorLayout::byNODES|byVDIM) and the tensor products modes can
-  be enabled before calling the Mult, Values, Derivatives, PhysDerivatives and
-  Determinants methods.
-
- Implemented a filter method for the Navier miniapp to stabilize highly
-  turbulent flows in direct numerical simulation.
-
- Added HIP support to the CMake build system.
-
- Added support for reading high-order Lagrange meshes in VTK format. Arbitrary-
-  orders and all element types are supported. See the VTK blog for more info:
-  https://blog.kitware.com/wp-content/uploads/2018/09/Source_Issue_43.pdf.
-
- Added support for reading VTK meshes in XML format.
-
- Added partial assembly and device support to Example 25/25p, with diagonal
-  preconditioning.
-
- Implemented a variable step-size IMEX (VSSIMEX) method for the Navier miniapp.
+- Added FMS support (https://github.com/CEED/FMS) to mfem. FMS can represent
+  unstructured high-order meshes with general high-order finite element fields
+  on them. When enabled, mfem can convert data collections to/from FMS data
+  collections in memory. In addition, an FMS data collection class was added so
+  the convert-dc miniapp can read and generate data files in FMS format.

 - Added new mesh quality metrics and improved the untangling capabilities of the
  TMOP-based mesh optimization algorithms.

- Added convective and skew-symmetric integrators for the nonlinear term in the
-  Navier-Stokes equations.
-
- Added new miniapp directory mtop/ with optimization-oriented block parametric
-  non-linear form and abstract integrators. Two new miniapps, ParHeat and
-  SeqHeat, demonstrate parallel and sequential implementation of gradients
-  evaluation for linear diffusion with discrete density.
-
- Changed the interface for the error estimator.
-
- Implemented the parallel Kelly error indicator for scalar-valued problems.
-
- Added new classes DenseSymmetricMatrix and SymmetricMatrixCoefficient for
-  efficient evaluation of symmetric matrix coefficients. This replaces the now
-  deprecated EvalSymmetric in MatrixCoefficient. Added DiagonalMatrixCoefficient
-  for clarity, which is a typedef of VectorCoefficient.
-
- Added support for AMG preconditioners for non-symmetric systems (e.g.
-  advection-dominated problems) using hypre's approximate ideal restriction
-  (AIR) AMG. Requires hypre version 2.14.0 or newer. Usage is illustrated in
-  example 9/9p.
-
- Implemented an adaptive linear solver tolerance option for NewtonSolver based
-  on the algorithm of Eisenstat and Walker.
-
- Added support for nonscalar coefficient with VectorDiffusionIntegrator.
-
- Extending support for L2 basis functions using MapTypes VALUE and INTEGRAL in
-  linear interpolators and GridFunction "GetValue" methods.
-
- Variable order spaces, p- and hp-refinement. This is the initial (serial)
-  support for variable-order FiniteElementCollection and FiniteElementSpace.
-  The new method FiniteElementSpace::SetElementOrder can be called to set an
-  arbitrary order for each mesh element. The conforming interpolation matrix
-  will now automatically constrain p- and hp- interfaces, enabling general
-  hp-refinement in both 2D and 3D, on uniform or mixed NC meshes. Support for
-  parallel variable-order spaces will follow shortly.
+- The TMOP mesh optimization algorithms were extended to GPU:
+  * QualityMetric 1, 2, 7, 77 are available in 2D, 302, 303, 315, 321 in 3D
+  * Both AnalyticAdaptTC and DiscreteAdaptTC TargetConstructor are available
+  * Kernels for normalization and limiting have been added
+  * The AdvectorCG now also supports AssemblyLevel::PARTIAL

 - Added support for creating refined meshes for all element types (e.g. by
  splitting high-order elements into low-order refined elements), including
  mixed meshes. The LOR Transfer miniapp (miniapps/tools/lor-transfer.cpp) now
  supports meshes with any element geometry.

- Gitlab CI: use Spack (and Uberenv) to automate the build of TPLs.
-
- Added new miniapps demonstrating: 1) the use of GSLIB for overlapping grids,
-  see gslib/schwarz_ex1, and 2) coupling different physics in different domains,
-  see navier/cht. Note that gslib v1.0.7 is require (see INSTALL for details).
-
- Added a new, very simple example (ex0 and parallel version ex0p). This
-  example solves a simple Poisson problem using H1 elements (the same problem as
-  ex1), but is intended to be extremely simple and approachable for new users.
-
 - Meshes consisting of any type of elements (including mixed meshes) can be
  converted to all-simplex meshes using Mesh::MakeSimplicial.

@@ -194,45 +169,147 @@ Version 4.2.1 (development)
  requisite periodic vertex mappings can be created with
  Mesh::CreatePeriodicVertexMapping.

- Added support for transferring dual fields between high-order and low-order
-  refined finite element spaces using the transposed versions of the
-  L2ProjectionGridTransfer operators. This functionality is illustrated in the
-  lor-transfer miniapp.
-
- Improved interface for using the Ginkgo library, including: support for matrix-
-  free operators in Ginkgo solvers, new wrappers for Ginkgo preconditioners, HIP
-  support, and reduction of unnecessary data copies. 
-
- Added initial support for hypre's mixed integer (mixedint) capability, which
-  uses different data types for local and global indices in order to save memory
-  in large problems. This capability requires that hypre was configured with the
-  --enable-mixedint option. Note that this option is currently tested only in
-  ex1p and may not work in more general settings.
-
- Added new functionality for constructing low-order refined discretizations and
-  solvers, see the LORDiscretization and LORSolver classes. A new basis type for
-  H(curl) and H(div) spaces is introduced to give spectral equivalence. This
-  functionality is illustrated in the LOR solvers miniapp in miniapps/solvers.
+- Added support for 1D non-conforming meshes (which can be useful for parallel
+  load balancing and derefinement).

 - Added sample meshes in the `data` subdirectory showing the reference elements
  of the six currently supported element types; ref-segment.mesh,
  ref-triangle.mesh, ref-square.mesh, ref-tetrahedron.mesh, ref-cube.mesh, and
  ref-prism.mesh.

-libCEED integration improvements
--------------------------------
- Refactor the libCEED integration
+High-performance computing
+--------------------------
+- Added initial support for GPU-accelerated versions of PETSc that works with
+  MFEM_USE_CUDA if PETSc has been configured with CUDA support. Examples 1 and 9
+  in the examples/petsc directory have been modified to work with --device cuda.
+  Examples with GAMG (ex1p) and SLEPc (ex11p) are also provided.

- Add support for VectorCoefficient with libCEED backends.
+- Added support for explicit vectorization in the high-performance templated
+  code for Fujitsu's A64FX ARM microprocessor architecture.

- Add support for ConvectionIntegrator, and VectorConvectionNLFIntegrator with
-  libCEED backends.
+- Added support for different modes of QuadratureInterpolator on GPU.
+  The layout (QVectorLayout::byNODES|byVDIM) and the tensor products modes can
+  be enabled before calling the Mult, Values, Derivatives, PhysDerivatives and
+  Determinants methods.
+
+- Added method Device::SetMemoryTypes that can be used to change the default
+  host and device MemoryTypes before Device setup.
+
+- In class MemoryManager, added methods GetDualMemoryType and SetDualMemoryType;
+  dual MemoryTypes are used to determine the second MemoryType (host or device)
+  when only one MemoryType is specified in methods of class Memory.
+
+- Added Memory constructor for setting both the host and device MemoryTypes.
+
+- Switched the default behavior of device memory allocations so that they are
+  deferred until the device pointer is needed.
+
+- Added a second Umpire device MemoryType, DEVICE_UMPIRE_2, with corresponding
+  allocator that can be set with the method SetUmpireDevice2AllocatorName.
+
+- Added HOST_PINNED MemoryType and a pinned host allocator for CUDA and HIP.
+
+- Added matrix-free GPU-enabled implementations of GradientInterpolator and
+  IdentityInterpolator.
+
+New and updated examples and miniapps
+-------------------------------------
+- Added a new, very simple example (ex0 and parallel version ex0p). This example
+  solves a simple Poisson problem using H1 elements (the same problem as ex1),
+  but is intended to be extremely simple and approachable for new users.
+
+- Added new miniapps demonstrating: 1) the use of GSLIB for overlapping grids,
+  see gslib/schwarz_ex1, and 2) coupling different physics in different domains,
+  see navier/cht. Note that gslib v1.0.7 is require (see INSTALL for details).
+
+- Added a new miniapp for computing (signed) distance functions to a point
+  source or zero level set. See miniapps/shifted/distance.cpp.
+
+- Added a high-order extension of the shifted boundary method to solve PDEs on
+  non body-fitted meshes. This is illustrated in the new Shifted Diffusion
+  miniapp, see miniapps/shifted/diffusion.cpp.
+
+- Added new miniapp directory mtop/ with optimization-oriented block parametric
+  non-linear form and abstract integrators. Two new miniapps, ParHeat and
+  SeqHeat, demonstrate parallel and sequential implementation of gradients
+  evaluation for linear diffusion with discrete density.
+
+- Added a new miniapp block-solvers that compares the performance of various
+  solvers for mixed finite element discretization of the second order scalar
+  elliptic equations. Currently available solvers in the miniapp include a
+  block-diagonal preconditioner that is based on approximate Schur complement
+  (implemented in ex5p), and a newly implemented solver DivFreeSolver, which
+  exploits a multilevel decomposition of the Raviart-Thomas space and its
+  divergence-free subspace. See the miniapps/solvers directory for more details.
+
+- Introduced new options for the mesh-explorer miniapp to visualize the actual
+  element attributes in parallel meshes while retaining the visualization of the
+  domain decomposition.
+
+- Added partial assembly and device support to Example 25/25p, with diagonal
+  preconditioning.
+
+- Implemented a filter method for the Navier miniapp to stabilize highly
+  turbulent flows in direct numerical simulation.
+
+Improved testing
+----------------
+- Transitioned from Travis to GitHub Action for testing/CI on GitHub.
+
+- Use Spack (and Uberenv) to automate TPL building in LLNL GitLab tests.
+
+- Extended `make test` to include GPU tests when MFEM is built with CUDA or HIP
+  support.
+
+- Added a set of suggested git hooks for developers in config/githooks.
+
+- Added support for Caliper: a library to integrate performance profiling
+  capabilities into applications. See examples/caliper for more details.
+
+- Added a new command line boolean option (`--all`) to the unit tests to launch
+  *all* non-regression tests.
+
+- Upgraded the Catch unit test framework from version 2.13.0 to version 2.13.2.
+
+Miscellaneous
+-------------
+- The following integrations have updated minimum version requirements:
+  * CUDA >= 10.1.168
+  * Ginkgo >= 1.4.0
+  * GSLIB >= 1.0.7
+  * HIOP >= 0.4
+  * HYPRE >= 2.20.0 for mixedint support
+  * HYPRE >= 2.22.0 for CUDA support
+  * libCEED >= 0.8
+  * PETSc >= 3.15.0 for CUDA support
+  * RAJA >= 0.13.0
+  see INSTALL for more details.
+
+- Added a "scaled Jacobian" visualization option in the Mesh Explorer miniapp to
+  help identify elements with poor mesh quality.
+
+- Added support for reading VTK meshes in XML format.
+
+- Added makefile rule to generate TAGS table for vi or Emacs users.
+
+- Added HIP support to the CMake build system.
+
+- Various other simplifications, extensions, and bugfixes in the code.
+
+API changes
+-----------
+- Added an abstract interface `mfem::FaceRestriction` for `H1FaceRestriction`
+  and `L2FaceRestriction`.
+  In order to conform with the semantic of `MultTranspose` in `mfem::Operator`,
+  `mfem::FaceRestriction::MultTranspose` now sets instead of adding values, and
+  `mfem::FaceRestriction::AddMultTranspose` should replace previous calls to
+  `mfem::FaceRestriction::MultTranspose`.


 Version 4.2, released on October 30, 2020
 =========================================

-High-Performance Computing
+High-performance computing
 --------------------------
 - Added support for explicit vectorization in the high-performance templated
  code, which can now take advantage of specific classes on the following
@@ -314,9 +391,6 @@ Linear and nonlinear solvers
  matrix with the function HypreParMatrixFromBlocks. This could be useful for
  solving block systems with parallel direct solvers such as STRUMPACK.

- Added CUDA support for SUNDIALS ODE integrators. See the updated SUNDIALS
-  modification of Example 9/9p.
-
 - Added wrappers for hypre's flexible GMRES solver and the new parallel ILU
  preconditioner. The latter requires hypre version 2.19.0 or later.

@@ -427,7 +501,7 @@ New and updated examples and miniapps
    L2, with partial assembly support in Example 24/24p.
  * Weak Dirichlet boundary conditions (Nitsche) to the NURBS miniapp.

-Data management and Visualization
+Data management and visualization
 ---------------------------------
 - Added support for ADIOS2 for parallel I/O with ParaView visualization. See
  Examples 5, 9, 12, 16. The classes adios2stream and ADIOS2DataCollection
@@ -0,0 +1,66 @@
+cff-version: 1.2.0
+message: "If you use MFEM, please cite it as follows."
+authors:
+- family-names: "MFEM Team"
+title: "MFEM: Modular Finite Element Methods [Software]"
+doi: 10.11578/dc.20171025.1248
+url: "https://mfem.org"
+preferred-citation:
+  type: article
+  authors:
+  - family-names: "Anderson"
+    given-names: "Robert"
+    orcid: "https://orcid.org/0000-0002-3508-9944"
+  - family-names: "Andrej"
+    given-names: "Julian"
+    orcid: "https://orcid.org/0000-0001-7661-4840"
+  - family-names: "Barker"
+    given-names: "Andrew"
+    orcid: "https://orcid.org/0000-0003-3572-911X"
+  - family-names: "Bramwell"
+    given-names: "Jamie"
+  - family-names: "Camier"
+    given-names: "Jean-Sylvain"
+    orcid: "https://orcid.org/0000-0003-2421-1999"
+  - family-names: "Cerveny"
+    given-names: "Jakub"
+    orcid: "https://orcid.org/0000-0003-4231-2531"
+  - family-names: "Dobrev"
+    given-names: "Veselin"
+    orcid: "https://orcid.org/0000-0003-1793-5622"
+  - family-names: "Dudouit"
+    given-names: "Yohann"
+    orcid: "https://orcid.org/0000-0001-5831-561X"
+  - family-names: "Fisher"
+    given-names: "Aaron"
+  - family-names: "Kolev"
+    given-names: "Tzanio"
+    orcid: "https://orcid.org/0000-0002-2810-3090"
+  - family-names: "Pazner"
+    given-names: "Will"
+    orcid: "https://orcid.org/0000-0003-4885-2934"
+  - family-names: "Stowell"
+    given-names: "Mark"
+    orcid: "https://orcid.org/0000-0002-5389-7435"
+  - family-names: "Tomov"
+    given-names: "Vladimir"
+    orcid: "https://orcid.org/0000-0002-1846-6816"
+  - family-names: "Akkerman"
+    given-names: "Ido"
+    orcid: "https://orcid.org/0000-0002-5937-0300"
+  - family-names: "Dahm"
+    given-names: "Johann"
+    orcid: "https://orcid.org/0000-0001-9657-3564"
+  - family-names: "Medina"
+    given-names: "David"
+  - family-names: "Zampini"
+    given-names: "Stefano"
+    orcid: "https://orcid.org/0000-0002-0435-0433"
+  doi: "10.1016/j.camwa.2020.06.009"
+  journal: "Computers \\& Mathematics with Applications"
+  month: 1
+  start: 42 # First page number
+  end: 74 # Last page number
+  title: "MFEM: A Modular Finite Element Methods Library"
+  volume: 81
+  year: 2021
@@ -16,7 +16,7 @@ set(USER_CONFIG "${CMAKE_CURRENT_SOURCE_DIR}/config/user.cmake" CACHE PATH

 # Require C++11 and disable compiler-specific extensions
 set(CMAKE_CXX_STANDARD 11)
-if (MFEM_USE_GINKGO) 
+if (MFEM_USE_GINKGO)
  set(CMAKE_CXX_STANDARD 14)
 endif()
 set(CMAKE_CXX_STANDARD_REQUIRED ON)
@@ -54,7 +54,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 4.2.1)
+set(${PROJECT_NAME}_VERSION 4.3.1)

 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -102,7 +102,7 @@ if (MFEM_USE_CUDA)
   endif()
   enable_language(CUDA)
   set(CMAKE_CUDA_STANDARD 11)
-   if (MFEM_USE_GINKGO) 
+   if (MFEM_USE_GINKGO)
     set(CMAKE_CUDA_STANDARD 14)
   endif()
   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
@@ -175,6 +175,10 @@ else()
  set(MFEM_DEBUG OFF)
 endif()

+if (WIN32)
+	add_definitions(-D_USE_MATH_DEFINES)
+endif()
+
 # MPI -> hypre; PETSc (optional)
 if (MFEM_USE_MPI)
  find_package(MPI REQUIRED)
@@ -246,6 +250,7 @@ if (MFEM_USE_OPENMP OR 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})
 endif()

 # SuiteSparse (before SUNDIALS which may depend on KLU)
@@ -330,6 +335,10 @@ if (MFEM_USE_CONDUIT)
    find_package(Conduit REQUIRED conduit relay blueprint )
 endif()

+if (MFEM_USE_FMS)
+    find_package(FMS REQUIRED fms )
+endif()
+
 # Axom/Sidre
 if (MFEM_USE_SIDRE)
  find_package(Axom REQUIRED Axom)
@@ -424,9 +433,10 @@ endif()
 #    integers, the METIS header (with 32-bit indices, as used by mfem) needs to
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP HYPRE BLAS LAPACK SuperLUDist METIS SuiteSparse SUNDIALS PETSC
-    SLEPC MESQUITE MUMPS STRUMPACK AXOM CONDUIT Ginkgo GNUTLS GSLIB NETCDF
+    SLEPC MESQUITE MUMPS STRUMPACK AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB NETCDF
    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE ADIOS2
    CUSPARSE MKL_CPARDISO AMGX CALIPER)
+
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")
@@ -445,6 +455,9 @@ include_directories(${TPL_INCLUDE_DIRS})
 if (OPENMP_FOUND)
  message(STATUS "MFEM: using package OpenMP")
  set(CMAKE_CXX_FLAGS "${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}")
@@ -4,7 +4,9 @@

 <p align="center">
 <a href="https://github.com/mfem/mfem/blob/master/LICENSE"><img alt="License" src="https://img.shields.io/badge/License-BSD-brightgreen.svg"></a>
-<a href="https://travis-ci.org/mfem/mfem"><img alt="Build Status" src="https://travis-ci.org/mfem/mfem.svg?branch=master"></a>
+<a href="https://github.com/mfem/mfem/actions?query=workflow%3Arepo-check+branch%3Amaster"><img alt="Repo check" src="https://github.com/mfem/mfem/actions/workflows/repo-check.yml/badge.svg?branch=master"></a>
+<a href="https://github.com/mfem/mfem/actions?query=workflow%3Abuild-analysis+branch%3Amaster"><img alt="Build Analysis" src="https://github.com/mfem/mfem/actions/workflows/mfem-analysis.yml/badge.svg?branch=master"></a>
+<a href="https://github.com/mfem/mfem/actions?query=workflow%3Abuilds-and-tests+branch%3Amaster"><img alt="Builds and Tests" src="https://github.com/mfem/mfem/actions/workflows/builds-and-tests.yml/badge.svg?branch=master"></a>
 <a href="https://ci.appveyor.com/project/mfem/mfem"><img alt="Build Status" src="https://ci.appveyor.com/api/projects/status/19non9sqm6msi2wy?svg=true"></a>
 <a href="https://mfem.github.io/doxygen/html/index.html"><img alt="Doxygen" src="https://img.shields.io/badge/code-documented-brightgreen.svg"></a>
 </p>
@@ -63,6 +65,8 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
  development branches off `mfem:master`.
 - Please follow the [developer guidelines](#developer-guidelines), in particular
  with regards to documentation and code styling.
+- Please do not commit large/binary files to the central repository (use a fork
+  instead).
 - Pull requests  should be issued toward `mfem:master`. Make sure
  to check the items off the [Pull Request Checklist](#pull-request-checklist).
 - When your contribution is fully working and ready to be reviewed, add
@@ -71,6 +75,7 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
  reviewers to evaluate the changes.
 - The reviewers have 3 weeks to evaluate the PR and work with the author to
  fix issues and implement improvements.
+- During review there should be no force pushes/rewriting history in the branch.
 - After approval, MFEM developers merge the PR manually in the [mfem:next branch](#masternext-workflow).
 - After a week of testing in `mfem:next`, the original PR is merged in `mfem:master`.
 - We use [milestones](https://github.com/mfem/mfem/milestones) to coordinate the
@@ -91,8 +96,8 @@ The MFEM source code has the following structure:
 ```
  .
  ├── config
-  │   └── cmake
-  │       └── ...
+  │   ├── cmake
+  │   └── githooks
  ├── data
  ├── doc
  ├── examples
@@ -129,10 +134,10 @@ The MFEM source code has the following structure:
  └── tests
      ├── convergence
      ├── gitlab
+      ├── mem_manager
      ├── par-mesh-format
      ├── scripts
      └── unit
-          └── ...
 ```

 #### Main directories and classes
@@ -363,6 +368,10 @@ Before you can start, you need a GitHub account, here are a few suggestions:
  two reviewers to evaluate the changes. The reviewers have 3 weeks to evaluate
  the PR and work with the author to implement improvements and fix issues.

+- Once the `ready-for-review` label has been applied and reviewers have been
+  assigned, the PR is considered under review. To help with the review process
+  there should be no force pushes/rewriting history in the branch.
+
 - After approval, the PR is [tested](#masternext-workflow) for a week with
  other approved PRs in the `mfem:next` branch.

@@ -370,16 +379,20 @@ Before you can start, you need a GitHub account, here are a few suggestions:
  `mfem:next`, see the [README](tests/scripts/README) file in that directory
  for more details.

- Track the Travis CI, Github Actions and Appveyor [continuous integration](#automated-testing)
+- Track the GitHub Actions and Appveyor [continuous integration](#automated-testing)
  builds at the end of the PR. These should generally run clean, so address any
  errors as soon as possible. Please ask if you are unsure how to do that.

- Note that some tests, such as the `branch-history` check in Travis and Github
-  Actions are safeguards that are allowed to fail in certain cases.
+- Note that some tests, such as the `branch-history` check in GitHub Actions
+  are safeguards that are allowed to fail in certain cases.

 - Other tests, such as the `code-style`, `documentation` and `gitignore`
-  checks in Travis and Github Actions enforce MFEM-specific rules which are
-  explained in the error messages and the `tests/scripts` directory.
+  checks in GitHub Actions enforce MFEM-specific rules which are explained in
+  the error messages and the `tests/scripts` directory.
+
+- Also note that the tests `branch-history` and `repos-checks` found in GitHub
+  Actions can be triggered automatically before each push using git hooks. See
+  the [git hooks README](config/githooks/README.md) for a detailed explanation.

 - If triggered, track the status of the LLNL GitLab tests. If failing, ask
  one of the _LLNL developers_ for details.
@@ -399,7 +412,7 @@ Before a PR can be merged, it should satisfy the following:
    - [ ] Does `make` or `cmake` have a new target?
    - [ ] Did the requirements or the installation process change? *(rare)*
 - [ ] Update continuous integration server configurations if necessary (e.g. with new version requirements for each of MFEM's dependencies)
-    - [ ] `.travis.yml`
+    - [ ] `.github`
    - [ ] `.appveyor.yml`
 - [ ] Update `.gitignore`:
    - [ ] Check if `make distclean; git status` shows any files that were generated from the source by the project (not an IDE) but we don't want to track in the repository.
@@ -516,7 +529,7 @@ MFEM uses a `master`/`next`-branch workflow as described below:
    - [ ] `doc/CodeDocumentation.conf.in`
 - [ ] Check that version requirements for each of MFEM's dependencies are documented in `INSTALL` and up-to-date
 - [ ] Check that continuous integration server configurations reflect the dependency version requirements of the new release
-    - [ ] `.travis.yml`
+    - [ ] `.github`
    - [ ] `.appveyor.yml`
 - [ ] Update the `CHANGELOG` to organize all release contributions
 - [ ] Review the whole source code once over
@@ -578,14 +591,17 @@ MFEM uses a `master`/`next`-branch workflow as described below:
 MFEM has several levels of automated testing running on GitHub, as well as on
 local Mac and Linux workstations, and Livermore Computing clusters at LLNL.

-### Linux and Mac smoke tests
-We use Travis CI and Github Actions to drive the default tests on the `master`
-and `next` branches. See the `.travis` file and the logs at
-[https://travis-ci.org/mfem/mfem](https://travis-ci.org/mfem/mfem).
+In addition, developers can set local git hooks to run some quick checks on
+commit or push, see the [README](config/githooks/README.md) in the `config/githooks`
+directory.

-Testing using Travis CI and Github Actions should be kept lightweight, as there
-is a time constraint on jobs. Two virtual machines are configured - Mac (OS X)
-and Linux.
+### Linux and Mac smoke tests
+We use GitHub Actions to drive the default tests on the `master` and `next`
+branches. See the `.github/workflows` files and the logs at
+[https://github.com/mfem/mfem/actions](https://github.com/mfem/mfem/actions).
+
+Testing using GitHub Actions should be kept lightweight, as there is a time
+constraint on jobs. Two virtual machines are configured - Mac (OS X) and Linux.

 - Tests on the `master` branch are triggered whenever a PR is issued on this branch.
 - Tests on the `next` branch are currently scheduled to run each night.
@@ -58,6 +58,7 @@ following package managers:

 - Spack, https://github.com/spack/spack
 - OpenHPC, http://openhpc.community
+- Conda-forge, https://conda-forge.org (pre-built binaries linked with OpenMPI/MPICH, hypre, and METIS)
 - Homebrew/Science, https://github.com/Homebrew/homebrew-science (deprecated)

 We also recommend downloading and building the MFEM-based GLVis visualization
@@ -473,7 +474,7 @@ MFEM_USE_HIP = YES/NO
   Enables support for AMD devices in MFEM. HIP is a heterogeneous-compute
   interface for portability developed by AMD that can target both AMD and
   NVIDIA GPUs. The variable HIP_ARCH is used to specify the AMD GPU processor
-   used during compilation (by default, HIP_ARCH=gfx900).  When enabled, this
+   used during compilation (by default, HIP_ARCH=gfx900). When enabled, this
   option uses the HIP_* build options, see below.

 MFEM_USE_RAJA = YES/NO
@@ -515,6 +516,13 @@ MFEM_USE_CALIPER = YES/NO
   profiling at runtime with Caliper's configuration API. Alternatively, one
   can configure Caliper through environment variables or config files.

+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
+   DataCollection class, see the header file fem/fmsconvert.hpp.
+
 MFEM_BUILD_TAG = (any value)
   An optional tag to characterize the build. Exported to config/config.mk.
   Can be used to identify the MFEM build from other makefiles.
@@ -539,8 +547,9 @@ The specific libraries and their options are:
  See also the "Specific options for hypre" section at the end of this file.
  URL: https://github.com/hypre-space/hypre and https://www.llnl.gov/casc/hypre
  Options: HYPRE_OPT, HYPRE_LIB.
-  Versions: HYPRE >= 2.10.0b,
-            HYPRE >= 2.20.0 for '--enable-mixedint' support.
+  Versions: HYPRE >= 2.10.0b  (HYPRE built without CUDA)
+            HYPRE >= 2.20.0   (HYPRE built with '--enable-mixedint')
+            HYPRE >= 2.22.1   (HYPRE built with CUDA)

 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
  MFEM_USE_METIS_5 = YES (default is to use METIS 4).
@@ -614,7 +623,7 @@ The specific libraries and their options are:
  and dependencies of specific modules, see the Ginkgo webpage below.
  URL: https://ginkgo-project.github.io
  Options: GINKGO_OPT, GINKGO_LIB, GINKGO_DIR, GINKGO_BUILD_TYPE (Release or Debug).
-  Versions: Ginkgo >= 1.4.0. 
+  Versions: Ginkgo >= 1.4.0.

 - AmgX (optional), used when MFEM_USE_AMGX = YES.
  URL: https://github.com/NVIDIA/AMGX
@@ -752,6 +761,11 @@ The specific libraries and their options are:
  URL: https://zlib.net
  Options: ZLIB_OPT, ZLIB_LIB.

+- FMS (optional), used when MFEM_USE_FMS = YES.
+  URL: https://github.com/CEED/FMS
+  Options: FMS_OPT, FMS_LIB.
+  Versions: FMS >= 0.2.
+
 Building with CMake
 ===================
 The MFEM build system consists of two steps: configuration and compilation.
@@ -883,6 +897,7 @@ MFEM_USE_RAJA
 MFEM_USE_UMPIRE
 MFEM_USE_SIDRE
 MFEM_USE_CALIPER
+MFEM_USE_FMS

 The following options are CMake specific:

@@ -937,6 +952,7 @@ The CMake build system adds auto-detection for the following packages/libraries:
 - UMPIRE
 - AXOM - Used when MFEM_USE_SIDRE is enabled
 - CALIPER
+ - FMS

 The following built-in CMake packages are also used:

@@ -954,7 +970,7 @@ config/config.hpp.in:

   cp config/config.hpp.in config/_config.hpp

-The file config/_config.hpp can then be edited to enable desired options.  The
+The file config/_config.hpp can then be edited to enable desired options. The
 MFEM library is simply a combination of all object files obtained by compiling
 the .cpp source files in the source directories: general, linalg, mesh, and fem.

@@ -962,7 +978,7 @@ the .cpp source files in the source directories: general, linalg, mesh, and fem.
 Specifying an MPI job launcher
 ==============================
 By default, MFEM will use 'mpirun -np #' to launch any of its parallel tests or
-miniapps, where # is the number of MPI tasks.  An alternate MPI launcher can be
+miniapps, where # is the number of MPI tasks. An alternate MPI launcher can be
 provided by setting the MFEM_MPIEXEC and MFEM_MPIEXEC_NP config variables.

 MFEM will expect the launcher command, plus the command line option to allow it
@@ -256,6 +256,10 @@ IF (DEFINED TPL_ENABLE_SIDRE)
  SET(MFEM_USE_SIDRE ${TPL_ENABLE_SIDRE} CACHE BOOL "Enable Axom/Sidre usage" FORCE)
 ENDIF()

+IF (DEFINED TPL_ENABLE_FMS)
+  SET(MFEM_USE_FMS ${TPL_ENABLE_FMS} CACHE BOOL "Enable FMS usage" FORCE)
+ENDIF()
+
 IF (DEFINED TPL_ENABLE_CONDUIT)
  SET(MFEM_USE_CONDUIT ${TPL_ENABLE_CONDUIT} CACHE BOOL "Enable Conduit usage" FORCE)
 ENDIF()
@@ -44,6 +44,7 @@ set(MFEM_USE_PETSC @MFEM_USE_PETSC@)
 set(MFEM_USE_SLEPC @MFEM_USE_SLEPC@)
 set(MFEM_USE_MPFR @MFEM_USE_MPFR@)
 set(MFEM_USE_SIDRE @MFEM_USE_SIDRE@)
+set(MFEM_USE_FMS @MFEM_USE_FMS@)
 set(MFEM_USE_CONDUIT @MFEM_USE_CONDUIT@)
 set(MFEM_USE_PUMI @MFEM_USE_PUMI@)
 set(MFEM_USE_CUDA @MFEM_USE_CUDA@)
@@ -119,6 +119,9 @@
 // Enable the use of SIMD in the high performance templated classes
 #cmakedefine MFEM_USE_SIMD

+// Enable MFEM functionality based on the FMS library
+#cmakedefine MFEM_USE_FMS
+
 // Enable MFEM functionality based on Conduit
 #cmakedefine MFEM_USE_CONDUIT

@@ -0,0 +1,20 @@
+# Copyright (c) 2010-2021, 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:
+#   - FMS_FOUND
+#   - FMS_LIBRARIES
+#   - FMS_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(FMS FMS FMS_DIR
+  "include" fms.h "lib" fms
+  "Paths to headers required by FMS." "Libraries required by FMS.")
@@ -117,6 +117,9 @@
 // Enable the use of SIMD in the high performance templated classes
 // #define MFEM_USE_SIMD

+// Enable FMS support
+// #define MFEM_USE_FMS
+
 // Enable Conduit support
 // #define MFEM_USE_CONDUIT

@@ -43,6 +43,7 @@ MFEM_USE_PETSC         = @MFEM_USE_PETSC@
 MFEM_USE_SLEPC         = @MFEM_USE_SLEPC@
 MFEM_USE_MPFR          = @MFEM_USE_MPFR@
 MFEM_USE_SIDRE         = @MFEM_USE_SIDRE@
+MFEM_USE_FMS           = @MFEM_USE_FMS@
 MFEM_USE_CONDUIT       = @MFEM_USE_CONDUIT@
 MFEM_USE_PUMI          = @MFEM_USE_PUMI@
 MFEM_USE_HIOP          = @MFEM_USE_HIOP@
@@ -45,6 +45,7 @@ option(MFEM_USE_PETSC "Enable PETSc support." OFF)
 option(MFEM_USE_SLEPC "Enable SLEPc support." OFF)
 option(MFEM_USE_MPFR "Enable MPFR usage." OFF)
 option(MFEM_USE_SIDRE "Enable Axom/Sidre usage" OFF)
+option(MFEM_USE_FMS "Enable FMS usage" OFF)
 option(MFEM_USE_CONDUIT "Enable Conduit usage" OFF)
 option(MFEM_USE_PUMI "Enable PUMI" OFF)
 option(MFEM_USE_HIOP "Enable HiOp" OFF)
@@ -96,6 +97,11 @@ set(HYPRE_DIR "${MFEM_DIR}/../hypre/src/hypre" CACHE PATH
 # If hypre was compiled to depend on BLAS and LAPACK:
 # set(HYPRE_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
 #     "Packages that HYPRE depends on.")
+if (MFEM_USE_CUDA)
+   # This is only necessary when hypre is built with cuda:
+   set(HYPRE_REQUIRED_LIBRARIES "-lcusparse" "-lcurand" CACHE STRING
+       "Libraries that HYPRE depends on.")
+endif()

 set(METIS_DIR "${MFEM_DIR}/../metis-4.0" CACHE PATH "Path to the METIS library.")

@@ -132,10 +138,10 @@ set(MUMPS_DIR "${MFEM_DIR}/../MUMPS_5.2.0" CACHE PATH
    "Path to the MUMPS library.")
 # Packages required by MUMPS, depending on how it was compiled.
 set(MUMPS_REQUIRED_PACKAGES "MPI" "BLAS" "METIS" "ScaLAPACK" CACHE STRING
-    "Additional packages required by MUMPS.")    
+    "Additional packages required by MUMPS.")
 # If the MPI package does not find all required Fortran libraries:
 # set(MUMPS_REQUIRED_LIBRARIES "gfortran" "mpi_mpifh" CACHE STRING
-#     "Additional libraries required by MUMPS.")    
+#     "Additional libraries required by MUMPS.")

 set(STRUMPACK_DIR "${MFEM_DIR}/../STRUMPACK-build" CACHE PATH
    "Path to the STRUMPACK library.")
@@ -187,6 +193,12 @@ set(SLEPC_ARCH "arch-linux2-c-debug" CACHE STRING "SLEPC build architecture.")

 set(MPFR_DIR "" CACHE PATH "Path to the MPFR library.")

+set(FMS_DIR "${MFEM_DIR}/../fms" CACHE PATH
+    "Path to the FMS library.")
+# If FMS is built with Conduit:
+# set(FMS_REQUIRED_PACKAGES "Conduit/relay" CACHE STRING
+#     "Additional packages required by FMS.")
+
 set(CONDUIT_DIR "${MFEM_DIR}/../conduit" CACHE PATH
    "Path to the Conduit library.")

@@ -18,6 +18,9 @@
 # Some choices below are based on the OS type:
 NOTMAC := $(subst Darwin,,$(shell uname -s))

+ETAGS_BIN = $(shell command -v etags 2> /dev/null)
+EGREP_BIN = $(shell command -v egrep 2> /dev/null)
+
 CXX = g++
 MPICXX = mpicxx

@@ -133,6 +136,7 @@ MFEM_USE_PETSC         = NO
 MFEM_USE_SLEPC         = NO
 MFEM_USE_MPFR          = NO
 MFEM_USE_SIDRE         = NO
+MFEM_USE_FMS           = NO
 MFEM_USE_CONDUIT       = NO
 MFEM_USE_PUMI          = NO
 MFEM_USE_HIOP          = NO
@@ -171,6 +175,10 @@ LIBUNWIND_LIB = $(if $(NOTMAC),-lunwind -ldl,)
 HYPRE_DIR = @MFEM_DIR@/../hypre/src/hypre
 HYPRE_OPT = -I$(HYPRE_DIR)/include
 HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
+ifeq (YES,$(MFEM_USE_CUDA))
+   # This is only necessary when hypre is built with cuda:
+   HYPRE_LIB += -lcusparse -lcurand
+endif

 # METIS library configuration
 ifeq ($(MFEM_USE_SUPERLU)$(MFEM_USE_STRUMPACK)$(MFEM_USE_MUMPS),NONONO)
@@ -354,6 +362,11 @@ endif
 MPFR_OPT =
 MPFR_LIB = -lmpfr

+# FMS and required libraries configuration
+FMS_DIR = $(MFEM_DIR)/../fms
+FMS_OPT = -I$(FMS_DIR)/include
+FMS_LIB = -Wl,-rpath,$(FMS_DIR)/lib -L$(FMS_DIR)/lib -lfms
+
 # Conduit and required libraries configuration
 CONDUIT_DIR = @MFEM_DIR@/../conduit
 CONDUIT_OPT = -I$(CONDUIT_DIR)/include/conduit
@@ -0,0 +1,41 @@
+                    Finite Element Discretization Library
+                                   __
+                       _ __ ___   / _|  ___  _ __ ___
+                      | '_ ` _ \ | |_  / _ \| '_ ` _ \
+                      | | | | | ||  _||  __/| | | | | |
+                      |_| |_| |_||_|   \___||_| |_| |_|
+
+                               https://mfem.org
+
+
+This directory contains recommended git hooks, which are scripts that can be
+used to improve your development experience with MFEM:
+
+### The hooks
+
+* `pre-commit` is a hook that will be applied before each commit and run
+`astyle` on the code. This will ensure that your changes comply with the MFEM
+code styling guidelines.
+
+* `pre-push` is a hook that will be applied before each push to run a quick set
+of tests that verify that your files headers are in compliance, and that you did
+not add any large files to the repo.
+
+### Setup
+
+To setup the git hooks, run `make hooks`, which creates symlinks to the hooks in
+the `.git/hooks` directory. Individual hooks can be enabled by manually creating
+symlinks.
+
+(You may also copy the scripts directly and customize them further, but this way
+you may miss additional updates in the future.)
+
+### Failures
+
+The `branch-history` check can fail in some cases when the history is OK. For
+example, when a large number of files were modified for a legitimate reason, or
+when a picture was added for documentation.
+
+If that is the case, make sure the failure is indeed justified, and rerun the
+push command with the `--no-verify` option. This will skip the hooks, allowing
+you to push those changes.
@@ -0,0 +1,4 @@
+#!/bin/sh
+
+# Apply automated code formatting
+make -C $(git rev-parse --show-toplevel) style
@@ -0,0 +1,107 @@
+#!/bin/bash
+
+# Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+option=${1:-""}
+
+if [[ "${option}" == "--help" ]]; then
+  echo "This script runs checks on the repository."
+  echo "It has 2 modes: with and without an option."
+  echo ""
+  echo "Options are used in GitHub Actions and can be:"
+  echo "  --copyright"
+  echo "  --license"
+  echo "  --release"
+  echo "  --style"
+  echo "  --history"
+  echo ""
+  echo "As a githook, the script is used without options."
+  echo "In that case, it will run all the checks except style."
+  echo ""
+  echo "Use --help to print this help message."
+fi
+
+cd $(git rev-parse --show-toplevel)
+
+# copyright check
+copyright=true
+if [[ "${option}" == "--copyright" || "${option}" == "" ]]; then
+  if git grep -l "^\(#\|//\).*\(\-2020\|\ 2010,\)" > matches.txt; then
+    echo "Please update the following files to Copyright (c) 2010-2021:"
+    cat matches.txt
+    copyright=false
+  fi
+fi
+
+# license check
+license=true
+if [[ "${option}" == "--license" || "${option}" == "" ]]; then
+  if git grep -li "^\(#\|//\).*GNU\ Lesser\ General\ Public\ License" > matches.txt; then
+    echo "Please update the following files to the BSD-3 license:"
+    cat matches.txt
+    license=false
+  fi
+fi
+
+# release check
+release=true
+if [[ "${option}" == "--release" || "${option}" == "" ]]; then
+  if git grep -l "^\(#\|//\).*LLNL\-CODE\-443211" > matches.txt
+  then
+    echo "Please update the following files to LLNL-CODE-806117:"
+    cat matches.txt
+    release=false
+  fi
+fi
+
+# wrap-up
+code=0
+if ! $copyright ; then
+  echo "copyright check failed, unroll log for details"
+  code=1
+fi
+if ! $license ; then
+  echo "license check failed, unroll log for details"
+  code=1
+fi
+if ! $release ; then
+  echo "release check failed, unroll log for details"
+  code=1
+fi
+
+# `code-style` is not just a check, it will actually reformat the code if
+# necessary. This means that if one pushes while the repo is in dirty state
+# (changes not staged), those changes may be mixed with format changes.
+# To activate this, you will need to hard-copy this hook script in the hook
+# directory and uncomment only then. (See README.md)
+#
+## style check
+#if [[ "${option}" == "--style" || "${option}" == "" ]]; then
+if [[ "${option}" == "--style" ]]; then
+  if which astyle && [[ "$(astyle --version)" == "Artistic Style Version 2.05.1" ]]; then
+    cd tests/scripts
+    if ! ./runtest code-style; then code=1; fi
+    cd -
+  else
+    echo "Warning: astyle not found or version is not 2.05.1"
+  fi
+fi
+
+# branch-history
+if [[ "${option}" == "--history" || "${option}" == "" ]]; then
+  git fetch origin master:master
+  cd tests/scripts
+  if ! ./runtest branch-history; then code=1; fi
+  cd -
+fi
+
+exit $code
@@ -57,22 +57,27 @@ TIMECMD := $(word 1,$(TIMECMD))
 ifneq (,$(filter test%,$(MAKECMDGOALS)))
   MAKEFLAGS += -k
 endif
-# Test runs of the examples/miniapps with parameters - check exit code
+# Test runs of the examples/miniapps with parameters - check exit code:
+# 0 means success, 255 means the test was skipped, anything else means error
 mfem-test = \
   printf "   $(3) [$(2) $(1) ... ]: "; \
   $(call $(TIMEFUN),$(TIMECMD),$(2) ./$(1) $(if $(5),,-no-vis )$(4) \
     > $(1).stderr 2>&1); \
-   if [ "$$3" = 0 ]; \
-   then $(PRINT_OK); else $(PRINT_FAILED); cat $(1).stderr; fi; \
-   rm -f $(1).stderr; exit $$3
+   err="$$3"; \
+   if [ "$$3" = 0 ]; then $(PRINT_OK); \
+   else if [ "$$3" = 255 ]; then $(PRINT_SKIP); err=0; \
+   else $(PRINT_FAILED); cat $(1).stderr; fi; fi; \
+   rm -f $(1).stderr; exit $$err

 # Test runs of the examples/miniapps - check exit code and if a file exists
+# See mfem-test for the interpretation of the error code
 mfem-test-file = \
   printf "   $(3) [$(2) $(1) ... ]: "; \
   $(call $(TIMEFUN),$(TIMECMD),$(2) ./$(1) -no-vis > $(1).stderr 2>&1); \
   err="$$3"; \
-   if [ "$$3" = 0 ] && [ -e $(4) ]; \
-   then $(PRINT_OK); else $(PRINT_FAILED); cat $(1).stderr; err=64; fi; \
+   if [ "$$3" = 0 ] && [ -e $(4) ]; then $(PRINT_OK); \
+   else if [ "$$3" = 255 ] && [ -e $(4) ]; then $(PRINT_SKIP); err=0; \
+   else $(PRINT_FAILED); cat $(1).stderr; err=64; fi; fi; \
   rm -f $(1).stderr; exit $$err

 .PHONY: test test-par-YES test-par-NO test-ser test-par test-clean test-print
@@ -80,6 +85,26 @@ mfem-test-file = \
 # What sets of tests to run in serial and parallel
 test-par-YES: $(PAR_$(MFEM_TESTS):=-test-par) $(SEQ_$(MFEM_TESTS):=-test-seq)
 test-par-NO:  $(SEQ_$(MFEM_TESTS):=-test-seq)
+ifeq ($(MFEM_USE_CUDA),YES)
+.PHONY: test-par-YES-cuda test-par-NO-cuda test-ser-cuda test-par-cuda test-cuda
+test-par-YES: test-par-YES-cuda
+test-par-NO:  test-par-NO-cuda
+test-par-YES-cuda: test-par-cuda test-ser-cuda
+test-par-NO-cuda:  test-ser-cuda
+test-ser-cuda: $(SEQ_DEVICE_$(MFEM_TESTS):=-test-seq-cuda)
+test-par-cuda: $(PAR_DEVICE_$(MFEM_TESTS):=-test-par-cuda)
+test-cuda: test-par-$(MFEM_USE_MPI)-cuda clean-exec
+endif
+ifeq ($(MFEM_USE_HIP),YES)
+.PHONY: test-par-YES-hip test-par-NO-hip test-ser-hip test-par-hip test-hip
+test-par-YES: test-par-YES-hip
+test-par-NO:  test-par-NO-hip
+test-par-YES-hip: test-par-hip test-ser-hip
+test-par-NO-hip:  test-ser-hip
+test-ser-hip: $(SEQ_DEVICE_$(MFEM_TESTS):=-test-seq-hip)
+test-par-hip: $(PAR_DEVICE_$(MFEM_TESTS):=-test-par-hip)
+test-hip: test-par-$(MFEM_USE_MPI)-hip clean-exec
+endif
 test-ser:     test-par-NO
 test-par:     test-par-YES
 test:         all test-par-$(MFEM_USE_MPI) clean-exec
@@ -0,0 +1,9 @@
+MFEM INLINE mesh v1.0
+
+type = pyramid
+nx = 4
+ny = 4
+nz = 4
+sx = 1.0
+sy = 1.0
+sz = 1.0
@@ -0,0 +1,43 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+# PYRAMID     = 7
+#
+
+dimension
+3
+
+elements
+2
+1 7 4 3 2 1 0
+1 7 1 2 3 4 5
+
+boundary
+8
+1 2 0 2 1
+2 2 0 3 2
+3 2 0 4 3
+4 2 0 1 4
+5 2 1 2 5
+6 2 2 3 5
+7 2 3 4 5
+8 2 4 1 5
+
+vertices
+6
+3
+0 0 -1
+1 0 0
+0 1 0
+-1 0 0
+0 -1 0
+0 0 1
@@ -0,0 +1,38 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+# PYRAMID     = 7
+#
+
+dimension
+3
+
+elements
+1
+1 7 0 1 2 3 4
+
+boundary
+5
+1 3 3 2 1 0
+2 2 0 1 4
+3 2 1 2 4
+4 2 2 3 4
+5 2 3 0 4
+
+vertices
+5
+3
+0 0 0
+1 0 0
+1 1 0
+0 1 0
+0 0 1
@@ -0,0 +1,246 @@
+FMS: 100
+DataCollection/Name: star
+DataCollection/NumberOfFieldDescriptors: 1
+DataCollection/FieldDescriptors/0/Name: CoordsDescriptor
+DataCollection/FieldDescriptors/0/ComponentName: volume
+DataCollection/FieldDescriptors/0/Type: 0
+DataCollection/FieldDescriptors/0/FixedOrder/Size: 3
+DataCollection/FieldDescriptors/0/FixedOrder/Type: FMS_UINT64
+DataCollection/FieldDescriptors/0/FixedOrder/Values: [0, 1, 3]
+DataCollection/FieldDescriptors/0/NumDofs: 211
+DataCollection/NumberOfFields: 1
+DataCollection/Fields/0/Name: Coords
+DataCollection/Fields/0/LayoutType: 0
+DataCollection/Fields/0/NumberOfVectorComponents: 2
+DataCollection/Fields/0/FieldDescriptorName: CoordsDescriptor
+DataCollection/Fields/0/Data/Size: 422
+DataCollection/Fields/0/Data/Type: FMS_DOUBLE
+DataCollection/Fields/0/Data/Values: [-0.016886, 1.000000, 0.309017, 
+1.309020, -0.809017, -0.500000, 
+-0.809017, -1.618030, 0.309017, 
+-0.500000, 1.309020, 0.519420, 
+1.154510, 0.809019, 0.147680, 
+-0.095492, -0.654508, -0.415586, 
+-1.213520, -1.213520, -0.392210, 
+-0.654508, -0.095492, 0.139949, 
+0.809019, 1.154510, 0.660184, 
+-0.264063, -0.800064, -0.231060, 
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+0.595190, 0.846237, 0.671735, 
+1.051500, 1.103010, 0.964008, 
+0.821603, 1.257520, 1.206010, 
+1.142350, 0.975686, 0.781273, 
+0.717257, 0.475684, 0.642352, 
+0.268930, 0.211049, 0.174181, 
+0.039345, -0.147746, -0.177481, 
+-0.365164, -0.230328, -0.551503, 
+-0.603005, -0.497587, -0.389864, 
+-0.757514, -0.706011, -0.675487, 
+-0.528946, -0.943851, -1.078690, 
+-1.087600, -0.955467, -1.483190, 
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+-0.206896, 0.174181, 0.039345, 
+0.268468, 0.222269, 0.475684, 
+0.642352, 0.759791, 0.719381, 
+1.142350, 0.975686, 1.257520, 
+1.206010, 0.972837, 0.836119, 
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+-0.206969, -0.027946, -0.184969, 
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+0.430781, 0.718277, 0.885068, 
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+1.024530, 0.934099, 1.093820, 
+0.348422, 0.524463, 0.404903, 
+0.587376, 0.054525, 0.146431, 
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+-0.296404, -1.063310, -1.244950, 
+-0.453865, -0.951057, -0.475529, 
+0.466620, 0.792932, -0.013913, 
+-0.748783, -0.497528, 0.021382, 
+-0.017158, 0.172591, 0.330125, 
+0.458568, 0.457971, 0.137740, 
+0.299049, 0.588394, 0.667324, 
+0.432341, 0.634346, 0.117322, 
+0.193603, 0.211702, 0.098278, 
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+-0.216296, -0.458634, -0.592374, 
+-0.563926, -0.680404, -0.135751, 
+-0.302942, -0.469005, -0.453640, 
+-0.182727, -0.314240, 0.024270, 
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+0.485799, 0.492951, 0.792548, 
+0.634038, 0.951057, 0.951057, 
+0.777915, 0.613430, 0.951057, 
+0.951057, 0.793994, 0.635800, 
+1.049020, 1.146990, 1.084480, 
+0.924310, 1.440880, 1.342910, 
+1.380330, 1.221820, 0.948209, 
+0.856297, 0.746293, 0.904802, 
+0.476242, 0.393234, 0.489821, 
+0.391857, 0.194471, 0.075751, 
+0.097964, 0.195929, -0.097964, 
+-0.195928, -0.173234, -0.078922, 
+-0.489821, -0.391856, -0.467007, 
+-0.397859, -0.746293, -0.904802, 
+-0.945206, -0.849559, -1.380330, 
+-1.221820, -1.440880, -1.342910, 
+-1.100830, -0.923191, -1.049020, 
+-1.146990, -0.774515, -0.621542, 
+-0.951057, -0.951057, -0.803055, 
+-0.635255, -0.951057, -0.951057, 
+-0.792548, -0.634038, -0.454301, 
+-0.479369, -0.158510, -0.317019, 
+0.149331, 0.178643, 0.295860, 
+0.306275, 0.246225, 0.406610, 
+0.367954, 0.498458, -0.014929, 
+0.084917, -0.094272, -0.000726, 
+-0.245374, -0.340755, -0.435351, 
+-0.490564, -0.176355, -0.294974, 
+-0.148010, -0.328246, 0.136248, 
+0.182883, 0.328957, 0.309903, 
+0.646446, 0.622546, 0.800859, 
+0.801803, 0.643087, 0.654473, 
+0.796963, 0.816799, 0.748189, 
+0.898148, 0.819092, 0.970033, 
+1.049540, 1.162660, 1.115310, 
+1.266700, 0.539960, 0.728396, 
+0.656318, 0.783152, 0.302716, 
+0.403858, 0.219006, 0.309252, 
+0.009667, 0.107161, -0.118211, 
+0.011786, -0.284704, -0.179858, 
+-0.411567, -0.296676, -0.570168, 
+-0.635348, -0.726784, -0.793211, 
+-1.016860, -1.112970, -1.170910, 
+-1.281530, -0.737860, -0.851723, 
+-0.883732, -0.995070, -0.653153, 
+-0.769939, -0.631918, -0.797688, 
+-0.616289, -0.806819, -0.638485, 
+-0.790356, -0.136399, -0.322769, 
+-0.165339, -0.309622]
+DataCollection/Mesh/PartitionInfo/Size: 2
+DataCollection/Mesh/PartitionInfo/Type: FMS_UINT64
+DataCollection/Mesh/PartitionInfo/Values: [0, 1]
+DataCollection/Mesh/NumDomainNames: 1
+DataCollection/Mesh/NumComponents: 1
+DataCollection/Mesh/NumTags: 0
+DataCollection/Mesh/DomainNames/0/Name: Domain
+DataCollection/Mesh/DomainNames/0/NumDomains: 1
+DataCollection/Mesh/DomainNames/0/Domains/0/Dimension: 2
+DataCollection/Mesh/DomainNames/0/Domains/0/NumVertices: 31
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/0/EntityType: FMS_EDGE
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/0/NumEntities: 50
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/0/Size: 100
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/0/Type: FMS_INT32
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/0/Values: [11, 0, 26, 
+11, 26, 14, 
+14, 0, 27, 
+14, 27, 17, 
+17, 0, 28, 
+17, 28, 20, 
+20, 0, 29, 
+20, 29, 23, 
+23, 0, 30, 
+23, 30, 11, 
+11, 1, 12, 
+1, 26, 12, 
+12, 3, 13, 
+3, 26, 13, 
+13, 2, 14, 
+2, 15, 2, 
+27, 15, 15, 
+5, 16, 5, 
+27, 16, 16, 
+4, 17, 4, 
+18, 4, 28, 
+18, 18, 7, 
+19, 7, 28, 
+19, 19, 6, 
+20, 6, 21, 
+6, 29, 21, 
+21, 9, 22, 
+9, 29, 22, 
+22, 8, 23, 
+8, 24, 8, 
+30, 24, 24, 
+10, 25, 10, 
+30, 25, 25, 1]
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/1/EntityType: FMS_QUADRILATERAL
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/1/NumEntities: 20
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/1/Size: 80
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/1/Type: FMS_INT32
+DataCollection/Mesh/DomainNames/0/Domains/0/Entities/1/Values: [0, 1, 2, 
+3, 3, 4, 
+5, 6, 6, 
+7, 8, 9, 
+9, 10, 11, 
+12, 12, 13, 
+14, 0, 15, 
+16, 17, 1, 
+17, 18, 19, 
+20, 2, 20, 
+21, 22, 22, 
+23, 24, 4, 
+24, 25, 26, 
+27, 5, 27, 
+28, 29, 29, 
+30, 31, 7, 
+31, 32, 33, 
+34, 8, 34, 
+35, 36, 36, 
+37, 38, 10, 
+38, 39, 40, 
+41, 11, 41, 
+42, 43, 43, 
+44, 45, 13, 
+45, 46, 47, 
+48, 14, 48, 
+49, 15]
+DataCollection/Mesh/Components/0/Name: volume
+DataCollection/Mesh/Components/0/Dimension: 2
+DataCollection/Mesh/Components/0/NumEntities: 20
+DataCollection/Mesh/Components/0/Coordinates: Coords
+DataCollection/Mesh/Components/0/NumParts: 1
+DataCollection/Mesh/Components/0/Parts/0/DomainName: Domain
+DataCollection/Mesh/Components/0/Parts/0/DomainID: 0
+DataCollection/Mesh/Components/0/Parts/0/FullDomain: Yes
+DataCollection/Mesh/Components/0/Relations/Size: 0
+DataCollection/Mesh/Components/0/Relations/Type: FMS_UINT64
@@ -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         = v4.2.1
+PROJECT_NUMBER         = v4.3.1

 # 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
@@ -189,6 +189,7 @@ namespace mfem {
 * - <a class="el" href="field-diff_8cpp_source.html">Field Diff</a>: compare grid functions on different meshes
 * - <a class="el" href="field-interp_8cpp_source.html">Field Interp</a>: transfer a grid functions between meshes
 * - <a class="el" href="distance_8cpp_source.html">Distance</a>: finite element distance function solver
+ * - <a class="el" href="diffusion_8cpp_source.html">Shifted Diffusion</a>: shifted boundary diffusion solver
 * - <a class="el" href="distance_8cpp_source.html">Block Solvers</a>: comparison of saddle point system solvers
 * - <a class="el" href="parheat_8cpp_source.html">Optimization gradients</a>: Gradients of PDE-constrained function
 * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Laplace problem
@@ -84,8 +84,9 @@ foreach(SRC_FILE ${ALL_EXE_SRCS})
  get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
  string(REPLACE ".cpp" "" TEST_NAME ${SRC_FILENAME})

-  if (NOT (${TEST_NAME} MATCHES "ex0p?"))
-    set(THIS_TEST_OPTIONS "-no-vis")
+  set(THIS_TEST_OPTIONS "-no-vis")
+  if (${TEST_NAME} MATCHES "ex0p?")
+    set(THIS_TEST_OPTIONS)
  endif()
  if (${TEST_NAME} MATCHES "ex10p*")
    list(APPEND THIS_TEST_OPTIONS "-tf" "5")
@@ -107,6 +108,34 @@ foreach(SRC_FILE ${ALL_EXE_SRCS})
  endif()
 endforeach()

+# Add CUDA/HIP tests.
+set(DEVICE_EXAMPLES
+    # serial examples with device support:
+    ex1 ex3 ex4 ex5 ex6 ex9 ex22 ex24 ex25 ex26
+    # parallel examples with device support:
+    ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex22p ex24p ex25p ex26p)
+set(MFEM_TEST_DEVICE)
+if (MFEM_USE_CUDA)
+  set(MFEM_TEST_DEVICE "cuda")
+elseif (MFEM_USE_HIP)
+  set(MFEM_TEST_DEVICE "hip")
+endif()
+if (MFEM_TEST_DEVICE)
+  foreach(TEST_NAME ${DEVICE_EXAMPLES})
+    set(THIS_TEST_OPTIONS "-no-vis" "-d" "${MFEM_TEST_DEVICE}")
+    if (NOT (${TEST_NAME} MATCHES ".*p$"))
+      add_test(NAME ${TEST_NAME}_${MFEM_TEST_DEVICE}_ser
+        COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})
+    elseif (MFEM_USE_MPI)
+      add_test(NAME ${TEST_NAME}_${MFEM_TEST_DEVICE}_np=${MFEM_MPI_NP}
+        COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
+        ${MPIEXEC_PREFLAGS}
+        $<TARGET_FILE:${TEST_NAME}> ${THIS_TEST_OPTIONS}
+        ${MPIEXEC_POSTFLAGS})
+    endif()
+  endforeach()
+endif()
+
 # If STRUMPACK is enabled, add a test run that uses it.
 if (MFEM_USE_STRUMPACK)
  add_test(NAME ex11p_strumpack_np=${MFEM_MPI_NP}
@@ -0,0 +1,18 @@
+                    Finite Element Discretization Library
+                                   __
+                       _ __ ___   / _|  ___  _ __ ___
+                      | '_ ` _ \ | |_  / _ \| '_ ` _ \
+                      | | | | | ||  _||  __/| | | | | |
+                      |_| |_| |_||_|   \___||_| |_| |_|
+
+                               https://mfem.org
+
+This directory contains modifications of the example codes that illustrate the
+use of MFEM features based on the Caliper performance profiling library.
+
+To build these examples, make sure that MFEM is configured with the option
+"MFEM_USE_CALIPER = YES", see the top-level INSTALL file for details (version
+2.5.0 of Caliper is recommended, though older versions may work too).
+
+We recommend comparing the original example codes with the corresponding files
+in the current directory.
@@ -206,9 +206,9 @@ int main(int argc, char *argv[])
   cout << "Size of linear system: " << A->Height() << endl;

   // 11. Solve the linear system A X = B.
-   MFEM_PERF_BEGIN("Solve A X=B");
   if (!pa)
   {
+      MFEM_PERF_SCOPE("Solve A X=B (FA)");
 #ifndef MFEM_USE_SUITESPARSE
      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
      GSSmoother M((SparseMatrix&)(*A));
@@ -223,6 +223,7 @@ int main(int argc, char *argv[])
   }
   else // Jacobi preconditioning in partial assembly mode
   {
+      MFEM_PERF_SCOPE("Solve A X=B (PA)");
      if (UsesTensorBasis(fespace))
      {
         OperatorJacobiSmoother M(a, ess_tdof_list);
@@ -233,7 +234,6 @@ int main(int argc, char *argv[])
         CG(*A, B, X, 1, 400, 1e-12, 0.0);
      }
   }
-   MFEM_PERF_END("Solve A X=B");
   // 12. Recover the solution as a finite element grid function.
   a.RecoverFEMSolution(X, b, x);

@@ -231,28 +231,29 @@ int main(int argc, char *argv[])
   // 13. Solve the linear system A X = B.
   //     * With full assembly, use the BoomerAMG preconditioner from hypre.
   //     * With partial assembly, use Jacobi smoothing, for now.
-   MFEM_PERF_BEGIN("Solve A X = B");
-   Solver *prec = NULL;
-   if (pa)
   {
-      if (UsesTensorBasis(fespace))
+      MFEM_PERF_SCOPE("Solve A X=B");
+      Solver *prec = NULL;
+      if (pa)
      {
-         prec = new OperatorJacobiSmoother(a, ess_tdof_list);
+         if (UsesTensorBasis(fespace))
+         {
+            prec = new OperatorJacobiSmoother(a, ess_tdof_list);
+         }
      }
+      else
+      {
+         prec = new HypreBoomerAMG;
+      }
+      CGSolver cg(MPI_COMM_WORLD);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(2000);
+      cg.SetPrintLevel(1);
+      if (prec) { cg.SetPreconditioner(*prec); }
+      cg.SetOperator(*A);
+      cg.Mult(B, X);
+      delete prec;
   }
-   else
-   {
-      prec = new HypreBoomerAMG;
-   }
-   CGSolver cg(MPI_COMM_WORLD);
-   cg.SetRelTol(1e-12);
-   cg.SetMaxIter(2000);
-   cg.SetPrintLevel(1);
-   if (prec) { cg.SetPreconditioner(*prec); }
-   cg.SetOperator(*A);
-   cg.Mult(B, X);
-   delete prec;
-   MFEM_PERF_END("Solve A X = B");
   // 14. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
   a.RecoverFEMSolution(X, b, x);
@@ -9,6 +9,7 @@
 //               ex1 -m ../data/fichera.mesh
 //               ex1 -m ../data/fichera-mixed.mesh
 //               ex1 -m ../data/toroid-wedge.mesh
+//               ex1 -m ../data/octahedron.mesh -o 1
 //               ex1 -m ../data/periodic-annulus-sector.msh
 //               ex1 -m ../data/periodic-torus-sector.msh
 //               ex1 -m ../data/square-disc-p2.vtk -o 2
@@ -55,6 +55,7 @@ int main(int argc, char *argv[])
   int order = 1;
   int nev = 5;
   bool visualization = 1;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -71,6 +72,8 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -86,13 +89,18 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 3. Read the (serial) mesh from the given mesh file on all processors. We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors. We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 4. Refine the serial mesh on all processors to increase the resolution. In
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
   //    this example we do 'ref_levels' of uniform refinement (2 by default, or
   //    specified on the command line with -rs).
   for (int lev = 0; lev < ser_ref_levels; lev++)
@@ -100,7 +108,7 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution (1 time by
   //    default, or specified on the command line with -rp). Once the parallel
   //    mesh is defined, the serial mesh can be deleted.
@@ -110,9 +118,8 @@ int main(int argc, char *argv[])
   {
      pmesh->UniformRefinement();
   }
-   pmesh->ReorientTetMesh();

-   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Nedelec finite elements of the specified order.
   FiniteElementCollection *fec = new ND_FECollection(order, dim);
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
@@ -122,7 +129,7 @@ int main(int argc, char *argv[])
      cout << "Number of unknowns: " << size << endl;
   }

-   // 7. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
+   // 8. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
   //    element space. The first corresponds to the curl curl, while the second
   //    is a simple mass matrix needed on the right hand side of the
   //    generalized eigenvalue problem below. The boundary conditions are
@@ -164,7 +171,7 @@ int main(int argc, char *argv[])
   delete a;
   delete m;

-   // 8. Define and configure the AME eigensolver and the AMS preconditioner for
+   // 9. Define and configure the AME eigensolver and the AMS preconditioner for
   //    A to be used within the solver. Set the matrices which define the
   //    generalized eigenproblem A x = lambda M x.
   HypreAMS *ams = new HypreAMS(*A,fespace);
@@ -180,15 +187,15 @@ int main(int argc, char *argv[])
   ame->SetMassMatrix(*M);
   ame->SetOperator(*A);

-   // 9. Compute the eigenmodes and extract the array of eigenvalues. Define a
-   //    parallel grid function to represent each of the eigenmodes returned by
-   //    the solver.
+   // 10. Compute the eigenmodes and extract the array of eigenvalues. Define a
+   //     parallel grid function to represent each of the eigenmodes returned by
+   //     the solver.
   Array<double> eigenvalues;
   ame->Solve();
   ame->GetEigenvalues(eigenvalues);
   ParGridFunction x(fespace);

-   // 10. Save the refined mesh and the modes in parallel. This output can be
+   // 11. Save the refined mesh and the modes in parallel. This output can be
   //     viewed later using GLVis: "glvis -np <np> -m mesh -g mode".
   {
      ostringstream mesh_name, mode_name;
@@ -213,7 +220,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 11. Send the solution by socket to a GLVis server.
+   // 12. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -253,7 +260,7 @@ int main(int argc, char *argv[])
      mode_sock.close();
   }

-   // 12. Free the used memory.
+   // 13. Free the used memory.
   delete ame;
   delete ams;
   delete M;
@@ -19,6 +19,14 @@
 //               ex15 -m ../data/square-disc.mesh
 //               ex15 -m ../data/escher.mesh -r 2 -tf 0.3
 //
+//               Kelly estimator:
+//
+//               ex15 -est 1 -e 0.0001
+//               ex15 -est 1 -o 1 -y 0.4
+//               ex15 -est 1 -o 4 -y 0.1
+//               ex15 -est 1 -n 5
+//               ex15 -est 1 -p 1 -n 3
+//
 // Description:  Building on Example 6, this example demonstrates dynamic AMR.
 //               The mesh is adapted to a time-dependent solution by refinement
 //               as well as by derefinement. For simplicity, the solution is
@@ -28,10 +36,10 @@
 //               At each outer iteration the right hand side function is changed
 //               to mimic a time dependent problem.  Within each inner iteration
 //               the problem is solved on a sequence of meshes which are locally
-//               refined according to a simple ZZ error estimator.  At the end
-//               of the inner iteration the error estimates are also used to
-//               identify any elements which may be over-refined and a single
-//               derefinement step is performed.
+//               refined according to a simple ZZ or Kelly error estimator.  At
+//               the end of the inner iteration the error estimates are also
+//               used to identify any elements which may be over-refined and a
+//               single derefinement step is performed.
 //
 //               The example demonstrates MFEM's capability to refine and
 //               derefine nonconforming meshes, in 2D and 3D, and on linear,
@@ -78,6 +86,7 @@ int main(int argc, char *argv[])
   int nc_limit = 3;         // maximum level of hanging nodes
   bool visualization = true;
   bool visit = false;
+   int which_estimator = 0;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -98,6 +107,9 @@ int main(int argc, char *argv[])
                  "Maximum level of hanging nodes.");
   args.AddOption(&t_final, "-tf", "--t-final",
                  "Final time; start time is 0.");
+   args.AddOption(&which_estimator, "-est", "--estimator",
+                  "Which estimator to use: "
+                  "0 = ZZ, 1 = Kelly. Defaults to ZZ.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -186,19 +198,38 @@ int main(int argc, char *argv[])
   visit_dc.RegisterField("solution", &x);
   int vis_cycle = 0;

-   // 9. As in Example 6, we set up a Zienkiewicz-Zhu estimator that will be
-   //    used to obtain element error indicators. The integrator needs to
-   //    provide the method ComputeElementFlux. The smoothed flux space is a
-   //    vector valued H1 space here.
-   FiniteElementSpace flux_fespace(&mesh, &fec, sdim);
-   ZienkiewiczZhuEstimator estimator(*integ, x, flux_fespace);
+   // 9. As in Example 6, we set up an estimator that will be used to obtain
+   //    element error indicators. The integrator needs to provide the method
+   //    ComputeElementFlux. The smoothed flux space is a vector valued H1 (ZZ)
+   //    or L2 (Kelly) space here.
+   L2_FECollection flux_fec(order, dim);
+   ErrorEstimator* estimator{nullptr};
+
+   switch (which_estimator)
+   {
+      case 1:
+      {
+         auto flux_fes = new FiniteElementSpace(&mesh, &flux_fec, sdim);
+         estimator = new KellyErrorEstimator(*integ, x, flux_fes);
+         break;
+      }
+
+      default:
+         std::cout << "Unknown estimator. Falling back to ZZ." << std::endl;
+      case 0:
+      {
+         auto flux_fes = new FiniteElementSpace(&mesh, &fec, sdim);
+         estimator = new ZienkiewiczZhuEstimator(*integ, x, flux_fes);
+         break;
+      }
+   }

   // 10. As in Example 6, we also need a refiner. This time the refinement
   //     strategy is based on a fixed threshold that is applied locally to each
   //     element. The global threshold is turned off by setting the total error
   //     fraction to zero. We also enforce a maximum refinement ratio between
   //     adjacent elements.
-   ThresholdRefiner refiner(estimator);
+   ThresholdRefiner refiner(*estimator);
   refiner.SetTotalErrorFraction(0.0); // use purely local threshold
   refiner.SetLocalErrorGoal(max_elem_error);
   refiner.PreferConformingRefinement();
@@ -207,7 +238,7 @@ int main(int argc, char *argv[])
   // 11. A derefiner selects groups of elements that can be coarsened to form
   //     a larger element. A conservative enough threshold needs to be set to
   //     prevent derefining elements that would immediately be refined again.
-   ThresholdDerefiner derefiner(estimator);
+   ThresholdDerefiner derefiner(*estimator);
   derefiner.SetThreshold(hysteresis * max_elem_error);
   derefiner.SetNCLimit(nc_limit);

@@ -308,6 +339,8 @@ int main(int argc, char *argv[])
      b.Update();
   }

+   delete estimator;
+
   return 0;
 }

@@ -223,13 +223,14 @@ int main(int argc, char *argv[])
   visit_dc.RegisterField("solution", &x);
   int vis_cycle = 0;

-   // 10. As in Example 6p, we set up a Zienkiewicz-Zhu estimator that will be
-   //     used to obtain element error indicators. The integrator needs to
-   //     provide the method ComputeElementFlux. We supply an L2 space for the
-   //     discontinuous flux and an H(div) space for the smoothed flux.
+   // 10. As in Example 6p, we set up an estimator that will be used to obtain
+   //     element error indicators. The integrator needs to provide the method
+   //     ComputeElementFlux. We supply an L2 space for the discontinuous flux
+   //     and an H(div) space for the smoothed flux.
   L2_FECollection flux_fec(order, dim);
   RT_FECollection smooth_flux_fec(order-1, dim);
-   ErrorEstimator* estimator;
+   ErrorEstimator* estimator{nullptr};
+
   switch (which_estimator)
   {
      case 1:
@@ -248,7 +249,7 @@ int main(int argc, char *argv[])
      default:
         if (myid == 0)
         {
-            std::cout << "Unkown estimator. Falling back to L2ZZ." << std::endl;
+            std::cout << "Unknown estimator. Falling back to L2ZZ." << std::endl;
         }
      case 0:
      {
@@ -24,7 +24,10 @@
 //               class ConductionOperator defining C(u)), as well as their
 //               implicit time integration. Note that implementing the method
 //               ConductionOperator::ImplicitSolve is the only requirement for
-//               high-order implicit (SDIRK) time integration.
+//               high-order implicit (SDIRK) time integration. In this example,
+//               the diffusion operator is linearized by evaluating with the
+//               lagged solution from the previous timestep, so there is only
+//               a linear solve.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -326,8 +329,8 @@ ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
 void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 {
   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
+   //    du_dt = M^{-1}*-Ku
+   // for du_dt, where K is linearized by using u from the previous timestep
   Kmat.Mult(u, z);
   z.Neg(); // z = -z
   M_solver.Mult(z, du_dt);
@@ -338,7 +341,7 @@ void ConductionOperator::ImplicitSolve(const double dt,
 {
   // Solve the equation:
   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
+   // for du_dt, where K is linearized by using u from the previous timestep
   if (!T)
   {
      T = Add(1.0, Mmat, dt, Kmat);
@@ -24,8 +24,11 @@
 //               class ConductionOperator defining C(u)), as well as their
 //               implicit time integration. Note that implementing the method
 //               ConductionOperator::ImplicitSolve is the only requirement for
-//               high-order implicit (SDIRK) time integration. Optional saving
-//               with ADIOS2 (adios2.readthedocs.io) is also illustrated.
+//               high-order implicit (SDIRK) time integration. In this example,
+//               the diffusion operator is linearized by evaluating with the
+//               lagged solution from the previous timestep, so there is only
+//               a linear solve. Optional saving with ADIOS2
+//               (adios2.readthedocs.io) is also illustrated.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -420,8 +423,8 @@ ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
 void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 {
   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
+   //    du_dt = M^{-1}*-Ku
+   // for du_dt, where K is linearized by using u from the previous timestep
   Kmat.Mult(u, z);
   z.Neg(); // z = -z
   M_solver.Mult(z, du_dt);
@@ -432,7 +435,7 @@ void ConductionOperator::ImplicitSolve(const double dt,
 {
   // Solve the equation:
   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
+   // for du_dt, where K is linearized by using u from the previous timestep
   if (!T)
   {
      T = Add(1.0, Mmat, dt, Kmat);
@@ -196,6 +196,12 @@ void InitialDeformation(const Vector &x, Vector &y);

 int main(int argc, char *argv[])
 {
+#ifdef HYPRE_USING_CUDA
+   cout << "\nAs of mfem-4.3 and hypre-2.22.0 (July 2021) this example\n"
+        << "is NOT supported with the CUDA version of hypre.\n\n";
+   return 255;
+#endif
+
   // 1. Initialize MPI
   MPI_Session mpi;
   const int myid = mpi.WorldRank();
@@ -438,16 +444,20 @@ JacobianPreconditioner::JacobianPreconditioner(Array<ParFiniteElementSpace *>
 void JacobianPreconditioner::Mult(const Vector &k, Vector &y) const
 {
   // Extract the blocks from the input and output vectors
-   Vector disp_in(k.GetData() + block_trueOffsets[0],
-                  block_trueOffsets[1]-block_trueOffsets[0]);
-   Vector pres_in(k.GetData() + block_trueOffsets[1],
-                  block_trueOffsets[2]-block_trueOffsets[1]);
-
-   Vector disp_out(y.GetData() + block_trueOffsets[0],
+   Vector disp_in;
+   disp_in.MakeRef(const_cast<Vector&>(k), block_trueOffsets[0],
                   block_trueOffsets[1]-block_trueOffsets[0]);
-   Vector pres_out(y.GetData() + block_trueOffsets[1],
+   Vector pres_in;
+   pres_in.MakeRef(const_cast<Vector&>(k), block_trueOffsets[1],
                   block_trueOffsets[2]-block_trueOffsets[1]);

+   Vector disp_out;
+   disp_out.MakeRef(y, block_trueOffsets[0],
+                    block_trueOffsets[1]-block_trueOffsets[0]);
+   Vector pres_out;
+   pres_out.MakeRef(y, block_trueOffsets[1],
+                    block_trueOffsets[2]-block_trueOffsets[1]);
+
   Vector temp(block_trueOffsets[1]-block_trueOffsets[0]);
   Vector temp2(block_trueOffsets[1]-block_trueOffsets[0]);

@@ -459,6 +469,9 @@ void JacobianPreconditioner::Mult(const Vector &k, Vector &y) const
   subtract(disp_in, temp, temp2);

   stiff_pcg->Mult(temp2, disp_out);
+
+   disp_out.SyncAliasMemory(y);
+   pres_out.SyncAliasMemory(y);
 }

 void JacobianPreconditioner::SetOperator(const Operator &op)
@@ -473,7 +486,10 @@ void JacobianPreconditioner::SetOperator(const Operator &op)

      if (!spaces[0]->GetParMesh()->Nonconforming())
      {
+#ifndef HYPRE_USING_CUDA
+         // Not available yet when hypre is built with CUDA
         stiff_prec_amg->SetElasticityOptions(spaces[0]);
+#endif
      }

      stiff_prec = stiff_prec_amg;
@@ -9,6 +9,7 @@
 //               mpirun -np 4 ex1p -m ../data/fichera.mesh
 //               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
 //               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
+//               mpirun -np 4 ex1p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex1p -m ../data/periodic-annulus-sector.msh
 //               mpirun -np 4 ex1p -m ../data/periodic-torus-sector.msh
 //               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
@@ -89,7 +90,8 @@ int main(int argc, char *argv[])
   args.AddOption(&device_config, "-d", "--device",
                  "Device configuration string, see Device::Configure().");
 #ifdef MFEM_USE_CEED
-   args.AddOption(&algebraic_ceed, "-a", "--algebraic", "-no-a", "--no-algebraic",
+   args.AddOption(&algebraic_ceed, "-a", "--algebraic",
+                  "-no-a", "--no-algebraic",
                  "Use algebraic Ceed solver");
 #endif
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -197,15 +199,15 @@ int main(int argc, char *argv[])
   b.AddDomainIntegrator(new DomainLFIntegrator(one));
   b.Assemble();

-   // 10. Define the solution vector x as a parallel finite element grid function
-   //     corresponding to fespace. Initialize x with initial guess of zero,
-   //     which satisfies the boundary conditions.
+   // 10. Define the solution vector x as a parallel finite element grid
+   //     function corresponding to fespace. Initialize x with initial guess of
+   //     zero, which satisfies the boundary conditions.
   ParGridFunction x(&fespace);
   x = 0.0;

   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
-   //     corresponding to the Laplacian operator -Delta, by adding the Diffusion
-   //     domain integrator.
+   //     corresponding to the Laplacian operator -Delta, by adding the
+   //     Diffusion domain integrator.
   ParBilinearForm a(&fespace);
   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   a.AddDomainIntegrator(new DiffusionIntegrator(one));
@@ -3,6 +3,10 @@
 // Compile with: make ex20
 //
 // Sample runs:  ex20
+//               ex20 -p 1 -o 1 -n 120 -dt 0.1
+//               ex20 -p 1 -o 2 -n 60 -dt 0.2
+//               ex20 -p 1 -o 3 -n 40 -dt 0.3
+//               ex20 -p 1 -o 4 -n 30 -dt 0.4
 //
 // Description: This example demonstrates the use of the variable order,
 //              symplectic ODE integration algorithm.  Symplectic integration
@@ -231,6 +235,7 @@ int main(int argc, char *argv[])
   // 9. Finalize the GLVis output
   if (visualization)
   {
+      mesh.FinalizeQuadMesh(1);
      H1_FECollection fec(order = 1, 2);
      FiniteElementSpace fespace(&mesh, &fec);
      GridFunction energy(&fespace);
@@ -3,6 +3,10 @@
 // Compile with: make ex20p
 //
 // Sample runs:  mpirun -np 4 ex20p
+//               mpirun -np 4 ex20p -p 1 -o 1 -n 120 -dt 0.1
+//               mpirun -np 4 ex20p -p 1 -o 2 -n 60 -dt 0.2
+//               mpirun -np 4 ex20p -p 1 -o 3 -n 40 -dt 0.3
+//               mpirun -np 4 ex20p -p 1 -o 4 -n 30 -dt 0.4
 //
 // Description: This example demonstrates the use of the variable order,
 //              symplectic ODE integration algorithm.  Symplectic integration
@@ -168,7 +172,7 @@ int main(int argc, char *argv[])
   }

   // 6. Create a Mesh for visualization in phase space
-   int nverts = (visualization) ? (num_procs+1)*(nsteps+1) : 0;
+   int nverts = (visualization) ? 2*num_procs*(nsteps+1) : 0;
   int nelems = (visualization) ? (nsteps * num_procs) : 0;
   Mesh mesh(2, nverts, nelems, 0, 3);

@@ -190,9 +194,9 @@ int main(int argc, char *argv[])

         if (visualization)
         {
-            mesh.AddVertex(x0);
            for (int j = 0; j < num_procs; j++)
            {
+               mesh.AddVertex(x0);
               x1[0] = q(0);
               x1[1] = p(0);
               x1[2] = 0.0;
@@ -216,17 +220,17 @@ int main(int argc, char *argv[])
      if (visualization)
      {
         x0[2] = t;
-         mesh.AddVertex(x0);
         for (int j = 0; j < num_procs; j++)
         {
+            mesh.AddVertex(x0);
            x1[0] = q(0);
            x1[1] = p(0);
            x1[2] = t;
            mesh.AddVertex(x1);
-            v[0] = (num_procs + 1) * i;
-            v[1] = (num_procs + 1) * (i + 1);
-            v[2] = (num_procs + 1) * (i + 1) + j + 1;
-            v[3] = (num_procs + 1) * i + j + 1;
+            v[0] = 2 * num_procs * i + 2 * j;
+            v[1] = 2 * num_procs * (i + 1) + 2 * j;
+            v[2] = 2 * num_procs * (i + 1) + 2 * j + 1;
+            v[3] = 2 * num_procs * i + 2 * j + 1;
            mesh.AddQuad(v);
            part[num_procs * i + j] = j;
         }
@@ -13,6 +13,8 @@
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 1
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa
+//               ex22 -m ../data/inline-wedge.mesh -o 1
+//               ex22 -m ../data/inline-pyramid.mesh -o 1
 //               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0
 //
 // Device sample runs:
@@ -13,6 +13,8 @@
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 1
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 2
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa
+//               mpirun -np 4 ex22p -m ../data/inline-wedge.mesh -o 1
+//               mpirun -np 4 ex22p -m ../data/inline-pyramid.mesh -o 1
 //               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0
 //
 // Device sample runs:
@@ -113,7 +113,6 @@ int main(int argc, char *argv[])
         mesh->UniformRefinement();
      }
   }
-   mesh->ReorientTetMesh();

   // 5. Define a finite element space on the mesh. Here we use Nedelec or
   //    Raviart-Thomas finite elements of the specified order.
@@ -141,7 +141,6 @@ int main(int argc, char *argv[])
         pmesh->UniformRefinement();
      }
   }
-   pmesh->ReorientTetMesh();

   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use Nedelec or Raviart-Thomas finite elements of the specified order.
@@ -92,7 +92,7 @@ class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
   CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , Vector &);
+   void (*Function)(const Vector &, CartesianPML *, Vector &);
 public:
   PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
                                              Vector &),
@@ -277,10 +277,8 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 6. Reorient mesh in case of a tet mesh
-   mesh->ReorientTetMesh();
-
-   // Set element attributes in order to distinguish elements in the PML region
+   // 6. Set element attributes in order to distinguish elements in the
+   //    PML region
   pml->SetAttributes(mesh);

   // 7. Define a finite element space on the mesh. Here we use the Nedelec
@@ -92,7 +92,7 @@ class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
   CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , Vector &);
+   void (*Function)(const Vector &, CartesianPML *, Vector &);
 public:
   PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
                                              Vector &),
@@ -316,9 +316,6 @@ int main(int argc, char *argv[])
      }
   }

-   // 7a. Reorient mesh in case of a tet mesh
-   pmesh->ReorientTetMesh();
-
   // 8. Set element attributes in order to distinguish elements in the PML
   pml->SetAttributes(pmesh);

@@ -105,7 +105,7 @@ private:
      Vector diag(fespace.GetTrueVSize());
      bfs.Last()->AssembleDiagonal(diag);

-      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), diag,
+      Solver* smoother = new OperatorChebyshevSmoother(*opr, diag,
                                                       *essentialTrueDofs.Last(), 2);
      AddLevel(opr.Ptr(), smoother, true, true);
   }
@@ -115,7 +115,7 @@ private:
      Vector diag(fespace.GetTrueVSize());
      bfs.Last()->AssembleDiagonal(diag);

-      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), diag,
+      Solver* smoother = new OperatorChebyshevSmoother(*opr, diag,
                                                       *essentialTrueDofs.Last(), 2, fespace.GetParMesh()->GetComm());

      AddLevel(opr.Ptr(), smoother, true, true);
@@ -81,6 +81,12 @@ Mesh * build_trapezoid_mesh(double offset)

 int main(int argc, char *argv[])
 {
+#ifdef HYPRE_USING_CUDA
+   cout << "\nAs of mfem-4.3 and hypre-2.22.0 (July 2021) this example\n"
+        << "is NOT supported with the CUDA version of hypre.\n\n";
+   return 255;
+#endif
+
   // 1. Initialize MPI.
   int num_procs, myid;
   MPI_Init(&argc, &argv);
@@ -360,6 +366,7 @@ int main(int argc, char *argv[])
   }
   delete pmesh;

+   // HYPRE_Finalize();
   MPI_Finalize();

   return 0;
@@ -61,6 +61,7 @@ int main(int argc, char *argv[])
   bool visualization = 1;
   bool amg_elast = 0;
   bool reorder_space = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -78,6 +79,8 @@ int main(int argc, char *argv[])
                  "Enable or disable GLVis visualization.");
   args.AddOption(&reorder_space, "-nodes", "--by-nodes", "-vdim", "--by-vdim",
                  "Use byNODES ordering of vector space instead of byVDIM");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -93,7 +96,12 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
@@ -109,14 +117,14 @@ int main(int argc, char *argv[])
      return 3;
   }

-   // 4. Select the order of the finite element discretization space. For NURBS
+   // 5. Select the order of the finite element discretization space. For NURBS
   //    meshes, we increase the order by degree elevation.
   if (mesh->NURBSext)
   {
      mesh->DegreeElevate(order, order);
   }

-   // 5. Refine the serial mesh on all processors to increase the resolution. In
+   // 6. Refine the serial mesh on all processors to increase the resolution. In
   //    this example we do 'ref_levels' of uniform refinement. We choose
   //    'ref_levels' to be the largest number that gives a final mesh with no
   //    more than 1,000 elements.
@@ -129,7 +137,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 7. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution. Once the
   //    parallel mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
@@ -142,7 +150,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 7. Define a parallel finite element space on the parallel mesh. Here we
+   // 8. Define a parallel finite element space on the parallel mesh. Here we
   //    use vector finite elements, i.e. dim copies of a scalar finite element
   //    space. We use the ordering by vector dimension (the last argument of
   //    the FiniteElementSpace constructor) which is expected in the systems
@@ -175,7 +183,7 @@ int main(int argc, char *argv[])
           << "Assembling: " << flush;
   }

-   // 8. Determine the list of true (i.e. parallel conforming) essential
+   // 9. Determine the list of true (i.e. parallel conforming) essential
   //    boundary dofs. In this example, the boundary conditions are defined by
   //    marking only boundary attribute 1 from the mesh as essential and
   //    converting it to a list of true dofs.
@@ -184,14 +192,14 @@ int main(int argc, char *argv[])
   ess_bdr[0] = 1;
   fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);

-   // 9. Set up the parallel linear form b(.) which corresponds to the
-   //    right-hand side of the FEM linear system. In this case, b_i equals the
-   //    boundary integral of f*phi_i where f represents a "pull down" force on
-   //    the Neumann part of the boundary and phi_i are the basis functions in
-   //    the finite element fespace. The force is defined by the object f, which
-   //    is a vector of Coefficient objects. The fact that f is non-zero on
-   //    boundary attribute 2 is indicated by the use of piece-wise constants
-   //    coefficient for its last component.
+   // 10. Set up the parallel linear form b(.) which corresponds to the
+   //     right-hand side of the FEM linear system. In this case, b_i equals the
+   //     boundary integral of f*phi_i where f represents a "pull down" force on
+   //     the Neumann part of the boundary and phi_i are the basis functions in
+   //     the finite element fespace. The force is defined by the object f, which
+   //     is a vector of Coefficient objects. The fact that f is non-zero on
+   //     boundary attribute 2 is indicated by the use of piece-wise constants
+   //     coefficient for its last component.
   VectorArrayCoefficient f(dim);
   for (int i = 0; i < dim-1; i++)
   {
@@ -212,13 +220,13 @@ int main(int argc, char *argv[])
   }
   b->Assemble();

-   // 10. Define the solution vector x as a parallel finite element grid
+   // 11. Define the solution vector x as a parallel finite element grid
   //     function corresponding to fespace. Initialize x with initial guess of
   //     zero, which satisfies the boundary conditions.
   ParGridFunction x(fespace);
   x = 0.0;

-   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
+   // 12. Set up the parallel bilinear form a(.,.) on the finite element space
   //     corresponding to the linear elasticity integrator with piece-wise
   //     constants coefficient lambda and mu.
   Vector lambda(pmesh->attributes.Max());
@@ -233,7 +241,7 @@ int main(int argc, char *argv[])
   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));

-   // 12. Assemble the parallel bilinear form and the corresponding linear
+   // 13. Assemble the parallel bilinear form and the corresponding linear
   //     system, applying any necessary transformations such as: parallel
   //     assembly, eliminating boundary conditions, applying conforming
   //     constraints for non-conforming AMR, static condensation, etc.
@@ -250,7 +258,7 @@ int main(int argc, char *argv[])
      cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
   }

-   // 13. Define and apply a parallel PCG solver for A X = B with the BoomerAMG
+   // 14. Define and apply a parallel PCG solver for A X = B with the BoomerAMG
   //     preconditioner from hypre.
   HypreBoomerAMG *amg = new HypreBoomerAMG(A);
   if (amg_elast && !a->StaticCondensationIsEnabled())
@@ -268,11 +276,11 @@ int main(int argc, char *argv[])
   pcg->SetPreconditioner(*amg);
   pcg->Mult(B, X);

-   // 14. Recover the parallel grid function corresponding to X. This is the
+   // 15. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
   a->RecoverFEMSolution(X, *b, x);

-   // 15. For non-NURBS meshes, make the mesh curved based on the finite element
+   // 16. For non-NURBS meshes, make the mesh curved based on the finite element
   //     space. This means that we define the mesh elements through a fespace
   //     based transformation of the reference element.  This allows us to save
   //     the displaced mesh as a curved mesh when using high-order finite
@@ -284,7 +292,7 @@ int main(int argc, char *argv[])
      pmesh->SetNodalFESpace(fespace);
   }

-   // 16. Save in parallel the displaced mesh and the inverted solution (which
+   // 17. Save in parallel the displaced mesh and the inverted solution (which
   //     gives the backward displacements to the original grid). This output
   //     can be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
   {
@@ -305,7 +313,7 @@ int main(int argc, char *argv[])
      x.Save(sol_ofs);
   }

-   // 17. Send the above data by socket to a GLVis server.  Use the "n" and "b"
+   // 18. Send the above data by socket to a GLVis server.  Use the "n" and "b"
   //     keys in GLVis to visualize the displacements.
   if (visualization)
   {
@@ -317,7 +325,7 @@ int main(int argc, char *argv[])
      sol_sock << "solution\n" << *pmesh << x << flush;
   }

-   // 18. Free the used memory.
+   // 19. Free the used memory.
   delete pcg;
   delete amg;
   delete a;
@@ -16,6 +16,8 @@
 //               ex3 -m ../data/beam-hex-nurbs.mesh
 //               ex3 -m ../data/amr-hex.mesh
 //               ex3 -m ../data/fichera-amr.mesh
+//               ex3 -m ../data/ref-prism.mesh -o 1
+//               ex3 -m ../data/octahedron.mesh -o 1
 //               ex3 -m ../data/star-surf.mesh -o 1
 //               ex3 -m ../data/mobius-strip.mesh -f 0.1
 //               ex3 -m ../data/klein-bottle.mesh -f 0.1
@@ -113,7 +115,6 @@ int main(int argc, char *argv[])
         mesh->UniformRefinement();
      }
   }
-   mesh->ReorientTetMesh();

   // 5. Define a finite element space on the mesh. Here we use the Nedelec
   //    finite elements of the specified order.
@@ -16,6 +16,8 @@
 //               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
 //               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
 //               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
+//               mpirun -np 4 ex3p -m ../data/ref-prism.mesh -o 1
+//               mpirun -np 4 ex3p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
 //               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
 //               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
@@ -103,6 +105,7 @@ int main(int argc, char *argv[])
      {
         args.PrintUsage(cout);
      }
+      // HYPRE_Finalize();
      MPI_Finalize();
      return 1;
   }
@@ -138,9 +141,7 @@ int main(int argc, char *argv[])

   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them.
+   //    parallel mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -150,7 +151,6 @@ int main(int argc, char *argv[])
         pmesh->UniformRefinement();
      }
   }
-   pmesh->ReorientTetMesh();

   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Nedelec finite elements of the specified order.
@@ -19,6 +19,8 @@
 //               ex4 -m ../data/amr-hex.mesh
 //               ex4 -m ../data/amr-hex.mesh -o 2 -hb
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
+//               ex4 -m ../data/ref-prism.mesh -o 1
+//               ex4 -m ../data/octahedron.mesh -o 1
 //               ex4 -m ../data/star-surf.mesh -o 1
 //
 // Device sample runs:
@@ -19,6 +19,8 @@
 //               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
+//               mpirun -np 4 ex4p -m ../data/ref-prism.mesh -o 1
+//               mpirun -np 4 ex4p -m ../data/octahedron.mesh -o 1
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb
 //
 // Device sample runs:
@@ -135,9 +137,7 @@ int main(int argc, char *argv[])

   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them (this is needed in the ADS solver below).
+   //    parallel mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -147,7 +147,6 @@ int main(int argc, char *argv[])
         pmesh->UniformRefinement();
      }
   }
-   pmesh->ReorientTetMesh();

   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Raviart-Thomas finite elements of the specified order.
@@ -197,6 +197,7 @@ int main(int argc, char *argv[])
      SparseMatrix &M(mVarf->SpMat());
      SparseMatrix &B(bVarf->SpMat());
      B *= -1.;
+      if (Device::IsEnabled()) { B.BuildTranspose(); }
      Bt = new TransposeOperator(&B);

      darcyOp.SetBlock(0,0, &M);
@@ -240,6 +241,7 @@ int main(int argc, char *argv[])
   {
      SparseMatrix &M(mVarf->SpMat());
      M.GetDiag(Md);
+      Md.HostReadWrite();

      SparseMatrix &B(bVarf->SpMat());
      MinvBt = Transpose(B);
@@ -287,12 +289,18 @@ int main(int argc, char *argv[])
   chrono.Stop();

   if (solver.GetConverged())
+   {
      std::cout << "MINRES converged in " << solver.GetNumIterations()
-                << " iterations with a residual norm of " << solver.GetFinalNorm() << ".\n";
+                << " iterations with a residual norm of "
+                << solver.GetFinalNorm() << ".\n";
+   }
   else
+   {
      std::cout << "MINRES did not converge in " << solver.GetNumIterations()
-                << " iterations. Residual norm is " << solver.GetFinalNorm() << ".\n";
-   std::cout << "MINRES solver took " << chrono.RealTime() << "s. \n";
+                << " iterations. Residual norm is " << solver.GetFinalNorm()
+                << ".\n";
+   }
+   std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";

   // 12. Create the grid functions u and p. Compute the L2 error norms.
   GridFunction u, p;
@@ -47,6 +47,7 @@ int main(int argc, char *argv[])
   int order = 2;
   bool always_snap = false;
   bool visualization = 1;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&elem_type, "-e", "--elem",
@@ -65,6 +66,8 @@ int main(int argc, char *argv[])
                  "--snap-at-the-end",
                  "If true, snap nodes to the sphere initially and after each refinement "
                  "otherwise, snap only after the last refinement");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -80,7 +83,12 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 3. Generate an initial high-order (surface) mesh on the unit sphere. The
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Generate an initial high-order (surface) mesh on the unit sphere. The
   //    Mesh object represents a 2D mesh in 3 spatial dimensions. We first add
   //    the elements and the vertices of the mesh, and then make it high-order
   //    by specifying a finite element space for its nodes.
@@ -146,7 +154,7 @@ int main(int argc, char *argv[])
   FiniteElementSpace nodal_fes(mesh, &fec, mesh->SpaceDimension());
   mesh->SetNodalFESpace(&nodal_fes);

-   // 4. Refine the mesh while snapping nodes to the sphere. Number of parallel
+   // 5. Refine the mesh while snapping nodes to the sphere. Number of parallel
   //    refinements is fixed to 2.
   for (int l = 0; l <= ref_levels; l++)
   {
@@ -218,7 +226,7 @@ int main(int argc, char *argv[])
      SnapNodes(*pmesh);
   }

-   // 5. Define a finite element space on the mesh. Here we use isoparametric
+   // 6. Define a finite element space on the mesh. Here we use isoparametric
   //    finite elements -- the same as the mesh nodes.
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, &fec);
   HYPRE_BigInt size = fespace->GlobalTrueVSize();
@@ -227,7 +235,7 @@ int main(int argc, char *argv[])
      cout << "Number of unknowns: " << size << endl;
   }

-   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
   //    the basis functions in the finite element fespace.
   ParLinearForm *b = new ParLinearForm(fespace);
@@ -237,27 +245,27 @@ int main(int argc, char *argv[])
   b->AddDomainIntegrator(new DomainLFIntegrator(rhs_coef));
   b->Assemble();

-   // 7. Define the solution vector x as a finite element grid function
+   // 8. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x with initial guess of zero.
   ParGridFunction x(fespace);
   x = 0.0;

-   // 8. Set up the bilinear form a(.,.) on the finite element space
+   // 9. Set up the bilinear form a(.,.) on the finite element space
   //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
   //    and Mass domain integrators.
   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new DiffusionIntegrator(one));
   a->AddDomainIntegrator(new MassIntegrator(one));

-   // 9. Assemble the parallel linear system, applying any transformations
-   //    such as: parallel assembly, applying conforming constraints, etc.
+   // 10. Assemble the parallel linear system, applying any transformations
+   //     such as: parallel assembly, applying conforming constraints, etc.
   a->Assemble();
   HypreParMatrix A;
   Vector B, X;
   Array<int> empty_tdof_list;
   a->FormLinearSystem(empty_tdof_list, x, *b, A, X, B);

-   // 10. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
+   // 11. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
   //     preconditioner from hypre. Extract the parallel grid function x
   //     corresponding to the finite element approximation X. This is the local
   //     solution on each processor.
@@ -273,14 +281,14 @@ int main(int argc, char *argv[])
   delete a;
   delete b;

-   // 11. Compute and print the L^2 norm of the error.
+   // 12. Compute and print the L^2 norm of the error.
   double err = x.ComputeL2Error(sol_coef);
   if (myid == 0)
   {
      cout << "\nL2 norm of error: " << err << endl;
   }

-   // 12. Save the refined mesh and the solution. This output can be viewed
+   // 13. Save the refined mesh and the solution. This output can be viewed
   //     later using GLVis: "glvis -np <np> -m sphere_refined -g sol".
   {
      ostringstream mesh_name, sol_name;
@@ -296,7 +304,7 @@ int main(int argc, char *argv[])
      x.Save(sol_ofs);
   }

-   // 13. Send the solution by socket to a GLVis server.
+   // 14. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -307,7 +315,7 @@ int main(int argc, char *argv[])
      sol_sock << "solution\n" << *pmesh << x << flush;
   }

-   // 14. Free the used memory.
+   // 15. Free the used memory.
   delete pcg;
   delete amg;
   delete fespace;
@@ -106,7 +106,6 @@ int main(int argc, char *argv[])
         pmesh->UniformRefinement();
      }
   }
-   pmesh->ReorientTetMesh();

   // 6. Define the trial, interfacial (trace) and test DPG spaces:
   //    - The trial space, x0_space, contains the non-interfacial unknowns and
@@ -216,7 +216,7 @@ int main(int argc, char *argv[])
 {
   // 1. Parse command-line options.
   problem = 0;
-   optimizer_type = 1;
+   optimizer_type = 2;
   const char *mesh_file = "../../data/periodic-hexagon.mesh";
   int ref_levels = 2;
   int order = 3;
@@ -247,7 +247,7 @@ int main(int argc, char *argv[])

   // 2. Parse command-line options.
   problem = 0;
-   optimizer_type = 1;
+   optimizer_type = 2;
   const char *mesh_file = "../../data/periodic-hexagon.mesh";
   int ser_ref_levels = 2;
   int par_ref_levels = 0;
@@ -50,6 +50,13 @@ endif
 MFEM_TESTS = EXAMPLES
 include $(MFEM_TEST_MK)

+# Testing: Parallel vs. serial runs
+RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
+%-test-par: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel example)
+%-test-seq: %
+	@$(call mfem-test,$<,, Serial example)
+
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk

 # Generate an error message if the MFEM library is not built and exit
@@ -26,6 +26,9 @@ SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
 PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
  ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
  ex25p ex26p ex27p ex28p ex29p
+SEQ_DEVICE_EXAMPLES = ex1 ex3 ex4 ex5 ex6 ex9 ex22 ex24 ex25 ex26
+PAR_DEVICE_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex22p \
+  ex24p ex25p ex26p

 ifeq ($(MFEM_USE_MPI),NO)
   EXAMPLES = $(SEQ_EXAMPLES)
@@ -99,6 +102,14 @@ RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example)
 %-test-seq: %
 	@$(call mfem-test,$<,, Serial example)
+%-test-par-cuda: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel CUDA example,-d cuda)
+%-test-seq-cuda: %
+	@$(call mfem-test,$<,, Serial CUDA example,-d cuda)
+%-test-par-hip: %
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel HIP example,-d hip)
+%-test-seq-hip: %
+	@$(call mfem-test,$<,, Serial HIP example,-d hip)

 # Testing: Specific execution options
 ex0-test-seq: ex0
@@ -121,9 +121,7 @@ int main(int argc, char *argv[])

   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them.
+   //    parallel mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -133,7 +131,6 @@ int main(int argc, char *argv[])
         pmesh->UniformRefinement();
      }
   }
-   pmesh->ReorientTetMesh();

   // 6. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Nedelec finite elements of the specified order.
@@ -122,9 +122,7 @@ int main(int argc, char *argv[])

   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution. Once the
-   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
-   //    meshes need to be reoriented before we can define high-order Nedelec
-   //    spaces on them (this is needed in the ADS solver below).
+   //    parallel mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -134,7 +132,6 @@ int main(int argc, char *argv[])
         pmesh->UniformRefinement();
      }
   }
-   pmesh->ReorientTetMesh();

   // 6. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Raviart-Thomas finite elements of the specified order.
@@ -282,6 +282,10 @@ int main(int argc, char *argv[])
   superlu->SetOperator(*SLU_A);
   superlu->SetPrintStatistics(true);
   superlu->Mult(B, X);
+   superlu->DismantleGrid();
+
+   delete SLU_A;
+   delete superlu;

   // 14. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
@@ -39,6 +39,7 @@ set(SRCS
  complex_fem.cpp
  convergence.cpp
  datacollection.cpp
+  doftrans.cpp
  eltrans.cpp
  estimators.cpp
  fe.cpp
@@ -105,6 +106,7 @@ set(SRCS
  tmop/tmop_pa_w3.cpp
  tmop/tmop_pa_w3_c0.cpp
  tmop_tools.cpp
+  tmop_amr.cpp
  gslib.cpp
  transfer.cpp
  lor.cpp
@@ -118,6 +120,7 @@ set(HDRS
  complex_fem.hpp
  convergence.hpp
  datacollection.hpp
+  doftrans.hpp
  eltrans.hpp
  estimators.hpp
  fe.hpp
@@ -164,6 +167,7 @@ set(HDRS
  tmop.hpp
  tmop/tmop_pa.hpp
  tmop_tools.hpp
+  tmop_amr.hpp
  gslib.hpp
  transfer.hpp
  lor.hpp
@@ -184,6 +188,11 @@ if (MFEM_USE_ADIOS2)
  list(APPEND HDRS adios2datacollection.hpp)
 endif()

+if (MFEM_USE_FMS)
+  list(APPEND SRCS fmsdatacollection.cpp fmsconvert.cpp)
+  list(APPEND HDRS fmsdatacollection.hpp fmsconvert.hpp)
+endif()
+
 if (MFEM_USE_MPI)
  list(APPEND SRCS
    pbilinearform.cpp
@@ -31,7 +31,7 @@ void BilinearForm::AllocMat()
   const Table &elem_dof = fes->GetElementToDofTable();
   Table dof_dof;

-   if (fbfi.Size() > 0)
+   if (interior_face_integs.Size() > 0)
   {
      // the sparsity pattern is defined from the map: face->element->dof
      Table face_dof, dof_face;
@@ -99,15 +99,15 @@ BilinearForm::BilinearForm (FiniteElementSpace * f, BilinearForm * bf, int ps)
   ext = NULL;

   // Copy the pointers to the integrators
-   dbfi = bf->dbfi;
+   domain_integs = bf->domain_integs;

-   bbfi = bf->bbfi;
-   bbfi_marker = bf->bbfi_marker;
+   boundary_integs = bf->boundary_integs;
+   boundary_integs_marker = bf->boundary_integs_marker;

-   fbfi = bf->fbfi;
+   interior_face_integs = bf->interior_face_integs;

-   bfbfi = bf->bfbfi;
-   bfbfi_marker = bf->bfbfi_marker;
+   boundary_face_integs = bf->boundary_face_integs;
+   boundary_face_integs_marker = bf->boundary_face_integs_marker;

   AllocMat();
 }
@@ -234,38 +234,47 @@ void BilinearForm::Finalize (int skip_zeros)

 void BilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi)
 {
-   dbfi.Append(bfi);
+   domain_integs.Append(bfi);
+   domain_integs_marker.Append(NULL); // NULL marker means apply everywhere
+}
+
+void BilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi,
+                                       Array<int> &elem_marker)
+{
+   domain_integs.Append(bfi);
+   domain_integs_marker.Append(&elem_marker);
 }

 void BilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
 {
-   bbfi.Append (bfi);
-   bbfi_marker.Append(NULL); // NULL marker means apply everywhere
+   boundary_integs.Append (bfi);
+   boundary_integs_marker.Append(NULL); // NULL marker means apply everywhere
 }

 void BilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
                                          Array<int> &bdr_marker)
 {
-   bbfi.Append (bfi);
-   bbfi_marker.Append(&bdr_marker);
+   boundary_integs.Append (bfi);
+   boundary_integs_marker.Append(&bdr_marker);
 }

-void BilinearForm::AddInteriorFaceIntegrator (BilinearFormIntegrator * bfi)
+void BilinearForm::AddInteriorFaceIntegrator(BilinearFormIntegrator * bfi)
 {
-   fbfi.Append (bfi);
+   interior_face_integs.Append (bfi);
 }

 void BilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi)
 {
-   bfbfi.Append(bfi);
-   bfbfi_marker.Append(NULL); // NULL marker means apply everywhere
+   boundary_face_integs.Append(bfi);
+   // NULL marker means apply everywhere
+   boundary_face_integs_marker.Append(NULL);
 }

 void BilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
                                        Array<int> &bdr_marker)
 {
-   bfbfi.Append(bfi);
-   bfbfi_marker.Append(&bdr_marker);
+   boundary_face_integs.Append(bfi);
+   boundary_face_integs_marker.Append(&bdr_marker);
 }

 void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
@@ -277,14 +286,14 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
      return;
   }

-   if (dbfi.Size())
+   if (domain_integs.Size())
   {
      const FiniteElement &fe = *fes->GetFE(i);
      ElementTransformation *eltrans = fes->GetElementTransformation(i);
-      dbfi[0]->AssembleElementMatrix(fe, *eltrans, elmat);
-      for (int k = 1; k < dbfi.Size(); k++)
+      domain_integs[0]->AssembleElementMatrix(fe, *eltrans, elmat);
+      for (int k = 1; k < domain_integs.Size(); k++)
      {
-         dbfi[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
+         domain_integs[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
         elmat += elemmat;
      }
   }
@@ -298,14 +307,14 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)

 void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
 {
-   if (bbfi.Size())
+   if (boundary_integs.Size())
   {
      const FiniteElement &be = *fes->GetBE(i);
      ElementTransformation *eltrans = fes->GetBdrElementTransformation(i);
-      bbfi[0]->AssembleElementMatrix(be, *eltrans, elmat);
-      for (int k = 1; k < bbfi.Size(); k++)
+      boundary_integs[0]->AssembleElementMatrix(be, *eltrans, elmat);
+      for (int k = 1; k < boundary_integs.Size(); k++)
      {
-         bbfi[k]->AssembleElementMatrix(be, *eltrans, elemmat);
+         boundary_integs[k]->AssembleElementMatrix(be, *eltrans, elemmat);
         elmat += elemmat;
      }
   }
@@ -382,6 +391,7 @@ void BilinearForm::Assemble(int skip_zeros)
   }

   ElementTransformation *eltrans;
+   DofTransformation * doftrans;
   Mesh *mesh = fes -> GetMesh();
   DenseMatrix elmat, *elmat_p;

@@ -399,24 +409,59 @@ void BilinearForm::Assemble(int skip_zeros)
   }
 #endif

-   if (dbfi.Size())
+   if (domain_integs.Size())
   {
+      for (int k = 0; k < domain_integs.Size(); k++)
+      {
+         if (domain_integs_marker[k] != NULL)
+         {
+            MFEM_VERIFY(mesh->attributes.Size() ==
+                        domain_integs_marker[k]->Size(),
+                        "invalid element marker for domain integrator #"
+                        << k << ", counting from zero");
+         }
+      }
+
      for (int i = 0; i < fes -> GetNE(); i++)
      {
-         fes->GetElementVDofs(i, vdofs);
+         int elem_attr = fes->GetMesh()->GetAttribute(i);
+         doftrans = fes->GetElementVDofs(i, vdofs);
         if (element_matrices)
         {
            elmat_p = &(*element_matrices)(i);
         }
         else
         {
-            const FiniteElement &fe = *fes->GetFE(i);
-            eltrans = fes->GetElementTransformation(i);
-            dbfi[0]->AssembleElementMatrix(fe, *eltrans, elmat);
-            for (int k = 1; k < dbfi.Size(); k++)
+            elmat.SetSize(0);
+            for (int k = 0; k < domain_integs.Size(); k++)
            {
-               dbfi[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
-               elmat += elemmat;
+               if ( domain_integs_marker[k] == NULL ||
+                    (*(domain_integs_marker[k]))[elem_attr-1] == 1)
+               {
+                  const FiniteElement &fe = *fes->GetFE(i);
+                  eltrans = fes->GetElementTransformation(i);
+                  domain_integs[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
+                  if (elmat.Size() == 0)
+                  {
+                     elmat = elemmat;
+                  }
+                  else
+                  {
+                     elmat += elemmat;
+                  }
+               }
+            }
+            if (elmat.Size() == 0)
+            {
+               continue;
+            }
+            else
+            {
+               elmat_p = &elmat;
+            }
+            if (doftrans)
+            {
+               doftrans->TransformDual(elmat);
            }
            elmat_p = &elmat;
         }
@@ -435,20 +480,20 @@ void BilinearForm::Assemble(int skip_zeros)
      }
   }

-   if (bbfi.Size())
+   if (boundary_integs.Size())
   {
      // Which boundary attributes need to be processed?
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
-      for (int k = 0; k < bbfi.Size(); k++)
+      for (int k = 0; k < boundary_integs.Size(); k++)
      {
-         if (bbfi_marker[k] == NULL)
+         if (boundary_integs_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *bbfi_marker[k];
+         Array<int> &bdr_marker = *boundary_integs_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary integrator #"
                     << k << ", counting from zero");
@@ -464,42 +509,47 @@ void BilinearForm::Assemble(int skip_zeros)
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }

         const FiniteElement &be = *fes->GetBE(i);
-         fes -> GetBdrElementVDofs (i, vdofs);
+         doftrans = fes -> GetBdrElementVDofs (i, vdofs);
         eltrans = fes -> GetBdrElementTransformation (i);
         int k = 0;
-         for (; k < bbfi.Size(); k++)
+         for (; k < boundary_integs.Size(); k++)
         {
-            if (bbfi_marker[k] &&
-                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }
+            if (boundary_integs_marker[k] &&
+                (*boundary_integs_marker[k])[bdr_attr-1] == 0) { continue; }

-            bbfi[k]->AssembleElementMatrix(be, *eltrans, elmat);
+            boundary_integs[k]->AssembleElementMatrix(be, *eltrans, elmat);
            k++;
            break;
         }
-         for (; k < bbfi.Size(); k++)
+         for (; k < boundary_integs.Size(); k++)
         {
-            if (bbfi_marker[k] &&
-                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }
+            if (boundary_integs_marker[k] &&
+                (*boundary_integs_marker[k])[bdr_attr-1] == 0) { continue; }

-            bbfi[k]->AssembleElementMatrix(be, *eltrans, elemmat);
+            boundary_integs[k]->AssembleElementMatrix(be, *eltrans, elemmat);
            elmat += elemmat;
         }
+         if (doftrans)
+         {
+            doftrans->TransformDual(elmat);
+         }
+         elmat_p = &elmat;
         if (!static_cond)
         {
-            mat->AddSubMatrix(vdofs, vdofs, elmat, skip_zeros);
+            mat->AddSubMatrix(vdofs, vdofs, *elmat_p, skip_zeros);
            if (hybridization)
            {
-               hybridization->AssembleBdrMatrix(i, elmat);
+               hybridization->AssembleBdrMatrix(i, *elmat_p);
            }
         }
         else
         {
-            static_cond->AssembleBdrMatrix(i, elmat);
+            static_cond->AssembleBdrMatrix(i, *elmat_p);
         }
      }
   }

-   if (fbfi.Size())
+   if (interior_face_integs.Size())
   {
      FaceElementTransformations *tr;
      Array<int> vdofs2;
@@ -513,18 +563,19 @@ void BilinearForm::Assemble(int skip_zeros)
            fes -> GetElementVDofs (tr -> Elem1No, vdofs);
            fes -> GetElementVDofs (tr -> Elem2No, vdofs2);
            vdofs.Append (vdofs2);
-            for (int k = 0; k < fbfi.Size(); k++)
+            for (int k = 0; k < interior_face_integs.Size(); k++)
            {
-               fbfi[k] -> AssembleFaceMatrix (*fes -> GetFE (tr -> Elem1No),
-                                              *fes -> GetFE (tr -> Elem2No),
-                                              *tr, elemmat);
+               interior_face_integs[k]->
+               AssembleFaceMatrix(*fes->GetFE(tr->Elem1No),
+                                  *fes->GetFE(tr->Elem2No),
+                                  *tr, elemmat);
               mat -> AddSubMatrix (vdofs, vdofs, elemmat, skip_zeros);
            }
         }
      }
   }

-   if (bfbfi.Size())
+   if (boundary_face_integs.Size())
   {
      FaceElementTransformations *tr;
      const FiniteElement *fe1, *fe2;
@@ -533,14 +584,14 @@ void BilinearForm::Assemble(int skip_zeros)
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
-      for (int k = 0; k < bfbfi.Size(); k++)
+      for (int k = 0; k < boundary_face_integs.Size(); k++)
      {
-         if (bfbfi_marker[k] == NULL)
+         if (boundary_face_integs_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *bfbfi_marker[k];
+         Array<int> &bdr_marker = *boundary_face_integs_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary face integrator #"
                     << k << ", counting from zero");
@@ -564,12 +615,14 @@ void BilinearForm::Assemble(int skip_zeros)
            // but we can't dereference a NULL pointer, and we don't want to
            // actually make a fake element.
            fe2 = fe1;
-            for (int k = 0; k < bfbfi.Size(); k++)
+            for (int k = 0; k < boundary_face_integs.Size(); k++)
            {
-               if (bfbfi_marker[k] &&
-                   (*bfbfi_marker[k])[bdr_attr-1] == 0) { continue; }
+               if (boundary_face_integs_marker[k] &&
+                   (*boundary_face_integs_marker[k])[bdr_attr-1] == 0)
+               { continue; }

-               bfbfi[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elemmat);
+               boundary_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr,
+                                                              elemmat);
               mat -> AddSubMatrix (vdofs, vdofs, elemmat, skip_zeros);
            }
         }
@@ -683,8 +736,8 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
      {
         // A, X and B point to the same data as mat, x and b
         EliminateVDofsInRHS(ess_tdof_list, x, b);
-         X.NewMemoryAndSize(x.GetMemory(), x.Size(), false);
-         B.NewMemoryAndSize(b.GetMemory(), b.Size(), false);
+         X.MakeRef(x, 0, x.Size());
+         B.MakeRef(b, 0, b.Size());
         if (!copy_interior) { X.SetSubVectorComplement(ess_tdof_list, 0.0); }
      }
   }
@@ -820,7 +873,7 @@ void BilinearForm::RecoverFEMSolution(const Vector &X,

 void BilinearForm::ComputeElementMatrices()
 {
-   if (element_matrices || dbfi.Size() == 0 || fes->GetNE() == 0)
+   if (element_matrices || domain_integs.Size() == 0 || fes->GetNE() == 0)
   {
      return;
   }
@@ -849,11 +902,11 @@ void BilinearForm::ComputeElementMatrices()
 #endif
      fes->GetElementTransformation(i, &eltrans);

-      dbfi[0]->AssembleElementMatrix(fe, eltrans, elmat);
-      for (int k = 1; k < dbfi.Size(); k++)
+      domain_integs[0]->AssembleElementMatrix(fe, eltrans, elmat);
+      for (int k = 1; k < domain_integs.Size(); k++)
      {
         // note: some integrators may not be thread-safe
-         dbfi[k]->AssembleElementMatrix(fe, eltrans, tmp);
+         domain_integs[k]->AssembleElementMatrix(fe, eltrans, tmp);
         elmat += tmp;
      }
      elmat.ClearExternalData();
@@ -1068,10 +1121,12 @@ BilinearForm::~BilinearForm()
   if (!extern_bfs)
   {
      int k;
-      for (k=0; k < dbfi.Size(); k++) { delete dbfi[k]; }
-      for (k=0; k < bbfi.Size(); k++) { delete bbfi[k]; }
-      for (k=0; k < fbfi.Size(); k++) { delete fbfi[k]; }
-      for (k=0; k < bfbfi.Size(); k++) { delete bfbfi[k]; }
+      for (k=0; k < domain_integs.Size(); k++) { delete domain_integs[k]; }
+      for (k=0; k < boundary_integs.Size(); k++) { delete boundary_integs[k]; }
+      for (k=0; k < interior_face_integs.Size(); k++)
+      { delete interior_face_integs[k]; }
+      for (k=0; k < boundary_face_integs.Size(); k++)
+      { delete boundary_face_integs[k]; }
   }

   delete ext;
@@ -1104,13 +1159,13 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
   ext = NULL;

   // Copy the pointers to the integrators
-   dbfi = mbf->dbfi;
-   bbfi = mbf->bbfi;
-   tfbfi = mbf->tfbfi;
-   btfbfi = mbf->btfbfi;
+   domain_integs = mbf->domain_integs;
+   boundary_integs = mbf->boundary_integs;
+   trace_face_integs = mbf->trace_face_integs;
+   boundary_trace_face_integs = mbf->boundary_trace_face_integs;

-   bbfi_marker = mbf->bbfi_marker;
-   btfbfi_marker = mbf->btfbfi_marker;
+   boundary_integs_marker = mbf->boundary_integs_marker;
+   boundary_trace_face_integs_marker = mbf->boundary_trace_face_integs_marker;

   assembly = AssemblyLevel::LEGACY;
   ext = NULL;
@@ -1199,7 +1254,8 @@ MatrixInverse * MixedBilinearForm::Inverse() const
 {
   if (assembly != AssemblyLevel::LEGACY)
   {
-      MFEM_WARNING("MixedBilinearForm::Inverse not possible with this assembly level!");
+      MFEM_WARNING("MixedBilinearForm::Inverse not possible with this "
+                   "assembly level!");
      return NULL;
   }
   else
@@ -1230,38 +1286,39 @@ void MixedBilinearForm::GetBlocks(Array2D<SparseMatrix *> &blocks) const

 void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi)
 {
-   dbfi.Append (bfi);
+   domain_integs.Append (bfi);
 }

 void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
 {
-   bbfi.Append (bfi);
-   bbfi_marker.Append(NULL); // NULL marker means apply everywhere
+   boundary_integs.Append (bfi);
+   boundary_integs_marker.Append(NULL); // NULL marker means apply everywhere
 }

 void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
                                               Array<int> &bdr_marker)
 {
-   bbfi.Append (bfi);
-   bbfi_marker.Append(&bdr_marker);
+   boundary_integs.Append (bfi);
+   boundary_integs_marker.Append(&bdr_marker);
 }

 void MixedBilinearForm::AddTraceFaceIntegrator (BilinearFormIntegrator * bfi)
 {
-   tfbfi.Append (bfi);
+   trace_face_integs.Append (bfi);
 }

 void MixedBilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator *bfi)
 {
-   btfbfi.Append(bfi);
-   btfbfi_marker.Append(NULL); // NULL marker means apply everywhere
+   boundary_trace_face_integs.Append(bfi);
+   // NULL marker means apply everywhere
+   boundary_trace_face_integs_marker.Append(NULL);
 }

 void MixedBilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator *bfi,
                                                  Array<int> &bdr_marker)
 {
-   btfbfi.Append(bfi);
-   btfbfi_marker.Append(&bdr_marker);
+   boundary_trace_face_integs.Append(bfi);
+   boundary_trace_face_integs_marker.Append(&bdr_marker);
 }

 void MixedBilinearForm::Assemble (int skip_zeros)
@@ -1272,9 +1329,10 @@ void MixedBilinearForm::Assemble (int skip_zeros)
      return;
   }

-   Array<int> tr_vdofs, te_vdofs;
   ElementTransformation *eltrans;
-   DenseMatrix elemmat;
+   DofTransformation * dom_dof_trans;
+   DofTransformation * ran_dof_trans;
+   DenseMatrix elmat;

   Mesh *mesh = test_fes -> GetMesh();

@@ -1283,37 +1341,45 @@ void MixedBilinearForm::Assemble (int skip_zeros)
      mat = new SparseMatrix(height, width);
   }

-   if (dbfi.Size())
+   if (domain_integs.Size())
   {
      for (int i = 0; i < test_fes -> GetNE(); i++)
      {
-         trial_fes -> GetElementVDofs (i, tr_vdofs);
-         test_fes  -> GetElementVDofs (i, te_vdofs);
+         dom_dof_trans = trial_fes -> GetElementVDofs (i, trial_vdofs);
+         ran_dof_trans = test_fes  -> GetElementVDofs (i, test_vdofs);
         eltrans = test_fes -> GetElementTransformation (i);
-         for (int k = 0; k < dbfi.Size(); k++)
+
+         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+         elmat = 0.0;
+         for (int k = 0; k < domain_integs.Size(); k++)
         {
-            dbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
-                                               *test_fes  -> GetFE(i),
-                                               *eltrans, elemmat);
-            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
+            domain_integs[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
+                                                        *test_fes  -> GetFE(i),
+                                                        *eltrans, elemmat);
+            elmat += elemmat;
         }
+         if (ran_dof_trans || dom_dof_trans)
+         {
+            TransformDual(ran_dof_trans, dom_dof_trans, elmat);
+         }
+         mat -> AddSubMatrix (test_vdofs, trial_vdofs, elmat, skip_zeros);
      }
   }

-   if (bbfi.Size())
+   if (boundary_integs.Size())
   {
      // Which boundary attributes need to be processed?
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
-      for (int k = 0; k < bbfi.Size(); k++)
+      for (int k = 0; k < boundary_integs.Size(); k++)
      {
-         if (bbfi_marker[k] == NULL)
+         if (boundary_integs_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *bbfi_marker[k];
+         Array<int> &bdr_marker = *boundary_integs_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary integrator #"
                     << k << ", counting from zero");
@@ -1328,40 +1394,48 @@ void MixedBilinearForm::Assemble (int skip_zeros)
         const int bdr_attr = mesh->GetBdrAttribute(i);
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }

-         trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
-         test_fes  -> GetBdrElementVDofs (i, te_vdofs);
+         dom_dof_trans = trial_fes -> GetBdrElementVDofs (i, trial_vdofs);
+         ran_dof_trans = test_fes  -> GetBdrElementVDofs (i, test_vdofs);
         eltrans = test_fes -> GetBdrElementTransformation (i);
-         for (int k = 0; k < bbfi.Size(); k++)
-         {
-            if (bbfi_marker[k] &&
-                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }

-            bbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetBE(i),
-                                               *test_fes  -> GetBE(i),
-                                               *eltrans, elemmat);
-            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
+         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+         elmat = 0.0;
+         for (int k = 0; k < boundary_integs.Size(); k++)
+         {
+            if (boundary_integs_marker[k] &&
+                (*boundary_integs_marker[k])[bdr_attr-1] == 0) { continue; }
+
+            boundary_integs[k]->AssembleElementMatrix2 (*trial_fes -> GetBE(i),
+                                                        *test_fes  -> GetBE(i),
+                                                        *eltrans, elemmat);
+            elmat += elemmat;
         }
+         if (ran_dof_trans || dom_dof_trans)
+         {
+            TransformDual(ran_dof_trans, dom_dof_trans, elmat);
+         }
+         mat -> AddSubMatrix (test_vdofs, trial_vdofs, elmat, skip_zeros);
      }
   }

-   if (tfbfi.Size())
+   if (trace_face_integs.Size())
   {
      FaceElementTransformations *ftr;
-      Array<int> te_vdofs2;
+      Array<int> test_vdofs2;
      const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;

      int nfaces = mesh->GetNumFaces();
      for (int i = 0; i < nfaces; i++)
      {
         ftr = mesh->GetFaceElementTransformations(i);
-         trial_fes->GetFaceVDofs(i, tr_vdofs);
-         test_fes->GetElementVDofs(ftr->Elem1No, te_vdofs);
+         trial_fes->GetFaceVDofs(i, trial_vdofs);
+         test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
         trial_face_fe = trial_fes->GetFaceElement(i);
         test_fe1 = test_fes->GetFE(ftr->Elem1No);
         if (ftr->Elem2No >= 0)
         {
-            test_fes->GetElementVDofs(ftr->Elem2No, te_vdofs2);
-            te_vdofs.Append(te_vdofs2);
+            test_fes->GetElementVDofs(ftr->Elem2No, test_vdofs2);
+            test_vdofs.Append(test_vdofs2);
            test_fe2 = test_fes->GetFE(ftr->Elem2No);
         }
         else
@@ -1371,16 +1445,16 @@ void MixedBilinearForm::Assemble (int skip_zeros)
            // want to actually make a fake element.
            test_fe2 = test_fe1;
         }
-         for (int k = 0; k < tfbfi.Size(); k++)
+         for (int k = 0; k < trace_face_integs.Size(); k++)
         {
-            tfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
-                                         *ftr, elemmat);
-            mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
+            trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
+                                                     *test_fe2, *ftr, elemmat);
+            mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
         }
      }
   }

-   if (btfbfi.Size())
+   if (boundary_trace_face_integs.Size())
   {
      FaceElementTransformations *ftr;
      Array<int> te_vdofs2;
@@ -1390,17 +1464,17 @@ void MixedBilinearForm::Assemble (int skip_zeros)
      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
                                 mesh->bdr_attributes.Max() : 0);
      bdr_attr_marker = 0;
-      for (int k = 0; k < btfbfi.Size(); k++)
+      for (int k = 0; k < boundary_trace_face_integs.Size(); k++)
      {
-         if (btfbfi_marker[k] == NULL)
+         if (boundary_trace_face_integs_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *btfbfi_marker[k];
+         Array<int> &bdr_marker = *boundary_trace_face_integs_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
-                     "invalid boundary marker for boundary trace face integrator #"
-                     << k << ", counting from zero");
+                     "invalid boundary marker for boundary trace face"
+                     "integrator #" << k << ", counting from zero");
         for (int i = 0; i < bdr_attr_marker.Size(); i++)
         {
            bdr_attr_marker[i] |= bdr_marker[i];
@@ -1415,22 +1489,25 @@ void MixedBilinearForm::Assemble (int skip_zeros)
         ftr = mesh->GetBdrFaceTransformations(i);
         if (ftr)
         {
-            trial_fes->GetFaceVDofs(ftr->ElementNo, tr_vdofs);
-            test_fes->GetElementVDofs(ftr->Elem1No, te_vdofs);
+            trial_fes->GetFaceVDofs(ftr->ElementNo, trial_vdofs);
+            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
            trial_face_fe = trial_fes->GetFaceElement(ftr->ElementNo);
            test_fe1 = test_fes->GetFE(ftr->Elem1No);
            // The test_fe2 object is really a dummy and not used on the
            // boundaries, but we can't dereference a NULL pointer, and we don't
            // want to actually make a fake element.
            test_fe2 = test_fe1;
-            for (int k = 0; k < btfbfi.Size(); k++)
+            for (int k = 0; k < boundary_trace_face_integs.Size(); k++)
            {
-               if (btfbfi_marker[k] &&
-                   (*btfbfi_marker[k])[bdr_attr-1] == 0) { continue; }
+               if (boundary_trace_face_integs_marker[k] &&
+                   (*boundary_trace_face_integs_marker[k])[bdr_attr-1] == 0)
+               { continue; }

-               btfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
-                                             *ftr, elemmat);
-               mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
+               boundary_trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe,
+                                                                 *test_fe1,
+                                                                 *test_fe2,
+                                                                 *ftr, elemmat);
+               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
            }
         }
      }
@@ -1520,15 +1597,17 @@ void MixedBilinearForm::ConformingAssemble()

 void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
 {
-   if (dbfi.Size())
+   if (domain_integs.Size())
   {
      const FiniteElement &trial_fe = *trial_fes->GetFE(i);
      const FiniteElement &test_fe = *test_fes->GetFE(i);
      ElementTransformation *eltrans = test_fes->GetElementTransformation(i);
-      dbfi[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans, elmat);
-      for (int k = 1; k < dbfi.Size(); k++)
+      domain_integs[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans,
+                                               elmat);
+      for (int k = 1; k < domain_integs.Size(); k++)
      {
-         dbfi[k]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans, elemmat);
+         domain_integs[k]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans,
+                                                  elemmat);
         elmat += elemmat;
      }
   }
@@ -1543,15 +1622,17 @@ void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)

 void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
 {
-   if (bbfi.Size())
+   if (boundary_integs.Size())
   {
      const FiniteElement &trial_be = *trial_fes->GetBE(i);
      const FiniteElement &test_be = *test_fes->GetBE(i);
      ElementTransformation *eltrans = test_fes->GetBdrElementTransformation(i);
-      bbfi[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans, elmat);
-      for (int k = 1; k < bbfi.Size(); k++)
+      boundary_integs[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans,
+                                                 elmat);
+      for (int k = 1; k < boundary_integs.Size(); k++)
      {
-         bbfi[k]->AssembleElementMatrix2(trial_be, test_be, *eltrans, elemmat);
+         boundary_integs[k]->AssembleElementMatrix2(trial_be, test_be, *eltrans,
+                                                    elemmat);
         elmat += elemmat;
      }
   }
@@ -1651,10 +1732,10 @@ void MixedBilinearForm::EliminateTestDofs (const Array<int> &bdr_attr_is_ess)
      }
 }

-void MixedBilinearForm::FormRectangularSystemMatrix(const Array<int>
-                                                    &trial_tdof_list,
-                                                    const Array<int> &test_tdof_list,
-                                                    OperatorHandle &A)
+void MixedBilinearForm::FormRectangularSystemMatrix(
+   const Array<int> &trial_tdof_list,
+   const Array<int> &test_tdof_list,
+   OperatorHandle &A)

 {
   if (ext)
@@ -1692,17 +1773,17 @@ void MixedBilinearForm::FormRectangularSystemMatrix(const Array<int>
   A.Reset(mat, false);
 }

-void MixedBilinearForm::FormRectangularLinearSystem(const Array<int>
-                                                    &trial_tdof_list,
-                                                    const Array<int> &test_tdof_list,
-                                                    Vector &x, Vector &b,
-                                                    OperatorHandle &A,
-                                                    Vector &X, Vector &B)
+void MixedBilinearForm::FormRectangularLinearSystem(
+   const Array<int> &trial_tdof_list,
+   const Array<int> &test_tdof_list,
+   Vector &x, Vector &b,
+   OperatorHandle &A,
+   Vector &X, Vector &B)
 {
   if (ext)
   {
-      ext->FormRectangularLinearSystem(trial_tdof_list, test_tdof_list, x, b, A, X,
-                                       B);
+      ext->FormRectangularLinearSystem(trial_tdof_list, test_tdof_list,
+                                       x, b, A, X, B);
      return;
   }

@@ -1740,10 +1821,13 @@ MixedBilinearForm::~MixedBilinearForm()
   if (!extern_bfs)
   {
      int i;
-      for (i = 0; i < dbfi.Size(); i++) { delete dbfi[i]; }
-      for (i = 0; i < bbfi.Size(); i++) { delete bbfi[i]; }
-      for (i = 0; i < tfbfi.Size(); i++) { delete tfbfi[i]; }
-      for (i = 0; i < btfbfi.Size(); i++) { delete btfbfi[i]; }
+      for (i = 0; i < domain_integs.Size(); i++) { delete domain_integs[i]; }
+      for (i = 0; i < boundary_integs.Size(); i++)
+      { delete boundary_integs[i]; }
+      for (i = 0; i < trace_face_integs.Size(); i++)
+      { delete trace_face_integs[i]; }
+      for (i = 0; i < boundary_trace_face_integs.Size(); i++)
+      { delete boundary_trace_face_integs[i]; }
   }
   delete ext;
 }
@@ -1785,6 +1869,8 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)

   Array<int> dom_vdofs, ran_vdofs;
   ElementTransformation *T;
+   DofTransformation * dom_dof_trans;
+   DofTransformation * ran_dof_trans;
   const FiniteElement *dom_fe, *ran_fe;
   DenseMatrix totelmat, elmat;

@@ -1793,27 +1879,33 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
      mat = new SparseMatrix(height, width);
   }

-   if (dbfi.Size() > 0)
+   if (domain_integs.Size() > 0)
   {
      for (int i = 0; i < test_fes->GetNE(); i++)
      {
-         trial_fes->GetElementVDofs(i, dom_vdofs);
-         test_fes->GetElementVDofs(i, ran_vdofs);
+         dom_dof_trans = trial_fes->GetElementVDofs(i, dom_vdofs);
+         ran_dof_trans = test_fes->GetElementVDofs(i, ran_vdofs);
         T = test_fes->GetElementTransformation(i);
         dom_fe = trial_fes->GetFE(i);
         ran_fe = test_fes->GetFE(i);

-         dbfi[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
-         for (int j = 1; j < dbfi.Size(); j++)
+         domain_integs[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
+                                                  totelmat);
+         for (int j = 1; j < domain_integs.Size(); j++)
         {
-            dbfi[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
+            domain_integs[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
+                                                     elmat);
            totelmat += elmat;
         }
+         if (ran_dof_trans || dom_dof_trans)
+         {
+            TransformPrimal(ran_dof_trans, dom_dof_trans, totelmat);
+         }
         mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
      }
   }

-   if (tfbfi.Size())
+   if (trace_face_integs.Size())
   {
      const int nfaces = test_fes->GetMesh()->GetNumFaces();
      for (int i = 0; i < nfaces; i++)
@@ -1824,10 +1916,12 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
         dom_fe = trial_fes->GetFaceElement(i);
         ran_fe = test_fes->GetFaceElement(i);

-         tfbfi[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
-         for (int j = 1; j < tfbfi.Size(); j++)
+         trace_face_integs[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
+                                                      totelmat);
+         for (int j = 1; j < trace_face_integs.Size(); j++)
         {
-            tfbfi[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
+            trace_face_integs[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
+                                                         elmat);
            totelmat += elmat;
         }
         mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
@@ -84,23 +84,29 @@ protected:
       the BilinearForm. */
   long sequence;

-   /** @brief Indicates the BilinearFormIntegrator%s stored in #dbfi, #bbfi,
-       #fbfi, and #bfbfi are owned by another BilinearForm. */
+   /** @brief Indicates the BilinearFormIntegrator%s stored in #domain_integs,
+       #boundary_integs, #interior_face_integs, and #boundary_face_integs are
+       owned by another BilinearForm. */
   int extern_bfs;

   /// Set of Domain Integrators to be applied.
-   Array<BilinearFormIntegrator*> dbfi;
+   Array<BilinearFormIntegrator*> domain_integs;
+   /// Element attribute marker (should be of length mesh->attributes)
+   /// Includes all by default.
+   /// 0 - ignore attribute
+   /// 1 - include attribute
+   Array<Array<int>*>             domain_integs_marker;

   /// Set of Boundary Integrators to be applied.
-   Array<BilinearFormIntegrator*> bbfi;
-   Array<Array<int>*>             bbfi_marker; ///< Entries are not owned.
+   Array<BilinearFormIntegrator*> boundary_integs;
+   Array<Array<int>*> boundary_integs_marker; ///< Entries are not owned.

   /// Set of interior face Integrators to be applied.
-   Array<BilinearFormIntegrator*> fbfi;
+   Array<BilinearFormIntegrator*> interior_face_integs;

   /// Set of boundary face Integrators to be applied.
-   Array<BilinearFormIntegrator*> bfbfi;
-   Array<Array<int>*>             bfbfi_marker; ///< Entries are not owned.
+   Array<BilinearFormIntegrator*> boundary_face_integs;
+   Array<Array<int>*> boundary_face_integs_marker; ///< Entries are not owned.

   DenseMatrix elemmat;
   Array<int>  vdofs;
@@ -226,24 +232,25 @@ public:
   void AllocateMatrix() { if (mat == NULL) { AllocMat(); } }

   /// Access all the integrators added with AddDomainIntegrator().
-   Array<BilinearFormIntegrator*> *GetDBFI() { return &dbfi; }
+   Array<BilinearFormIntegrator*> *GetDBFI() { return &domain_integs; }

   /// Access all the integrators added with AddBoundaryIntegrator().
-   Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
+   Array<BilinearFormIntegrator*> *GetBBFI() { return &boundary_integs; }
   /** @brief Access all boundary markers added with AddBoundaryIntegrator().
       If no marker was specified when the integrator was added, the
       corresponding pointer (to Array<int>) will be NULL. */
-   Array<Array<int>*> *GetBBFI_Marker() { return &bbfi_marker; }
+   Array<Array<int>*> *GetBBFI_Marker() { return &boundary_integs_marker; }

   /// Access all integrators added with AddInteriorFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetFBFI() { return &fbfi; }
+   Array<BilinearFormIntegrator*> *GetFBFI() { return &interior_face_integs; }

   /// Access all integrators added with AddBdrFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetBFBFI() { return &bfbfi; }
+   Array<BilinearFormIntegrator*> *GetBFBFI() { return &boundary_face_integs; }
   /** @brief Access all boundary markers added with AddBdrFaceIntegrator().
       If no marker was specified when the integrator was added, the
       corresponding pointer (to Array<int>) will be NULL. */
-   Array<Array<int>*> *GetBFBFI_Marker() { return &bfbfi_marker; }
+   Array<Array<int>*> *GetBFBFI_Marker()
+   { return &boundary_face_integs_marker; }

   /// Returns a reference to: \f$ M_{ij} \f$
   const double &operator()(int i, int j) { return (*mat)(i,j); }
@@ -332,6 +339,10 @@ public:

   /// Adds new Domain Integrator. Assumes ownership of @a bfi.
   void AddDomainIntegrator(BilinearFormIntegrator *bfi);
+   /// Adds new Domain Integrator restricted to certain elements specified by
+   /// the @a elem_attr_marker.
+   void AddDomainIntegrator(BilinearFormIntegrator *bfi,
+                            Array<int> &elem_marker);

   /// Adds new Boundary Integrator. Assumes ownership of @a bfi.
   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi);
@@ -643,23 +654,25 @@ protected:
       Partial Assembly (PA), or Matrix Free assembly (MF). */
   MixedBilinearFormExtension *ext;

-   /** @brief Indicates the BilinearFormIntegrator%s stored in #dbfi, #bbfi,
-       #tfbfi and #btfbfi are owned by another MixedBilinearForm. */
+   /** @brief Indicates the BilinearFormIntegrator%s stored in #domain_integs,
+       #boundary_integs, #trace_face_integs and #boundary_trace_face_integs
+       are owned by another MixedBilinearForm. */
   int extern_bfs;

   /// Domain integrators.
-   Array<BilinearFormIntegrator*> dbfi;
+   Array<BilinearFormIntegrator*> domain_integs;

   /// Boundary integrators.
-   Array<BilinearFormIntegrator*> bbfi;
-   Array<Array<int>*>             bbfi_marker;///< Entries are not owned.
+   Array<BilinearFormIntegrator*> boundary_integs;
+   Array<Array<int>*> boundary_integs_marker; ///< Entries are not owned.

   /// Trace face (skeleton) integrators.
-   Array<BilinearFormIntegrator*> tfbfi;
+   Array<BilinearFormIntegrator*> trace_face_integs;

   /// Boundary trace face (skeleton) integrators.
-   Array<BilinearFormIntegrator*> btfbfi;
-   Array<Array<int>*>             btfbfi_marker;///< Entries are not owned.
+   Array<BilinearFormIntegrator*> boundary_trace_face_integs;
+   /// Entries are not owned.
+   Array<Array<int>*> boundary_trace_face_integs_marker;

   DenseMatrix elemmat;
   Array<int>  trial_vdofs, test_vdofs;
@@ -753,24 +766,26 @@ public:
                                   Array<int> &bdr_marker);

   /// Access all integrators added with AddDomainIntegrator().
-   Array<BilinearFormIntegrator*> *GetDBFI() { return &dbfi; }
+   Array<BilinearFormIntegrator*> *GetDBFI() { return &domain_integs; }

   /// Access all integrators added with AddBoundaryIntegrator().
-   Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
+   Array<BilinearFormIntegrator*> *GetBBFI() { return &boundary_integs; }
   /** @brief Access all boundary markers added with AddBoundaryIntegrator().
       If no marker was specified when the integrator was added, the
       corresponding pointer (to Array<int>) will be NULL. */
-   Array<Array<int>*> *GetBBFI_Marker() { return &bbfi_marker; }
+   Array<Array<int>*> *GetBBFI_Marker() { return &boundary_integs_marker; }

   /// Access all integrators added with AddTraceFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetTFBFI() { return &tfbfi; }
+   Array<BilinearFormIntegrator*> *GetTFBFI() { return &trace_face_integs; }

   /// Access all integrators added with AddBdrTraceFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetBTFBFI() { return &btfbfi; }
+   Array<BilinearFormIntegrator*> *GetBTFBFI()
+   { return &boundary_trace_face_integs; }
   /** @brief Access all boundary markers added with AddBdrTraceFaceIntegrator().
       If no marker was specified when the integrator was added, the
       corresponding pointer (to Array<int>) will be NULL. */
-   Array<Array<int>*> *GetBTFBFI_Marker() { return &btfbfi_marker; }
+   Array<Array<int>*> *GetBTFBFI_Marker()
+   { return &boundary_trace_face_integs_marker; }

   /// Sets all sparse values of \f$ M \f$ to @a a.
   void operator=(const double a) { *mat = a; }
@@ -995,7 +1010,7 @@ public:
   { AddTraceFaceIntegrator(di); }

   /// Access all interpolators added with AddDomainInterpolator().
-   Array<BilinearFormIntegrator*> *GetDI() { return &dbfi; }
+   Array<BilinearFormIntegrator*> *GetDI() { return &domain_integs; }

   /// Set the desired assembly level. The default is AssemblyLevel::FULL.
   /** This method must be called before assembly. */
@@ -160,7 +160,7 @@ void MFBilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultMF(faceIntX, faceIntY);
         }
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
+         int_face_restrict_lex->AddMultTranspose(faceIntY, y);
      }
   }

@@ -176,7 +176,7 @@ void MFBilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultMF(faceBdrX, faceBdrY);
         }
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
      }
   }
 }
@@ -217,7 +217,7 @@ void MFBilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultTransposeMF(faceIntX, faceIntY);
         }
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
+         int_face_restrict_lex->AddMultTranspose(faceIntY, y);
      }
   }

@@ -233,7 +233,7 @@ void MFBilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultTransposeMF(faceBdrX, faceBdrY);
         }
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
      }
   }
 }
@@ -417,7 +417,7 @@ void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultPA(faceIntX, faceIntY);
         }
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
+         int_face_restrict_lex->AddMultTranspose(faceIntY, y);
      }
   }

@@ -433,7 +433,7 @@ void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultPA(faceBdrX, faceBdrY);
         }
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
      }
   }
 }
@@ -474,7 +474,7 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultTransposePA(faceIntX, faceIntY);
         }
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
+         int_face_restrict_lex->AddMultTranspose(faceIntY, y);
      }
   }

@@ -490,7 +490,7 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultTransposePA(faceBdrX, faceBdrY);
         }
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
      }
   }
 }
@@ -657,7 +657,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
            Y(j, 0, f) += res;
         });
         // Apply the Interior Face Restriction transposed
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
+         int_face_restrict_lex->AddMultTranspose(faceIntY, y);
      }
   }

@@ -688,7 +688,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
            Y(j, f) += res;
         });
         // Apply the Boundary Face Restriction transposed
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
      }
   }
 }
@@ -783,7 +783,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
            Y(j, 0, f) += res;
         });
         // Apply the Interior Face Restriction transposed
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
+         int_face_restrict_lex->AddMultTranspose(faceIntY, y);
      }
   }

@@ -814,7 +814,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
            Y(j, f) += res;
         });
         // Apply the Boundary Face Restriction transposed
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
      }
   }
 }
@@ -72,8 +72,8 @@ protected:
   mutable Vector faceIntX, faceIntY;
   mutable Vector faceBdrX, faceBdrY;
   const Operator *elem_restrict; // Not owned
-   const Operator *int_face_restrict_lex; // Not owned
-   const Operator *bdr_face_restrict_lex; // Not owned
+   const FaceRestriction *int_face_restrict_lex; // Not owned
+   const FaceRestriction *bdr_face_restrict_lex; // Not owned

 public:
   PABilinearFormExtension(BilinearForm*);
@@ -143,8 +143,8 @@ protected:
   mutable Vector faceIntX, faceIntY;
   mutable Vector faceBdrX, faceBdrY;
   const Operator *elem_restrict; // Not owned
-   const Operator *int_face_restrict_lex; // Not owned
-   const Operator *bdr_face_restrict_lex; // Not owned
+   const FaceRestriction *int_face_restrict_lex; // Not owned
+   const FaceRestriction *bdr_face_restrict_lex; // Not owned

 public:
   MFBilinearFormExtension(BilinearForm *form);
@@ -175,6 +175,11 @@ void BilinearFormIntegrator::AssembleFaceVector(
   elmat.Mult(elfun, elvect);
 }

+void TransposeIntegrator::SetIntRule(const IntegrationRule *ir)
+{
+   IntRule = ir;
+   bfi->SetIntRule(ir);
+}

 void TransposeIntegrator::AssembleElementMatrix (
   const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
@@ -202,6 +207,12 @@ void TransposeIntegrator::AssembleFaceMatrix (
   elmat.Transpose (bfi_elmat);
 }

+void LumpedIntegrator::SetIntRule(const IntegrationRule *ir)
+{
+   IntRule = ir;
+   bfi->SetIntRule(ir);
+}
+
 void LumpedIntegrator::AssembleElementMatrix (
   const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 {
@@ -209,6 +220,12 @@ void LumpedIntegrator::AssembleElementMatrix (
   elmat.Lump();
 }

+void InverseIntegrator::SetIntRule(const IntegrationRule *ir)
+{
+   IntRule = ir;
+   integrator->SetIntRule(ir);
+}
+
 void InverseIntegrator::AssembleElementMatrix(
   const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 {
@@ -216,6 +233,15 @@ void InverseIntegrator::AssembleElementMatrix(
   elmat.Invert();
 }

+void SumIntegrator::SetIntRule(const IntegrationRule *ir)
+{
+   IntRule = ir;
+   for (int i = 0; i < integrators.Size(); i++)
+   {
+      integrators[i]->SetIntRule(ir);
+   }
+}
+
 void SumIntegrator::AssembleElementMatrix(
   const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 {
@@ -1751,15 +1777,16 @@ void DerivativeIntegrator::AssembleElementMatrix2 (
   int dim = trial_fe.GetDim();
   int trial_nd = trial_fe.GetDof();
   int test_nd = test_fe.GetDof();
+   int spaceDim = Trans.GetSpaceDim();

   int i, l;
   double det;

   elmat.SetSize (test_nd,trial_nd);
   dshape.SetSize (trial_nd,dim);
-   dshapedxt.SetSize(trial_nd,dim);
+   dshapedxt.SetSize(trial_nd, spaceDim);
   dshapedxi.SetSize(trial_nd);
-   invdfdx.SetSize(dim);
+   invdfdx.SetSize(dim, spaceDim);
   shape.SetSize (test_nd);

   const IntegrationRule *ir = IntRule;
@@ -21,7 +21,11 @@ namespace mfem

 // Local maximum size of dofs and quads in 1D
 constexpr int HCURL_MAX_D1D = 5;
+#ifdef MFEM_USE_HIP
+constexpr int HCURL_MAX_Q1D = 5;
+#else
 constexpr int HCURL_MAX_Q1D = 6;
+#endif

 constexpr int HDIV_MAX_D1D = 5;
 constexpr int HDIV_MAX_Q1D = 6;
@@ -257,6 +261,8 @@ public:
   TransposeIntegrator (BilinearFormIntegrator *bfi_, int own_bfi_ = 1)
   { bfi = bfi_; own_bfi = own_bfi_; }

+   virtual void SetIntRule(const IntegrationRule *ir);
+
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
@@ -324,6 +330,8 @@ public:
   LumpedIntegrator (BilinearFormIntegrator *bfi_, int own_bfi_ = 1)
   { bfi = bfi_; own_bfi = own_bfi_; }

+   virtual void SetIntRule(const IntegrationRule *ir);
+
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
@@ -342,6 +350,8 @@ public:
   InverseIntegrator(BilinearFormIntegrator *integ, int own_integ = 1)
   { integrator = integ; own_integrator = own_integ; }

+   virtual void SetIntRule(const IntegrationRule *ir);
+
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
@@ -360,6 +370,8 @@ private:
 public:
   SumIntegrator(int own_integs = 1) { own_integrators = own_integs; }

+   virtual void SetIntRule(const IntegrationRule *ir);
+
   void AddIntegrator(BilinearFormIntegrator *integ)
   { integrators.Append(integ); }

@@ -699,7 +711,7 @@ protected:
   {
      return "MixedScalarDerivativeIntegrator:  "
             "Trial and test spaces must both be scalar fields in 1D "
-             "and the trial space must implement CaldDShape.";
+             "and the trial space must implement CalcDShape.";
   }

   inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
@@ -2924,11 +2936,11 @@ public:

    - F. Bassi and S. Rebay. A high order discontinuous Galerkin method for
      compressible turbulent flows. In B. Cockburn, G. E. Karniadakis, and
-      C.-W. Shu, editors, Discontinuous Galerkin Methods, pages 77–88. Springer
+      C.-W. Shu, editors, Discontinuous Galerkin Methods, pages 77-88. Springer
      Berlin Heidelberg, 2000.
    - D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini. Unified analysis
      of discontinuous Galerkin methods for elliptic problems. SIAM Journal on
-      Numerical Analysis, 39(5):1749–1779, 2002.
+      Numerical Analysis, 39(5):1749-1779, 2002.
 */
 class DGDiffusionBR2Integrator : public BilinearFormIntegrator
 {
@@ -17,14 +17,14 @@ namespace mfem
 {

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble1D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EAConvectionAssemble1D(const int NE,
+                            const Array<double> &b,
+                            const Array<double> &g,
+                            const Vector &padata,
+                            Vector &eadata,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -69,14 +69,14 @@ static void EAConvectionAssemble1D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble2D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EAConvectionAssemble2D(const int NE,
+                            const Array<double> &b,
+                            const Array<double> &g,
+                            const Vector &padata,
+                            Vector &eadata,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -146,14 +146,14 @@ static void EAConvectionAssemble2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble3D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EAConvectionAssemble3D(const int NE,
+                            const Array<double> &b,
+                            const Array<double> &g,
+                            const Vector &padata,
+                            Vector &eadata,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -21,13 +21,13 @@ namespace mfem
 // PA Convection Integrator

 // PA Convection Assemble 2D kernel
-static void PAConvectionSetup2D(const int NQ,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const Vector &vel,
-                                const double alpha,
-                                Vector &op)
+void PAConvectionSetup2D(const int NQ,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const Vector &vel,
+                         const double alpha,
+                         Vector &op)
 {
   constexpr int DIM = 2;

@@ -60,13 +60,13 @@ static void PAConvectionSetup2D(const int NQ,
 }

 // PA Convection Assemble 3D kernel
-static void PAConvectionSetup3D(const int NQ,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const Vector &vel,
-                                const double alpha,
-                                Vector &op)
+void PAConvectionSetup3D(const int NQ,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const Vector &vel,
+                         const double alpha,
+                         Vector &op)
 {
   constexpr int DIM = 3;
   constexpr int SDIM = DIM;
@@ -135,7 +135,7 @@ static void PAConvectionSetup(const int dim,
 }

 // PA Convection Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PAConvectionApply2D(const int ne,
                         const Array<double> &b,
                         const Array<double> &g,
@@ -254,7 +254,7 @@ void PAConvectionApply2D(const int ne,
 }

 // Optimized PA Convection Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
 void SmemPAConvectionApply2D(const int ne,
                             const Array<double> &b,
                             const Array<double> &g,
@@ -382,7 +382,7 @@ void SmemPAConvectionApply2D(const int ne,
 }

 // PA Convection Apply 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PAConvectionApply3D(const int ne,
                         const Array<double> &b,
                         const Array<double> &g,
@@ -563,7 +563,7 @@ void PAConvectionApply3D(const int ne,
 }

 // Optimized PA Convection Apply 3D kernel
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void SmemPAConvectionApply3D(const int ne,
                             const Array<double> &b,
                             const Array<double> &g,
@@ -768,6 +768,8 @@ void SmemPAConvectionApply3D(const int ne,

 void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
+   const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
+                         Device::GetDeviceMemoryType() : pa_mt;
   // Assumes tensor-product elements
   Mesh *mesh = fes.GetMesh();
   const FiniteElement &el = *fes.GetFE(0);
@@ -784,11 +786,11 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   const int nq = ir->GetNPoints();
   dim = mesh->Dimension();
   ne = fes.GetNE();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS, mt);
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
+   pa_data.SetSize(symmDims * nq * ne, mt);
   Vector vel;
   if (VectorConstantCoefficient *cQ =
          dynamic_cast<VectorConstantCoefficient*>(Q))
@@ -798,7 +800,7 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   else if (VectorGridFunctionCoefficient *vgfQ =
               dynamic_cast<VectorGridFunctionCoefficient*>(Q))
   {
-      vel.SetSize(dim * nq * ne);
+      vel.SetSize(dim * nq * ne, mt);

      const GridFunction *gf = vgfQ->GetGridFunction();
      const FiniteElementSpace &gf_fes = *gf->FESpace();
@@ -809,7 +811,7 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
                                          ElementDofOrdering::NATIVE;
      const Operator *R = gf_fes.GetElementRestriction(ordering);

-      Vector xe(R->Height(), Device::GetMemoryType());
+      Vector xe(R->Height(), mt);
      xe.UseDevice(true);

      R->Mult(*gf, xe);
@@ -16,12 +16,12 @@
 namespace mfem
 {

-static void EADGTraceAssemble1DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   const bool add)
+void EADGTraceAssemble1DInt(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_int,
+                            Vector &eadata_ext,
+                            const bool add)
 {
   auto D = Reshape(padata.Read(), 2, 2, NF);
   auto A_int = Reshape(eadata_int.ReadWrite(), 2, NF);
@@ -50,11 +50,11 @@ static void EADGTraceAssemble1DInt(const int NF,
   });
 }

-static void EADGTraceAssemble1DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   const bool add)
+void EADGTraceAssemble1DBdr(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_bdr,
+                            const bool add)
 {
   auto D = Reshape(padata.Read(), 2, 2, NF);
   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), NF);
@@ -72,14 +72,14 @@ static void EADGTraceAssemble1DBdr(const int NF,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble2DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble2DInt(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_int,
+                            Vector &eadata_ext,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -128,13 +128,13 @@ static void EADGTraceAssemble2DInt(const int NF,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble2DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble2DBdr(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_bdr,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -170,14 +170,14 @@ static void EADGTraceAssemble2DBdr(const int NF,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble3DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble3DInt(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_int,
+                            Vector &eadata_ext,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -268,13 +268,13 @@ static void EADGTraceAssemble3DInt(const int NF,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble3DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   const bool add,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void EADGTraceAssemble3DBdr(const int NF,
+                            const Array<double> &basis,
+                            const Vector &padata,
+                            Vector &eadata_bdr,
+                            const bool add,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -19,16 +19,16 @@ using namespace std;
 namespace mfem
 {
 // PA DG Trace Integrator
-static void PADGTraceSetup2D(const int Q1D,
-                             const int NF,
-                             const Array<double> &w,
-                             const Vector &det,
-                             const Vector &nor,
-                             const Vector &rho,
-                             const Vector &vel,
-                             const double alpha,
-                             const double beta,
-                             Vector &op)
+void PADGTraceSetup2D(const int Q1D,
+                      const int NF,
+                      const Array<double> &w,
+                      const Vector &det,
+                      const Vector &nor,
+                      const Vector &rho,
+                      const Vector &vel,
+                      const double alpha,
+                      const double beta,
+                      Vector &op)
 {
   const int VDIM = 2;

@@ -61,16 +61,16 @@ static void PADGTraceSetup2D(const int Q1D,
   });
 }

-static void PADGTraceSetup3D(const int Q1D,
-                             const int NF,
-                             const Array<double> &w,
-                             const Vector &det,
-                             const Vector &nor,
-                             const Vector &rho,
-                             const Vector &vel,
-                             const double alpha,
-                             const double beta,
-                             Vector &op)
+void PADGTraceSetup3D(const int Q1D,
+                      const int NF,
+                      const Array<double> &w,
+                      const Vector &det,
+                      const Vector &nor,
+                      const Vector &rho,
+                      const Vector &vel,
+                      const double alpha,
+                      const double beta,
+                      Vector &op)
 {
   const int VDIM = 3;

@@ -301,7 +301,7 @@ void DGTraceIntegrator::AssemblePABoundaryFaces(const FiniteElementSpace& fes)
 }

 // PA DGTrace Apply 2D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApply2D(const int NF,
                      const Array<double> &b,
                      const Array<double> &bt,
@@ -392,7 +392,7 @@ void PADGTraceApply2D(const int NF,
 }

 // PA DGTrace Apply 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApply3D(const int NF,
                      const Array<double> &b,
                      const Array<double> &bt,
@@ -537,7 +537,7 @@ void PADGTraceApply3D(const int NF,
 }

 // Optimized PA DGTrace Apply 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
 void SmemPADGTraceApply3D(const int NF,
                          const Array<double> &b,
                          const Array<double> &bt,
@@ -701,7 +701,7 @@ static void PADGTraceApply(const int dim,
 }

 // PA DGTrace Apply 2D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApplyTranspose2D(const int NF,
                               const Array<double> &b,
                               const Array<double> &bt,
@@ -797,7 +797,7 @@ void PADGTraceApplyTranspose2D(const int NF,
 }

 // PA DGTrace Apply Transpose 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0> static
+template<int T_D1D = 0, int T_Q1D = 0>
 void PADGTraceApplyTranspose3D(const int NF,
                               const Array<double> &b,
                               const Array<double> &bt,
@@ -953,7 +953,7 @@ void PADGTraceApplyTranspose3D(const int NF,
 }

 // Optimized PA DGTrace Apply Transpose 3D kernel for Gauss-Lobatto/Bernstein
-template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
 void SmemPADGTraceApplyTranspose3D(const int NF,
                                   const Array<double> &b,
                                   const Array<double> &bt,
@@ -17,14 +17,14 @@ namespace mfem
 {

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble1D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  const bool add,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void EADiffusionAssemble1D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &padata,
+                           Vector &eadata,
+                           const bool add,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -68,14 +68,14 @@ static void EADiffusionAssemble1D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble2D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  const bool add,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void EADiffusionAssemble2D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &padata,
+                           Vector &eadata,
+                           const bool add,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -145,14 +145,14 @@ static void EADiffusionAssemble2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble3D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  const bool add,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void EADiffusionAssemble3D(const int NE,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &padata,
+                           Vector &eadata,
+                           const bool add,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -351,6 +351,8 @@ static void PADiffusionSetup(const int dim,

 void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
+   const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
+                         Device::GetDeviceMemoryType() : pa_mt;
   // Assuming the same element type
   fespace = &fes;
   Mesh *mesh = fes.GetMesh();
@@ -371,7 +373,7 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   const int nq = ir->GetNPoints();
   dim = mesh->Dimension();
   ne = fes.GetNE();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS, mt);
   const int sdim = mesh->SpaceDimension();
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
@@ -488,21 +490,20 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
         }
      }
   }
-   pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne,
-                   Device::GetDeviceMemoryType());
+   pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne, mt);
   PADiffusionSetup(dim, sdim, dofs1D, quad1D, coeffDim, ne, ir->GetWeights(),
                    geom->J, coeff, pa_data);
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionDiagonal2D(const int NE,
-                                  const bool symmetric,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &d,
-                                  Vector &y,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void PADiffusionDiagonal2D(const int NE,
+                           const bool symmetric,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &d,
+                           Vector &y,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -561,14 +562,14 @@ static void PADiffusionDiagonal2D(const int NE,

 // Shared memory PA Diffusion Diagonal 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPADiffusionDiagonal2D(const int NE,
-                                      const bool symmetric,
-                                      const Array<double> &b_,
-                                      const Array<double> &g_,
-                                      const Vector &d_,
-                                      Vector &y_,
-                                      const int d1d = 0,
-                                      const int q1d = 0)
+void SmemPADiffusionDiagonal2D(const int NE,
+                               const bool symmetric,
+                               const Array<double> &b_,
+                               const Array<double> &g_,
+                               const Vector &d_,
+                               Vector &y_,
+                               const int d1d = 0,
+                               const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -655,14 +656,14 @@ static void SmemPADiffusionDiagonal2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionDiagonal3D(const int NE,
-                                  const bool symmetric,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &d,
-                                  Vector &y,
-                                  const int d1d = 0,
-                                  const int q1d = 0)
+void PADiffusionDiagonal3D(const int NE,
+                           const bool symmetric,
+                           const Array<double> &b,
+                           const Array<double> &g,
+                           const Vector &d,
+                           Vector &y,
+                           const int d1d = 0,
+                           const int q1d = 0)
 {
   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -756,14 +757,14 @@ static void PADiffusionDiagonal3D(const int NE,

 // Shared memory PA Diffusion Diagonal 3D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPADiffusionDiagonal3D(const int NE,
-                                      const bool symmetric,
-                                      const Array<double> &b_,
-                                      const Array<double> &g_,
-                                      const Vector &d_,
-                                      Vector &y_,
-                                      const int d1d = 0,
-                                      const int q1d = 0)
+void SmemPADiffusionDiagonal3D(const int NE,
+                               const bool symmetric,
+                               const Array<double> &b_,
+                               const Array<double> &g_,
+                               const Vector &d_,
+                               Vector &y_,
+                               const int d1d = 0,
+                               const int q1d = 0)
 {
   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -1033,17 +1034,17 @@ static void OccaPADiffusionApply3D(const int D1D,

 // PA Diffusion Apply 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionApply2D(const int NE,
-                               const bool symmetric,
-                               const Array<double> &b_,
-                               const Array<double> &g_,
-                               const Array<double> &bt_,
-                               const Array<double> &gt_,
-                               const Vector &d_,
-                               const Vector &x_,
-                               Vector &y_,
-                               const int d1d = 0,
-                               const int q1d = 0)
+void PADiffusionApply2D(const int NE,
+                        const bool symmetric,
+                        const Array<double> &b_,
+                        const Array<double> &g_,
+                        const Array<double> &bt_,
+                        const Array<double> &gt_,
+                        const Vector &d_,
+                        const Vector &x_,
+                        Vector &y_,
+                        const int d1d = 0,
+                        const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1155,15 +1156,15 @@ static void PADiffusionApply2D(const int NE,

 // Shared memory PA Diffusion Apply 2D kernel
 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPADiffusionApply2D(const int NE,
-                                   const bool symmetric,
-                                   const Array<double> &b_,
-                                   const Array<double> &g_,
-                                   const Vector &d_,
-                                   const Vector &x_,
-                                   Vector &y_,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void SmemPADiffusionApply2D(const int NE,
+                            const bool symmetric,
+                            const Array<double> &b_,
+                            const Array<double> &g_,
+                            const Vector &d_,
+                            const Vector &x_,
+                            Vector &y_,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1313,16 +1314,16 @@ static void SmemPADiffusionApply2D(const int NE,

 // PA Diffusion Apply 3D kernel
 template<int T_D1D = 0, int T_Q1D = 0>
-static void PADiffusionApply3D(const int NE,
-                               const bool symmetric,
-                               const Array<double> &b,
-                               const Array<double> &g,
-                               const Array<double> &bt,
-                               const Array<double> &gt,
-                               const Vector &d_,
-                               const Vector &x_,
-                               Vector &y_,
-                               int d1d = 0, int q1d = 0)
+void PADiffusionApply3D(const int NE,
+                        const bool symmetric,
+                        const Array<double> &b,
+                        const Array<double> &g,
+                        const Array<double> &bt,
+                        const Array<double> &gt,
+                        const Vector &d_,
+                        const Vector &x_,
+                        Vector &y_,
+                        int d1d = 0, int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1532,15 +1533,15 @@ static MFEM_HOST_DEVICE inline double sign(const int q, const int d)
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPADiffusionApply3D(const int NE,
-                                   const bool symmetric,
-                                   const Array<double> &b_,
-                                   const Array<double> &g_,
-                                   const Vector &d_,
-                                   const Vector &x_,
-                                   Vector &y_,
-                                   const int d1d = 0,
-                                   const int q1d = 0)
+void SmemPADiffusionApply3D(const int NE,
+                            const bool symmetric,
+                            const Array<double> &b_,
+                            const Array<double> &g_,
+                            const Vector &d_,
+                            const Vector &x_,
+                            Vector &y_,
+                            const int d1d = 0,
+                            const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -21,12 +21,12 @@ namespace mfem
 // PA Divergence Integrator

 // PA Divergence Assemble 2D kernel
-static void PADivergenceSetup2D(const int Q1D,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const double COEFF,
-                                Vector &op)
+void PADivergenceSetup2D(const int Q1D,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const double COEFF,
+                         Vector &op)
 {
   const int NQ = Q1D*Q1D;
   auto W = w.Read();
@@ -51,12 +51,12 @@ static void PADivergenceSetup2D(const int Q1D,
 }

 // PA Divergence Assemble 3D kernel
-static void PADivergenceSetup3D(const int Q1D,
-                                const int NE,
-                                const Array<double> &w,
-                                const Vector &j,
-                                const double COEFF,
-                                Vector &op)
+void PADivergenceSetup3D(const int Q1D,
+                         const int NE,
+                         const Array<double> &w,
+                         const Vector &j,
+                         const double COEFF,
+                         Vector &op)
 {
   const int NQ = Q1D*Q1D*Q1D;
   auto W = w.Read();
@@ -160,16 +160,16 @@ void VectorDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,

 // PA Divergence Apply 2D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApply2D(const int NE,
-                                const Array<double> &b,
-                                const Array<double> &g,
-                                const Array<double> &bt,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                const int tr_d1d = 0,
-                                const int te_d1d = 0,
-                                const int q1d = 0)
+void PADivergenceApply2D(const int NE,
+                         const Array<double> &b,
+                         const Array<double> &g,
+                         const Array<double> &bt,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         const int tr_d1d = 0,
+                         const int te_d1d = 0,
+                         const int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -281,16 +281,16 @@ static void PADivergenceApply2D(const int NE,
 // Shared memory PA Divergence Apply 2D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0,
         const int T_NBZ = 0>
-static void SmemPADivergenceApply2D(const int NE,
-                                    const Array<double> &b_,
-                                    const Array<double> &g_,
-                                    const Array<double> &bt_,
-                                    const Vector &op_,
-                                    const Vector &x_,
-                                    Vector &y_,
-                                    const int tr_d1d = 0,
-                                    const int te_d1d = 0,
-                                    const int q1d = 0)
+void SmemPADivergenceApply2D(const int NE,
+                             const Array<double> &b_,
+                             const Array<double> &g_,
+                             const Array<double> &bt_,
+                             const Vector &op_,
+                             const Vector &x_,
+                             Vector &y_,
+                             const int tr_d1d = 0,
+                             const int te_d1d = 0,
+                             const int q1d = 0)
 {
   // TODO
   MFEM_ASSERT(false, "SHARED MEM NOT PROGRAMMED YET");
@@ -298,16 +298,16 @@ static void SmemPADivergenceApply2D(const int NE,

 // PA Divergence Apply 2D kernel transpose
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApplyTranspose2D(const int NE,
-                                         const Array<double> &bt,
-                                         const Array<double> &gt,
-                                         const Array<double> &b,
-                                         const Vector &op_,
-                                         const Vector &x_,
-                                         Vector &y_,
-                                         const int tr_d1d = 0,
-                                         const int te_d1d = 0,
-                                         const int q1d = 0)
+void PADivergenceApplyTranspose2D(const int NE,
+                                  const Array<double> &bt,
+                                  const Array<double> &gt,
+                                  const Array<double> &b,
+                                  const Vector &op_,
+                                  const Vector &x_,
+                                  Vector &y_,
+                                  const int tr_d1d = 0,
+                                  const int te_d1d = 0,
+                                  const int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -414,16 +414,16 @@ static void PADivergenceApplyTranspose2D(const int NE,

 // PA Vector Divergence Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApply3D(const int NE,
-                                const Array<double> &b,
-                                const Array<double> &g,
-                                const Array<double> &bt,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                int tr_d1d = 0,
-                                int te_d1d = 0,
-                                int q1d = 0)
+void PADivergenceApply3D(const int NE,
+                         const Array<double> &b,
+                         const Array<double> &g,
+                         const Array<double> &bt,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         int tr_d1d = 0,
+                         int te_d1d = 0,
+                         int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -597,16 +597,16 @@ static void PADivergenceApply3D(const int NE,

 // PA Vector Divergence Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PADivergenceApplyTranspose3D(const int NE,
-                                         const Array<double> &bt,
-                                         const Array<double> &gt,
-                                         const Array<double> &b,
-                                         const Vector &op_,
-                                         const Vector &x_,
-                                         Vector &y_,
-                                         int tr_d1d = 0,
-                                         int te_d1d = 0,
-                                         int q1d = 0)
+void PADivergenceApplyTranspose3D(const int NE,
+                                  const Array<double> &bt,
+                                  const Array<double> &gt,
+                                  const Array<double> &b,
+                                  const Vector &op_,
+                                  const Vector &x_,
+                                  Vector &y_,
+                                  int tr_d1d = 0,
+                                  int te_d1d = 0,
+                                  int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -775,16 +775,16 @@ static void PADivergenceApplyTranspose3D(const int NE,

 // Shared memory PA Vector Divergence Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void SmemPADivergenceApply3D(const int NE,
-                                    const Array<double> &b_,
-                                    const Array<double> &g_,
-                                    const Array<double> &bt_,
-                                    const Vector &q_,
-                                    const Vector &x_,
-                                    Vector &y_,
-                                    const int tr_d1d = 0,
-                                    const int te_d1d = 0,
-                                    const int q1d = 0)
+void SmemPADivergenceApply3D(const int NE,
+                             const Array<double> &b_,
+                             const Array<double> &g_,
+                             const Array<double> &bt_,
+                             const Vector &q_,
+                             const Vector &x_,
+                             Vector &y_,
+                             const int tr_d1d = 0,
+                             const int te_d1d = 0,
+                             const int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -25,7 +25,7 @@ namespace mfem
   \b Q1D number of quadrature points in one dimension.
   \b w quadrature weights.
   \b j element Jacobians.
-   \b COEFF coefficient at quadrature points.
+   \b c coefficient at quadrature points.

   The function is used precompute data needed at quadrature points during
   the action. */
@@ -70,18 +70,22 @@ namespace mfem
   the \b MFEM_SHARED keyword for local arrays. */

 // PA Gradient Assemble 2D kernel
-static void PAGradientSetup2D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              const double COEFF,
-                              Vector &op)
+void PAGradientSetup2D(const int Q1D,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       const Vector &c,
+                       Vector &op)
 {
   const int NQ = Q1D*Q1D;
   auto W = w.Read();
   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
   auto y = Reshape(op.Write(), NQ, 2, 2, NE);

+   const bool const_c = c.Size() == 1;
+   const auto C = const_c ? Reshape(c.Read(), 1,1) :
+                  Reshape(c.Read(), NQ, NE);
+
   MFEM_FORALL(e, NE,
   {
      for (int q = 0; q < NQ; ++q)
@@ -91,30 +95,38 @@ static void PAGradientSetup2D(const int Q1D,
         const double J21 = J(q,1,0,e);
         const double J22 = J(q,1,1,e);
         // Store wq * Q * adj(J)
-         y(q,0,0,e) = W[q] * COEFF *  J22; // 1,1
-         y(q,0,1,e) = W[q] * COEFF * -J12; // 1,2
-         y(q,1,0,e) = W[q] * COEFF * -J21; // 2,1
-         y(q,1,1,e) = W[q] * COEFF *  J11; // 2,2
+         const double Co = const_c ? C(0,0) : C(q,e);
+         y(q,0,0,e) = W[q] * Co *  J22; // 1,1
+         y(q,0,1,e) = W[q] * Co * -J12; // 1,2
+         y(q,1,0,e) = W[q] * Co * -J21; // 2,1
+         y(q,1,1,e) = W[q] * Co *  J11; // 2,2
      }
   });
 }

 // PA Gradient Assemble 3D kernel
-static void PAGradientSetup3D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              const double COEFF,
-                              Vector &op)
+void PAGradientSetup3D(const int Q1D,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       const Vector &c,
+                       Vector &op)
 {
   const int NQ = Q1D*Q1D*Q1D;
   auto W = w.Read();
   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
   auto y = Reshape(op.Write(), NQ, 3, 3, NE);
+
+   const bool const_c = c.Size() == 1;
+   const auto C = const_c ? Reshape(c.Read(), 1,1) :
+                  Reshape(c.Read(), NQ,NE);
+
   MFEM_FORALL(e, NE,
   {
      for (int q = 0; q < NQ; ++q)
      {
+         const double Co = const_c ? C(0,0) : C(q,e);
+
         const double J11 = J(q,0,0,e);
         const double J21 = J(q,1,0,e);
         const double J31 = J(q,2,0,e);
@@ -124,7 +136,7 @@ static void PAGradientSetup3D(const int Q1D,
         const double J13 = J(q,0,2,e);
         const double J23 = J(q,1,2,e);
         const double J33 = J(q,2,2,e);
-         const double cw  = W[q] * COEFF;
+         const double cw  = W[q] * Co;
         // adj(J)
         const double A11 = (J22 * J33) - (J23 * J32);
         const double A12 = (J32 * J13) - (J12 * J33);
@@ -156,7 +168,7 @@ static void PAGradientSetup(const int dim,
                            const int NE,
                            const Array<double> &W,
                            const Vector &J,
-                            const double COEFF,
+                            const Vector &COEFF,
                            Vector &op)
 {
   if (dim == 1) { MFEM_ABORT("dim==1 not supported in PAGradientSetup"); }
@@ -196,29 +208,62 @@ void GradientIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
   MFEM_ASSERT(quad1D == test_maps->nqpt,
               "PA requires test and trial space to have same number of quadrature points!");
   pa_data.SetSize(nq * dimsToStore * ne, Device::GetMemoryType());
-   double coeff = 1.0;
-   if (Q)
+
+   Vector coeff;
+
+   if (Q == nullptr)
   {
-      ConstantCoefficient *cQ = dynamic_cast<ConstantCoefficient*>(Q);
-      MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
-      coeff = cQ->constant;
+      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* cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == ne*nq,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
+   else
+   {
+      coeff.SetSize(nq * ne);
+      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));
+         }
+      }
+   }
+
   PAGradientSetup(dim, trial_dofs1D, test_dofs1D, quad1D,
                   ne, ir->GetWeights(), geom->J, coeff, pa_data);
 }

 // PA Gradient Apply 2D kernel
 template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_Q1D = 0>
-static void PAGradientApply2D(const int NE,
-                              const Array<double> &b,
-                              const Array<double> &g,
-                              const Array<double> &bt,
-                              const Vector &op_,
-                              const Vector &x_,
-                              Vector &y_,
-                              const int tr_d1d = 0,
-                              const int te_d1d = 0,
-                              const int q1d = 0)
+void PAGradientApply2D(const int NE,
+                       const Array<double> &b,
+                       const Array<double> &g,
+                       const Array<double> &bt,
+                       const Vector &op_,
+                       const Vector &x_,
+                       Vector &y_,
+                       const int tr_d1d = 0,
+                       const int te_d1d = 0,
+                       const int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -339,16 +384,16 @@ static void PAGradientApplyTranspose2D(const int NE,

 // PA Gradient Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void PAGradientApply3D(const int NE,
-                              const Array<double> &b,
-                              const Array<double> &g,
-                              const Array<double> &bt,
-                              const Vector &op_,
-                              const Vector &x_,
-                              Vector &y_,
-                              int tr_d1d = 0,
-                              int te_d1d = 0,
-                              int q1d = 0)
+void PAGradientApply3D(const int NE,
+                       const Array<double> &b,
+                       const Array<double> &g,
+                       const Array<double> &bt,
+                       const Vector &op_,
+                       const Vector &x_,
+                       Vector &y_,
+                       int tr_d1d = 0,
+                       int te_d1d = 0,
+                       int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -534,16 +579,16 @@ static void PAGradientApplyTranspose3D(const int NE,

 // Shared memory PA Gradient Apply 3D kernel
 template<const int T_TR_D1D = 0, const int T_TE_D1D = 0, const int T_Q1D = 0>
-static void SmemPAGradientApply3D(const int NE,
-                                  const Array<double> &b_,
-                                  const Array<double> &g_,
-                                  const Array<double> &bt_,
-                                  const Vector &d_,
-                                  const Vector &x_,
-                                  Vector &y_,
-                                  const int tr_d1d = 0,
-                                  const int te_d1d = 0,
-                                  const int q1d = 0)
+void SmemPAGradientApply3D(const int NE,
+                           const Array<double> &b_,
+                           const Array<double> &g_,
+                           const Array<double> &bt_,
+                           const Vector &d_,
+                           const Vector &x_,
+                           Vector &y_,
+                           const int tr_d1d = 0,
+                           const int te_d1d = 0,
+                           const int q1d = 0)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -791,12 +791,12 @@ void SmemPAHcurlMassApply3D(const int D1D,
 }

 // PA H(curl) curl-curl assemble 2D kernel
-static void PACurlCurlSetup2D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              Vector &coeff,
-                              Vector &op)
+void PACurlCurlSetup2D(const int Q1D,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       Vector &coeff,
+                       Vector &op)
 {
   const int NQ = Q1D*Q1D;
   auto W = w.Read();
@@ -818,13 +818,13 @@ static void PACurlCurlSetup2D(const int Q1D,
 }

 // PA H(curl) curl-curl assemble 3D kernel
-static void PACurlCurlSetup3D(const int Q1D,
-                              const int coeffDim,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              Vector &coeff,
-                              Vector &op)
+void PACurlCurlSetup3D(const int Q1D,
+                       const int coeffDim,
+                       const int NE,
+                       const Array<double> &w,
+                       const Vector &j,
+                       Vector &coeff,
+                       Vector &op)
 {
   const int NQ = Q1D*Q1D*Q1D;
   const bool symmetric = (coeffDim != 9);
@@ -1045,16 +1045,16 @@ void CurlCurlIntegrator::AssemblePA(const FiniteElementSpace &fes)
   }
 }

-static void PACurlCurlApply2D(const int D1D,
-                              const int Q1D,
-                              const int NE,
-                              const Array<double> &bo,
-                              const Array<double> &bot,
-                              const Array<double> &gc,
-                              const Array<double> &gct,
-                              const Vector &pa_data,
-                              const Vector &x,
-                              Vector &y)
+void PACurlCurlApply2D(const int D1D,
+                       const int Q1D,
+                       const int NE,
+                       const Array<double> &bo,
+                       const Array<double> &bot,
+                       const Array<double> &gc,
+                       const Array<double> &gct,
+                       const Vector &pa_data,
+                       const Vector &x,
+                       Vector &y)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HCURL_MAX_D1D;
@@ -1166,19 +1166,19 @@ static void PACurlCurlApply2D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PACurlCurlApply3D(const int D1D,
-                              const int Q1D,
-                              const bool symmetric,
-                              const int NE,
-                              const Array<double> &bo,
-                              const Array<double> &bc,
-                              const Array<double> &bot,
-                              const Array<double> &bct,
-                              const Array<double> &gc,
-                              const Array<double> &gct,
-                              const Vector &pa_data,
-                              const Vector &x,
-                              Vector &y)
+void PACurlCurlApply3D(const int D1D,
+                       const int Q1D,
+                       const bool symmetric,
+                       const int NE,
+                       const Array<double> &bo,
+                       const Array<double> &bc,
+                       const Array<double> &bot,
+                       const Array<double> &bct,
+                       const Array<double> &gc,
+                       const Array<double> &gct,
+                       const Vector &pa_data,
+                       const Vector &x,
+                       Vector &y)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -1677,19 +1677,19 @@ static void PACurlCurlApply3D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPACurlCurlApply3D(const int D1D,
-                                  const int Q1D,
-                                  const bool symmetric,
-                                  const int NE,
-                                  const Array<double> &bo,
-                                  const Array<double> &bc,
-                                  const Array<double> &bot,
-                                  const Array<double> &bct,
-                                  const Array<double> &gc,
-                                  const Array<double> &gct,
-                                  const Vector &pa_data,
-                                  const Vector &x,
-                                  Vector &y)
+void SmemPACurlCurlApply3D(const int D1D,
+                           const int Q1D,
+                           const bool symmetric,
+                           const int NE,
+                           const Array<double> &bo,
+                           const Array<double> &bc,
+                           const Array<double> &bot,
+                           const Array<double> &bct,
+                           const Array<double> &gc,
+                           const Array<double> &gct,
+                           const Vector &pa_data,
+                           const Vector &x,
+                           Vector &y)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -2032,13 +2032,13 @@ void CurlCurlIntegrator::AddMultPA(const Vector &x, Vector &y) const
   }
 }

-static void PACurlCurlAssembleDiagonal2D(const int D1D,
-                                         const int Q1D,
-                                         const int NE,
-                                         const Array<double> &bo,
-                                         const Array<double> &gc,
-                                         const Vector &pa_data,
-                                         Vector &diag)
+void PACurlCurlAssembleDiagonal2D(const int D1D,
+                                  const int Q1D,
+                                  const int NE,
+                                  const Array<double> &bo,
+                                  const Array<double> &gc,
+                                  const Vector &pa_data,
+                                  Vector &diag)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
@@ -2087,16 +2087,16 @@ static void PACurlCurlAssembleDiagonal2D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void PACurlCurlAssembleDiagonal3D(const int D1D,
-                                         const int Q1D,
-                                         const bool symmetric,
-                                         const int NE,
-                                         const Array<double> &bo,
-                                         const Array<double> &bc,
-                                         const Array<double> &go,
-                                         const Array<double> &gc,
-                                         const Vector &pa_data,
-                                         Vector &diag)
+void PACurlCurlAssembleDiagonal3D(const int D1D,
+                                  const int Q1D,
+                                  const bool symmetric,
+                                  const int NE,
+                                  const Array<double> &bo,
+                                  const Array<double> &bc,
+                                  const Array<double> &go,
+                                  const Array<double> &gc,
+                                  const Vector &pa_data,
+                                  Vector &diag)
 {
   constexpr static int VDIM = 3;
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
@@ -2273,16 +2273,16 @@ static void PACurlCurlAssembleDiagonal3D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPACurlCurlAssembleDiagonal3D(const int D1D,
-                                             const int Q1D,
-                                             const bool symmetric,
-                                             const int NE,
-                                             const Array<double> &bo,
-                                             const Array<double> &bc,
-                                             const Array<double> &go,
-                                             const Array<double> &gc,
-                                             const Vector &pa_data,
-                                             Vector &diag)
+void SmemPACurlCurlAssembleDiagonal3D(const int D1D,
+                                      const int Q1D,
+                                      const bool symmetric,
+                                      const int NE,
+                                      const Array<double> &bo,
+                                      const Array<double> &bc,
+                                      const Array<double> &go,
+                                      const Array<double> &gc,
+                                      const Vector &pa_data,
+                                      Vector &diag)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -2955,18 +2955,18 @@ void MixedVectorCurlIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
 // Apply to x corresponding to DOF's 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,
-                             const int Q1D,
-                             const int coeffDim,
-                             const int NE,
-                             const Array<double> &bo,
-                             const Array<double> &bc,
-                             const Array<double> &bot,
-                             const Array<double> &bct,
-                             const Array<double> &gc,
-                             const Vector &pa_data,
-                             const Vector &x,
-                             Vector &y)
+void PAHcurlL2Apply3D(const int D1D,
+                      const int Q1D,
+                      const int coeffDim,
+                      const int NE,
+                      const Array<double> &bo,
+                      const Array<double> &bc,
+                      const Array<double> &bot,
+                      const Array<double> &bct,
+                      const Array<double> &gc,
+                      const Vector &pa_data,
+                      const Vector &x,
+                      Vector &y)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -3297,16 +3297,16 @@ static void PAHcurlL2Apply3D(const int D1D,
 // Apply to x corresponding to DOF's 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,
-                                 const int Q1D,
-                                 const int coeffDim,
-                                 const int NE,
-                                 const Array<double> &bo,
-                                 const Array<double> &bc,
-                                 const Array<double> &gc,
-                                 const Vector &pa_data,
-                                 const Vector &x,
-                                 Vector &y)
+void SmemPAHcurlL2Apply3D(const int D1D,
+                          const int Q1D,
+                          const int coeffDim,
+                          const int NE,
+                          const Array<double> &bo,
+                          const Array<double> &bc,
+                          const Array<double> &gc,
+                          const Vector &pa_data,
+                          const Vector &x,
+                          Vector &y)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -3585,18 +3585,18 @@ static void SmemPAHcurlL2Apply3D(const int D1D,
 // Apply to x corresponding to DOF's 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,
-                               const int D1Dtest,
-                               const int Q1D,
-                               const int NE,
-                               const Array<double> &bo,
-                               const Array<double> &bc,
-                               const Array<double> &bot,
-                               const Array<double> &bct,
-                               const Array<double> &gc,
-                               const Vector &pa_data,
-                               const Vector &x,
-                               Vector &y)
+void PAHcurlHdivApply3D(const int D1D,
+                        const int D1Dtest,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &bo,
+                        const Array<double> &bc,
+                        const Array<double> &bot,
+                        const Array<double> &bct,
+                        const Array<double> &gc,
+                        const Vector &pa_data,
+                        const Vector &x,
+                        Vector &y)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -4071,18 +4071,18 @@ void MixedVectorWeakCurlIntegrator::AssemblePA(const FiniteElementSpace
 // Apply to x corresponding to DOF's 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,
-                                      const int Q1D,
-                                      const int coeffDim,
-                                      const int NE,
-                                      const Array<double> &bo,
-                                      const Array<double> &bc,
-                                      const Array<double> &bot,
-                                      const Array<double> &bct,
-                                      const Array<double> &gct,
-                                      const Vector &pa_data,
-                                      const Vector &x,
-                                      Vector &y)
+void PAHcurlL2Apply3DTranspose(const int D1D,
+                               const int Q1D,
+                               const int coeffDim,
+                               const int NE,
+                               const Array<double> &bo,
+                               const Array<double> &bc,
+                               const Array<double> &bot,
+                               const Array<double> &bct,
+                               const Array<double> &gct,
+                               const Vector &pa_data,
+                               const Vector &x,
+                               Vector &y)
 {
   // See PAHcurlL2Apply3D for comments.

@@ -4413,16 +4413,16 @@ static void PAHcurlL2Apply3DTranspose(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-static void SmemPAHcurlL2Apply3DTranspose(const int D1D,
-                                          const int Q1D,
-                                          const int coeffDim,
-                                          const int NE,
-                                          const Array<double> &bo,
-                                          const Array<double> &bc,
-                                          const Array<double> &gc,
-                                          const Vector &pa_data,
-                                          const Vector &x,
-                                          Vector &y)
+void SmemPAHcurlL2Apply3DTranspose(const int D1D,
+                                   const int Q1D,
+                                   const int coeffDim,
+                                   const int NE,
+                                   const Array<double> &bo,
+                                   const Array<double> &bc,
+                                   const Array<double> &gc,
+                                   const Vector &pa_data,
+                                   const Vector &x,
+                                   Vector &y)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -4675,13 +4675,13 @@ void MixedVectorWeakCurlIntegrator::AddMultPA(const Vector &x, Vector &y) const
 // Apply to x corresponding to DOFs in H^1 (domain) the (topological) gradient
 // to get a dof in H(curl) (range). You can think of the range as the "test" space
 // and the domain as the "trial" space, but there's no integration.
-static void PAHcurlApplyGradient2D(const int c_dofs1D,
-                                   const int o_dofs1D,
-                                   const int NE,
-                                   const Array<double> &B_,
-                                   const Array<double> &G_,
-                                   const Vector &x_,
-                                   Vector &y_)
+void PAHcurlApplyGradient2D(const int c_dofs1D,
+                            const int o_dofs1D,
+                            const int NE,
+                            const Array<double> &B_,
+                            const Array<double> &G_,
+                            const Vector &x_,
+                            Vector &y_)
 {
   auto B = Reshape(B_.Read(), c_dofs1D, c_dofs1D);
   auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
@@ -4753,12 +4753,12 @@ static void PAHcurlApplyGradient2D(const int c_dofs1D,
 }

 // Specialization of PAHcurlApplyGradient2D to the case where B is identity
-static void PAHcurlApplyGradient2DBId(const int c_dofs1D,
-                                      const int o_dofs1D,
-                                      const int NE,
-                                      const Array<double> &G_,
-                                      const Vector &x_,
-                                      Vector &y_)
+void PAHcurlApplyGradient2DBId(const int c_dofs1D,
+                               const int o_dofs1D,
+                               const int NE,
+                               const Array<double> &G_,
+                               const Vector &x_,
+                               Vector &y_)
 {
   auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);

@@ -4822,7 +4822,7 @@ static void PAHcurlApplyGradient2DBId(const int c_dofs1D,
   });
 }

-static void PAHcurlApplyGradientTranspose2D(
+void PAHcurlApplyGradientTranspose2D(
   const int c_dofs1D, const int o_dofs1D, const int NE,
   const Array<double> &B_, const Array<double> &G_,
   const Vector &x_, Vector &y_)
@@ -4898,7 +4898,7 @@ static void PAHcurlApplyGradientTranspose2D(

 // Specialization of PAHcurlApplyGradientTranspose2D to the case where
 // B is identity
-static void PAHcurlApplyGradientTranspose2DBId(
+void PAHcurlApplyGradientTranspose2DBId(
   const int c_dofs1D, const int o_dofs1D, const int NE,
   const Array<double> &G_,
   const Vector &x_, Vector &y_)
@@ -4965,13 +4965,13 @@ static void PAHcurlApplyGradientTranspose2DBId(
   });
 }

-static void PAHcurlApplyGradient3D(const int c_dofs1D,
-                                   const int o_dofs1D,
-                                   const int NE,
-                                   const Array<double> &B_,
-                                   const Array<double> &G_,
-                                   const Vector &x_,
-                                   Vector &y_)
+void PAHcurlApplyGradient3D(const int c_dofs1D,
+                            const int o_dofs1D,
+                            const int NE,
+                            const Array<double> &B_,
+                            const Array<double> &G_,
+                            const Vector &x_,
+                            Vector &y_)
 {
   auto B = Reshape(B_.Read(), c_dofs1D, c_dofs1D);
   auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
@@ -5154,12 +5154,12 @@ static void PAHcurlApplyGradient3D(const int c_dofs1D,
 }

 // Specialization of PAHcurlApplyGradient3D to the case where
-static void PAHcurlApplyGradient3DBId(const int c_dofs1D,
-                                      const int o_dofs1D,
-                                      const int NE,
-                                      const Array<double> &G_,
-                                      const Vector &x_,
-                                      Vector &y_)
+void PAHcurlApplyGradient3DBId(const int c_dofs1D,
+                               const int o_dofs1D,
+                               const int NE,
+                               const Array<double> &G_,
+                               const Vector &x_,
+                               Vector &y_)
 {
   auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);

@@ -5322,7 +5322,7 @@ static void PAHcurlApplyGradient3DBId(const int c_dofs1D,
   });
 }

-static void PAHcurlApplyGradientTranspose3D(
+void PAHcurlApplyGradientTranspose3D(
   const int c_dofs1D, const int o_dofs1D, const int NE,
   const Array<double> &B_, const Array<double> &G_,
   const Vector &x_, Vector &y_)
@@ -5507,7 +5507,7 @@ static void PAHcurlApplyGradientTranspose3D(
 }

 // Specialization of PAHcurlApplyGradientTranspose3D to the case where
-static void PAHcurlApplyGradientTranspose3DBId(
+void PAHcurlApplyGradientTranspose3DBId(
   const int c_dofs1D, const int o_dofs1D, const int NE,
   const Array<double> &G_,
   const Vector &x_, Vector &y_)
@@ -5789,14 +5789,14 @@ void GradientInterpolator::AddMultTransposePA(const Vector &x, Vector &y) const
   }
 }

-static void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
-                                        const int o_dofs1D,
-                                        const int NE,
-                                        const Array<double> &Bclosed,
-                                        const Array<double> &Bopen,
-                                        const Vector &pa_data,
-                                        const Vector &x_,
-                                        Vector &y_)
+void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
+                                 const int o_dofs1D,
+                                 const int NE,
+                                 const Array<double> &Bclosed,
+                                 const Array<double> &Bopen,
+                                 const Vector &pa_data,
+                                 const Vector &x_,
+                                 Vector &y_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6002,14 +6002,14 @@ static void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
   });
 }

-static void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
-                                                 const int o_dofs1D,
-                                                 const int NE,
-                                                 const Array<double> &Bclosed,
-                                                 const Array<double> &Bopen,
-                                                 const Vector &pa_data,
-                                                 const Vector &x_,
-                                                 Vector &y_)
+void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
+                                          const int o_dofs1D,
+                                          const int NE,
+                                          const Array<double> &Bclosed,
+                                          const Array<double> &Bopen,
+                                          const Vector &pa_data,
+                                          const Vector &x_,
+                                          Vector &y_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6228,14 +6228,14 @@ static void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
   });
 }

-static void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
-                                        const int o_dofs1D,
-                                        const int NE,
-                                        const Array<double> &Bclosed,
-                                        const Array<double> &Bopen,
-                                        const Vector &pa_data,
-                                        const Vector &x_,
-                                        Vector &y_)
+void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
+                                 const int o_dofs1D,
+                                 const int NE,
+                                 const Array<double> &Bclosed,
+                                 const Array<double> &Bopen,
+                                 const Vector &pa_data,
+                                 const Vector &x_,
+                                 Vector &y_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6327,14 +6327,14 @@ static void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
   });
 }

-static void PAHcurlVecH1IdentityApplyTranspose2D(const int c_dofs1D,
-                                                 const int o_dofs1D,
-                                                 const int NE,
-                                                 const Array<double> &Bclosed,
-                                                 const Array<double> &Bopen,
-                                                 const Vector &pa_data,
-                                                 const Vector &x_,
-                                                 Vector &y_)
+void PAHcurlVecH1IdentityApplyTranspose2D(const int c_dofs1D,
+                                          const int o_dofs1D,
+                                          const int NE,
+                                          const Array<double> &Bclosed,
+                                          const Array<double> &Bopen,
+                                          const Vector &pa_data,
+                                          const Vector &x_,
+                                          Vector &y_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -539,12 +539,12 @@ void PAHdivMassApply3D(const int D1D,

 // PA H(div) div-div assemble 2D kernel
 // NOTE: this is identical to PACurlCurlSetup3D
-static void PADivDivSetup2D(const int Q1D,
-                            const int NE,
-                            const Array<double> &w,
-                            const Vector &j,
-                            Vector &coeff_,
-                            Vector &op)
+void PADivDivSetup2D(const int Q1D,
+                     const int NE,
+                     const Array<double> &w,
+                     const Vector &j,
+                     Vector &coeff_,
+                     Vector &op)
 {
   const int NQ = Q1D*Q1D;
   auto W = w.Read();
@@ -565,12 +565,12 @@ static void PADivDivSetup2D(const int Q1D,
   });
 }

-static void PADivDivSetup3D(const int Q1D,
-                            const int NE,
-                            const Array<double> &w,
-                            const Vector &j,
-                            Vector &coeff_,
-                            Vector &op)
+void PADivDivSetup3D(const int Q1D,
+                     const int NE,
+                     const Array<double> &w,
+                     const Vector &j,
+                     Vector &coeff_,
+                     Vector &op)
 {
   const int NQ = Q1D*Q1D*Q1D;
   auto W = w.Read();
@@ -599,16 +599,16 @@ static void PADivDivSetup3D(const int Q1D,
   });
 }

-static void PADivDivApply2D(const int D1D,
-                            const int Q1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &Bot_,
-                            const Array<double> &Gct_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PADivDivApply2D(const int D1D,
+                     const int Q1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &Bot_,
+                     const Array<double> &Gct_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -718,16 +718,16 @@ static void PADivDivApply2D(const int D1D,
   }); // end of element loop
 }

-static void PADivDivApply3D(const int D1D,
-                            const int Q1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &Bot_,
-                            const Array<double> &Gct_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PADivDivApply3D(const int D1D,
+                     const int Q1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &Bot_,
+                     const Array<double> &Gct_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
   MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
   MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -967,13 +967,13 @@ void DivDivIntegrator::AddMultPA(const Vector &x, Vector &y) const
   }
 }

-static void PADivDivAssembleDiagonal2D(const int D1D,
-                                       const int Q1D,
-                                       const int NE,
-                                       const Array<double> &Bo_,
-                                       const Array<double> &Gc_,
-                                       const Vector &op_,
-                                       Vector &diag_)
+void PADivDivAssembleDiagonal2D(const int D1D,
+                                const int Q1D,
+                                const int NE,
+                                const Array<double> &Bo_,
+                                const Array<double> &Gc_,
+                                const Vector &op_,
+                                Vector &diag_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
@@ -1023,13 +1023,13 @@ static void PADivDivAssembleDiagonal2D(const int D1D,
   });
 }

-static void PADivDivAssembleDiagonal3D(const int D1D,
-                                       const int Q1D,
-                                       const int NE,
-                                       const Array<double> &Bo_,
-                                       const Array<double> &Gc_,
-                                       const Vector &op_,
-                                       Vector &diag_)
+void PADivDivAssembleDiagonal3D(const int D1D,
+                                const int Q1D,
+                                const int NE,
+                                const Array<double> &Bo_,
+                                const Array<double> &Gc_,
+                                const Vector &op_,
+                                Vector &diag_)
 {
   MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
   MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1104,11 +1104,11 @@ void DivDivIntegrator::AssembleDiagonalPA(Vector& diag)
 }

 // PA H(div)-L2 (div u, p) assemble 2D kernel
-static void PADivL2Setup2D(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           Vector &coeff_,
-                           Vector &op)
+void PADivL2Setup2D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    Vector &coeff_,
+                    Vector &op)
 {
   const int NQ = Q1D*Q1D;
   auto W = w.Read();
@@ -1123,11 +1123,11 @@ static void PADivL2Setup2D(const int Q1D,
   });
 }

-static void PADivL2Setup3D(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           Vector &coeff_,
-                           Vector &op)
+void PADivL2Setup3D(const int Q1D,
+                    const int NE,
+                    const Array<double> &w,
+                    Vector &coeff_,
+                    Vector &op)
 {
   const int NQ = Q1D*Q1D*Q1D;
   auto W = w.Read();
@@ -1225,16 +1225,16 @@ VectorFEDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,

 // Apply to x corresponding to DOF's 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,
-                            const int L2D1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &L2Bot_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PAHdivL2Apply3D(const int D1D,
+                     const int Q1D,
+                     const int L2D1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &L2Bot_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
   MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
   MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1388,16 +1388,16 @@ static void PAHdivL2Apply3D(const int D1D,

 // Apply to x corresponding to DOF's 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,
-                            const int L2D1D,
-                            const int NE,
-                            const Array<double> &Bo_,
-                            const Array<double> &Gc_,
-                            const Array<double> &L2Bot_,
-                            const Vector &op_,
-                            const Vector &x_,
-                            Vector &y_)
+void PAHdivL2Apply2D(const int D1D,
+                     const int Q1D,
+                     const int L2D1D,
+                     const int NE,
+                     const Array<double> &Bo_,
+                     const Array<double> &Gc_,
+                     const Array<double> &L2Bot_,
+                     const Vector &op_,
+                     const Vector &x_,
+                     Vector &y_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -1494,16 +1494,16 @@ static void PAHdivL2Apply2D(const int D1D,
   }); // end of element loop
 }

-static void PAHdivL2ApplyTranspose3D(const int D1D,
-                                     const int Q1D,
-                                     const int L2D1D,
-                                     const int NE,
-                                     const Array<double> &L2Bo_,
-                                     const Array<double> &Gct_,
-                                     const Array<double> &Bot_,
-                                     const Vector &op_,
-                                     const Vector &x_,
-                                     Vector &y_)
+void PAHdivL2ApplyTranspose3D(const int D1D,
+                              const int Q1D,
+                              const int L2D1D,
+                              const int NE,
+                              const Array<double> &L2Bo_,
+                              const Array<double> &Gct_,
+                              const Array<double> &Bot_,
+                              const Vector &op_,
+                              const Vector &x_,
+                              Vector &y_)
 {
   MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
   MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1656,16 +1656,16 @@ static void PAHdivL2ApplyTranspose3D(const int D1D,
   }); // end of element loop
 }

-static void PAHdivL2ApplyTranspose2D(const int D1D,
-                                     const int Q1D,
-                                     const int L2D1D,
-                                     const int NE,
-                                     const Array<double> &L2Bo_,
-                                     const Array<double> &Gct_,
-                                     const Array<double> &Bot_,
-                                     const Vector &op_,
-                                     const Vector &x_,
-                                     Vector &y_)
+void PAHdivL2ApplyTranspose2D(const int D1D,
+                              const int Q1D,
+                              const int L2D1D,
+                              const int NE,
+                              const Array<double> &L2Bo_,
+                              const Array<double> &Gct_,
+                              const Array<double> &Bot_,
+                              const Vector &op_,
+                              const Vector &x_,
+                              Vector &y_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -1791,16 +1791,16 @@ void VectorFEDivergenceIntegrator::AddMultTransposePA(const Vector &x,
   }
 }

-static void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
-                                             const int Q1D,
-                                             const int L2D1D,
-                                             const int NE,
-                                             const Array<double> &L2Bo_,
-                                             const Array<double> &Gct_,
-                                             const Array<double> &Bot_,
-                                             const Vector &op_,
-                                             const Vector &D_,
-                                             Vector &diag_)
+void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
+                                      const int Q1D,
+                                      const int L2D1D,
+                                      const int NE,
+                                      const Array<double> &L2Bo_,
+                                      const Array<double> &Gct_,
+                                      const Array<double> &Bot_,
+                                      const Vector &op_,
+                                      const Vector &D_,
+                                      Vector &diag_)
 {
   MFEM_VERIFY(D1D <= HDIV_MAX_D1D, "Error: D1D > HDIV_MAX_D1D");
   MFEM_VERIFY(Q1D <= HDIV_MAX_Q1D, "Error: Q1D > HDIV_MAX_Q1D");
@@ -1916,16 +1916,16 @@ static void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
   }); // end of element loop
 }

-static void PAHdivL2AssembleDiagonal_ADAt_2D(const int D1D,
-                                             const int Q1D,
-                                             const int L2D1D,
-                                             const int NE,
-                                             const Array<double> &L2Bo_,
-                                             const Array<double> &Gct_,
-                                             const Array<double> &Bot_,
-                                             const Vector &op_,
-                                             const Vector &D_,
-                                             Vector &diag_)
+void PAHdivL2AssembleDiagonal_ADAt_2D(const int D1D,
+                                      const int Q1D,
+                                      const int L2D1D,
+                                      const int NE,
+                                      const Array<double> &L2Bo_,
+                                      const Array<double> &Gct_,
+                                      const Array<double> &Bot_,
+                                      const Vector &op_,
+                                      const Vector &D_,
+                                      Vector &diag_)
 {
   constexpr static int VDIM = 2;

@@ -17,13 +17,13 @@ namespace mfem
 {

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble1D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             const bool add,
-                             const int d1d = 0,
-                             const int q1d = 0)
+void EAMassAssemble1D(const int NE,
+                      const Array<double> &basis,
+                      const Vector &padata,
+                      Vector &eadata,
+                      const bool add,
+                      const int d1d = 0,
+                      const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -67,13 +67,13 @@ static void EAMassAssemble1D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble2D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             const bool add,
-                             const int d1d = 0,
-                             const int q1d = 0)
+void EAMassAssemble2D(const int NE,
+                      const Array<double> &basis,
+                      const Vector &padata,
+                      Vector &eadata,
+                      const bool add,
+                      const int d1d = 0,
+                      const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -139,13 +139,13 @@ static void EAMassAssemble2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble3D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             const bool add,
-                             const int d1d = 0,
-                             const int q1d = 0)
+void EAMassAssemble3D(const int NE,
+                      const Array<double> &basis,
+                      const Vector &padata,
+                      Vector &eadata,
+                      const bool add,
+                      const int d1d = 0,
+                      const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -25,6 +25,9 @@ namespace mfem

 void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
+   const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
+                         Device::GetDeviceMemoryType() : pa_mt;
+
   // Assuming the same element type
   fespace = &fes;
   Mesh *mesh = fes.GetMesh();
@@ -42,11 +45,11 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
   ne = fes.GetMesh()->GetNE();
   nq = ir->GetNPoints();
   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
-                                    GeometricFactors::JACOBIANS);
+                                    GeometricFactors::JACOBIANS, mt);
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
-   pa_data.SetSize(ne*nq, Device::GetDeviceMemoryType());
+   pa_data.SetSize(ne*nq, mt);
   Vector coeff;
   if (Q == nullptr)
   {
@@ -152,12 +155,12 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassAssembleDiagonal2D(const int NE,
-                                     const Array<double> &b,
-                                     const Vector &d,
-                                     Vector &y,
-                                     const int d1d = 0,
-                                     const int q1d = 0)
+void PAMassAssembleDiagonal2D(const int NE,
+                              const Array<double> &b,
+                              const Vector &d,
+                              Vector &y,
+                              const int d1d = 0,
+                              const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -198,12 +201,12 @@ static void PAMassAssembleDiagonal2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPAMassAssembleDiagonal2D(const int NE,
-                                         const Array<double> &b_,
-                                         const Vector &d_,
-                                         Vector &y_,
-                                         const int d1d = 0,
-                                         const int q1d = 0)
+void SmemPAMassAssembleDiagonal2D(const int NE,
+                                  const Array<double> &b_,
+                                  const Vector &d_,
+                                  Vector &y_,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -264,12 +267,12 @@ static void SmemPAMassAssembleDiagonal2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassAssembleDiagonal3D(const int NE,
-                                     const Array<double> &b,
-                                     const Vector &d,
-                                     Vector &y,
-                                     const int d1d = 0,
-                                     const int q1d = 0)
+void PAMassAssembleDiagonal3D(const int NE,
+                              const Array<double> &b,
+                              const Vector &d,
+                              Vector &y,
+                              const int d1d = 0,
+                              const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -333,12 +336,12 @@ static void PAMassAssembleDiagonal3D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPAMassAssembleDiagonal3D(const int NE,
-                                         const Array<double> &b_,
-                                         const Vector &d_,
-                                         Vector &y_,
-                                         const int d1d = 0,
-                                         const int q1d = 0)
+void SmemPAMassAssembleDiagonal3D(const int NE,
+                                  const Array<double> &b_,
+                                  const Vector &d_,
+                                  Vector &y_,
+                                  const int d1d = 0,
+                                  const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -566,14 +569,14 @@ static void OccaPAMassApply3D(const int D1D,
 #endif // MFEM_USE_OCCA

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassApply2D(const int NE,
-                          const Array<double> &b_,
-                          const Array<double> &bt_,
-                          const Vector &d_,
-                          const Vector &x_,
-                          Vector &y_,
-                          const int d1d = 0,
-                          const int q1d = 0)
+void PAMassApply2D(const int NE,
+                   const Array<double> &b_,
+                   const Array<double> &bt_,
+                   const Vector &d_,
+                   const Vector &x_,
+                   Vector &y_,
+                   const int d1d = 0,
+                   const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -658,14 +661,14 @@ static void PAMassApply2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0>
-static void SmemPAMassApply2D(const int NE,
-                              const Array<double> &b_,
-                              const Array<double> &bt_,
-                              const Vector &d_,
-                              const Vector &x_,
-                              Vector &y_,
-                              const int d1d = 0,
-                              const int q1d = 0)
+void SmemPAMassApply2D(const int NE,
+                       const Array<double> &b_,
+                       const Array<double> &bt_,
+                       const Vector &d_,
+                       const Vector &x_,
+                       Vector &y_,
+                       const int d1d = 0,
+                       const int q1d = 0)
 {
   MFEM_CONTRACT_VAR(bt_);
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -781,14 +784,14 @@ static void SmemPAMassApply2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAMassApply3D(const int NE,
-                          const Array<double> &b_,
-                          const Array<double> &bt_,
-                          const Vector &d_,
-                          const Vector &x_,
-                          Vector &y_,
-                          const int d1d = 0,
-                          const int q1d = 0)
+void PAMassApply3D(const int NE,
+                   const Array<double> &b_,
+                   const Array<double> &bt_,
+                   const Vector &d_,
+                   const Vector &x_,
+                   Vector &y_,
+                   const int d1d = 0,
+                   const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -922,14 +925,14 @@ static void PAMassApply3D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void SmemPAMassApply3D(const int NE,
-                              const Array<double> &b_,
-                              const Array<double> &bt_,
-                              const Vector &d_,
-                              const Vector &x_,
-                              Vector &y_,
-                              const int d1d = 0,
-                              const int q1d = 0)
+void SmemPAMassApply3D(const int NE,
+                       const Array<double> &b_,
+                       const Array<double> &bt_,
+                       const Vector &d_,
+                       const Vector &x_,
+                       Vector &y_,
+                       const int d1d = 0,
+                       const int q1d = 0)
 {
   MFEM_CONTRACT_VAR(bt_);
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -22,12 +22,12 @@ namespace mfem
 // PA Vector Diffusion Integrator

 // PA Diffusion Assemble 2D kernel
-static void PAVectorDiffusionSetup2D(const int Q1D,
-                                     const int NE,
-                                     const Array<double> &w,
-                                     const Vector &j,
-                                     const double COEFF,
-                                     Vector &op)
+void PAVectorDiffusionSetup2D(const int Q1D,
+                              const int NE,
+                              const Array<double> &w,
+                              const Vector &j,
+                              const Vector &c,
+                              Vector &op)
 {
   const int NQ = Q1D*Q1D;
   auto W = w.Read();
@@ -35,6 +35,11 @@ static void PAVectorDiffusionSetup2D(const int Q1D,
   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
   auto y = Reshape(op.Write(), NQ, 3, NE);

+   const bool const_c = c.Size() == 1;
+   const auto C = const_c ? Reshape(c.Read(), 1,1) :
+                  Reshape(c.Read(), NQ, NE);
+
+
   MFEM_FORALL(e, NE,
   {
      for (int q = 0; q < NQ; ++q)
@@ -43,7 +48,9 @@ static void PAVectorDiffusionSetup2D(const int Q1D,
         const double J21 = J(q,1,0,e);
         const double J12 = J(q,0,1,e);
         const double J22 = J(q,1,1,e);
-         const double c_detJ = W[q] * COEFF / ((J11*J22)-(J21*J12));
+
+         const double C1 = const_c ? C(0,0) : C(q,e);
+         const double c_detJ = W[q] * C1 / ((J11*J22)-(J21*J12));
         y(q,0,e) =  c_detJ * (J12*J12 + J22*J22); // 1,1
         y(q,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
         y(q,2,e) =  c_detJ * (J11*J11 + J21*J21); // 2,2
@@ -52,17 +59,23 @@ static void PAVectorDiffusionSetup2D(const int Q1D,
 }

 // PA Diffusion Assemble 3D kernel
-static void PAVectorDiffusionSetup3D(const int Q1D,
-                                     const int NE,
-                                     const Array<double> &w,
-                                     const Vector &j,
-                                     const double COEFF,
-                                     Vector &op)
+void PAVectorDiffusionSetup3D(const int Q1D,
+                              const int NE,
+                              const Array<double> &w,
+                              const Vector &j,
+                              const Vector &c,
+                              Vector &op)
 {
   const int NQ = Q1D*Q1D*Q1D;
   auto W = w.Read();
   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
   auto y = Reshape(op.Write(), NQ, 6, NE);
+
+   const bool const_c = c.Size() == 1;
+   const auto C = const_c ? Reshape(c.Read(), 1,1) :
+                  Reshape(c.Read(), NQ,NE);
+
+
   MFEM_FORALL(e, NE,
   {
      for (int q = 0; q < NQ; ++q)
@@ -79,7 +92,10 @@ static void PAVectorDiffusionSetup3D(const int Q1D,
         const double detJ = J11 * (J22 * J33 - J32 * J23) -
         /* */               J21 * (J12 * J33 - J32 * J13) +
         /* */               J31 * (J12 * J23 - J22 * J13);
-         const double c_detJ = W[q] * COEFF / detJ;
+
+         const double C1 = const_c ? C(0,0) : C(q,e);
+
+         const double c_detJ = W[q] * C1 / detJ;
         // adj(J)
         const double A11 = (J22 * J33) - (J23 * J32);
         const double A12 = (J32 * J13) - (J12 * J33);
@@ -106,7 +122,7 @@ static void PAVectorDiffusionSetup(const int dim,
                                   const int NE,
                                   const Array<double> &W,
                                   const Vector &J,
-                                   const double COEFF,
+                                   const Vector &C,
                                   Vector &op)
 {
   if (!(dim == 2 || dim == 3))
@@ -115,11 +131,11 @@ static void PAVectorDiffusionSetup(const int dim,
   }
   if (dim == 2)
   {
-      PAVectorDiffusionSetup2D(Q1D, NE, W, J, COEFF, op);
+      PAVectorDiffusionSetup2D(Q1D, NE, W, J, C, op);
   }
   if (dim == 3)
   {
-      PAVectorDiffusionSetup3D(Q1D, NE, W, J, COEFF, op);
+      PAVectorDiffusionSetup3D(Q1D, NE, W, J, C, op);
   }
 }

@@ -147,13 +163,47 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
   pa_data.SetSize(symmDims * nq * ne, Device::GetDeviceMemoryType());
-   double coeff = 1.0;
-   if (Q)
+
+   MFEM_VERIFY(!VQ && !MQ,
+               "Only scalar coefficient supported for partial assembly for VectorDiffusionIntegrator");
+   Vector coeff;
+   if (Q == nullptr)
   {
-      ConstantCoefficient *cQ = dynamic_cast<ConstantCoefficient*>(Q);
-      MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
-      coeff = cQ->constant;
+      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* cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == ne*nq,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
+   else
+   {
+      coeff.SetSize(nq * ne);
+      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));
+         }
+      }
+   }
+
   const Array<double> &w = ir->GetWeights();
   const Vector &j = geom->J;
   Vector &d = pa_data;
@@ -166,6 +216,11 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
      auto W = w.Read();
      auto J = Reshape(j.Read(), NQ, SDIM, DIM, ne);
      auto D = Reshape(d.Write(), NQ, SDIM, ne);
+
+      const bool const_c = coeff.Size() == 1;
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1) :
+                     Reshape(coeff.Read(), NQ,ne);
+
      MFEM_FORALL(e, ne,
      {
         for (int q = 0; q < NQ; ++q)
@@ -181,7 +236,8 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
            const double G = J12*J12 + J22*J22 + J32*J32;
            const double F = J11*J12 + J21*J22 + J31*J32;
            const double iw = 1.0 / sqrt(E*G - F*F);
-            const double alpha = wq * coeff * iw;
+            const double C1 = const_c ? C(0,0) : C(q,e);
+            const double alpha = wq * C1 * iw;
            D(q,0,e) =  alpha * G; // 1,1
            D(q,1,e) = -alpha * F; // 1,2
            D(q,2,e) =  alpha * E; // 2,2
@@ -195,7 +251,7 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }

 // PA Diffusion Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0> static
+template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0>
 void PAVectorDiffusionApply2D(const int NE,
                              const Array<double> &b,
                              const Array<double> &g,
@@ -318,7 +374,7 @@ void PAVectorDiffusionApply2D(const int NE,

 // PA Diffusion Apply 3D kernel
 template<const int T_D1D = 0,
-         const int T_Q1D = 0> static
+         const int T_Q1D = 0>
 void PAVectorDiffusionApply3D(const int NE,
                              const Array<double> &b,
                              const Array<double> &g,
@@ -550,13 +606,13 @@ void VectorDiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAVectorDiffusionDiagonal2D(const int NE,
-                                        const Array<double> &b,
-                                        const Array<double> &g,
-                                        const Vector &d,
-                                        Vector &y,
-                                        const int d1d = 0,
-                                        const int q1d = 0)
+void PAVectorDiffusionDiagonal2D(const int NE,
+                                 const Array<double> &b,
+                                 const Array<double> &g,
+                                 const Vector &d,
+                                 Vector &y,
+                                 const int d1d = 0,
+                                 const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -617,13 +673,13 @@ static void PAVectorDiffusionDiagonal2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-static void PAVectorDiffusionDiagonal3D(const int NE,
-                                        const Array<double> &b,
-                                        const Array<double> &g,
-                                        const Vector &d,
-                                        Vector &y,
-                                        const int d1d = 0,
-                                        const int q1d = 0)
+void PAVectorDiffusionDiagonal3D(const int NE,
+                                 const Array<double> &b,
+                                 const Array<double> &g,
+                                 const Vector &d,
+                                 Vector &y,
+                                 const int d1d = 0,
+                                 const int q1d = 0)
 {
   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -104,14 +104,14 @@ void VectorMassIntegrator::AssemblePA(const FiniteElementSpace &fes)

 template<const int T_D1D = 0,
         const int T_Q1D = 0>
-static void PAVectorMassApply2D(const int NE,
-                                const Array<double> &B_,
-                                const Array<double> &Bt_,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                const int d1d = 0,
-                                const int q1d = 0)
+void PAVectorMassApply2D(const int NE,
+                         const Array<double> &B_,
+                         const Array<double> &Bt_,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         const int d1d = 0,
+                         const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -201,14 +201,14 @@ static void PAVectorMassApply2D(const int NE,

 template<const int T_D1D = 0,
         const int T_Q1D = 0>
-static void PAVectorMassApply3D(const int NE,
-                                const Array<double> &B_,
-                                const Array<double> &Bt_,
-                                const Vector &op_,
-                                const Vector &x_,
-                                Vector &y_,
-                                const int d1d = 0,
-                                const int q1d = 0)
+void PAVectorMassApply3D(const int NE,
+                         const Array<double> &B_,
+                         const Array<double> &Bt_,
+                         const Vector &op_,
+                         const Vector &x_,
+                         Vector &y_,
+                         const int d1d = 0,
+                         const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -379,13 +379,13 @@ void VectorMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 }

 template<const int T_D1D = 0, const int T_Q1D = 0>
-static void PAVectorMassAssembleDiagonal2D(const int NE,
-                                           const Array<double> &B_,
-                                           const Array<double> &Bt_,
-                                           const Vector &op_,
-                                           Vector &diag_,
-                                           const int d1d = 0,
-                                           const int q1d = 0)
+void PAVectorMassAssembleDiagonal2D(const int NE,
+                                    const Array<double> &B_,
+                                    const Array<double> &Bt_,
+                                    const Vector &op_,
+                                    Vector &diag_,
+                                    const int d1d = 0,
+                                    const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -431,13 +431,13 @@ static void PAVectorMassAssembleDiagonal2D(const int NE,
 }

 template<const int T_D1D = 0, const int T_Q1D = 0>
-static void PAVectorMassAssembleDiagonal3D(const int NE,
-                                           const Array<double> &B_,
-                                           const Array<double> &Bt_,
-                                           const Vector &op_,
-                                           Vector &diag_,
-                                           const int d1d = 0,
-                                           const int q1d = 0)
+void PAVectorMassAssembleDiagonal3D(const int NE,
+                                    const Array<double> &B_,
+                                    const Array<double> &Bt_,
+                                    const Vector &op_,
+                                    Vector &diag_,
+                                    const int d1d = 0,
+                                    const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -143,7 +143,7 @@ Solver *BuildSmootherFromCeed(ConstrainedOperator &op, bool chebyshev)
   if (chebyshev)
   {
      const int cheb_order = 3;
-      out = new OperatorChebyshevSmoother(&op, t_diag, ess_tdofs, cheb_order);
+      out = new OperatorChebyshevSmoother(op, t_diag, ess_tdofs, cheb_order);
   }
   else
   {
@@ -1204,17 +1204,30 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
      });
      // Modify offdiagonal blocks (imaginary parts of the matrix) to conform
      // with standard essential BC treatment
-      ess_tdof_list.HostRead();
      if (A_i.Type() == Operator::Hypre_ParCSR)
      {
         HypreParMatrix * Ah;
         A_i.Get(Ah);
         hypre_ParCSRMatrix *Aih = *Ah;
+#ifndef HYPRE_USING_CUDA
+         ess_tdof_list.HostRead();
         for (int k = 0; k < n; k++)
         {
            const int j = ess_tdof_list[k];
            Aih->diag->data[Aih->diag->i[j]] = 0.0;
         }
+#else
+         Ah->HypreReadWrite();
+         const int *d_ess_tdof_list =
+            ess_tdof_list.GetMemory().Read(MemoryClass::DEVICE, n);
+         const int *d_diag_i = Aih->diag->i;
+         double *d_diag_data = Aih->diag->data;
+         CuWrap1D(n, [=] MFEM_DEVICE (int k)
+         {
+            const int j = d_ess_tdof_list[k];
+            d_diag_data[d_diag_i[j]] = 0.0;
+         });
+#endif
      }
      else
      {
@@ -17,6 +17,7 @@

 #include <cerrno>      // errno
 #include <sstream>
+#include <regex>

 #ifndef _WIN32
 #include <sys/stat.h>  // mkdir
@@ -764,7 +765,8 @@ ParaViewDataCollection::ParaViewDataCollection(const std::string&
   : DataCollection(collection_name, mesh_),
     levels_of_detail(1),
     pv_data_format(VTKFormat::BINARY),
-     high_order_output(false)
+     high_order_output(false),
+     restart_mode(false)
 {
 #ifdef MFEM_USE_ZLIB
   compression = -1; // default zlib compression level, equivalent to 6
@@ -842,17 +844,60 @@ void ParaViewDataCollection::Save()
   }
   // the directory is created

-   // create pvd file if needed
+   // create pvd file if needed. If we are not in restart mode, a new pvd file
+   // is always created. In restart mode, we keep any previously defined
+   // timestep values as long as they are less than the currently defined time.
+
   if (myid == 0 && !pvd_stream.is_open())
   {
      std::string dpath=GenerateCollectionPath();
      std::string pvdname=dpath+"/"+GeneratePVDFileName();
-      pvd_stream.open(pvdname.c_str(),std::ios::out);
-      // initialize the file
-      pvd_stream << "<?xml version=\"1.0\"?>\n";
-      pvd_stream << "<VTKFile type=\"Collection\" version=\"0.1\"";
-      pvd_stream << " byte_order=\"" << VTKByteOrder() << "\">\n";
-      pvd_stream << "<Collection>" << std::endl;
+
+      std::ifstream pvd_in;
+      if (restart_mode && (pvd_in.open(pvdname,std::ios::binary),pvd_in.good()))
+      {
+         // PVD file exists and restart mode enabled: preserve existing time
+         // steps less than the current time.
+         std::fstream::pos_type pos_begin = pvd_in.tellg();
+         std::fstream::pos_type pos_end = pos_begin;
+
+         std::regex regexp("timestep=\"([^[:space:]]+)\".*file=\"Cycle(\\d+)");
+         std::smatch match;
+
+         std::string line;
+         while (getline(pvd_in,line))
+         {
+            if (regex_search(line,match,regexp))
+            {
+               MFEM_ASSERT(match.size() == 3, "Unable to parse DataSet");
+               double tvalue = std::stod(match[1]);
+               if (tvalue >= GetTime()) { break; }
+               int cvalue = std::stoi(match[2]);
+               MFEM_VERIFY(cvalue < GetCycle(), "Cycle " << GetCycle() <<
+                           " is too small for restart mode: trying to overwrite"
+                           " existing data.");
+               pos_end = pvd_in.tellg();
+            }
+         }
+         size_t count = pos_end - pos_begin;
+         std::vector<char> buf(count);
+         pvd_in.clear();
+         pvd_in.seekg(pos_begin);
+         pvd_in.read(buf.data(), count);
+         pvd_in.close();
+         pvd_stream.open(pvdname.c_str(),std::ios::out);
+         pvd_stream.write(buf.data(), count);
+      }
+      else
+      {
+         // initialize new pvd file
+         pvd_stream.open(pvdname.c_str(),std::ios::out);
+         // initialize the file
+         pvd_stream << "<?xml version=\"1.0\"?>\n";
+         pvd_stream << "<VTKFile type=\"Collection\" version=\"0.1\"";
+         pvd_stream << " byte_order=\"" << VTKByteOrder() << "\">\n";
+         pvd_stream << "<Collection>" << std::endl;
+      }
   }

   // define the vtu file
@@ -1091,6 +1136,11 @@ void ParaViewDataCollection::SetCompression(bool compression_)
   }
 }

+void ParaViewDataCollection::UseRestartMode(bool restart_mode_)
+{
+   restart_mode = restart_mode_;
+}
+
 const char *ParaViewDataCollection::GetDataFormatString() const
 {
   if (pv_data_format == VTKFormat::ASCII)
@@ -488,6 +488,7 @@ private:
   std::fstream pvd_stream;
   VTKFormat pv_data_format;
   bool high_order_output;
+   bool restart_mode;

 protected:
   void SaveDataVTU(std::ostream &out, int ref);
@@ -545,6 +546,11 @@ public:
   /// by default). Reading high-order data requires ParaView 5.5 or later.
   void SetHighOrderOutput(bool high_order_output_);

+   /// Enable or disable restart mode. If restart is enabled, new writes will
+   /// preserve timestep metadata for any solutions prior to the currently
+   /// defined time.
+   void UseRestartMode(bool restart_mode_);
+
   /// Load the collection - not implemented in the ParaView writer
   virtual void Load(int cycle_ = 0) override;
 };
@@ -0,0 +1,358 @@
+// Copyright (c) 2010-2021, 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 "fem.hpp"
+
+namespace mfem
+{
+
+void DofTransformation::TransformPrimal(Vector &v) const
+{
+   TransformPrimal(v.GetData());
+}
+
+void DofTransformation::TransformPrimalCols(DenseMatrix &V) const
+{
+   for (int c=0; c<V.Width(); c++)
+   {
+      TransformPrimal(V.GetColumn(c));
+   }
+}
+
+void DofTransformation::TransformDual(Vector &v) const
+{
+   TransformDual(v.GetData());
+}
+
+void DofTransformation::TransformDual(DenseMatrix &V) const
+{
+   TransformDualCols(V);
+   TransformDualRows(V);
+}
+
+void DofTransformation::TransformDualRows(DenseMatrix &V) const
+{
+   Vector row;
+   for (int r=0; r<V.Height(); r++)
+   {
+      V.GetRow(r, row);
+      TransformDual(row);
+      V.SetRow(r, row);
+   }
+}
+
+void DofTransformation::TransformDualCols(DenseMatrix &V) const
+{
+   for (int c=0; c<V.Width(); c++)
+   {
+      TransformDual(V.GetColumn(c));
+   }
+}
+
+void DofTransformation::InvTransformPrimal(Vector &v) const
+{
+   InvTransformPrimal(v.GetData());
+}
+
+void TransformPrimal(const DofTransformation *ran_dof_trans,
+                     const DofTransformation *dom_dof_trans,
+                     DenseMatrix &elmat)
+{
+   if (ran_dof_trans && dom_dof_trans)
+   {
+      ran_dof_trans->TransformPrimalCols(elmat);
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else if (ran_dof_trans)
+   {
+      ran_dof_trans->TransformPrimalCols(elmat);
+   }
+   else if (dom_dof_trans)
+   {
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else
+   {
+      // If both transformations are NULL this function should not be called
+   }
+}
+
+void TransformDual(const DofTransformation *ran_dof_trans,
+                   const DofTransformation *dom_dof_trans,
+                   DenseMatrix &elmat)
+{
+   if (ran_dof_trans && dom_dof_trans)
+   {
+      ran_dof_trans->TransformDualCols(elmat);
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else if (ran_dof_trans)
+   {
+      ran_dof_trans->TransformDualCols(elmat);
+   }
+   else if (dom_dof_trans)
+   {
+      dom_dof_trans->TransformDualRows(elmat);
+   }
+   else
+   {
+      // If both transformations are NULL this function should not be called
+   }
+}
+
+void VDofTransformation::TransformPrimal(double *v) const
+{
+   int size = doftrans_->Size();
+
+   if ((Ordering::Type)ordering_ == Ordering::byNODES || vdim_ == 1)
+   {
+      for (int i=0; i<vdim_; i++)
+      {
+         doftrans_->TransformPrimal(&v[i*size]);
+      }
+   }
+   else
+   {
+      Vector vec(size);
+      for (int i=0; i<vdim_; i++)
+      {
+         for (int j=0; j<size; j++)
+         {
+            vec(j) = v[j*vdim_+i];
+         }
+         doftrans_->TransformPrimal(vec);
+         for (int j=0; j<size; j++)
+         {
+            v[j*vdim_+i] = vec(j);
+         }
+      }
+   }
+}
+
+void VDofTransformation::InvTransformPrimal(double *v) const
+{
+   int size = doftrans_->Height();
+
+   if ((Ordering::Type)ordering_ == Ordering::byNODES)
+   {
+      for (int i=0; i<vdim_; i++)
+      {
+         doftrans_->InvTransformPrimal(&v[i*size]);
+      }
+   }
+   else
+   {
+      Vector vec(size);
+      for (int i=0; i<vdim_; i++)
+      {
+         for (int j=0; j<size; j++)
+         {
+            vec(j) = v[j*vdim_+i];
+         }
+         doftrans_->InvTransformPrimal(vec);
+         for (int j=0; j<size; j++)
+         {
+            v[j*vdim_+i] = vec(j);
+         }
+      }
+   }
+}
+
+void VDofTransformation::TransformDual(double *v) const
+{
+   int size = doftrans_->Size();
+
+   if ((Ordering::Type)ordering_ == Ordering::byNODES)
+   {
+      for (int i=0; i<vdim_; i++)
+      {
+         doftrans_->TransformDual(&v[i*size]);
+      }
+   }
+   else
+   {
+      Vector vec(size);
+      for (int i=0; i<vdim_; i++)
+      {
+         for (int j=0; j<size; j++)
+         {
+            vec(j) = v[j*vdim_+i];
+         }
+         doftrans_->TransformDual(vec);
+         for (int j=0; j<size; j++)
+         {
+            v[j*vdim_+i] = vec(j);
+         }
+      }
+   }
+}
+
+const double ND_DofTransformation::T_data[24] =
+{
+   1.0,  0.0,  0.0,  1.0,
+   -1.0, -1.0,  0.0,  1.0,
+   0.0,  1.0, -1.0, -1.0,
+   1.0,  0.0, -1.0, -1.0,
+   -1.0, -1.0,  1.0,  0.0,
+   0.0,  1.0,  1.0,  0.0
+};
+
+const DenseTensor ND_DofTransformation
+::T(const_cast<double*>(ND_DofTransformation::T_data), 2, 2, 6);
+
+const double ND_DofTransformation::TInv_data[24] =
+{
+   1.0,  0.0,  0.0,  1.0,
+   -1.0, -1.0,  0.0,  1.0,
+   -1.0, -1.0,  1.0,  0.0,
+   1.0,  0.0, -1.0, -1.0,
+   0.0,  1.0, -1.0, -1.0,
+   0.0,  1.0,  1.0,  0.0
+};
+
+const DenseTensor ND_DofTransformation
+::TInv(const_cast<double*>(TInv_data), 2, 2, 6);
+
+ND_DofTransformation::ND_DofTransformation(int size, int p)
+   : DofTransformation(size),
+     order(p)
+{
+}
+
+ND_TriDofTransformation::ND_TriDofTransformation(int p)
+   : ND_DofTransformation(p*(p + 2), p)
+{
+}
+
+void ND_TriDofTransformation::TransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<1; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[3*nedofs + f*nfdofs + 2*i];
+         T(Fo[f]).Mult(v2, &v[3*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TriDofTransformation::InvTransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<1; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[3*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).Mult(v2, &v[3*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TriDofTransformation::TransformDual(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<1; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[3*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).MultTranspose(v2, &v[3*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+ND_TetDofTransformation::ND_TetDofTransformation(int p)
+   : ND_DofTransformation(p*(p + 2)*(p + 3)/2, p)
+{
+}
+
+void ND_TetDofTransformation::TransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<4; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[6*nedofs + f*nfdofs + 2*i];
+         T(Fo[f]).Mult(v2, &v[6*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TetDofTransformation::InvTransformPrimal(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<4; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[6*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).Mult(v2, &v[6*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+void
+ND_TetDofTransformation::TransformDual(double *v) const
+{
+   int nedofs = order; // number of DoFs per edge
+   int nfdofs = order*(order-1); // number of DoFs per face
+
+   double data[2];
+   Vector v2(data, 2);
+
+   // Transform face DoFs
+   for (int f=0; f<4; f++)
+   {
+      for (int i=0; i<nfdofs/2; i++)
+      {
+         v2 = &v[6*nedofs + f*nfdofs + 2*i];
+         TInv(Fo[f]).MultTranspose(v2, &v[6*nedofs + f*nfdofs + 2*i]);
+      }
+   }
+}
+
+} // namespace mfem
@@ -0,0 +1,277 @@
+// Copyright (c) 2010-2021, 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_DOFTRANSFORM
+#define MFEM_DOFTRANSFORM
+
+#include "../config/config.hpp"
+#include "../linalg/linalg.hpp"
+#include "intrules.hpp"
+#include "fe.hpp"
+
+namespace mfem
+{
+
+/** The DofTransformation class is an abstract base class for a family of
+    transformations that map local degrees of freedom (DoFs), contained within
+    individual elements, to global degrees of freedom, stored within
+    GridFunction objects. These transformations are necessary to ensure that
+    basis functions in neighboring elements align correctly. Closely related but
+    complementary transformations are required for the entries stored in
+    LinearForm and BilinearForm objects. The DofTransformation class is designed
+    to apply the action of both of these types of DoF transformations.
+
+    Let the "primal transformation" be given by the operator T. This means that
+    given a local element vector v the data that must be placed into a
+    GridFunction object is v_t = T * v.
+
+    We also need the inverse of the primal transformation T^{-1} so that we can
+    recover the local element vector from data read out of a GridFunction
+    e.g. v = T^{-1} * v_t.
+
+    We need to preserve the action of our linear forms applied to primal
+    vectors. In other words, if f is the local vector computed by a linear
+    form then f * v = f_t * v_t (where "*" represents an inner product of
+    vectors). This requires that f_t = T^{-T} * f i.e. the "dual transform" is
+    given by the transpose of the inverse of the primal transformation.
+
+    For bilinear forms we require that v^T * A * v = v_t^T * A_t * v_t. This
+    implies that A_t = T^{-T} * A * T^{-1}. This can be accomplished by
+    performing dual transformations of the rows and columns of the matrix A.
+
+    For discrete linear operators the range must be modified with the primal
+    transformation rather than the dual transformation because the result is a
+    primal vector rather than a dual vector. This leads to the transformation
+    D_t = T * D * T^{-1}. This can be accomplished by using a primal
+    transformation on the columns of D and a dual transformation on its rows.
+*/
+class DofTransformation
+{
+protected:
+   int size_;
+
+   Array<int> Fo;
+
+   DofTransformation(int size)
+      : size_(size) {}
+
+public:
+
+   inline int Size() const { return size_; }
+   inline int Height() const { return size_; }
+   inline int NumRows() const { return size_; }
+   inline int Width() const { return size_; }
+   inline int NumCols() const { return size_; }
+
+   /** @brief Configure the transformation using face orientations for the
+       current element. */
+   /// The face_orientation array can be obtained from Mesh::GetElementFaces.
+   inline void SetFaceOrientations(const Array<int> & face_orientation)
+   { Fo = face_orientation; }
+
+   inline const Array<int> & GetFaceOrientations() const { return Fo; }
+
+   /** Transform local DoFs to align with the global DoFs. For example, this
+       transformation can be used to map the local vector computed by
+       FiniteElement::Project() to the transformed vector stored within a
+       GridFunction object. */
+   virtual void TransformPrimal(double *v) const = 0;
+   virtual void TransformPrimal(Vector &v) const;
+
+   /// Transform groups of DoFs stored as dense matrices
+   virtual void TransformPrimalCols(DenseMatrix &V) const;
+
+   /** Inverse transform local DoFs. Used to transform DoFs from a global vector
+       back to their element-local form. For example, this must be used to
+       transform the vector obtained using GridFunction::GetSubVector before it
+       can be used to compute a local interpolation.
+   */
+   virtual void InvTransformPrimal(double *v) const = 0;
+   virtual void InvTransformPrimal(Vector &v) const;
+
+   /** Transform dual DoFs as computed by a LinearFormIntegrator before summing
+       into a LinearForm object. */
+   virtual void TransformDual(double *v) const = 0;
+   virtual void TransformDual(Vector &v) const;
+
+   /** Transform a matrix of dual DoFs entries as computed by a
+       BilinearFormIntegrator before summing into a BilinearForm object. */
+   virtual void TransformDual(DenseMatrix &V) const;
+
+   /// Transform groups of dual DoFs stored as dense matrices
+   virtual void TransformDualRows(DenseMatrix &V) const;
+   virtual void TransformDualCols(DenseMatrix &V) const;
+
+   virtual ~DofTransformation() {}
+};
+
+/** Transform a matrix of DoFs entries from different finite element spaces as
+    computed by a DiscreteInterpolator before copying into a
+    DiscreteLinearOperator.
+*/
+void TransformPrimal(const DofTransformation *ran_dof_trans,
+                     const DofTransformation *dom_dof_trans,
+                     DenseMatrix &elmat);
+
+/** Transform a matrix of dual DoFs entries from different finite element spaces
+    as computed by a BilinearFormIntegrator before summing into a
+    MixedBilinearForm object.
+*/
+void TransformDual(const DofTransformation *ran_dof_trans,
+                   const DofTransformation *dom_dof_trans,
+                   DenseMatrix &elmat);
+
+/** The VDofTransformation class implements a nested transformation where an
+    arbitrary DofTransformation is replicated with a vdim >= 1.
+*/
+class VDofTransformation : public DofTransformation
+{
+private:
+   int vdim_;
+   int ordering_;
+   DofTransformation * doftrans_;
+
+public:
+   /** @brief Default constructor which requires that SetDofTransformation be
+       called before use. */
+   VDofTransformation(int vdim = 1, int ordering = 0)
+      : DofTransformation(0),
+        vdim_(vdim), ordering_(ordering),
+        doftrans_(NULL) {}
+
+   /// Constructor with a known DofTransformation
+   VDofTransformation(DofTransformation & doftrans, int vdim = 1,
+                      int ordering = 0)
+      : DofTransformation(vdim * doftrans.Size()),
+        vdim_(vdim), ordering_(ordering),
+        doftrans_(&doftrans) {}
+
+   /// Set or change the vdim parameter
+   inline void SetVDim(int vdim)
+   {
+      vdim_ = vdim;
+      if (doftrans_)
+      {
+         size_ = vdim_ * doftrans_->Size();
+      }
+   }
+
+   /// Return the current vdim value
+   inline int GetVDim() const { return vdim_; }
+
+   /// Set or change the nested DofTransformation object
+   inline void SetDofTransformation(DofTransformation & doftrans)
+   {
+      size_ = vdim_ * doftrans.Size();
+      doftrans_ = &doftrans;
+   }
+
+   /// Return the nested DofTransformation object
+   inline DofTransformation * GetDofTransformation() const { return doftrans_; }
+
+   inline void SetFaceOrientation(const Array<int> & face_orientation)
+   { Fo = face_orientation; doftrans_->SetFaceOrientations(face_orientation); }
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+   void InvTransformPrimal(double *v) const;
+   void TransformDual(double *v) const;
+};
+
+/** Abstract base class for high-order Nedelec spaces on elements with
+    triangular faces.
+
+    The Nedelec DoFs on the interior of triangular faces come in pairs which
+    share an interpolation point but have different vector directions. These
+    directions depend on the orientation of the face and can therefore differ in
+    neighboring elements. The mapping required to transform these DoFs can be
+    implemented as series of 2x2 linear transformations. The raw data for these
+    linear transformations is stored in the T_data and TInv_data arrays and can
+    be accessed as DenseMatrices using the GetFaceTransform() and
+    GetFaceInverseTransform() methods.
+*/
+class ND_DofTransformation : public DofTransformation
+{
+protected:
+   static const double T_data[24];
+   static const double TInv_data[24];
+   static const DenseTensor T, TInv;
+   int order;
+
+   ND_DofTransformation(int size, int order);
+
+public:
+   // Return the 2x2 transformation operator for the given face orientation
+   static const DenseMatrix & GetFaceTransform(int ori) { return T(ori); }
+
+   // Return the 2x2 inverse transformation operator
+   static const DenseMatrix & GetFaceInverseTransform(int ori)
+   { return TInv(ori); }
+};
+
+/// DoF transformation implementation for the Nedelec basis on triangles
+class ND_TriDofTransformation : public ND_DofTransformation
+{
+public:
+   ND_TriDofTransformation(int order);
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+
+   void InvTransformPrimal(double *v) const;
+
+   void TransformDual(double *v) const;
+};
+
+/// DoF transformation implementation for the Nedelec basis on tetrahedra
+class ND_TetDofTransformation : public ND_DofTransformation
+{
+public:
+   ND_TetDofTransformation(int order);
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+
+   void InvTransformPrimal(double *v) const;
+
+   void TransformDual(double *v) const;
+};
+
+/// DoF transformation implementation for the Nedelec basis on wedge elements
+/** TODO: (Under development) */
+class ND_WedgeDofTransformation : public ND_DofTransformation
+{
+public:
+   ND_WedgeDofTransformation(int order);
+
+   using DofTransformation::TransformPrimal;
+   using DofTransformation::InvTransformPrimal;
+   using DofTransformation::TransformDual;
+
+   void TransformPrimal(double *v) const;
+
+   void InvTransformPrimal(double *v) const;
+
+   void TransformDual(double *v) const;
+};
+
+} // namespace mfem
+
+#endif // MFEM_DOFTRANSFORM
@@ -380,6 +380,7 @@ void IsoparametricTransformation::SetIdentityTransformation(
      case Geometry::TETRAHEDRON : FElem = &TetrahedronFE; break;
      case Geometry::CUBE :        FElem = &HexahedronFE; break;
      case Geometry::PRISM :       FElem = &WedgeFE; break;
+      case Geometry::PYRAMID :     FElem = &PyramidFE; break;
      default:
         MFEM_ABORT("unknown Geometry::Type!");
   }
@@ -316,7 +316,7 @@ public:

   /// Set the desired print level, useful for debugging.
   /** The valid options are: -1 - never print (default); 0 - print only errors;
-       1 - print the first and last last iterations; 2 - print every iteration;
+       1 - print the first and last iterations; 2 - print every iteration;
       and 3 - print every iteration including point coordinates. */
   void SetPrintLevel(int pr_level) { print_level = pr_level; }

@@ -48,29 +48,36 @@ void L2ZienkiewiczZhuEstimator::ComputeEstimates()
   current_sequence = solution->FESpace()->GetMesh()->GetSequence();
 }

+#endif // MFEM_USE_MPI

 KellyErrorEstimator::KellyErrorEstimator(BilinearFormIntegrator& di_,
-                                         ParGridFunction& sol_,
-                                         ParFiniteElementSpace& flux_fespace_,
+                                         GridFunction& sol_,
+                                         FiniteElementSpace& flux_fespace_,
                                         const Array<int> &attributes_)
   : attributes(attributes_)
   , flux_integrator(&di_)
   , solution(&sol_)
   , flux_space(&flux_fespace_)
   , own_flux_fespace(false)
+#ifdef MFEM_USE_MPI
+   , isParallel(dynamic_cast<ParFiniteElementSpace*>(sol_.FESpace()))
+#endif // MFEM_USE_MPI
 {
   ResetCoefficientFunctions();
 }

 KellyErrorEstimator::KellyErrorEstimator(BilinearFormIntegrator& di_,
-                                         ParGridFunction& sol_,
-                                         ParFiniteElementSpace* flux_fespace_,
+                                         GridFunction& sol_,
+                                         FiniteElementSpace* flux_fespace_,
                                         const Array<int> &attributes_)
   : attributes(attributes_)
   , flux_integrator(&di_)
   , solution(&sol_)
   , flux_space(flux_fespace_)
   , own_flux_fespace(true)
+#ifdef MFEM_USE_MPI
+   , isParallel(dynamic_cast<ParFiniteElementSpace*>(sol_.FESpace()))
+#endif // MFEM_USE_MPI
 {
   ResetCoefficientFunctions();
 }
@@ -85,29 +92,31 @@ KellyErrorEstimator::~KellyErrorEstimator()

 void KellyErrorEstimator::ResetCoefficientFunctions()
 {
-   compute_element_coefficient = [](ParMesh* pmesh, const int e)
+   compute_element_coefficient = [](Mesh* mesh, const int e)
   {
      return 1.0;
   };

-   compute_face_coefficient = [](ParMesh* pmesh, const int f,
+   compute_face_coefficient = [](Mesh* mesh, const int f,
                                 const bool shared_face)
   {
      auto FT = [&]()
      {
+#ifdef MFEM_USE_MPI
         if (shared_face)
         {
-            return pmesh->GetSharedFaceTransformations(f);
+            return dynamic_cast<ParMesh*>(mesh)->GetSharedFaceTransformations(f);
         }
-         return pmesh->GetFaceElementTransformations(f);
+#endif // MFEM_USE_MPI
+         return mesh->GetFaceElementTransformations(f);
      }();
      const auto order = FT->GetFE()->GetOrder();

      // Poor man's face diameter.
      double diameter = 0.0;

-      Vector p1(pmesh->SpaceDimension());
-      Vector p2(pmesh->SpaceDimension());
+      Vector p1(mesh->SpaceDimension());
+      Vector p2(mesh->SpaceDimension());
      // NOTE: We have no direct access to vertices for shared faces,
      // so we fall back to compute the positions from the element.
      // This can also be modified to compute the diameter for non-linear
@@ -148,17 +157,23 @@ void KellyErrorEstimator::ComputeEstimates()

   flux_space->Update(false);

-   auto xfes      = solution->ParFESpace();
+   auto xfes = solution->FESpace();
   MFEM_ASSERT(xfes->GetVDim() == 1,
               "Estimation for vector-valued problems not implemented yet.");
-   auto pmesh     = xfes->GetParMesh();
+   auto mesh = xfes->GetMesh();

   this->error_estimates.SetSize(xfes->GetNE());
   this->error_estimates = 0.0;

   // 1. Compute fluxes in discontinuous space
-   ParGridFunction flux(flux_space);
-   flux = 0.0;
+   GridFunction *flux =
+#ifdef MFEM_USE_MPI
+      isParallel ? new ParGridFunction(dynamic_cast<ParFiniteElementSpace*>
+                                       (flux_space)) :
+#endif // MFEM_USE_MPI
+      new GridFunction(flux_space);
+
+   *flux = 0.0;

   // We pre-sort the array to speed up the search in the following loops.
   if (attributes.Size())
@@ -184,21 +199,21 @@ void KellyErrorEstimator::ComputeEstimates()
                                          *flux_space->GetFE(e), el_f, true);

      flux_space->GetElementVDofs(e, fdofs);
-      flux.AddElementVector(fdofs, el_f);
+      flux->AddElementVector(fdofs, el_f);
   }

   // 2. Add error contribution from local interior faces
-   for (int f = 0; f < pmesh->GetNumFaces(); f++)
+   for (int f = 0; f < mesh->GetNumFaces(); f++)
   {
-      auto FT = pmesh->GetFaceElementTransformations(f);
+      auto FT = mesh->GetFaceElementTransformations(f);

      auto &int_rule = IntRules.Get(FT->FaceGeom, 2 * xfes->GetFaceOrder(f));
      const auto nip = int_rule.GetNPoints();

-      if (pmesh->FaceIsInterior(f))
+      if (mesh->FaceIsInterior(f))
      {
         int Inf1, Inf2, NCFace;
-         pmesh->GetFaceInfos(f, &Inf1, &Inf2, &NCFace);
+         mesh->GetFaceInfos(f, &Inf1, &Inf2, &NCFace);

         // Convention
         // * Conforming face: Face side with smaller element id handles
@@ -229,18 +244,18 @@ void KellyErrorEstimator::ComputeEstimates()
               FT->Loc1.Transform(fip, ip);

               Vector val(flux_space->GetVDim());
-               flux.GetVectorValue(FT->Elem1No, ip, val);
+               flux->GetVectorValue(FT->Elem1No, ip, val);

               // And build scalar product with normal
-               Vector normal(pmesh->SpaceDimension());
+               Vector normal(mesh->SpaceDimension());
               FT->Face->SetIntPoint(&fip);
-               if (pmesh->Dimension() == pmesh->SpaceDimension())
+               if (mesh->Dimension() == mesh->SpaceDimension())
               {
                  CalcOrtho(FT->Face->Jacobian(), normal);
               }
               else
               {
-                  Vector ref_normal(pmesh->Dimension());
+                  Vector ref_normal(mesh->Dimension());
                  FT->Loc1.Transf.SetIntPoint(&fip);
                  CalcOrtho(FT->Loc1.Transf.Jacobian(), ref_normal);
                  auto &e1 = FT->GetElement1Transformation();
@@ -260,18 +275,18 @@ void KellyErrorEstimator::ComputeEstimates()
               FT->Loc2.Transform(fip, ip);

               Vector val(flux_space->GetVDim());
-               flux.GetVectorValue(FT->Elem2No, ip, val);
+               flux->GetVectorValue(FT->Elem2No, ip, val);

               // And build scalar product with normal
-               Vector normal(pmesh->SpaceDimension());
+               Vector normal(mesh->SpaceDimension());
               FT->Face->SetIntPoint(&fip);
-               if (pmesh->Dimension() == pmesh->SpaceDimension())
+               if (mesh->Dimension() == mesh->SpaceDimension())
               {
                  CalcOrtho(FT->Face->Jacobian(), normal);
               }
               else
               {
-                  Vector ref_normal(pmesh->Dimension());
+                  Vector ref_normal(mesh->Dimension());
                  FT->Loc1.Transf.SetIntPoint(&fip);
                  CalcOrtho(FT->Loc1.Transf.Jacobian(), ref_normal);
                  auto &e1 = FT->GetElement1Transformation();
@@ -287,7 +302,7 @@ void KellyErrorEstimator::ComputeEstimates()
            {
               jumps(i) *= jumps(i);
            }
-            auto h_k_face = compute_face_coefficient(pmesh, f, false);
+            auto h_k_face = compute_face_coefficient(mesh, f, false);
            double jump_integral = h_k_face*jumps.Sum();

            // A local face is shared between two local elements, so we
@@ -300,9 +315,37 @@ void KellyErrorEstimator::ComputeEstimates()
      }
   }

+   current_sequence = solution->FESpace()->GetMesh()->GetSequence();
+
+#ifdef MFEM_USE_MPI
+   if (!isParallel)
+#endif // MFEM_USE_MPI
+   {
+      // Finalize element errors
+      for (int e = 0; e < xfes->GetNE(); e++)
+      {
+         auto factor = compute_element_coefficient(mesh, e);
+         // The sqrt belongs to the norm and hₑ to the indicator.
+         error_estimates(e) = sqrt(factor * error_estimates(e));
+      }
+
+      total_error = error_estimates.Norml2();
+      delete flux;
+      return;
+   }
+
+#ifdef MFEM_USE_MPI
+
   // 3. Add error contribution from shared interior faces
   // Synchronize face data.
-   flux.ExchangeFaceNbrData();
+
+   ParGridFunction *pflux = dynamic_cast<ParGridFunction*>(flux);
+   MFEM_VERIFY(pflux, "flux is not a ParGridFunction pointer");
+
+   ParMesh *pmesh = dynamic_cast<ParMesh*>(mesh);
+   MFEM_VERIFY(pmesh, "mesh is not a ParMesh pointer");
+
+   pflux->ExchangeFaceNbrData();

   for (int sf = 0; sf < pmesh->GetNSharedFaces(); sf++)
   {
@@ -330,17 +373,17 @@ void KellyErrorEstimator::ComputeEstimates()
         FT->Loc1.Transform(fip, ip);

         Vector val(flux_space->GetVDim());
-         flux.GetVectorValue(FT->Elem1No, ip, val);
+         flux->GetVectorValue(FT->Elem1No, ip, val);

-         Vector normal(pmesh->SpaceDimension());
+         Vector normal(mesh->SpaceDimension());
         FT->Face->SetIntPoint(&fip);
-         if (pmesh->Dimension() == pmesh->SpaceDimension())
+         if (mesh->Dimension() == mesh->SpaceDimension())
         {
            CalcOrtho(FT->Face->Jacobian(), normal);
         }
         else
         {
-            Vector ref_normal(pmesh->Dimension());
+            Vector ref_normal(mesh->Dimension());
            FT->Loc1.Transf.SetIntPoint(&fip);
            CalcOrtho(FT->Loc1.Transf.Jacobian(), ref_normal);
            auto &e1 = FT->GetElement1Transformation();
@@ -361,18 +404,18 @@ void KellyErrorEstimator::ComputeEstimates()
         FT->Loc2.Transform(fip, ip);

         Vector val(flux_space->GetVDim());
-         flux.GetVectorValue(FT->Elem2No, ip, val);
+         flux->GetVectorValue(FT->Elem2No, ip, val);

         // Evaluate gauss point
-         Vector normal(pmesh->SpaceDimension());
+         Vector normal(mesh->SpaceDimension());
         FT->Face->SetIntPoint(&fip);
-         if (pmesh->Dimension() == pmesh->SpaceDimension())
+         if (mesh->Dimension() == mesh->SpaceDimension())
         {
            CalcOrtho(FT->Face->Jacobian(), normal);
         }
         else
         {
-            Vector ref_normal(pmesh->Dimension());
+            Vector ref_normal(mesh->Dimension());
            CalcOrtho(FT->Loc1.Transf.Jacobian(), ref_normal);
            auto &e1 = FT->GetElement1Transformation();
            e1.AdjugateJacobian().MultTranspose(ref_normal, normal);
@@ -387,7 +430,7 @@ void KellyErrorEstimator::ComputeEstimates()
      {
         jumps(i) *= jumps(i);
      }
-      auto h_k_face = compute_face_coefficient(pmesh, sf, true);
+      auto h_k_face = compute_face_coefficient(mesh, sf, true);
      double jump_integral = h_k_face*jumps.Sum();

      error_estimates(FT->Elem1No) += jump_integral;
@@ -395,25 +438,26 @@ void KellyErrorEstimator::ComputeEstimates()
      // because the error is stored on the remote process and
      // recomputed there.
   }
+   delete flux;

   // Finalize element errors
   for (int e = 0; e < xfes->GetNE(); e++)
   {
-      auto factor = compute_element_coefficient(pmesh, e);
+      auto factor = compute_element_coefficient(mesh, e);
      // The sqrt belongs to the norm and hₑ to the indicator.
      error_estimates(e) = sqrt(factor * error_estimates(e));
   }

-   current_sequence = solution->FESpace()->GetMesh()->GetSequence();
-
   // Finish by computing the global error.
-   double process_local_error = error_estimates.Sum();
+   auto pfes = dynamic_cast<ParFiniteElementSpace*>(xfes);
+   MFEM_VERIFY(pfes, "xfes is not a ParFiniteElementSpace pointer");
+
+   double process_local_error = pow(error_estimates.Norml2(),2.0);
   MPI_Allreduce(&process_local_error, &total_error, 1, MPI_DOUBLE,
-                 MPI_SUM, xfes->GetComm());
-}
-
+                 MPI_SUM, pfes->GetComm());
+   total_error = sqrt(total_error);
 #endif // MFEM_USE_MPI
-
+}

 void LpErrorEstimator::ComputeEstimates()
 {
@@ -407,35 +407,37 @@ public:
 };


-#ifdef MFEM_USE_MPI
 /** @brief The KellyErrorEstimator class provides a fast error indication
    strategy for smooth scalar parallel problems.

    The Kelly error indicator is based on the following papers:

-    Kelly, D. W., et al. "A posteriori error analysis and adaptive processes in
-    the finite element method: Part I—Error analysis." International journal for
-    numerical methods in engineering 19.11 (1983): 1593-1619.
+    [1] Kelly, D. W., et al. "A posteriori error analysis and adaptive processes
+    in the finite element method: Part I—Error analysis." International journal
+    for numerical methods in engineering 19.11 (1983): 1593-1619.

-    De SR Gago, J. P., et al. "A posteriori error analysis and adaptive
+    [2] De SR Gago, J. P., et al. "A posteriori error analysis and adaptive
    processes in the finite element method: Part II—Adaptive mesh refinement."
    International journal for numerical methods in engineering 19.11 (1983):
    1621-1656.

    It can be roughly described by:
-        ||∇(u-uₕ)||ₑ ≦ √( C hₑ ∑ₖ (hₖ ∫ |J[∇uₕ]|²) dS )
+        ||∇(u-uₕ)||ₑ ≅ √( C hₑ ∑ₖ (hₖ ∫ |J[∇uₕ]|²) dS )
    where "e" denotes an element, ||⋅||ₑ the corresponding local norm and k the
    corresponding faces. u is the analytic solution and uₕ the discretized
-    solution. hₖ and hₑ are factors dependend on the face and element geometry.
+    solution. hₖ and hₑ are factors dependent on the face and element geometry.
    J is the jump function, i.e. the difference between the limits at each point
    for each side of the face. A custom method to compute hₖ can be provided. It
    is also possible to estimate the error only on a subspace by feeding this
    class an attribute array describing the subspace.

-    @note This algorithm is only for Poisson problems a proper error esimator.
-    The current implementation does not reflect this, because the "C" factor is
-    not included.
-    It further assumes that the approximation error at the boundary is small
+    @note This algorithm is appropriate only for problems with scalar diffusion
+    coefficients (e.g. Poisson problems), because it measures only the flux of
+    the gradient of the discrete solution. The current implementation also does
+    not include the volume term present in Equation 75 of Kelly et al [1].
+    Instead, it includes only the flux term recommended in Equation 82. The
+    current implementation also does not include the constant factor "C". It
+    furthermore assumes that the approximation error at the boundary is small
    enough, as the implementation ignores boundary faces.
 */
 class KellyErrorEstimator final : public ErrorEstimator
@@ -443,11 +445,11 @@ class KellyErrorEstimator final : public ErrorEstimator
 public:
   /// Function type to compute the local coefficient hₑ of an element.
   using ElementCoefficientFunction =
-      std::function<double(ParMesh*, const int)>;
+      std::function<double(Mesh*, const int)>;
   /** @brief Function type to compute the local coefficient hₖ of a face. The
       third argument is true for shared faces and false for local faces. */
   using FaceCoefficientFunction =
-      std::function<double(ParMesh*, const int, const bool)>;
+      std::function<double(Mesh*, const int, const bool)>;

 private:
   int current_sequence = -1;
@@ -478,12 +480,16 @@ private:
   FaceCoefficientFunction compute_face_coefficient;

   BilinearFormIntegrator* flux_integrator; ///< Not owned.
-   ParGridFunction* solution;               ///< Not owned.
+   GridFunction* solution;               ///< Not owned.

-   ParFiniteElementSpace*
+   FiniteElementSpace*
   flux_space; /**< @brief Ownership based on own_flux_fes. */
   bool own_flux_fespace; ///< Ownership flag for flux_space.

+#ifdef MFEM_USE_MPI
+   const bool isParallel;
+#endif
+
   /// Check if the mesh of the solution was modified.
   bool MeshIsModified()
   {
@@ -512,8 +518,8 @@ public:
                          error should be estimated. An empty array results in
                          estimating the error over the complete domain.
   */
-   KellyErrorEstimator(BilinearFormIntegrator& di_, ParGridFunction& sol_,
-                       ParFiniteElementSpace& flux_fes_,
+   KellyErrorEstimator(BilinearFormIntegrator& di_, GridFunction& sol_,
+                       FiniteElementSpace& flux_fes_,
                       const Array<int> &attributes_ = Array<int>());

   /** @brief Construct a new KellyErrorEstimator object for a scalar field.
@@ -524,8 +530,8 @@ public:
                          error should be estimated. An empty array results in
                          estimating the error over the complete domain.
   */
-   KellyErrorEstimator(BilinearFormIntegrator& di_, ParGridFunction& sol_,
-                       ParFiniteElementSpace* flux_fes_,
+   KellyErrorEstimator(BilinearFormIntegrator& di_, GridFunction& sol_,
+                       FiniteElementSpace* flux_fes_,
                       const Array<int> &attributes_ = Array<int>());

   ~KellyErrorEstimator();
@@ -572,8 +578,6 @@ public:
   void ResetCoefficientFunctions();
 };

-#endif // MFEM_USE_MPI
-
 } // namespace mfem

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