Merge branch 'master' into DST-maxwell-solver-dev

ParDST first commit in new (clean) branch
2021-06-16 10:30:33 -07:00 · 2020-12-21 11:36:56 -08:00
276 changed files with 13354 additions and 19246 deletions
@@ -47,36 +47,26 @@ jobs:
    strategy:
      matrix:
        os: [ubuntu-18.04, macos-10.15]
-        target: [dbg, opt]
-        mpi: [seq, par]
+        target: [debug, optim]
+        mpi: [sequential, parallel]
        build-system: [make]
-        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'
+        # 'include' allows us to
+        # - add a variable without creating a new matrix dimension.
+        # - add a new combination ('build-system: cmake' case here)
        #
        # note: we will gather coverage info for any non-debug run except the
        # CMake build.
        include:
-          - target: dbg
+          - target: debug
            codecov: NO
-          - target: opt
+          - target: optim
            codecov: YES
          - os: ubuntu-18.04
-            target: opt
+            target: optim
            codecov: NO
-            mpi: par
+            mpi: parallel
            build-system: cmake
-            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 }}
+    name: ${{ matrix.os }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.build-system }}

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

@@ -102,7 +92,7 @@ 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 == 'par' && matrix.os == 'ubuntu-18.04'
+      if: matrix.mpi == 'parallel' && matrix.os == 'ubuntu-18.04'
      run: |
        sudo apt-get install mpich libmpich-dev
        export MAKE_CXX_FLAG="MPICXX=mpic++"
@@ -113,11 +103,11 @@ jobs:
        sudo apt-get install lcov

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

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

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

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

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

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

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

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

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

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

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

    - 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 }}-v2.0
+        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2

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

    # MFEM build and test
    - name: build-mfem
-      uses: mfem/github-actions/build-mfem@v2.0
+      uses: mfem/github-actions/build-mfem@master
      with:
        os: ${{ runner.os }}
        target: optim
@@ -28,24 +28,49 @@ jobs:
        access_token: ${{ github.token }}
    - name: checkout mfem
      uses: actions/checkout@v2
+      with:
+        path: mfem

    - name: copyright check
      id: copyright
      run: |
-        ./config/githooks/pre-push --copyright
-
+        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
      continue-on-error: true

    - name: license check
      id: license
      run: |
-        ./config/githooks/pre-push --license
+        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
      continue-on-error: true

    - name: release check
      id: release
      run: |
-        ./config/githooks/pre-push --release
+        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
      continue-on-error: true

    - name: wrap-up
@@ -75,7 +100,8 @@ jobs:

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

  documentation:
    runs-on: ubuntu-18.04
@@ -107,4 +133,5 @@ jobs:
      run: |
        git fetch origin master:master
        git checkout -b gh-actions-branch-history
-        ./config/githooks/pre-push --history
+        cd tests/scripts
+        ./runtest branch-history
@@ -26,7 +26,6 @@ CMakeFiles/
 config/_config.hpp
 config/config.mk
 config/sample-runs-build.log
-config/user.mk
 doc/CodeDocumentation.conf
 doc/CodeDocumentation.html
 doc/CodeDocumentation
@@ -252,7 +251,6 @@ 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
@@ -297,7 +295,6 @@ 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
@@ -48,59 +48,39 @@ variables:
  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, 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.
+# 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.
 # - 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_baseline
+  - setup
  - baseline_check
  - baseline_to_autotest
  - baseline_publish

-# 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.
+# 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:
  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:
@@ -126,10 +106,10 @@ setup_baseline:
  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
@@ -22,13 +22,12 @@

 # 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: [setup]
+  needs: []

 opt_mpi_cuda_xl_16_1_1_8:
  variables:
-    SPEC: "%xl@16.1.1.8 +mpi +cuda cuda_arch=70"
+    SPEC: "%xl@16.1.1.8 +mpi +cuda cuda_arch=sm_70"
  extends: .build_and_test_on_lassen
@@ -16,13 +16,13 @@
    - shell
    - quartz
  rules:
-    # Don't run quartz jobs if...
+    # Don’t run quartz jobs if...
    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_QUARTZ == "OFF"'
      when: never
-    # Don't run autotest update if...
+    # Don’t run autotest update if...
    - if: '$CI_JOB_NAME =~ /update_autotest/ && $AUTOTEST != "YES"'
      when: never
-    # Don't run autotest update if...
+    # Don’t run autotest update if...
    - if: '$CI_JOB_NAME =~ /q_report/ && $AUTOTEST != "YES"'
      when: never
    # Report success on success status
@@ -37,18 +37,6 @@
    # 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:
@@ -77,11 +65,10 @@ q_report_success:
  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
+    - cd ${AUTOTEST_ROOT}/autotest && git pull
+    - mkdir -p ${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
@@ -93,11 +80,10 @@ q_report_failure:
  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
+    - cd ${AUTOTEST_ROOT}/autotest && git pull
+    - mkdir -p ${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))"
@@ -150,29 +136,24 @@ opt_par_gcc_6_1_0_pumi:
    SPEC: "%gcc@6.1.0 +pumi"
  extends: .build_and_test_on_quartz

-# 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.
-
+# Baseline
 baselinecheck_mfem_intel_quartz:
  extends: [.baselinecheck_mfem, .on_quartz]
-  needs: [setup_baseline]
+  needs: [setup]

 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
+    - cd ${AUTOTEST_ROOT}/autotest && git pull
+    - mkdir -p ${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 ${rundir}
@@ -0,0 +1,469 @@
+# Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+language: cpp
+
+os: linux
+dist: bionic
+
+stages:
+  - checks
+  - tests
+  - optional
+
+env:
+  global:
+    - HYPRE_ARCHIVE=v2.19.0.tar.gz
+      HYPRE_URL=https://github.com/hypre-space/hypre/archive/$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
@@ -8,87 +8,40 @@
                               https://mfem.org


-Version 4.3.1 (development)
+Version 4.2.1 (development)
 ===========================
- Added support for hr-adaptivity using TMOP-based error estimator.
+- 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.

- Adding lowest order Nedelec and Raviart-Thomas basis functions on wedge
-  shaped elements.
+- 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.

- 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 Caliper: a library to integrate performance profiling
+  capabilities into applications. See examples/caliper for more details.

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

- 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.
+- Added AlgebraicCeedSolver that does matrix-free algebraic p-multigrid for
+  diffusion problems with the Ceed backend.

-
-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 new options for the mesh-explorer miniapp to visualize the actual
+  element attributes in parallel meshes while retaining the visualization of
+  the domain decomposition.

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

- 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 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.

- 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 a new miniapp for computing (signed) distance functions to a point
+  source or zero level set. See miniapps/shifted/distance.cpp.

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

 - 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.
@@ -118,17 +72,6 @@ Linear and nonlinear solvers
 - 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
@@ -137,26 +80,109 @@ Meshing improvements
  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 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 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 new mesh quality metrics and improved the untangling capabilities of the
  TMOP-based mesh optimization algorithms.

- 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 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 Kelly error indicator for scalar-valued problems, supported
+  in serial and parallel builds.
+
+- 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.

 - 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.

@@ -169,147 +195,56 @@ Meshing improvements
  requisite periodic vertex mappings can be created with
  Mesh::CreatePeriodicVertexMapping.

- Added support for 1D non-conforming meshes (which can be useful for parallel
-  load balancing and derefinement).
+- 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 support for transferring fields (primary and dual) between high-order
+  and low-order refined H1 finite element spaces using the
+  L2ProjectionH1GridTransfer operators. This functionality is demonstrated
+  through the lor-transfer miniapp when run with the -h1 option.
+
+- 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 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.

-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.
-
- Added support for explicit vectorization in the high-performance templated
-  code for Fujitsu's A64FX ARM microprocessor architecture.
-
- 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.
+libCEED integration improvements
+--------------------------------
+- Refactor the libCEED integration

- Various other simplifications, extensions, and bugfixes in the code.
+- Add support for VectorCoefficient with libCEED backends.

-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`.
+- Add support for ConvectionIntegrator, and VectorConvectionNLFIntegrator with
+  libCEED backends.


 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
@@ -391,6 +326,9 @@ 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.

@@ -501,7 +439,7 @@ 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
@@ -1,66 +0,0 @@
-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(${PROJECT_NAME}_VERSION 4.3.1)
+set(${PROJECT_NAME}_VERSION 4.2.1)

 # 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)
@@ -175,10 +175,6 @@ 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)
@@ -250,7 +246,6 @@ 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)
@@ -335,10 +330,6 @@ 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)
@@ -433,10 +424,9 @@ endif()
 #    integers, the METIS header (with 32-bit indices, as used by mfem) needs to
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP HYPRE BLAS LAPACK SuperLUDist METIS SuiteSparse SUNDIALS PETSC
-    SLEPC MESQUITE MUMPS STRUMPACK AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB NETCDF
+    SLEPC MESQUITE MUMPS STRUMPACK AXOM 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 "")
@@ -455,9 +445,6 @@ 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}")
@@ -4,9 +4,7 @@

 <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://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://travis-ci.org/mfem/mfem"><img alt="Build Status" src="https://travis-ci.org/mfem/mfem.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>
@@ -65,8 +63,6 @@ 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
@@ -75,7 +71,6 @@ 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
@@ -96,8 +91,8 @@ The MFEM source code has the following structure:
 ```
  .
  ├── config
-  │   ├── cmake
-  │   └── githooks
+  │   └── cmake
+  │       └── ...
  ├── data
  ├── doc
  ├── examples
@@ -134,10 +129,10 @@ The MFEM source code has the following structure:
  └── tests
      ├── convergence
      ├── gitlab
-      ├── mem_manager
      ├── par-mesh-format
      ├── scripts
      └── unit
+          └── ...
 ```

 #### Main directories and classes
@@ -368,10 +363,6 @@ 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.

@@ -379,20 +370,16 @@ 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 GitHub Actions and Appveyor [continuous integration](#automated-testing)
+- Track the Travis CI, 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 GitHub Actions
-  are safeguards that are allowed to fail in certain cases.
+- 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.

 - Other tests, such as the `code-style`, `documentation` and `gitignore`
-  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.
+  checks in Travis and Github Actions enforce MFEM-specific rules which are
+  explained in the error messages and the `tests/scripts` directory.

 - If triggered, track the status of the LLNL GitLab tests. If failing, ask
  one of the _LLNL developers_ for details.
@@ -412,7 +399,7 @@ 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)
-    - [ ] `.github`
+    - [ ] `.travis.yml`
    - [ ] `.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.
@@ -529,7 +516,7 @@ 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
-    - [ ] `.github`
+    - [ ] `.travis.yml`
    - [ ] `.appveyor.yml`
 - [ ] Update the `CHANGELOG` to organize all release contributions
 - [ ] Review the whole source code once over
@@ -591,17 +578,14 @@ 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.

-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.
-
 ### 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).
+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).

-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.
+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.

 - 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.
@@ -474,7 +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
@@ -516,13 +516,6 @@ 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.
@@ -547,9 +540,8 @@ 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 built without CUDA)
-            HYPRE >= 2.20.0   (HYPRE built with '--enable-mixedint')
-            HYPRE >= 2.22.1   (HYPRE built with CUDA)
+  Versions: HYPRE >= 2.10.0b,
+            HYPRE >= 2.20.0 for '--enable-mixedint' support.

 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
  MFEM_USE_METIS_5 = YES (default is to use METIS 4).
@@ -623,7 +615,7 @@ 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
@@ -761,11 +753,6 @@ 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.
@@ -897,7 +884,6 @@ MFEM_USE_RAJA
 MFEM_USE_UMPIRE
 MFEM_USE_SIDRE
 MFEM_USE_CALIPER
-MFEM_USE_FMS

 The following options are CMake specific:

@@ -952,7 +938,6 @@ 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:

@@ -970,7 +955,7 @@ 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.

@@ -978,7 +963,7 @@ 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
@@ -256,10 +256,6 @@ 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()
@@ -44,7 +44,6 @@ 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@)
@@ -119,9 +119,6 @@
 // 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

@@ -1,20 +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.
-
-# 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.")
@@ -117,9 +117,6 @@
 // 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

@@ -43,7 +43,6 @@ 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@
@@ -45,7 +45,6 @@ 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)
@@ -97,11 +96,6 @@ 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.")

@@ -138,10 +132,10 @@ 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.")
@@ -193,12 +187,6 @@ 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.")

@@ -136,7 +136,6 @@ 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
@@ -175,10 +174,6 @@ 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)
@@ -362,11 +357,6 @@ 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
@@ -1,41 +0,0 @@
-                    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.
@@ -1,4 +0,0 @@
-#!/bin/sh
-
-# Apply automated code formatting
-make -C $(git rev-parse --show-toplevel) style
@@ -1,107 +0,0 @@
-#!/bin/bash
-
-# Copyright (c) 2010-2021, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
-
-option=${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
@@ -57,27 +57,22 @@ TIMECMD := $(word 1,$(TIMECMD))
 ifneq (,$(filter test%,$(MAKECMDGOALS)))
   MAKEFLAGS += -k
 endif
-# Test runs of the examples/miniapps with parameters - check exit code:
-# 0 means success, 255 means the test was skipped, anything else means error
+# Test runs of the examples/miniapps with parameters - check exit code
 mfem-test = \
   printf "   $(3) [$(2) $(1) ... ]: "; \
   $(call $(TIMEFUN),$(TIMECMD),$(2) ./$(1) $(if $(5),,-no-vis )$(4) \
     > $(1).stderr 2>&1); \
-   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
+   if [ "$$3" = 0 ]; \
+   then $(PRINT_OK); else $(PRINT_FAILED); cat $(1).stderr; fi; \
+   rm -f $(1).stderr; exit $$3

 # 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 if [ "$$3" = 255 ] && [ -e $(4) ]; then $(PRINT_SKIP); err=0; \
-   else $(PRINT_FAILED); cat $(1).stderr; err=64; fi; fi; \
+   if [ "$$3" = 0 ] && [ -e $(4) ]; \
+   then $(PRINT_OK); else $(PRINT_FAILED); cat $(1).stderr; err=64; fi; \
   rm -f $(1).stderr; exit $$err

 .PHONY: test test-par-YES test-par-NO test-ser test-par test-clean test-print
@@ -85,26 +80,6 @@ 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
@@ -1,9 +0,0 @@
-MFEM INLINE mesh v1.0
-
-type = pyramid
-nx = 4
-ny = 4
-nz = 4
-sx = 1.0
-sy = 1.0
-sz = 1.0
@@ -1,43 +0,0 @@
-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
@@ -1,38 +0,0 @@
-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
@@ -1,246 +0,0 @@
-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, 
-0.663691, 0.183114, 0.317639, 
-0.543082, 0.598483, 0.345112, 
-0.478298, 0.027703, 0.095229, 
-0.012368, -0.092534, -0.334412, 
-0.313767, -0.140526, -0.293881, 
-0.534056, -0.660290, -0.537646, 
-0.655590, -0.121396, -0.274504, 
-0.346497, -0.296570, 0.004737, 
-0.098835, 0.069287, 0.082675, 
-0.318799, 0.467183, 0.564505, 
-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, 
-1.348360, -1.483190, -1.348360, 
-1.085930, -0.938010, -0.943851, 
-1.078690, -0.681476, -0.540944, 
-0.757514, -0.706011, -0.540614, 
-0.367058, -0.551503, -0.603005, 
-0.365164, -0.230328, -0.138552, 
-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, 
-1.051500, 1.103010, 0.214572, 
-0.407449, 0.288323, 0.449827, 
-0.086700, -0.027358, -0.200560, 
-0.166595, -0.271802, -0.418426, 
-0.426131, -0.551441, -0.096117, 
-0.206969, -0.027946, -0.184969, 
-0.211136, 0.260131, 0.407172, 
-0.430781, 0.718277, 0.885068, 
-0.753103, 0.957692, 0.866273, 
-1.024530, 0.934099, 1.093820, 
-0.348422, 0.524463, 0.404903, 
-0.587376, 0.054525, 0.146431, 
-0.078026, -0.007795, -0.329488, 
-0.302967, -0.488115, -0.439332, 
-0.498515, -0.453527, -0.633059, 
-0.570251, -0.655787, -0.791132, 
-0.802013, -0.956872, -1.094720, 
-1.208560, -1.207720, -1.339910, 
-0.693371, -0.795404, -0.803594, 
-0.945068, -0.464668, -0.631721, 
-0.458968, -0.547876, -0.332878, 
-0.485696, -0.286385, -0.408481, 
-0.053021, -0.058200, 0.110846, 
-0.002086, 0.381384, 0.416784, 
-0.551133, 0.613261, 0.872474, 
-0.901208, 1.038300, 1.084660, 
-0.737459, 0.751250, 0.890002, 
-0.915210, 0.010915, 0.000000, 
-0.951057, 0.951057, 0.587785, 
-1.538840, -0.587785, 0.000000, 
-0.951057, -1.538840, -0.951057, 
-0.015847, 0.475529, 0.951057, 
-0.492248, 1.244950, 1.063310, 
-0.274399, 0.293893, -0.293892, 
-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, 
-0.199438, -0.077304, -0.082243, 
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@@ -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         = v4.3.1
+PROJECT_NUMBER         = v4.2.1

 # 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
@@ -84,9 +84,8 @@ foreach(SRC_FILE ${ALL_EXE_SRCS})
  get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
  string(REPLACE ".cpp" "" TEST_NAME ${SRC_FILENAME})

-  set(THIS_TEST_OPTIONS "-no-vis")
-  if (${TEST_NAME} MATCHES "ex0p?")
-    set(THIS_TEST_OPTIONS)
+  if (NOT (${TEST_NAME} MATCHES "ex0p?"))
+    set(THIS_TEST_OPTIONS "-no-vis")
  endif()
  if (${TEST_NAME} MATCHES "ex10p*")
    list(APPEND THIS_TEST_OPTIONS "-tf" "5")
@@ -108,34 +107,6 @@ 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}
@@ -1,18 +0,0 @@
-                    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));
@@ -223,7 +223,6 @@ 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);
@@ -234,6 +233,7 @@ 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);

@@ -231,29 +231,28 @@ 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)
   {
-      MFEM_PERF_SCOPE("Solve A X=B");
-      Solver *prec = NULL;
-      if (pa)
+      if (UsesTensorBasis(fespace))
      {
-         if (UsesTensorBasis(fespace))
-         {
-            prec = new OperatorJacobiSmoother(a, ess_tdof_list);
-         }
+         prec = new OperatorJacobiSmoother(a, ess_tdof_list);
      }
-      else
-      {
-         prec = new HypreBoomerAMG;
-      }
-      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);
@@ -9,7 +9,6 @@
 //               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
@@ -55,7 +55,6 @@ 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",
@@ -72,8 +71,6 @@ 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())
   {
@@ -89,18 +86,13 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 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
+   // 3. Read the (serial) mesh from the given mesh file on all processors. We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

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

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

-   // 7. Define a parallel finite element space on the parallel mesh. Here we
+   // 6. 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);
@@ -129,7 +122,7 @@ int main(int argc, char *argv[])
      cout << "Number of unknowns: " << size << endl;
   }

-   // 8. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
+   // 7. 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
@@ -171,7 +164,7 @@ int main(int argc, char *argv[])
   delete a;
   delete m;

-   // 9. Define and configure the AME eigensolver and the AMS preconditioner for
+   // 8. 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);
@@ -187,15 +180,15 @@ int main(int argc, char *argv[])
   ame->SetMassMatrix(*M);
   ame->SetOperator(*A);

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

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

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

-   // 13. Free the used memory.
+   // 12. Free the used memory.
   delete ame;
   delete ams;
   delete M;
@@ -24,10 +24,7 @@
 //               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. 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.
+//               high-order implicit (SDIRK) time integration.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -329,8 +326,8 @@ ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
 void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 {
   // Compute:
-   //    du_dt = M^{-1}*-Ku
-   // for du_dt, where K is linearized by using u from the previous timestep
+   //    du_dt = M^{-1}*-K(u)
+   // for du_dt
   Kmat.Mult(u, z);
   z.Neg(); // z = -z
   M_solver.Mult(z, du_dt);
@@ -341,7 +338,7 @@ void ConductionOperator::ImplicitSolve(const double dt,
 {
   // Solve the equation:
   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt, where K is linearized by using u from the previous timestep
+   // for du_dt
   if (!T)
   {
      T = Add(1.0, Mmat, dt, Kmat);
@@ -24,11 +24,8 @@
 //               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. 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.
+//               high-order implicit (SDIRK) time integration. Optional saving
+//               with ADIOS2 (adios2.readthedocs.io) is also illustrated.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -423,8 +420,8 @@ ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
 void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
 {
   // Compute:
-   //    du_dt = M^{-1}*-Ku
-   // for du_dt, where K is linearized by using u from the previous timestep
+   //    du_dt = M^{-1}*-K(u)
+   // for du_dt
   Kmat.Mult(u, z);
   z.Neg(); // z = -z
   M_solver.Mult(z, du_dt);
@@ -435,7 +432,7 @@ void ConductionOperator::ImplicitSolve(const double dt,
 {
   // Solve the equation:
   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt, where K is linearized by using u from the previous timestep
+   // for du_dt
   if (!T)
   {
      T = Add(1.0, Mmat, dt, Kmat);
@@ -196,12 +196,6 @@ 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();
@@ -444,19 +438,15 @@ 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;
-   disp_in.MakeRef(const_cast<Vector&>(k), block_trueOffsets[0],
-                   block_trueOffsets[1]-block_trueOffsets[0]);
-   Vector pres_in;
-   pres_in.MakeRef(const_cast<Vector&>(k), block_trueOffsets[1],
-                   block_trueOffsets[2]-block_trueOffsets[1]);
+   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;
-   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 disp_out(y.GetData() + block_trueOffsets[0],
+                   block_trueOffsets[1]-block_trueOffsets[0]);
+   Vector pres_out(y.GetData() + 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]);
@@ -469,9 +459,6 @@ 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)
@@ -486,10 +473,7 @@ 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;
@@ -9,7 +9,6 @@
 //               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
@@ -90,8 +89,7 @@ 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",
@@ -199,15 +197,15 @@ 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));
@@ -13,8 +13,6 @@
 //               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:
@@ -13,8 +13,6 @@
 //               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:
@@ -113,6 +113,7 @@ 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.
@@ -141,6 +141,7 @@ 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 &),
@@ -277,8 +277,10 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 6. Set element attributes in order to distinguish elements in the
-   //    PML region
+   // 6. Reorient mesh in case of a tet mesh
+   mesh->ReorientTetMesh();
+
+   // 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 &),
@@ -316,6 +316,9 @@ 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, diag,
+      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), 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, diag,
+      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), diag,
                                                       *essentialTrueDofs.Last(), 2, fespace.GetParMesh()->GetComm());

      AddLevel(opr.Ptr(), smoother, true, true);
@@ -81,12 +81,6 @@ 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);
@@ -366,7 +360,6 @@ int main(int argc, char *argv[])
   }
   delete pmesh;

-   // HYPRE_Finalize();
   MPI_Finalize();

   return 0;
@@ -61,7 +61,6 @@ 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",
@@ -79,8 +78,6 @@ 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())
   {
@@ -96,12 +93,7 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 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
+   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
@@ -117,14 +109,14 @@ int main(int argc, char *argv[])
      return 3;
   }

-   // 5. Select the order of the finite element discretization space. For NURBS
+   // 4. 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);
   }

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

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

-   // 8. 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 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
@@ -183,7 +175,7 @@ int main(int argc, char *argv[])
           << "Assembling: " << flush;
   }

-   // 9. Determine the list of true (i.e. parallel conforming) essential
+   // 8. 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.
@@ -192,14 +184,14 @@ int main(int argc, char *argv[])
   ess_bdr[0] = 1;
   fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);

-   // 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.
+   // 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.
   VectorArrayCoefficient f(dim);
   for (int i = 0; i < dim-1; i++)
   {
@@ -220,13 +212,13 @@ int main(int argc, char *argv[])
   }
   b->Assemble();

-   // 11. Define the solution vector x as a parallel finite element grid
+   // 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;

-   // 12. Set up the parallel bilinear form a(.,.) on the finite element space
+   // 11. 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());
@@ -241,7 +233,7 @@ int main(int argc, char *argv[])
   ParBilinearForm *a = new ParBilinearForm(fespace);
   a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func, mu_func));

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

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

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

-   // 16. For non-NURBS meshes, make the mesh curved based on the finite element
+   // 15. 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
@@ -292,7 +284,7 @@ int main(int argc, char *argv[])
      pmesh->SetNodalFESpace(fespace);
   }

-   // 17. Save in parallel the displaced mesh and the inverted solution (which
+   // 16. 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".
   {
@@ -313,7 +305,7 @@ int main(int argc, char *argv[])
      x.Save(sol_ofs);
   }

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

-   // 19. Free the used memory.
+   // 18. Free the used memory.
   delete pcg;
   delete amg;
   delete a;
@@ -16,8 +16,6 @@
 //               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
@@ -115,6 +113,7 @@ 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.
@@ -16,8 +16,6 @@
 //               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
@@ -105,7 +103,6 @@ int main(int argc, char *argv[])
      {
         args.PrintUsage(cout);
      }
-      // HYPRE_Finalize();
      MPI_Finalize();
      return 1;
   }
@@ -141,7 +138,9 @@ 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.
+   //    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.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -151,6 +150,7 @@ 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.
@@ -19,8 +19,6 @@
 //               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:
@@ -19,8 +19,6 @@
 //               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:
@@ -137,7 +135,9 @@ 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.
+   //    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).
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -147,6 +147,7 @@ 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.
@@ -197,7 +197,6 @@ 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);
@@ -241,7 +240,6 @@ int main(int argc, char *argv[])
   {
      SparseMatrix &M(mVarf->SpMat());
      M.GetDiag(Md);
-      Md.HostReadWrite();

      SparseMatrix &B(bVarf->SpMat());
      MinvBt = Transpose(B);
@@ -289,18 +287,12 @@ 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;
@@ -47,7 +47,6 @@ 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",
@@ -66,8 +65,6 @@ 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())
   {
@@ -83,12 +80,7 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 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
+   // 3. 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.
@@ -154,7 +146,7 @@ int main(int argc, char *argv[])
   FiniteElementSpace nodal_fes(mesh, &fec, mesh->SpaceDimension());
   mesh->SetNodalFESpace(&nodal_fes);

-   // 5. Refine the mesh while snapping nodes to the sphere. Number of parallel
+   // 4. 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++)
   {
@@ -226,7 +218,7 @@ int main(int argc, char *argv[])
      SnapNodes(*pmesh);
   }

-   // 6. Define a finite element space on the mesh. Here we use isoparametric
+   // 5. 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();
@@ -235,7 +227,7 @@ int main(int argc, char *argv[])
      cout << "Number of unknowns: " << size << endl;
   }

-   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
+   // 6. 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);
@@ -245,27 +237,27 @@ int main(int argc, char *argv[])
   b->AddDomainIntegrator(new DomainLFIntegrator(rhs_coef));
   b->Assemble();

-   // 8. Define the solution vector x as a finite element grid function
+   // 7. 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;

-   // 9. Set up the bilinear form a(.,.) on the finite element space
+   // 8. 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));

-   // 10. Assemble the parallel linear system, applying any transformations
-   //     such as: parallel assembly, applying conforming constraints, etc.
+   // 9. 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);

-   // 11. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
+   // 10. 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.
@@ -281,14 +273,14 @@ int main(int argc, char *argv[])
   delete a;
   delete b;

-   // 12. Compute and print the L^2 norm of the error.
+   // 11. 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;
   }

-   // 13. Save the refined mesh and the solution. This output can be viewed
+   // 12. 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;
@@ -304,7 +296,7 @@ int main(int argc, char *argv[])
      x.Save(sol_ofs);
   }

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

-   // 15. Free the used memory.
+   // 14. Free the used memory.
   delete pcg;
   delete amg;
   delete fespace;
@@ -106,6 +106,7 @@ 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
@@ -26,9 +26,6 @@ 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)
@@ -102,14 +99,6 @@ 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
@@ -0,0 +1,960 @@
+#include "DofMapsDST.hpp"
+
+double testcoeff(const Vector & x)
+{
+   return sin(3*M_PI*(x.Sum()));
+}
+
+int get_rank(int tdof, std::vector<int> & tdof_offsets)
+{
+   int size = tdof_offsets.size();
+   if (size == 1) { return 0; }
+   std::vector<int>::iterator up;
+   up=std::upper_bound(tdof_offsets.begin(), tdof_offsets.end(),tdof); // 
+   return std::distance(tdof_offsets.begin(),up)-1;
+}
+
+void ComputeTdofOffsets(const MPI_Comm & comm, const ParFiniteElementSpace * pfes, 
+                        std::vector<int> & tdof_offsets)
+{
+   int num_procs;
+   MPI_Comm_size(comm, &num_procs);
+   tdof_offsets.resize(num_procs);
+   int mytoffset = pfes->GetMyTDofOffset();
+   MPI_Allgather(&mytoffset,1,MPI_INT,&tdof_offsets[0],1,MPI_INT,comm);
+}
+
+void GetSubdomainijk(int ip, const Array<int> nxyz, Array<int> & ijk)
+{
+   ijk.SetSize(3);
+   ijk[2] = ip/(nxyz[0]*nxyz[1]);
+   ijk[1] = (ip-ijk[2]*nxyz[0]*nxyz[1])/nxyz[0];
+   ijk[0] = (ip-ijk[2]*nxyz[0]*nxyz[1])%nxyz[0];
+}
+void GetDirectionijk(int id, Array<int> & ijk)
+{
+   ijk.SetSize(3);
+   int n = 3;
+   ijk[2] = id/(n*n) - 1;
+   ijk[1] = (id-(ijk[2]+1)*n*n)/n - 1;
+   ijk[0] = (id-(ijk[2]+1)*n*n)%n - 1;
+}
+
+int GetSubdomainId(const Array<int> nxyz, Array<int> & ijk)
+{
+   int dim=ijk.Size();
+   int k = (dim==2)? 0 : ijk[2];
+   return k*nxyz[1]*nxyz[0] + ijk[1]*nxyz[0] + ijk[0];
+}
+
+int GetDirectionId(const Array<int> & ijk)
+{
+   int n = 3;
+   int dim = ijk.Size();
+   int k = (dim == 2) ? -1 : ijk[2];
+   return (k+1)*n*n + (ijk[1]+1)*n + ijk[0]+1; 
+}
+
+void DofMaps::Init()
+{
+   comm = pfes->GetComm();
+   MPI_Comm_size(comm, &num_procs);
+   MPI_Comm_rank(comm, &myid);
+
+   dim = pfes->GetParMesh()->Dimension();
+   ComputeTdofOffsets(comm, pfes, tdof_offsets);
+   myelemoffset = part->myelem_offset;
+   mytoffset = pfes->GetMyTDofOffset();
+   subdomain_rank = part->subdomain_rank;
+   nrsubdomains = part->nrsubdomains;
+   nxyz.SetSize(3);
+   for (int i = 0; i<3; i++) { nxyz[i] = part->nxyz[i]; }
+
+   //compute sign factors for tdofs
+   int lsize = pfes->GetVSize();
+   int tsize = pfes->GetTrueVSize();
+   tdof_sign.SetSize(tsize); 
+   for (int i = 0; i<lsize; i++)
+   {
+      int j = pfes->GetGlobalTDofNumber(i);
+      if (j<mytoffset || j>=mytoffset+tsize) continue;
+      tdof_sign[j-mytoffset] = pfes->GetDofSign(i);
+   }
+}
+
+DofMaps::DofMaps(ParFiniteElementSpace *pfes_, ParMeshPartition * part_, bool CompFlag_)
+: pfes(pfes_), part(part_), CompFlag(CompFlag_)
+{
+   Init();
+   Setup();
+}
+
+void DofMaps::Setup()
+{
+   // Setup the local FiniteElementSpaces
+   const FiniteElementCollection * fec = pfes->FEColl();
+   fes.SetSize(nrsubdomains);
+   for (int i = 0; i<nrsubdomains; i++)
+   {
+      fes[i] = nullptr; // initialize with null on all procs
+      if (myid == subdomain_rank[i])
+      {
+         fes[i] = new FiniteElementSpace(part->subdomain_mesh[i],fec);
+      }
+   }
+   // cout << "Computing Overlap Tdofs" << endl;
+   SubdomainToSubdomainMapsSetup();
+   // TestSubdomainToSubdomainMaps();
+
+   SubdomainToGlobalMapsSetup();
+   // TestSubdomainToGlobalMaps();
+}
+
+void DofMaps::SubdomainToSubdomainMapsSetup()
+{
+   ComputeOvlpElems();
+   ComputeOvlpTdofs();
+}
+
+void DofMaps::AddElementToOvlpLists(int l, int iel, 
+                            const Array<bool> & neg, const Array<bool> & pos)
+{
+   int kbeg = (dim == 2) ? 0 : -1;
+   int kend = (dim == 2) ? 0 :  1;
+   Array<int> dijk(3);
+   for (int k = kbeg; k<=kend; k++)
+   {
+      if (dim == 3)
+      {
+         if (k == -1 && !neg[2]) continue;   
+         if (k ==  1 && !pos[2]) continue;   
+      }   
+
+      for (int j = -1; j<=1; j++)
+      {
+         if (j== -1 && !neg[1]) continue;   
+         if (j==  1 && !pos[1]) continue;   
+         for (int i = -1; i<=1; i++)
+         {
+            // cases to skip 
+            if (i==-1 && !neg[0]) continue;   
+            if (i== 1 && !pos[0]) continue;   
+
+            if (i==0 && j==0 && k == 0) continue;
+            dijk[0] = i; dijk[1] = j; dijk[2] = (dim==2)?-1 : k;  
+            int DirId = GetDirectionId(dijk);
+            OvlpElems[l][DirId].Append(iel);
+         }
+      }
+   }
+}
+
+void DofMaps::ComputeOvlpElems()
+{
+   // first compute the element in the overlaps
+   OvlpElems.resize(nrsubdomains);
+   int nlayers = 2*part->OvlpNlayers; 
+   // loop through subdomains
+   for (int l = 0; l<nrsubdomains; l++)
+   {
+      if (myid == subdomain_rank[l])
+      {
+         Array<int> ijk;
+         GetSubdomainijk(l,nxyz,ijk);
+         Mesh * mesh = part->subdomain_mesh[l];
+         OvlpElems[l].resize(pow(3,dim)); 
+         Vector pmin, pmax;
+         mesh->GetBoundingBox(pmin,pmax);
+         double h = part->MeshSize;
+         // loop through the elements in the mesh and assign them to the 
+         // appropriate lists of overlaps
+         for (int iel=0; iel< mesh->GetNE(); iel++)
+         {
+            // Get element center
+            Vector center(dim);
+            int geom = mesh->GetElementBaseGeometry(iel);
+            ElementTransformation * tr = mesh->GetElementTransformation(iel);
+            tr->Transform(Geometries.GetCenter(geom),center);
+
+            Array<bool> pos(dim); pos = false;
+            Array<bool> neg(dim); neg = false;
+            // loop through dimensions   
+            for (int d=0;d<dim; d++)
+            {
+               if (ijk[d]>0 && center[d] < pmin[d]+h*nlayers)
+               {
+                  neg[d] = true;
+               }
+
+               if (ijk[d]<nxyz[d]-1 && center[d] > pmax[d]-h*nlayers) 
+               {
+                  pos[d] = true;
+               }
+            }
+            // Add the element to the appropriate lists
+            AddElementToOvlpLists(l,iel,neg,pos);        
+         }   
+      }
+   }
+}
+
+void DofMaps::ComputeOvlpTdofs()
+{
+   OvlpTDofs.resize(nrsubdomains);
+   int nrneighbors = pow(3,dim); // including its self
+
+   // loop through subdomains
+   for (int l = 0; l<nrsubdomains; l++)
+   {
+      if (myid != subdomain_rank[l]) continue;
+      int ntdofs = fes[l]->GetTrueVSize();
+      Array<int> tdof_marker(ntdofs); 
+      OvlpTDofs[l].resize(nrneighbors);
+      // loop through neighboring directions/neighbors
+      for (int d=0; d<nrneighbors; d++)
+      {
+         tdof_marker = 0;
+         Array<int> tdoflist;
+         // Get the direction
+         Array<int> dijk;
+         GetDirectionijk(l,dijk);
+         int nel = OvlpElems[l][d].Size();
+         Array<int>Elems = OvlpElems[l][d];
+         for (int iel = 0; iel<nel; ++iel)
+         {
+            int jel = Elems[iel];   
+            Array<int> ElemDofs;
+
+            fes[l]->GetElementDofs(jel,ElemDofs);
+            int ndof = ElemDofs.Size();
+            for (int i = 0; i<ndof; ++i)
+            {
+               int dof_ = ElemDofs[i];
+               int dof = (dof_ >= 0) ? dof_ : abs(dof_) - 1;
+               if (!tdof_marker[dof])
+               {
+                  tdoflist.Append(dof); // dofs of ip0 in ovlp
+                  tdof_marker[dof] = 1;
+               }
+            }
+         }
+         OvlpTDofs[l][d] = tdoflist; 
+         if (CompFlag)
+         {
+            for (int i=0; i<tdoflist.Size(); i++)
+            {
+               tdoflist[i] += fes[l]->GetTrueVSize();
+            }
+            OvlpTDofs[l][d].Append(tdoflist);
+         }
+      }
+   }
+}
+
+void DofMaps::PrintOvlpTdofs()
+{
+   int nrneighbors = pow(3,dim); // including its self
+   if (myid == 0)
+   {
+      for (int i = 0; i<nrsubdomains; i++)
+      {
+         if (myid != subdomain_rank[i]) continue;
+         Array<int> ijk;
+         GetSubdomainijk(i,nxyz,ijk);
+         cout << "subdomain = " ; ijk.Print();
+         cout << "myid = " << myid << endl;
+         cout << "ip   = " << i << endl;
+         for (int d = 0; d<nrneighbors; d++)
+         {
+            Array<int> dijk;
+            GetDirectionijk(d,dijk);
+            cout << "direction = " ; dijk.Print();
+
+            if (OvlpTDofs[i][d].Size())
+            {
+               cout << "OvlpTdofs = " ; 
+               OvlpTDofs[i][d].Print(cout,OvlpTDofs[i][d].Size() );
+            }
+         }
+      }
+   }
+}
+
+void DofMaps::TransferToNeighbors(const Array<int> & SubdomainIds, const Array<Vector *> & x,
+std::vector<std::vector<Vector * >> & OvlpSol)
+{
+   // 2D for now....
+   MFEM_VERIFY(SubdomainIds.Size() == x.Size(), "TransferToNeighbors: Size inconsistency");
+   int nrsendIds = SubdomainIds.Size();
+   int nrneighbors = pow(3,dim);
+   MPI_Request *recv_requests = new MPI_Request[nrsendIds*nrneighbors];
+   MPI_Request *send_requests = new MPI_Request[nrsendIds*nrneighbors];
+   MPI_Status  *recv_statuses = new MPI_Status[nrsendIds*nrneighbors];
+   MPI_Status  *send_statuses = new MPI_Status[nrsendIds*nrneighbors];
+   Array<Vector * > send_buffer(nrsendIds*nrneighbors);
+   Array<Vector * > recv_buffer(nrsendIds*nrneighbors);
+   int send_counter = 0;
+   int recv_counter = 0;
+   for (int is = 0; is<nrsendIds; is++)
+   {
+      int i0 = SubdomainIds[is];
+      Array<int> ijk;
+      GetSubdomainijk(i0,nxyz,ijk);
+      for (int d=0;d<nrneighbors; d++)
+      {
+         Array<int>directions;
+         GetDirectionijk(d,directions);
+
+         if (dim == 2 && directions[0] == 0 && directions[1] == 0) continue;
+         if (dim == 3 && directions[0] == 0 
+                      && directions[1] == 0 
+                      && directions[2] == 0) continue;
+         int i = ijk[0] + directions[0];
+         if (i<0 || i>=nxyz[0]) continue;
+         int j = ijk[1] + directions[1];
+         if (j<0 || j>=nxyz[1]) continue;
+         int k = (dim ==3 ) ? ijk[2] + directions[2] : 0;
+         if (k<0 || k>=nxyz[2]) continue;
+         Array<int>ijk1(3);
+         ijk1[0] = i;
+         ijk1[1] = j;
+         ijk1[2] = k;
+         int i1 = GetSubdomainId(nxyz,ijk1);
+         if (myid == subdomain_rank[i0])
+         {
+            Array<int> tdofs0 = OvlpTDofs[i0][d]; // map of dofs in the overlap
+            send_buffer[send_counter] = new Vector(tdofs0.Size());
+            x[is]->GetSubVector(tdofs0,*send_buffer[send_counter]);
+            // Destination rank
+            int dest = subdomain_rank[i1];
+            int tag = i0 * nrneighbors + d;
+
+            int count = tdofs0.Size();
+            MPI_Isend(send_buffer[send_counter]->GetData(),count,MPI_DOUBLE,dest,
+                      tag,comm,&send_requests[send_counter]);
+            send_counter++;
+
+         }
+         if (myid == subdomain_rank[i1])
+         {
+            Array<int> direction1(3); direction1 = -1;
+            for (int dd=0;dd<dim;dd++) 
+            { 
+               direction1[dd] = -directions[dd];
+            }
+            int d1 = GetDirectionId(direction1);
+
+            int count = OvlpTDofs[i1][d1].Size();
+            recv_buffer[recv_counter] = new Vector(count); 
+            int src = subdomain_rank[i0];
+            int tag = i0 * nrneighbors + d;
+            MPI_Irecv(recv_buffer[recv_counter]->GetData(), count,MPI_DOUBLE,src,
+                      tag,comm, &recv_requests[recv_counter]);
+            recv_counter++;
+         }
+      }   
+   }
+   MPI_Waitall(send_counter, send_requests, send_statuses);
+   MPI_Waitall(recv_counter, recv_requests, recv_statuses);
+
+   delete [] send_statuses;
+   delete [] send_requests;
+   delete [] recv_statuses;
+   delete [] recv_requests;
+
+   for (int i = 0; i<send_counter; i++)
+   {
+      delete send_buffer[i];
+   }
+   send_buffer.DeleteAll();
+
+
+   // Extract the transfered solutions
+   recv_counter = 0;
+   for (int is = 0; is<nrsendIds; is++)
+   {
+      int i0 = SubdomainIds[is];
+      Array<int> ijk;
+      GetSubdomainijk(i0,nxyz,ijk);
+      for (int d=0;d<nrneighbors; d++)
+      {
+         Array<int>directions;
+         GetDirectionijk(d,directions);
+         if (dim == 2 && directions[0] == 0 && directions[1] == 0) continue;
+         if (dim == 3 && directions[0] == 0 
+                      && directions[1] == 0 
+                      && directions[2] == 0) continue;
+         int i = ijk[0] + directions[0];
+         if (i<0 || i>=nxyz[0]) continue;
+         int j = ijk[1] + directions[1];
+         if (j<0 || j>=nxyz[1]) continue;
+         int k = (dim ==3 ) ? ijk[2] + directions[2] : 0;
+         if (k<0 || k>=nxyz[2]) continue;
+
+         Array<int>ijk1(3);
+         ijk1[0] = i;
+         ijk1[1] = j;
+         ijk1[2] = k;
+         int i1 = GetSubdomainId(nxyz,ijk1);
+         if (myid == subdomain_rank[i1])
+         {
+            Array<int> direction1(3); direction1 = -1;
+            for (int d=0;d<dim;d++) 
+            { 
+               direction1[d] = -directions[d];
+            }
+            int d1 = GetDirectionId(direction1);
+            Array<int> tdofs1 = OvlpTDofs[i1][d1];
+            if (!OvlpSol[i1][d1])
+            {
+               OvlpSol[i1][d1] = new Vector(2*fes[i1]->GetTrueVSize());
+            }
+            *OvlpSol[i1][d1] = 0.0;
+            OvlpSol[i1][d1]->SetSubVector(tdofs1,*recv_buffer[recv_counter]);
+            recv_counter++;
+         }
+      }   
+   }
+   for (int i = 0; i<recv_counter; i++)
+   {
+      delete recv_buffer[i];
+   }
+   recv_buffer.DeleteAll();
+}
+
+void DofMaps::TestSubdomainToSubdomainMaps()
+{
+      // testing inter-subdomain communication
+   FunctionCoefficient c1(testcoeff);
+   int nrsub = nrsubdomains;
+   Array<int> subdomain_ids(nrsub);
+   Array<Vector*> x(nrsub);
+   for (int i = 0; i<nrsub; i++)
+   {
+      x[i] = nullptr;
+      subdomain_ids[i] = i;
+      if (fes[i])
+      {
+         ComplexGridFunction gf(fes[i]);
+         gf = 0.0;
+         gf.ProjectCoefficient(c1,c1);
+         x[i] = new Vector(2*fes[i]->GetTrueVSize());
+         *x[i] = gf;
+      }
+   }
+
+   std::vector<std::vector<Vector * >> OvlpSol;
+
+   OvlpSol.resize(nrsubdomains);
+   int nrneighbors = pow(3,dim);
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      if (myid == subdomain_rank[ip])
+      {
+         OvlpSol[ip].resize(nrneighbors);
+      }
+   }
+
+
+   TransferToNeighbors(subdomain_ids,x,OvlpSol);
+
+   string keys = "keys amrRljc\n";
+   for (int i0 = 0 ; i0< nrsubdomains; i0++)
+   {
+      if (fes[i0])
+      {
+         ComplexGridFunction gf0(fes[i0]);
+         for (int d = 0; d<nrneighbors; d++)
+         {
+            if(OvlpSol[i0][d])
+            {
+               Array<int>dijk;
+               GetDirectionijk(d,dijk);
+               Array<int>ijk;
+               GetSubdomainijk(i0,nxyz,ijk);
+               ostringstream oss;
+               oss << "myid: " << myid 
+                     << ", subdomain: (" << ijk[0] << "," << ijk[1] <<")"
+                     << ", direction: (" << dijk[0] << "," << dijk[1] <<")";
+
+               gf0 = 0.0;
+               gf0.real().SetVector(*OvlpSol[i0][d],0);
+               gf0.imag().SetVector(*OvlpSol[i0][d],fes[i0]->GetTrueVSize());
+               char vishost[] = "localhost";
+               int  visport   = 19916;
+               socketstream sol_sock(vishost, visport);
+               sol_sock.precision(8);
+               sol_sock << "solution\n" << *(part->subdomain_mesh[i0]) << gf0.real() 
+               << keys
+               << "window_title '" << oss.str() << "'" << flush;
+            }
+         }
+      }
+   }
+   for (int i = 0; i<nrsub; i++)
+   {
+      delete x[i];
+   }
+}
+
+void DofMaps::SubdomainToGlobalMapsSetup()
+{
+   // workspace for MPI_AlltoAll
+   send_count.SetSize(num_procs);  send_count = 0;
+   send_displ.SetSize(num_procs);  send_displ = 0; 
+   recv_count.SetSize(num_procs);  recv_count = 0;
+   recv_displ.SetSize(num_procs);  recv_displ = 0;
+
+   // 1. Communicate to the subdomain rank the list of tdofs 
+   // a. Compute send count
+   for (int ip = 0; ip<nrsubdomains; ++ip)
+   {
+      // avoid any communication if on subdomain rank
+      int nel = part->local_element_map[ip].Size();
+
+      for (int iel = 0; iel<nel; iel++)
+      {
+         int elem_idx = part->local_element_map[ip][iel] - myelemoffset;
+         // int ndofs = local_tdofs[ip].Size();
+         int ndofs = pfes->GetFE(elem_idx)->GetDof();
+
+         send_count[subdomain_rank[ip]] += 2 + ndofs; 
+      }
+   }
+   // b. Compute receive count
+   MPI_Alltoall(send_count,1,MPI_INT,recv_count,1,MPI_INT,comm);
+   for (int k=0; k<num_procs-1; k++)
+   {
+      send_displ[k+1] = send_displ[k] + send_count[k];
+      recv_displ[k+1] = recv_displ[k] + recv_count[k];
+   }
+   sbuff_size = send_count.Sum();
+   rbuff_size = recv_count.Sum();
+   // c. Allocate and fill the send buffer
+   Array<int> sendbuf(sbuff_size);  sendbuf = 0;
+   Array<int> soffs(num_procs); soffs = 0;
+   for (int ip = 0; ip<nrsubdomains; ++ip)
+   {
+      int nel = part->local_element_map[ip].Size();
+      for (int iel = 0; iel<nel; iel++)
+      {
+         int elem_idx = part->local_element_map[ip][iel] - myelemoffset;
+         Array<int>ElemDofs;
+         pfes->GetElementDofs(elem_idx,ElemDofs);
+         int ndofs = ElemDofs.Size();
+
+         int j = send_displ[subdomain_rank[ip]] + soffs[subdomain_rank[ip]];
+         sendbuf[j] = ip;
+         sendbuf[j+1] = ndofs;
+
+         for (int k = 0; k < ndofs ; ++k)
+         {
+            int edof_ = ElemDofs[k];
+            int edof = (edof_ >= 0) ? edof_ : abs(edof_) - 1;
+            sendbuf[j+2+k] = pfes->GetGlobalTDofNumber(edof);
+         }
+         soffs[subdomain_rank[ip]] +=  2 + ndofs;
+      }
+   }
+
+   // d. Communication
+   Array<int> recvbuf(rbuff_size);
+   MPI_Alltoallv(sendbuf, send_count, send_displ, MPI_INT, recvbuf,
+                 recv_count, recv_displ, MPI_INT, comm);
+
+   // 3. Extract from recv_buffer
+   std::vector<Array<int>> global_tdofs(nrsubdomains);
+   int k=0;
+   while (k<rbuff_size)
+   {
+      int ip = recvbuf[k++]; 
+      int ndofs = recvbuf[k++];
+      for (int i = 0; i < ndofs; ++i)
+      {
+         global_tdofs[ip].Append(recvbuf[i+k]); 
+      }
+      k += ndofs;
+   }
+
+   SubdomainGTrueDofs.resize(nrsubdomains);
+   // 4. Construct SubdomainTdof to Global mesh tdof maps
+   for (int ip=0; ip<nrsubdomains; ++ip)
+   {
+      if (myid != subdomain_rank[ip]) continue;
+      int nrdof = fes[ip]->GetTrueVSize();
+
+      SubdomainGTrueDofs[ip].SetSize(nrdof);
+      int nel = part->element_map[ip].Size();
+      int k = 0;
+      for (int iel = 0; iel<nel; ++iel)
+      {
+         Array<int> elem_dofs;
+         fes[ip]->GetElementDofs(iel,elem_dofs);
+         int ndof = elem_dofs.Size();
+         for (int i = 0; i<ndof; ++i)
+         {
+            int edof_ = elem_dofs[i];
+            int edof = (edof_ >= 0) ? edof_ : abs(edof_) - 1;
+            // rearranging dofs from serial fespace to pfes ordering
+            SubdomainGTrueDofs[ip][edof] = global_tdofs[ip][k++];
+         }
+      }
+   }
+
+   // 5. Communicate SubdomainGTrueDofs to participating ranks 
+   send_count = 0;  send_displ = 0;
+   recv_count = 0;  recv_displ = 0;
+
+   for (int ip = 0; ip < nrsubdomains; ++ip)
+   {
+      if (myid != subdomain_rank[ip]) continue;
+      int ndofs = SubdomainGTrueDofs[ip].Size();
+      for (int i = 0; i<ndofs; ++i)
+      {
+         int tdof = SubdomainGTrueDofs[ip][i];
+         int rank = get_rank(tdof,tdof_offsets);
+         if (rank == subdomain_rank[ip]) continue; // <--------------
+         send_count[rank] += 2; // 1 for the dof and 1 for the ip that goes to 
+      }
+   }
+
+   // communicate so that recv_count is constructed
+   MPI_Alltoall(send_count,1,MPI_INT,recv_count,1,MPI_INT,comm);
+   //
+   for (int k=0; k<num_procs-1; k++)
+   {
+      send_displ[k+1] = send_displ[k] + send_count[k];
+      recv_displ[k+1] = recv_displ[k] + recv_count[k];
+   }
+   sbuff_size = send_count.Sum();
+   rbuff_size = recv_count.Sum();
+
+   sendbuf.SetSize(sbuff_size);  
+   sendbuf = 0; soffs = 0;
+
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid != subdomain_rank[ip]) continue;
+      int ndofs = SubdomainGTrueDofs[ip].Size();
+      // loop through dofs
+      for (int i = 0; i<ndofs; ++i)
+      {
+         int tdof = SubdomainGTrueDofs[ip][i];
+         int irank = get_rank(tdof,tdof_offsets);
+         if (irank == subdomain_rank[ip]) continue; // <--------------
+         int j = send_displ[irank] + soffs[irank];
+         sendbuf[j] = ip;
+         sendbuf[j+1] = SubdomainGTrueDofs[ip][i];
+         soffs[irank] +=  2 ;
+      }
+   }
+
+   recvbuf.SetSize(rbuff_size);
+   MPI_Alltoallv(sendbuf, send_count, send_displ, MPI_INT, recvbuf,
+                 recv_count, recv_displ, MPI_INT, comm);
+
+   // List of tdofs owned by the processor for subdomains not owned
+   SubdomainLTrueDofs.resize(nrsubdomains); 
+   for (int k=0; k<rbuff_size/2; k++)
+   {
+      int ip = recvbuf[2*k];
+      int tdof = recvbuf[2*k+1];
+      SubdomainLTrueDofs[ip].Append(tdof);
+   }    
+}
+
+// Restriction of global residual to subdomain residuals
+void DofMaps::GlobalToSubdomains(const Vector & y, Array<Vector*> & x)
+{
+   send_count = 0; send_displ = 0;
+   recv_count = 0; recv_displ = 0;
+
+   // Compute send_counts
+   int m = (CompFlag) ? 2 : 1 ;
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid == subdomain_rank[ip]) continue;  // <---------------
+      int ndofs = SubdomainLTrueDofs[ip].Size();
+      send_count[subdomain_rank[ip]] += m * ndofs;
+   }
+
+    // communicate so that recv_count is constructed
+   MPI_Alltoall(send_count,1,MPI_INT,recv_count,1,MPI_INT,comm);
+
+   for (int k=0; k<num_procs-1; k++)
+   {
+      send_displ[k+1] = send_displ[k] + send_count[k];
+      recv_displ[k+1] = recv_displ[k] + recv_count[k];
+   }
+   sbuff_size = send_count.Sum();
+   rbuff_size = recv_count.Sum();
+
+   Array<double> sendbuf(sbuff_size); sendbuf = 0;
+   Array<int> soffs(num_procs); soffs = 0;
+
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid == subdomain_rank[ip]) continue;  // <---------------
+      int ndofs = SubdomainLTrueDofs[ip].Size();
+      for (int i = 0; i<ndofs; i++)
+      {
+         int tdof = SubdomainLTrueDofs[ip][i];
+         int j = send_displ[subdomain_rank[ip]] + soffs[subdomain_rank[ip]];
+         soffs[subdomain_rank[ip]] +=m;
+         int k = tdof - mytoffset;
+         // sendbuf[j] = y[k];
+         sendbuf[j] = tdof_sign[k]*y[k];
+         if (CompFlag)
+         {  // if complex valued 
+            int tsize = pfes->GetTrueVSize();
+            // sendbuf[j+1] = y[k+tsize];
+            sendbuf[j+1] = tdof_sign[k]*y[k+tsize];
+         }
+      }
+   }
+
+   // communication
+   Array<double> recvbuf(rbuff_size);
+   MPI_Alltoallv(sendbuf, send_count, send_displ, MPI_DOUBLE, recvbuf,
+                 recv_count, recv_displ, MPI_DOUBLE, comm);
+   Array<int> roffs(num_procs);
+   roffs = 0;
+   // Now each process will construct the res vector
+   x.SetSize(nrsubdomains);
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid != subdomain_rank[ip]) continue;
+      int ndof = SubdomainGTrueDofs[ip].Size();
+      if (!x[ip]) x[ip] = new Vector(m*ndof); 
+      *x[ip] = 0.0;
+      // extract the data from receiv buffer
+      for (int i=0; i<ndof; i++)
+      {
+         // pick up the tdof and find its rank
+         int tdof = SubdomainGTrueDofs[ip][i];
+         int tdof_rank = get_rank(tdof,tdof_offsets);
+         if (tdof_rank != subdomain_rank[ip])  // <---------------
+         {
+            int k = recv_displ[tdof_rank] + roffs[tdof_rank];
+            roffs[tdof_rank] += m;
+            (*x[ip])[i] = recvbuf[k];
+            if (CompFlag)
+            {  
+               (*x[ip])[i+ndof] = recvbuf[k+1];
+            }
+         }
+         else
+         {
+            int k = tdof - mytoffset;
+            // (*x[ip])[i] = y[k];
+            (*x[ip])[i] = tdof_sign[k]*y[k];
+            if (CompFlag)
+            {  
+               int gtsize = pfes->GetTrueVSize();
+               (*x[ip])[i+ndof] = tdof_sign[k]*y[k+gtsize];
+            }
+         }
+      }
+   }
+}
+
+// Prolongation of subdomain solutions to the global solution
+void DofMaps::SubdomainsToGlobal(const Array<Vector*> & x, Vector & y)
+{
+   send_count = 0; send_displ = 0;
+   recv_count = 0; recv_displ = 0;
+
+   // Compute send_counts
+   int m = (CompFlag) ? 2 : 1 ;
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid != subdomain_rank[ip]) continue;
+      int ndofs = SubdomainGTrueDofs[ip].Size();
+      for (int i=0; i<ndofs; i++)
+      {
+         // pick up the tdof and find its rank
+         int tdof = SubdomainGTrueDofs[ip][i];
+         int tdof_rank = get_rank(tdof,tdof_offsets);
+         if (tdof_rank == subdomain_rank[ip]) continue;
+         send_count[tdof_rank] +=m;
+      }
+   }
+
+   MPI_Alltoall(send_count,1,MPI_INT,recv_count,1,MPI_INT,comm);
+
+   for (int k=0; k<num_procs-1; k++)
+   {
+      send_displ[k+1] = send_displ[k] + send_count[k];
+      recv_displ[k+1] = recv_displ[k] + recv_count[k];
+   }
+   sbuff_size = send_count.Sum();
+   rbuff_size = recv_count.Sum();
+
+   Array<double> sendbuf(sbuff_size); sendbuf = 0;
+   Array<int> soffs(num_procs); soffs = 0;
+
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid != subdomain_rank[ip]) continue;
+      int ndofs = SubdomainGTrueDofs[ip].Size();
+      // loop through dofs
+      for (int i=0; i<ndofs; i++)
+      {
+         //  pick up the dof and find its tdof_rank
+         int tdof = SubdomainGTrueDofs[ip][i];
+         int tdof_rank = get_rank(tdof,tdof_offsets);
+         // offset
+         if (tdof_rank == subdomain_rank[ip]) continue;
+         int k = send_displ[tdof_rank] + soffs[tdof_rank];
+         soffs[tdof_rank] +=m;
+         sendbuf[k] = (*x[ip])[i];
+         if (CompFlag)
+         {
+            sendbuf[k+1] = (*x[ip])[i+ndofs];
+         }
+      }
+   }
+
+   Array<double> recvbuf(rbuff_size);
+   Array<int> roffs(num_procs); roffs = 0;
+   MPI_Alltoallv(sendbuf, send_count, send_displ, MPI_DOUBLE, recvbuf,
+                 recv_count, recv_displ, MPI_DOUBLE, comm);
+
+   for (int ip = 0; ip < nrsubdomains; ip++)
+   {
+      if (myid == subdomain_rank[ip]) 
+      {
+         int ndofs = SubdomainGTrueDofs[ip].Size();
+         for (int i = 0; i<ndofs; i++)
+         {
+            int tdof = SubdomainGTrueDofs[ip][i];
+            int k = tdof - mytoffset;
+            if (k<0 || k>=pfes->GetTrueVSize()) continue;
+            y[k] += tdof_sign[k] * (*x[ip])[i];
+            if (CompFlag)
+            {  
+               int gtsize = pfes->GetTrueVSize();
+               y[k+gtsize] += tdof_sign[k]*(*x[ip])[i+ndofs];
+            }
+         }
+      }
+      else
+      {
+         int ndofs = SubdomainLTrueDofs[ip].Size();
+         for (int i = 0; i<ndofs; i++)
+         {
+            int tdof = SubdomainLTrueDofs[ip][i];
+            int k = tdof - mytoffset;
+            int j = recv_displ[subdomain_rank[ip]] + roffs[subdomain_rank[ip]];
+            roffs[subdomain_rank[ip]] +=m;
+            y[k] += tdof_sign[k] * recvbuf[j];
+            if (CompFlag)
+            {
+               int tsize = pfes->GetTrueVSize();
+               y[k+tsize] += tdof_sign[k]*recvbuf[j+1];
+            }
+         }
+      }
+   }              
+}
+
+void DofMaps::TestSubdomainToGlobalMaps()
+{
+   cout << "Testing Subdomain To Global Maps" << endl;
+   FunctionCoefficient c1(testcoeff);
+   Array<Vector*> x(nrsubdomains);
+   Vector y(pfes->GetTrueVSize()); y = 0.0;
+   for (int i = 0 ; i<nrsubdomains; i++)
+   {
+      if (myid != subdomain_rank[i]) continue;
+      x[i] = new Vector(fes[i]->GetTrueVSize());
+      GridFunction gf(fes[i]);
+      gf = 0.0;
+
+      if (i==3) gf.ProjectCoefficient(c1);
+      *x[i] = gf;
+   }
+
+   SubdomainsToGlobal(x,y);
+
+   // cout << "1: myid = " <<  myid << ", y = "; y.Print();
+
+   string keys = (dim==2) ? "keys amrRljc\n": "keys m\n";
+   ParGridFunction pgf(pfes);
+
+   const Operator &P = *pfes->GetProlongationMatrix();
+   P.Mult(y, pgf);
+   
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock(vishost, visport);
+   sol_sock.precision(8);
+   sol_sock << "parallel " << num_procs << " " << myid << "\n"
+               << "solution\n" << *pfes->GetParMesh() << pgf 
+               << keys << flush;
+
+   ParGridFunction pgf1(pfes);
+   pgf1.ProjectCoefficient(c1);
+   Vector y1(pfes->GetTrueVSize());
+   const SparseMatrix * R = pfes->GetRestrictionMatrix();
+
+   R->Mult(pgf1,y1);
+   // P.MultTranspose(pgf1,y1);
+   Array<Vector*> x1;
+   GlobalToSubdomains(y1,x1);
+
+
+   // for (int i = 0 ; i<nrsubdomains; i++)
+   // {
+   //    if (myid != subdomain_rank[i]) continue;
+   //    ostringstream mesh_name;
+   //    mesh_name << "output/mesh." << setfill('0') << setw(6) << i;
+   //    ofstream mesh_ofs(mesh_name.str().c_str());
+   //    mesh_ofs.precision(8);
+   //    fes[i]->GetMesh()->Print(mesh_ofs);
+   //    GridFunction gf(fes[i]);
+   //    gf = x1[i];
+   //    ostringstream gf_name;
+   //    gf_name << "output/gf." << setfill('0') << setw(6) << i;
+   //    ofstream gf_ofs(gf_name.str().c_str());
+   //    gf_ofs.precision(8);
+   //    gf.Save(gf_ofs);
+   // }
+
+
+
+   int nrsub = nrsubdomains;
+   for (int i = 0 ; i<nrsub; i++)
+   {
+      if (myid == subdomain_rank[i])
+      {
+         socketstream sol_sock1(vishost, visport);
+         sol_sock1.precision(8);
+         sol_sock1 << "parallel " << nrsub << " " << i << "\n";
+         GridFunction gf(fes[i]);
+         GridFunction gf1(fes[i]);
+         gf1.ProjectCoefficient(c1);
+         gf = *x1[i];
+         gf1-=gf;
+         cout << "ip, Diff norm = " <<i<<", " << gf1.Norml2() << endl;
+         sol_sock1 << "solution\n" << *fes[i]->GetMesh() << gf
+                   << keys << flush;
+      }
+      MPI_Barrier(MPI_COMM_WORLD);
+   }
+
+   socketstream gf_sock(vishost, visport);
+   gf_sock.precision(8);
+   gf_sock << "parallel " << num_procs << " " << myid << "\n"
+           << "solution\n" << *pfes->GetParMesh() << pgf1 
+           << keys << flush;
+}
+
+
+DofMaps::~DofMaps()
+{
+   for (int i = 0; i<nrsubdomains; i++)
+   {
+      delete fes[i];
+   }
+}
@@ -0,0 +1,109 @@
+#pragma once
+#include "../common/Utilities.hpp"
+#include "../common/PML.hpp"
+using namespace std;
+using namespace mfem;
+
+double testcoeff(const Vector & x);
+int get_rank(int tdof, std::vector<int> & tdof_offsets);
+
+
+void ComputeTdofOffsets(const MPI_Comm & comm, const ParFiniteElementSpace * pfes, 
+                        std::vector<int> & tdof_offsets);
+
+void GetSubdomainijk(int ip, const Array<int> nxyz, Array<int> & ijk);
+void GetDirectionijk(int id, Array<int> & ijk);
+int GetSubdomainId(const Array<int> nxyz, Array<int> & ijk);
+int GetDirectionId(const Array<int> & ijk);
+
+
+// class handling two types of dof maps
+// 1. Subdomain truedofs ---> Global truedofs
+// 2. Subdomain truedofs ---> Neighbor truedofs 
+class DofMaps
+{
+private:
+   // The FE space of the problem (H1/Hcurl)
+   ParFiniteElementSpace *pfes = nullptr;
+
+   // The given partition of the parmesh
+   ParMeshPartition *part = nullptr;
+   // partition in x-y-z
+   Array<int> nxyz;
+
+   // MPI parameters
+   MPI_Comm comm = MPI_COMM_WORLD;
+   int num_procs, myid;
+
+   // true dof offset and element offset of the processor
+   vector<int> tdof_offsets;
+   int mytoffset;
+   int myelemoffset;
+   
+   int dim;
+   // Total number of subdomains
+   int nrsubdomains;
+   
+   // Array specifying the subdomain rank
+   Array<int> subdomain_rank;
+
+   // Complex flag
+   bool CompFlag;
+
+   // sign factors
+   Array<int> tdof_sign;
+   // Initializing mpi and helper parameters
+   void Init();
+
+   // 1. Setting up the subdomains FE spaces
+   // 2. Setting up the subdomains-to-subdomains maps
+   // 3. Setting up the subdomain-to-global maps
+   void Setup();
+
+   // -----------------------------------------------
+   //           Subdomain to Subdomain maps
+   // -----------------------------------------------
+   std::vector<std::vector<Array<int>>> OvlpElems;
+   void AddElementToOvlpLists(int l, int iel, 
+                            const Array<bool> & neg, 
+                            const Array<bool> & pos);
+   std::vector<std::vector<Array<int>>> OvlpTDofs;
+   void SubdomainToSubdomainMapsSetup();
+   void ComputeOvlpElems();
+   void ComputeOvlpTdofs();
+   void PrintOvlpTdofs();
+
+   // -----------------------------------------------
+   //           Subdomain to Global maps
+   // -----------------------------------------------
+   std::vector<Array<int>> SubdomainGTrueDofs; // Subdomain Tdofs to Global Tdofs
+   std::vector<Array<int>> SubdomainLTrueDofs; // Subdomain Tdofs to Local (on rank) Tdofs
+
+   Array<int> send_count, send_displ;  
+   Array<int> recv_count, recv_displ;  
+   int sbuff_size = 0;
+   int rbuff_size = 0;
+   void SubdomainToGlobalMapsSetup();
+
+   // Testing
+   void TestSubdomainToGlobalMaps();
+   void TestSubdomainToSubdomainMaps();
+
+public:
+   // constructor
+
+   // FiniteElementSpaces of the subdomains
+   Array<FiniteElementSpace *> fes;
+
+   DofMaps(ParFiniteElementSpace *fespace_, ParMeshPartition * part_, bool CompFlag_ = false);
+   ~DofMaps();
+   // Transfering from subdomains SubdomainIds to all their neighbors
+   void TransferToNeighbors(const Array<int> & SubdomainIds, const Array<Vector *> & x, 
+   std::vector<std::vector<Vector * >> & OvlpSol);
+
+   // Prolongation of subdomain solutions to the global solution
+   void SubdomainsToGlobal(const Array<Vector*> & x, Vector & y);
+   // Restriction of global residual to subdomain residuals
+   // bool comp: true for complex valued problems
+   void GlobalToSubdomains(const Vector & y, Array<Vector*> & x);
+};
@@ -0,0 +1,849 @@
+//Parallel Diagonal Source Transfer Preconditioner
+
+#include "ParDST.hpp"
+
+ParDST::ParDST(ParSesquilinearForm * bf_, Array2D<double> & Pmllength_, 
+         double omega_, Coefficient * Q_,  int nrlayers_ , int nx_, int ny_, int nz_)
+   : Solver(2*bf_->ParFESpace()->GetTrueVSize(), 2*bf_->ParFESpace()->GetTrueVSize()), 
+     bf(bf_), Pmllength(Pmllength_), omega(omega_), 
+     Q(Q_), nrlayers(nrlayers_)
+{
+   nx = nx_; ny = ny_; nz = nz_;
+   Init();
+}
+ParDST::ParDST(ParSesquilinearForm * bf_, Array2D<double> & Pmllength_, 
+         double omega_, VectorCoefficient * VQ_,  int nrlayers_ , int nx_, int ny_, int nz_)
+   : Solver(2*bf_->ParFESpace()->GetTrueVSize(), 2*bf_->ParFESpace()->GetTrueVSize()), 
+     bf(bf_), Pmllength(Pmllength_), omega(omega_), 
+     VQ(VQ_), nrlayers(nrlayers_)
+{
+   nx = nx_; ny = ny_; nz = nz_;
+   Init();
+}
+ParDST::ParDST(ParSesquilinearForm * bf_, Array2D<double> & Pmllength_, 
+         double omega_, MatrixCoefficient * MQ_,  int nrlayers_ , int nx_, int ny_, int nz_)
+   : Solver(2*bf_->ParFESpace()->GetTrueVSize(), 2*bf_->ParFESpace()->GetTrueVSize()), 
+     bf(bf_), Pmllength(Pmllength_), omega(omega_), 
+     MQ(MQ_), nrlayers(nrlayers_)
+{
+   nx = nx_; ny = ny_; nz = nz_;
+   Init();
+}
+
+void ParDST::Init()
+{
+   pfes = bf->ParFESpace();
+   fec = pfes->FEColl();
+ 
+   comm = pfes->GetComm();
+   MPI_Comm_size(comm, &num_procs);
+   MPI_Comm_rank(comm, &myid);
+
+   //1. Indentify problem ... Helmholtz or Maxwell
+   prob_kind = fec->GetContType();
+   if (myid == 0)
+   {
+      cout << " 1. Indentify problem to be solved ... " << endl;
+      if (prob_kind == 0) cout << "    Helmholtz" << endl;
+      if (prob_kind == 1) cout << "    Maxwell" << endl; 
+   }
+
+   //2. Create the parallel mesh partition
+   pmesh = pfes->GetParMesh();
+   dim = pmesh->Dimension();
+   if (myid == 0)
+   {
+      cout << "\n 2. Generating ParMesh partitioning ... " << endl;
+   }
+   ovlpnrlayers = nrlayers+1;
+   part = new ParMeshPartition(pmesh,nx,ny,nz,ovlpnrlayers);
+   nxyz.SetSize(3);
+   nxyz[0] = nx = part->nxyz[0]; 
+   nxyz[1] = ny = part->nxyz[1];  
+   nxyz[2] = nz = part->nxyz[2];
+
+   nrsubdomains = part->nrsubdomains;
+   SubdomainRank = part->subdomain_rank;
+
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      if (myid == SubdomainRank[ip])
+      {
+         RankSubdomains.Append(ip);
+      }
+   }
+
+   cout << " myid: " << myid 
+        << ", nrsubdomains: " << RankSubdomains.Size() << endl;
+
+   MPI_Barrier(comm);
+
+   if (myid == 0)
+   {
+      cout << "    Done ! " << endl;
+   }
+   //3. Setup info for sweeps
+   if (myid == 0)
+   {
+      cout << "\n 3. Computing sweeps info ..." << endl; 
+   }
+   sweeps = new Sweep(dim);
+   if (myid == 0)
+   {
+      cout << "    Done ! " << endl;
+   }
+   //4. Create LocalToGlobal maps 
+   //   (local GridFunctions/Vector to Global ParGridFunction/Vector) 
+   if (myid == 0)
+   {
+      cout << "\n 4. Computing true dofs maps ..." << endl; 
+   }
+
+   // if (myid == SubdomainRank[0])
+   // {
+   //    cout << "myid = " << myid << endl;
+   //    char vishost[] = "localhost";
+   //    int visport = 19916;
+   //    socketstream mesh_sock1(vishost, visport);
+   //    mesh_sock1.precision(8);
+   //    mesh_sock1 << "mesh\n"
+   //               << *part->subdomain_mesh[0] << "window_title 'Subdomain'" << flush;
+   //    part->subdomain_mesh[0]->Print();
+   
+   // }
+   bool comp = true;
+
+   dmaps = new DofMaps(pfes,part, comp);
+   
+   if (myid == 0)
+   {
+      cout << "    Done ! " << endl;
+   }
+   // 4. Setting up the local problems 
+   if (myid == 0)
+   {
+      cout << "\n 5. Setting up the subdomain problems ..." << endl; 
+   }
+
+   SetupSubdomainProblems();
+   
+   if (myid == 0)
+   {
+      cout << "    Done ! " << endl;
+   }
+   if (myid == 0)
+   {
+      cout << "\n 6. Mark subdomain overlap truedofs ..." << endl; 
+   }
+   MarkSubdomainOverlapDofs(comp);
+   if (myid == 0)
+   {
+      cout << "    Done ! " << endl;
+   }
+}
+
+void ParDST::Mult(const Vector &r, Vector &z) const
+{
+   // Initialize transfered residuals to 0.0;
+   for (int ip=0; ip<nrsubdomains; ip++)
+   {
+      if (myid != SubdomainRank[ip]) continue;
+      for (int i=0;i<sweeps->nsweeps; i++)
+      {
+         *f_transf[ip][i] = 0.0;
+      }
+   }
+
+   // restrict given residual to subdomains
+   dmaps->GlobalToSubdomains(r,f_orig);
+
+   for (int ip=0; ip<nrsubdomains; ip++)
+   {
+      if (myid != SubdomainRank[ip]) continue;
+      Array<int> ijk(3);
+      GetSubdomainijk(ip,nxyz,ijk);
+      Array2D<int> direct(dim,2); direct = 0;
+      for (int d=0;d<dim; d++)
+      {
+         if (ijk[d] > 0) direct[d][0] = 1; 
+         if (ijk[d] < part->nxyz[d]-1) direct[d][1] = 1; 
+      }
+      GetChiRes(*f_orig[ip],ip,direct);
+   }
+
+   z = 0.0; 
+   int nsteps;
+   switch(dim)
+   {
+      case 1: nsteps = nx; break;
+      case 2: nsteps = nx+ny-1; break;
+      default: nsteps = nx+ny+nz-2; break;
+   }
+   int nsweeps = sweeps->nsweeps;
+   // 1. Loop through sweeps
+   if (dim == 3 && nz == 1) { nsweeps = 4; } // x-y partition only;
+   for (int l=0; l<nsweeps; l++)
+   {  
+      // 2. loop through diagonals/steps of each sweep   
+      for (int s = 0; s<nsteps; s++)
+      {
+         Array2D<int> subdomains;
+         GetStepSubdomains(l,s,subdomains);
+         int nsubdomains = subdomains.NumRows();
+
+         // 3. Loop through the subdomains on the diagonal
+         Array<int> subdomain_ids;
+         for (int sb=0; sb < nsubdomains; sb++)
+         {
+            Array<int> ijk(dim); ijk = 0;
+            for (int d=0; d<dim; d++) ijk[d] = subdomains[sb][d]; 
+            int ip = GetSubdomainId(nxyz,ijk);
+            subdomain_ids.Append(ip);
+            if (myid != SubdomainRank[ip]) continue;
+
+            int n = dmaps->fes[ip]->GetTrueVSize();
+            Vector res_local(2*n); res_local = 0.0;
+
+            if (l==0)  { res_local += *f_orig[ip]; }
+            res_local += *f_transf[ip][l];
+            if (res_local.Norml2() < 1e-12) 
+            {
+               *subdomain_sol[ip] = 0.0;
+               continue;
+            }
+            PmlMatInv[ip]->Mult(res_local, *subdomain_sol[ip]);
+         }
+         // 4. Transfer solutions to neighbors so that the subdomain
+         // residuals are updated
+         TransferSources(l,subdomain_ids);
+      }
+      // 5. Update the global solution 
+      dmaps->SubdomainsToGlobal(subdomain_sol,z);
+   }
+}
+
+void ParDST::SetupSubdomainProblems()
+{
+   sqf.SetSize(nrsubdomains);
+   Optr.SetSize(nrsubdomains);
+   PmlMat.SetSize(nrsubdomains);
+   PmlMatInv.SetSize(nrsubdomains);
+   f_orig.SetSize(nrsubdomains);
+   f_transf.SetSize(nrsubdomains);
+   subdomain_sol.SetSize(nrsubdomains);
+   for (int ip=0; ip<nrsubdomains; ip++)
+   {
+      sqf[ip] = nullptr;
+      f_orig[ip] = nullptr;
+      subdomain_sol[ip] = nullptr;
+      PmlMat[ip] = nullptr;
+      PmlMatInv[ip] = nullptr;
+      Optr[ip] = nullptr;
+
+      if (myid != SubdomainRank[ip]) continue;
+      subdomain_sol[ip] = new Vector(2*dmaps->fes[ip]->GetTrueVSize());
+      if (prob_kind == 0)
+      {
+         SetHelmholtzPmlSystemMatrix(ip);
+      }
+      else if (prob_kind == 1)
+      {
+         SetMaxwellPmlSystemMatrix(ip);
+      }
+      PmlMat[ip] = Optr[ip]->As<ComplexSparseMatrix>();
+
+      PmlMatInv[ip] = new ComplexUMFPackSolver;
+      PmlMatInv[ip]->Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      PmlMatInv[ip]->SetOperator(*PmlMat[ip]);
+
+      // HYPRE_Int rowstarts[2]; rowstarts[0] = 0;
+      // rowstarts[1] = dmaps->fes[ip]->GetTrueVSize();
+      // HypreParMatrix * HypreMat_r =
+      //    new HypreParMatrix(MPI_COMM_SELF,rowstarts[1],rowstarts,
+      //                       &(PmlMat[ip]->real()));
+      // HypreParMatrix * HypreMat_i =
+      //    new HypreParMatrix(MPI_COMM_SELF,rowstarts[1],rowstarts,
+      //                       &(PmlMat[ip]->imag()));
+      // ComplexHypreParMatrix * HypreMat =
+      //    new ComplexHypreParMatrix(HypreMat_r,HypreMat_i,true,true);
+      // PmlMatInv[ip] = new ComplexMUMPSSolver;
+      // PmlMatInv[ip]->SetOperator(*HypreMat);
+      // delete HypreMat;
+      int ndofs = dmaps->fes[ip]->GetTrueVSize();
+      f_transf[ip].SetSize(sweeps->nsweeps);
+      for (int i=0;i<sweeps->nsweeps; i++)
+      {
+         f_transf[ip][i] = new Vector(2*ndofs);
+      }
+   }
+}
+
+
+
+void ParDST::SetHelmholtzPmlSystemMatrix(int ip)
+{
+   MFEM_VERIFY(part->subdomain_mesh[ip], "Null mesh pointer");
+   Mesh * mesh = part->subdomain_mesh[ip];
+   double h = part->MeshSize;
+   Array2D<double> length(dim,2);
+   length = h*(nrlayers);
+
+   Array<int> ijk;
+   GetSubdomainijk(ip,nxyz,ijk);
+   int i = ijk[0];
+   int j = ijk[1];
+   int k = ijk[2];
+
+   if (i == 0 )    length[0][0] = Pmllength[0][0];
+   if (i == nx-1 ) length[0][1] = Pmllength[0][1];
+   if (dim  > 1)
+   {
+      if (j == 0 )    length[1][0] = Pmllength[1][0];
+      if (j == ny-1 ) length[1][1] = Pmllength[1][1];
+   }
+   if (dim  == 3)
+   {
+      if (k == 0 )    length[2][0] = Pmllength[2][0];
+      if (k == nz-1 ) length[2][1] = Pmllength[2][1];
+   }
+   
+   CartesianPML pml(mesh, length);
+   pml.SetOmega(omega);
+
+   Array <int> ess_tdof_list;
+   if (mesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      dmaps->fes[ip]->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient sigma(-pow(omega, 2));
+   PmlMatrixCoefficient c1_re(dim,pml_detJ_JT_J_inv_Re,&pml);
+   PmlMatrixCoefficient c1_im(dim,pml_detJ_JT_J_inv_Im,&pml);
+   PmlCoefficient detJ_re(pml_detJ_Re,&pml);
+   PmlCoefficient detJ_im(pml_detJ_Im,&pml);
+   ProductCoefficient c2_re0(sigma, detJ_re);
+   ProductCoefficient c2_im0(sigma, detJ_im);
+   ProductCoefficient c2_re(c2_re0, *Q);
+   ProductCoefficient c2_im(c2_im0, *Q);
+   sqf[ip] = new SesquilinearForm (dmaps->fes[ip],bf->GetConvention());
+
+   sqf[ip]->AddDomainIntegrator(new DiffusionIntegrator(c1_re),
+                         new DiffusionIntegrator(c1_im));
+   sqf[ip]->AddDomainIntegrator(new MassIntegrator(c2_re),
+                         new MassIntegrator(c2_im));
+   sqf[ip]->Assemble(0);
+
+   Optr[ip] = new OperatorPtr;
+   sqf[ip]->FormSystemMatrix(ess_tdof_list,*Optr[ip]);
+}
+
+void ParDST::SetMaxwellPmlSystemMatrix(int ip)
+{
+   MFEM_VERIFY(part->subdomain_mesh[ip], "Null mesh pointer");
+   Mesh * mesh = part->subdomain_mesh[ip];
+   double h = part->MeshSize;
+   Array2D<double> length(dim,2);
+   length = h*(nrlayers);
+
+   Array<int> ijk;
+   GetSubdomainijk(ip,nxyz,ijk);
+   int i = ijk[0];
+   int j = ijk[1];
+   int k = ijk[2];
+
+   if (i == 0 )    length[0][0] = Pmllength[0][0];
+   if (i == nx-1 ) length[0][1] = Pmllength[0][1];
+   if (dim  > 1)
+   {
+      if (j == 0 )    length[1][0] = Pmllength[1][0];
+      if (j == ny-1 ) length[1][1] = Pmllength[1][1];
+   }
+   if (dim  == 3)
+   {
+      if (k == 0 )    length[2][0] = Pmllength[2][0];
+      if (k == nz-1 ) length[2][1] = Pmllength[2][1];
+   }
+   
+   CartesianPML pml(mesh, length);
+   pml.SetOmega(omega);
+   Array <int> ess_tdof_list;
+   if (mesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      dmaps->fes[ip]->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   ConstantCoefficient omeg(-pow(omega, 2));
+   int cdim = (dim == 2) ? 1 : dim;
+
+   PmlMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, &pml);
+   PmlMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, &pml);
+
+   PmlMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,&pml);
+   PmlMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,&pml);
+   ScalarMatrixProductCoefficient c2_Re0(omeg,pml_c2_Re);
+   ScalarMatrixProductCoefficient c2_Im0(omeg,pml_c2_Im);
+
+   MatrixCoefficient * c2_Re=nullptr;
+   MatrixCoefficient * c2_Im=nullptr;
+
+   if (Q)
+   {
+      c2_Re = new ScalarMatrixProductCoefficient(*Q,c2_Re0);
+      c2_Im = new ScalarMatrixProductCoefficient(*Q,c2_Im0);
+   }
+   else if (VQ)
+   {
+      MFEM_ABORT("Vector Coeffiecient not supported ");
+   }
+   else if (MQ)
+   {
+      c2_Re = new MatrixMatrixProductCoefficient(c2_Re0,*MQ);
+      c2_Im = new MatrixMatrixProductCoefficient(c2_Im0,*MQ);
+   }
+   
+   sqf[ip] = new SesquilinearForm(dmaps->fes[ip],bf->GetConvention());
+
+   sqf[ip]->AddDomainIntegrator(new CurlCurlIntegrator(pml_c1_Re),
+                         new CurlCurlIntegrator(pml_c1_Im));
+   sqf[ip]->AddDomainIntegrator(new VectorFEMassIntegrator(*c2_Re),
+                         new VectorFEMassIntegrator(*c2_Im));
+   sqf[ip]->Assemble(0);
+
+   Optr[ip] = new OperatorPtr;
+   sqf[ip]->FormSystemMatrix(ess_tdof_list,*Optr[ip]);
+   delete c2_Re;
+   delete c2_Im;
+}
+
+
+void ParDST::MarkSubdomainOverlapDofs(const bool comp)
+{
+   // First mark the elements
+         // cout<< "Compute Overlap Elements (in each possible direction) " << endl;
+      // Lists of elements
+      // x,y,z = +/- 1 ovlp 
+   NovlpElems.resize(nrsubdomains);
+
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      if (myid != SubdomainRank[ip]) continue;
+      Array<int> ijk;
+      GetSubdomainijk(ip,nxyz,ijk);
+
+      Mesh * mesh = dmaps->fes[ip]->GetMesh();
+      NovlpElems[ip].resize(2*dim);
+
+      Vector pmin, pmax;
+      mesh->GetBoundingBox(pmin,pmax);
+      double h = part->MeshSize;
+      // Loop through elements
+      for (int iel=0; iel<mesh->GetNE(); iel++)
+      {
+         // Get element center
+         Vector center(dim);
+         int geom = mesh->GetElementBaseGeometry(iel);
+         ElementTransformation * tr = mesh->GetElementTransformation(iel);
+         tr->Transform(Geometries.GetCenter(geom),center);
+
+         // Assign elements to the appropriate lists
+         for (int d=0;d<dim; d++)
+         {
+            if (ijk[d]>0)
+            {
+               if (center[d] >= pmin[d]+h*ovlpnrlayers) 
+               {
+                  NovlpElems[ip][d].Append(iel);
+               }
+            }
+            else
+            {
+               NovlpElems[ip][d].Append(iel);
+            }
+               
+            if (ijk[d]<nxyz[d]-1)
+            {
+               if (center[d] <= pmax[d]-h*ovlpnrlayers) 
+               {
+                  NovlpElems[ip][dim+d].Append(iel);
+               }
+            }
+            else
+            {
+               NovlpElems[ip][dim+d].Append(iel);
+            }
+         }
+      }
+   }
+
+      // mark dofs
+   NovlpDofs.resize(nrsubdomains);
+   int mm = (comp) ? 2 : 1; // complex or real valued
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      if (myid != SubdomainRank[ip]) continue;
+      FiniteElementSpace * fes = dmaps->fes[ip];
+      // Loop through the marked elements
+      NovlpDofs[ip].resize(2*dim);
+      int n = fes->GetTrueVSize();
+      Array<int> marker(n);
+      for (int d=0;d<2*dim; d++)
+      {
+         marker = 0;
+         int m = 0;
+         int melems = NovlpElems[ip][d].Size(); 
+         for (int iel=0; iel<melems; iel++)
+         {
+            Array<int> ElemDofs;
+            int el =  NovlpElems[ip][d][iel];
+            fes->GetElementDofs(el,ElemDofs);
+            int ndof = ElemDofs.Size();
+            for (int i = 0; i<ndof; ++i)
+            {
+               int eldof = ElemDofs[i];
+               int tdof = (eldof >= 0) ? eldof : abs(eldof) - 1; 
+               if (marker[tdof] == 1) continue;
+               marker[tdof] = 1;
+               m++;
+            }
+         }
+         int k = mm*(n-m);
+         NovlpDofs[ip][d].SetSize(k);
+         int l = 0;
+         for (int i = 0; i<n; i++)
+         {
+            if (marker[i]==0) 
+            {
+               NovlpDofs[ip][d][l] = i;  // real dofs
+               if (comp) 
+               {
+                  NovlpDofs[ip][d][l+k/2] = i+fes->GetTrueVSize();
+               }
+               l++;
+            }
+         }
+      }
+   }
+}
+
+void ParDST::GetChiRes(Vector & res, int ip, Array2D<int> direct) const
+{
+   for (int d=0; d<dim; d++)
+   {
+      // negative direction
+      if (direct[d][0]==1) res.SetSubVector(NovlpDofs[ip][d],0.0);
+      // possitive direction
+      if (direct[d][1]==1) res.SetSubVector(NovlpDofs[ip][d+dim],0.0);
+   }
+}
+
+
+
+void ParDST::PlotLocal(Vector & sol, socketstream & sol_sock, int ip) const
+{
+   FiniteElementSpace * fes = dmaps->fes[ip];
+   Mesh * mesh = fes->GetMesh();
+   GridFunction gf(fes);
+   double * data = sol.GetData();
+   gf.SetData(data);
+   
+   string keys;
+   keys = "keys mrRljc\n";
+   sol_sock << "solution\n" << *mesh << gf << keys << flush;
+}
+
+
+void ParDST::GetStepSubdomains(const int sweep, const int step, Array2D<int> & subdomains) const
+{
+   Array<int> aux;
+   switch(dim)
+   {
+      case 2: 
+      for (int i=nx-1;i>=0; i--)
+      {  
+         int j;
+         switch (sweep)
+         {
+            case 0:  j = step-i;         break;
+            case 1:  j = step-nx+i+1;    break;
+            case 2:  j = nx+i-step-1;    break;
+            default: j = nx+ny-i-step-2; break;
+         }
+         if (j<0 || j>=ny) continue;
+         aux.Append(i); aux.Append(j);
+      }
+      break; 
+      default:
+      for (int i=nx-1;i>=0; i--)
+      {  
+         for (int j=ny-1;j>=0; j--)
+         {
+            int k;
+            switch (sweep)
+            {
+               case 0:  k = step-i-j;            break;
+               case 1:  k = step-nx+i+1-j;       break;
+               case 2:  k = step-ny+j+1-i;       break;
+               case 3:  k = step-nx-ny+i+j+2;    break;
+               case 4:  k = i+j+nz-1-step;       break;
+               case 5:  k = nx+nz-i+j-step-2;    break;
+               case 6:  k = ny+nz+i-j-step-2;    break;
+               default: k = nx+ny+nz-i-j-step-3; break;
+            }
+            if (k<0 || k>=nz) continue;   
+            aux.Append(i); aux.Append(j); aux.Append(k); 
+         }
+      }
+      break;
+   }
+
+   int nrows = aux.Size()/dim;
+   int ncols = dim;
+
+   subdomains.SetSize(nrows,ncols);
+   for (int r=0;r<nrows; r++)
+   {
+      for (int c=0; c<ncols; c++)
+      {
+         int k = r*ncols + c;
+         subdomains[r][c] = aux[k];
+      }
+   }
+}
+
+
+void ParDST::TransferSources(int sweep, const Array<int> & subdomain_ids) const
+{
+   OvlpSol.resize(nrsubdomains);
+   int nrneighbors = pow(3,dim);
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      if (myid == SubdomainRank[ip])
+      {
+         OvlpSol[ip].resize(nrneighbors);
+      }
+   }
+   int m = subdomain_ids.Size();
+   Array<Vector *> x(m);
+   for (int i = 0; i<m; i++)
+   {
+      x[i] = nullptr;
+      int ip = subdomain_ids[i];
+      if (myid != SubdomainRank[ip]) continue;
+      x[i] = new Vector(subdomain_sol[ip]->GetData(),subdomain_sol[ip]->Size());
+   }
+   dmaps->TransferToNeighbors(subdomain_ids,x,OvlpSol);
+   for (int i = 0; i<m; i++)
+   {
+      delete x[i]; x[i] = nullptr;
+   }
+   // Update residuals
+//   Find all neighbors of patch ip0
+   for (int is = 0; is<m; is++)
+   {
+      int ip0 = subdomain_ids[is];
+      Array<int> ijk;
+      Array<int> ijk1(3);
+      GetSubdomainijk(ip0,nxyz,ijk);
+      Array<int> directions(3);   
+      for (int i=-1; i<2; i++)
+      {
+         int i1 = ijk[0] + i;
+         if (i1 <0 || i1>=nx) continue;
+         directions[0] = i;
+         ijk1[0] = i1;
+         for (int j=-1; j<2; j++)
+         {
+            int j1 = ijk[1] + j;
+            if (j1 <0 || j1>=ny) continue;
+            directions[1] = j;
+            ijk1[1] = j1;
+            int kbeg = (dim == 2) ? 0 : -1;
+            int kend = (dim == 2) ? 1 :  2;
+            for (int k=kbeg; k<kend; k++)
+            {
+               int k1 = ijk[2] + k;
+               if (k1 <0 || k1>=nz) continue;
+               directions[2] = (dim == 3) ? k : -1 ;
+               if (i==0 && j==0 && k==0) continue;
+
+               int l = GetSweepToTransfer(sweep,directions);
+               if (l == -1) continue;
+               ijk1[2] = k1;
+               int ip1 = GetSubdomainId(nxyz,ijk1);
+
+               if (myid != SubdomainRank[ip1]) continue;
+               Array<int>directions1(3); directions1 = -1;
+               for (int i = 0; i<dim; i++) directions1[i] = -directions[i];
+               int dir = GetDirectionId(directions1);
+               int n = dmaps->fes[ip1]->GetTrueVSize();
+               Vector res(2*n);
+               PmlMat[ip1]->Mult(*OvlpSol[ip1][dir],res);
+
+               Array2D<int> direct(dim,2); direct = 0;
+               for (int d = 0; d<dim; d++)
+               {
+                  if (directions[d]==1)  direct[d][0] = 1;
+                  if (directions[d]==-1) direct[d][1] = 1;
+               }   
+               GetChiRes(res,ip1,direct);
+               *f_transf[ip1][l] -= res;
+            }
+         }  
+      }
+   }
+
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      if (myid == SubdomainRank[ip])
+      {
+         for (int i = 0; i<nrneighbors; i++)
+         {
+            if (OvlpSol[ip][i])
+            {
+               delete OvlpSol[ip][i];
+            }
+         }
+         OvlpSol[ip].clear();
+      }
+   }
+}
+
+int ParDST::GetSweepToTransfer(const int s, Array<int> directions) const
+{
+   int l1=-1;
+   int nsweeps = sweeps->nsweeps;
+   Array<int> sweep0;   
+   sweeps->GetSweep(s,sweep0);
+   switch (dim)
+   {
+      case 2:
+      for (int l=s; l<nsweeps; l++)
+      {
+         // Rule 1: the transfer source direction has to be similar with 
+         // the sweep direction
+         Array<int> sweep1;   
+         sweeps->GetSweep(l,sweep1);
+         int ddot = 0;
+         for (int d=0; d<dim; d++) ddot+= sweep1[d] * directions[d];
+         if (ddot <= 0) continue;
+
+         // Rule 2: The horizontal or vertical transfer source cannot be used
+         // Case of horizontal or vertical transfer source 
+         // (it can't be both 0 cause it's skipped)
+         if (directions[0]==0 || directions[1] == 0) 
+         {
+            if (sweep0[0] == -sweep1[0] && sweep0[1] == -sweep1[1]) continue;
+         }
+         l1 = l;
+         break;
+      }
+      break;
+      default:
+      for (int l=s; l<nsweeps; l++)
+      {
+         // Rule 1: (similar directions) the transfer source direction has to be similar with 
+         // the sweep direction
+         Array<int> sweep1;   
+         sweeps->GetSweep(l,sweep1);
+         int ddot = 0;
+         bool similar = true;
+         for (int d=0; d<dim; d++) 
+         {
+            if (sweep1[d] * directions[d] < 0) similar = false;
+            ddot+= sweep1[d] * directions[d];
+         }
+         if (!similar || ddot<=0) continue; // not similar
+
+         // Rule 2: (oposite directions) the transfer source direction has to be similar with 
+         // the sweep direction
+         // 
+         // check any of the projections onto the planes
+         // (xy, xz, yz)
+
+         if ( (directions[0]==0 && directions[1] != 0) || 
+              (directions[0]!=0 && directions[1] == 0) ||
+              (directions[0]==0 && directions[2] != 0) || 
+              (directions[0]!=0 && directions[2] == 0) ||
+              (directions[2]==0 && directions[1] != 0) || 
+              (directions[2]!=0 && directions[1] == 0) ) 
+         {
+            if (sweep0[0] == -sweep1[0] && 
+                sweep0[1] == -sweep1[1] && 
+                sweep0[2] == -sweep1[2]) continue;
+         }
+         l1 = l;
+         break;
+      }
+      break;
+   }
+
+   return l1;   
+}
+
+void ParDST::CorrectOrientation(int ip,Vector &x) const
+{
+   FiniteElementSpace * fespace = dmaps->fes[ip];
+   Mesh * mesh = fespace->GetMesh();
+   int nrelems = mesh->GetNE();
+   // GridFunction test; 
+   // test.SetFromTrueDofs(x)
+   Array<int> signs(fespace->GetTrueVSize()); signs = 0;
+   for (int iel=0; iel<nrelems; iel++)
+   {
+      Array<int> ElemDofs;
+      fespace->GetElementDofs(iel,ElemDofs);
+      int ndofs = ElemDofs.Size();
+      ElemDofs.Print();
+      for (int i = 0; i< ndofs; i++)
+      {
+         int pdof_ = ElemDofs[i];
+         if (pdof_ < 0) 
+         {
+            signs[abs(pdof_)-1] += 1.0 ; 
+         }
+         else
+         {
+            signs[pdof_] -= 1.0 ; 
+         }
+      }
+   }
+
+   cout << "signs = " ; signs.Print();
+   for (int i = 0; i<fespace->GetTrueVSize(); i++)
+   {
+      if (signs[i]<0) 
+      {
+         x(i) *= -1.0;
+         x(i+fespace->GetTrueVSize()) *= -1.0;
+      }
+   }
+}
+
+
+ParDST::~ParDST()
+{
+
+   for (int ip=0; ip<nrsubdomains; ip++)
+   {
+      delete Optr[ip];
+      delete subdomain_sol[ip];
+      delete PmlMatInv[ip];
+      delete sqf[ip];
+      if (myid != SubdomainRank[ip]) continue;
+      for (int i=0;i<sweeps->nsweeps; i++)
+      {
+         delete f_transf[ip][i];
+      }
+      delete f_orig[ip];
+   }
+   f_orig.DeleteAll();
+   delete dmaps;
+   delete sweeps;
+   delete part;
+
+}
@@ -0,0 +1,70 @@
+#pragma once
+#include "../common/Utilities.hpp"
+#include "../common/PML.hpp"
+#include "DofMapsDST.hpp"
+using namespace std;
+using namespace mfem;
+
+
+class ParDST : public Solver//
+{
+private:
+   MPI_Comm comm = MPI_COMM_WORLD;
+   int num_procs, myid;
+   // Constructor inputs
+   int prob_kind;
+   ParSesquilinearForm *bf=nullptr;
+   ParFiniteElementSpace * pfes = nullptr;
+   ParMesh * pmesh = nullptr;
+   ParMeshPartition * part = nullptr;
+   Array<int> SubdomainRank;
+   Array<int> RankSubdomains;
+   const FiniteElementCollection * fec = nullptr;
+   Array2D<double> Pmllength;
+   int dim = 2;
+   double omega = 0.5;
+   Coefficient * Q=nullptr;
+   VectorCoefficient * VQ=nullptr;
+   MatrixCoefficient * MQ=nullptr;
+   int nrlayers;
+   int ovlpnrlayers;
+   int nrsubdomains = 0;
+   int nx,ny,nz;
+   Array<int> nxyz;
+   Sweep * sweeps = nullptr;
+   DofMaps * dmaps = nullptr;
+   Array< SesquilinearForm * > sqf;
+   Array< OperatorPtr * > Optr;
+   Array<ComplexSparseMatrix *> PmlMat;
+   Array<ComplexUMFPackSolver *> PmlMatInv;
+//    Array<ComplexMUMPSSolver *> PmlMatInv;
+   mutable Array<Vector *> f_orig;
+   mutable Array<Array<Vector * >> f_transf;
+   mutable Array<Vector * > subdomain_sol;
+   mutable std::vector<std::vector<Vector * >> OvlpSol;
+   void SetupSubdomainProblems();
+   std::vector<std::vector<Array<int>>> NovlpElems;
+   std::vector<std::vector<Array<int>>> NovlpDofs;
+   void MarkSubdomainOverlapDofs(const bool comp = false);
+   void SetHelmholtzPmlSystemMatrix(int ip);   
+   void SetMaxwellPmlSystemMatrix(int ip);
+   void GetChiRes(Vector & res, int ip, Array2D<int> direct) const;
+   void PlotLocal(Vector & sol, socketstream & sol_sock, int ip) const;
+   void GetStepSubdomains(const int sweep, const int step, Array2D<int> & subdomains) const;
+   void TransferSources(int sweep, const Array<int> & subdomain_ids) const;
+   int GetSweepToTransfer(const int s, Array<int> directions) const;
+   void CorrectOrientation(int ip, Vector & x) const;
+   void Init();
+public:
+   ParDST(ParSesquilinearForm * bf_, Array2D<double> & Pmllength_, 
+       double omega_, Coefficient * Q_, int nrlayers_, int nx_=2, int ny_=2, int nz_=2);
+   ParDST(ParSesquilinearForm * bf_, Array2D<double> & Pmllength_, 
+       double omega_, VectorCoefficient * VQ_, int nrlayers_, int nx_=2, int ny_=2, int nz_=2);
+   ParDST(ParSesquilinearForm * bf_, Array2D<double> & Pmllength_, 
+       double omega_, MatrixCoefficient * MQ_, int nrlayers_, int nx_=2, int ny_=2, int nz_=2);              
+   virtual void SetOperator(const Operator &op) {}
+   virtual void Mult(const Vector &r, Vector &z) const;
+   virtual ~ParDST();
+};
+
+
@@ -0,0 +1,151 @@
+#pragma once
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+using namespace std;
+using namespace mfem;
+
+
+struct UniqueIndexGenerator
+{
+   int counter = 0;
+   std::unordered_map<int,int> idx;
+   int Get(int i)
+   {
+      std::unordered_map<int,int>::iterator f = idx.find(i);
+      if (f == idx.end())
+      {
+         idx[i] = counter;
+         return counter++;
+      }
+      else
+      {
+         return (*f).second;
+      }
+   }
+   void Reset()
+   {
+      counter = 0;
+      idx.clear();
+   }
+};
+
+
+double GetUniformMeshElementSize(Mesh * mesh);
+Mesh * ExtendMesh(Mesh * mesh, const Array<int> & directions);
+
+class CartesianMeshPartition 
+{
+private:
+   Mesh *mesh=nullptr;
+public:
+   int nrpatch;
+   int nxyz[3];
+   double MeshSize;
+   std::vector<Array<int>> element_map;
+   Array3D<int>subdomains;
+   // constructor
+   CartesianMeshPartition(Mesh * mesh_,int & nx, int & ny, int & nz);
+   ~CartesianMeshPartition() {};
+};
+
+class OverlappingCartesianMeshPartition 
+{
+private:
+   Mesh *mesh=nullptr;
+public:
+   int nrpatch;
+   double MeshSize;
+   int nxyz[3];
+   std::vector<Array<int>> element_map;
+   Array3D<int> subdomains;
+   // constructor
+   OverlappingCartesianMeshPartition(Mesh * mesh_,int & nx, int & ny, int & nz);
+   OverlappingCartesianMeshPartition(Mesh * mesh_,int & nx, int & ny, int & nz, int ovlp_nlayers);
+   ~OverlappingCartesianMeshPartition() {};
+};
+
+class STPOverlappingCartesianMeshPartition // Special layered partition for STP
+{
+private:
+   Mesh *mesh=nullptr;
+public:
+   int nrpatch;
+   int nx, ny, nz;
+   std::vector<Array<int>> element_map;
+   // constructor
+   STPOverlappingCartesianMeshPartition(Mesh * mesh_);
+   ~STPOverlappingCartesianMeshPartition() {};
+};
+
+class MeshPartition
+{
+private:
+   Mesh *mesh=nullptr;
+   void AddElementToMesh(Mesh * mesh,mfem::Element::Type elem_type,int * ind);
+   void GetNumVertices(int type, mfem::Element::Type & elem_type, int & nrvert);
+   void PrintElementMap();
+public:
+   int nrpatch;
+   double MeshSize;
+   std::vector<Array<int>> element_map;
+   Array3D<int> subdomains;
+   Array<Mesh *> patch_mesh;
+   int partition_kind;
+   int nxyz[3];
+   // constructor
+   MeshPartition(Mesh * mesh_, int part, int mx=1, int my=1, int mz=1, int ovl_nlayers=0);
+   ~MeshPartition();
+};
+
+void SaveMeshPartition(Array<Mesh * > meshes, 
+                       string mfilename="output/mesh.",
+                       string sfilename="output/sol.");
+
+
+#ifdef MFEM_USE_MPI
+
+class CartesianParMeshPartition 
+{
+private:
+   ParMesh *pmesh=nullptr;
+public:
+   int nrsubdomains;
+   int nxyz[3];
+   double MeshSize;
+   std::vector<Array<int>> local_element_map;
+   Array<int> subdomain_rank;
+   Array3D<int>subdomains;
+   // constructor
+   CartesianParMeshPartition(ParMesh * pmesh_,int & nx, int & ny, int & nz, 
+                             int ovlp_nlayers);
+   ~CartesianParMeshPartition() {};
+};
+
+class ParMeshPartition
+{
+private:
+   MPI_Comm comm;
+   ParMesh *pmesh=nullptr;
+   void AddElementToMesh(Mesh * mesh,mfem::Element::Type elem_type,int * ind);
+   void GetNumVertices(int type, mfem::Element::Type & elem_type, int & nrvert);
+   void PrintElementMap();
+public:
+   int nrsubdomains;
+   int OvlpNlayers;
+   int myelem_offset = 0;
+   double MeshSize;
+   std::vector<Array<int>> element_map;
+   std::vector<Array<int>> local_element_map;
+   Array3D<int> subdomains;
+   Array<Mesh *> subdomain_mesh;
+   Array<int> subdomain_rank;
+   int partition_kind;
+   int nxyz[3];
+   // constructor
+   ParMeshPartition(ParMesh * pmesh_, int mx=1, int my=1, int mz=1, int ovl_nlayers=0);
+   void SaveMeshPartition();
+   ~ParMeshPartition();
+};
+
+#endif
@@ -0,0 +1,570 @@
+#include "PML.hpp"
+
+CartesianPML::CartesianPML(Mesh *mesh_, Array2D<double> length_)
+   : mesh(mesh_), length(length_)
+{
+   dim = mesh->Dimension();
+   SetBoundaries();
+}
+
+void CartesianPML::SetBoundaries()
+{
+   comp_dom_bdr.SetSize(dim, 2);
+   dom_bdr.SetSize(dim, 2);
+   // initialize
+   for (int i = 0; i < dim; i++)
+   {
+      dom_bdr(i, 0) = infinity();
+      dom_bdr(i, 1) = -infinity();
+   }
+
+   for (int i = 0; i < mesh->GetNBE(); i++)
+   {
+      Array<int> bdr_vertices;
+      mesh->GetBdrElementVertices(i, bdr_vertices);
+      for (int j = 0; j < bdr_vertices.Size(); j++)
+      {
+         for (int k = 0; k < dim; k++)
+         {
+            dom_bdr(k, 0) = min(dom_bdr(k, 0), mesh->GetVertex(bdr_vertices[j])[k]);
+            dom_bdr(k, 1) = max(dom_bdr(k, 1), mesh->GetVertex(bdr_vertices[j])[k]);
+         }
+      }
+   }
+
+#ifdef MFEM_USE_MPI
+   ParMesh * pmesh = dynamic_cast<ParMesh *>(mesh);
+   if (pmesh)
+   {
+      for (int d=0; d<dim; d++)
+      {
+         MPI_Allreduce(MPI_IN_PLACE,&dom_bdr(d,0),1,MPI_DOUBLE,MPI_MIN,pmesh->GetComm());
+         MPI_Allreduce(MPI_IN_PLACE,&dom_bdr(d,1),1,MPI_DOUBLE,MPI_MAX,pmesh->GetComm());
+      }
+   }
+#endif
+
+   for (int i = 0; i < dim; i++)
+   {
+      comp_dom_bdr(i, 0) = dom_bdr(i, 0) + length(i, 0);
+      comp_dom_bdr(i, 1) = dom_bdr(i, 1) - length(i, 1);
+   }
+}
+
+void CartesianPML::SetAttributes(Mesh *mesh_)
+{
+   int nrelem = mesh_->GetNE();
+   elems.SetSize(nrelem);
+
+   for (int i = 0; i < nrelem; ++i)
+   {
+      elems[i] = 1;
+      bool in_pml = false;
+      Element *el = mesh_->GetElement(i);
+      Array<int> vertices;
+      // Initialize Attribute
+      el->SetAttribute(1);
+      el->GetVertices(vertices);
+      int nrvert = vertices.Size();
+      // Check if any vertex is in the pml
+      for (int iv = 0; iv < nrvert; ++iv)
+      {
+         int vert_idx = vertices[iv];
+         double *coords = mesh_->GetVertex(vert_idx);
+         for (int comp = 0; comp < dim; ++comp)
+         {
+            if (coords[comp] > comp_dom_bdr(comp, 1) ||
+                coords[comp] < comp_dom_bdr(comp, 0))
+            {
+               in_pml = true;
+               break;
+            }
+         }
+      }
+      if (in_pml)
+      {
+         elems[i] = 0;
+         el->SetAttribute(2);
+      }
+   }
+   mesh_->SetAttributes();
+}
+
+void CartesianPML::StretchFunction(const Vector &x,
+                                   vector<complex<double>> &dxs, double omega)
+{
+   complex<double> zi = complex<double>(0., 1.);
+
+   double n = 2.0;
+   double c = 10.0;
+   // double c = log(omega);
+   double coeff;
+   // Stretch in each direction independently
+   for (int i = 0; i < dim; ++i)
+   {
+      dxs[i] = 1.0;
+      if (x(i) >= comp_dom_bdr(i, 1))
+      {
+         coeff = n * c / omega / pow(length(i, 1), n);
+         dxs[i] = 1.0 + zi * coeff * abs(pow(x(i) - comp_dom_bdr(i, 1), n - 1.0));
+      }
+      if (x(i) <= comp_dom_bdr(i, 0))
+      {
+         coeff = n * c / omega / pow(length(i, 0), n);
+         dxs[i] = 1.0 + zi * coeff * abs(pow(x(i) - comp_dom_bdr(i, 0), n - 1.0));
+      }
+   }
+}
+
+ToroidPML::ToroidPML(Mesh *mesh_)
+   : mesh(mesh_)
+{
+   dim = mesh->Dimension();
+   zlim.SetSize(2);
+   rlim.SetSize(2);
+   alim.SetSize(2);
+   zpml_thickness.SetSize(2);
+   rpml_thickness.SetSize(2);
+   apml_thickness.SetSize(2);
+   SetBoundaries();
+}
+
+void ToroidPML::SetBoundaries()
+{
+   mesh->EnsureNodes();
+   int nrnodes = mesh->GetNodalFESpace()->GetTrueVSize()/dim;
+   double zmin = infinity();
+   double zmax = -infinity();
+   double rmin = infinity();
+   double rmax = -infinity();
+   double amin = infinity(); // in degrees
+   double amax = -infinity(); // in degrees
+   for (int i = 0; i<nrnodes; i++)
+   {
+      Vector coord(dim);
+      mesh->GetNode(i,coord);
+      for (int d = 0; d<dim; d++)
+      {
+         if (abs(coord[d])<1e-13) coord[d] = 0.0;
+      }
+      // Find r and a for this point
+      double x = coord[0];
+      double y = coord[1];
+      double z = 0.0;
+      if (dim == 3) z = coord[2];
+      double a = GetAngle(x,y);
+      double r = sqrt(x*x + y*y);
+      
+      zmin = min(zmin,z);
+      zmax = max(zmax,z);
+      rmin = min(rmin,r);
+      rmax = max(rmax,r);
+      amin = min(amin,a);
+      amax = max(amax,a);
+   }
+
+   zlim[0] = zmin;
+   zlim[1] = zmax;
+   rlim[0] = rmin;
+   rlim[1] = rmax;
+   alim[0] = amin;
+   alim[1] = amax;
+
+
+#ifdef MFEM_USE_MPI
+   ParMesh * pmesh = dynamic_cast<ParMesh *>(mesh);
+   if (pmesh)
+   {
+      MPI_Allreduce(MPI_IN_PLACE,&zlim[0],1,MPI_DOUBLE,MPI_MIN,pmesh->GetComm());
+      MPI_Allreduce(MPI_IN_PLACE,&zlim[1],1,MPI_DOUBLE,MPI_MAX,pmesh->GetComm());
+      MPI_Allreduce(MPI_IN_PLACE,&rlim[0],1,MPI_DOUBLE,MPI_MIN,pmesh->GetComm());
+      MPI_Allreduce(MPI_IN_PLACE,&rlim[1],1,MPI_DOUBLE,MPI_MAX,pmesh->GetComm());
+      MPI_Allreduce(MPI_IN_PLACE,&alim[0],1,MPI_DOUBLE,MPI_MIN,pmesh->GetComm());
+      MPI_Allreduce(MPI_IN_PLACE,&alim[1],1,MPI_DOUBLE,MPI_MAX,pmesh->GetComm());
+   }
+#endif
+}
+
+void ToroidPML::SetAttributes(Mesh *mesh_)
+{
+   int nrelem = mesh_->GetNE();
+   elems.SetSize(nrelem);
+
+   // Loop through the elements and identify which of them are in the PML
+   for (int i = 0; i < nrelem; ++i)
+   {
+      // initialize with 1
+      elems[i] = 1;
+      Element *el = mesh_->GetElement(i);
+      // Initialize attribute
+      el->SetAttribute(1);
+
+      Array<int> vertices;
+      el->GetVertices(vertices);
+      int nrvert = vertices.Size();
+      // Check if any vertex is in the pml
+      bool in_pml = false;
+      for (int iv = 0; iv < nrvert; ++iv)
+      {
+         int vert_idx = vertices[iv];
+         double *coords = mesh_->GetVertex(vert_idx);
+         double x = coords[0];
+         double y = coords[1];
+         double a = GetAngle(x,y);
+         double r = sqrt(x*x + y*y);
+
+         if (astretch)
+         {
+            if ( (a <= alim[0]+apml_thickness[0]) ||
+                 (a >= alim[1]-apml_thickness[1]) )
+            {
+               in_pml = true;
+               break;  
+            }
+         }
+
+         if (rstretch)
+         {
+            if ( (r <= rlim[0]+rpml_thickness[0]) ||
+                 (r >= rlim[1]-rpml_thickness[1]) )
+            {
+               in_pml = true;
+               break;  
+            }
+         }
+      }
+      if (in_pml)
+      {
+         elems[i] = 0;
+         el->SetAttribute(2);
+      }
+
+      // Vector center;
+      // mesh_->GetElementCenter(i,center);
+      // double x = center[0];
+      // double y = center[1];
+      // double a = GetAngle(x,y);
+      // double r = sqrt(x*x + y*y);
+      // // check upper and lower bound
+      // if (astretch)
+      // {
+      //    if ( (a <= alim[0]+apml_thickness[0]) ||
+      //      (a >= alim[1]-apml_thickness[1]) )
+      //    {
+      //       elems[i] = 0;
+      //       el->SetAttribute(2);
+      //    }
+      // }
+      // if (rstretch)
+      // {
+      //    if ( (r <= rlim[0]+rpml_thickness[0]) ||
+      //         (r >= rlim[1]-rpml_thickness[1]) )
+      //    {
+      //       elems[i] = 0;
+      //       el->SetAttribute(2);
+      //    }
+      // }
+   }
+   mesh_->SetAttributes();
+}
+
+
+double ToroidPML::GetAngle(const double x, const double y)
+{
+   // Find r and a for this point
+   double arad;
+   if (x == 0.0)
+   {
+      arad = (y > 0.0)? M_PI/2.0 : 3.0 * M_PI/2.0;
+   }
+   else
+   {
+      arad = atan(y/x);
+      int k = 0;
+      if (x<0)
+      {
+         k = 1;
+      }
+      else if (y<0)
+      {
+         k = 2;
+      }
+      arad += k*M_PI;
+   }
+   return arad * 180.0/M_PI;
+}
+
+// void ToroidPML::StretchFunction(const Vector &X,
+//                                    vector<complex<double>> &dxs, double omega)
+void ToroidPML::StretchFunction(const Vector &X, ComplexDenseMatrix & J, double omega)
+
+{
+   complex<double> zi = complex<double>(0., 1.);
+
+   double n = 2.0;
+   double c = 10.0;
+   // double c = log(omega);
+   // Stretch in the azimuthal direction
+   double x = X[0];
+   double y = X[1];
+   if (abs(x) < 1e-12) x = 0.0;
+   if (abs(y) < 1e-12) y = 0.0;
+   double a = GetAngle(x,y);
+   double r = sqrt(x*x + y*y);
+   // dxs[0] = 1.0;
+   // dxs[1] = 1.0;
+   J = 0.0;
+   J(0,0) = 1.0;
+   J(1,1) = 1.0;
+   if (dim == 3) J(2,2) = 1.0;
+
+   if (astretch)
+   {
+      double th = a * M_PI/180.0;
+      double thl, thL, thH;
+      bool in_pml = false;
+      // negative direction 
+      if (a <= alim[0]+apml_thickness[0])
+      {
+         in_pml = true;
+         thL = alim[1] * M_PI/180.0;
+         thH = apml_thickness[1] * M_PI/180.0;
+         thl = thL + thH;
+      }
+      // positive direction 
+      if (a >= alim[1]-apml_thickness[1])
+      {
+         in_pml = true;
+         thL = alim[1] * M_PI/180.0;
+         thH = apml_thickness[1] * M_PI/180.0;
+         thl = thL - thH;
+      }
+      // double c1 = min(20.0*M_PI/180.0,thH);
+      if (in_pml)
+      {
+         double c1 = thH;
+         double coeff = n * c / omega / pow(c1,n);
+         double f_th = pow(th - thl,n-1);
+         double th_x = - y / (r * r);
+         double th_y =   x / (r * r);
+
+         J(0,0) = 1.0 + zi * coeff * abs(f_th * th_x);
+         J(0,1) = zi * f_th * th_y;
+         J(1,0) = zi * f_th * th_x;
+         J(1,1) = 1.0 + zi * coeff * abs(f_th * th_y);
+      }
+   }
+   // Stretch in the radial direction
+   if (rstretch)
+   {  // negative
+      double rl, rL, rH;
+      bool in_pml = false;
+      if (r <= rlim[0]+rpml_thickness[0])
+      {
+         in_pml = true;
+         rL = rlim[0];     
+         rH = rpml_thickness[0];
+         rl = rL + rH;
+      }
+      // positive direction 
+      if (r >= rlim[1]-rpml_thickness[1])
+      {
+         in_pml = true;
+         rL = rlim[1];     
+         rH = rpml_thickness[1];
+         rl = rL - rH;
+      }
+
+      if (in_pml)
+      {
+         double coeff = n * c / omega / pow (rH,n);
+         double f_r =  pow(r-rl,n-1.0);
+         double r_x = x / r;
+         double r_y = y / r;
+
+         J(0,0) = 1.0 + zi * coeff * abs(f_r*r_x);
+         J(0,1) = zi * f_r * r_y;
+         J(1,0) = zi * f_r * r_x;
+         J(1,1) = 1.0 + zi * coeff * abs(f_r*r_y);
+      }
+   }
+}
+
+double pml_detJ_Re(const Vector & x, CartesianPML * pml)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   std::vector<std::complex<double>> dxs(dim);
+   complex<double> det(1.0,0.0);
+   pml->StretchFunction(x, dxs, omega);
+   for (int i=0; i<dim; ++i) det *= dxs[i];
+   return det.real();
+}
+
+double pml_detJ_Im(const Vector & x, CartesianPML * pml)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   std::vector<std::complex<double>> dxs(dim);
+   complex<double> det(1.0,0.0);
+   pml->StretchFunction(x, dxs, omega);
+   for (int i=0; i<dim; ++i) det *= dxs[i];
+   return det.imag();
+}
+
+void pml_detJ_JT_J_inv_Re(const Vector & x, CartesianPML * pml , DenseMatrix & M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   std::vector<std::complex<double>> dxs(dim);
+   complex<double> det(1.0,0.0);
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i<dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   M=0.0;
+   for (int i = 0; i<dim; ++i)
+   {
+      M(i,i) = (det / pow(dxs[i],2)).real();
+   }
+}
+
+void pml_detJ_JT_J_inv_Im(const Vector & x, CartesianPML * pml , DenseMatrix & M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+
+   std::vector<std::complex<double>> dxs(dim);
+   complex<double> det = 1.0;
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i<dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   M=0.0;
+   for (int i = 0; i<dim; ++i)
+   {
+      M(i,i) = (det / pow(dxs[i],2)).imag();
+   }
+}
+
+
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   vector<complex<double>> dxs(dim);
+   complex<double> det(1.0, 0.0);
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i < dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   M = 0.0;
+   for (int i = 0; i < dim; ++i)
+   {
+      M(i, i) = (det / pow(dxs[i], 2)).real();
+   }
+}
+
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   vector<complex<double>> dxs(dim);
+   complex<double> det = 1.0;
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i < dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   M = 0.0;
+   for (int i = 0; i < dim; ++i)
+   {
+      M(i, i) = (det / pow(dxs[i], 2)).imag();
+   }
+}
+
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   vector<complex<double>> dxs(dim);
+   complex<double> det = 1.0;
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i < dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   M = 0.0;
+   for (int i = 0; i < dim; ++i)
+   {
+      M(i, i) = abs(det / pow(dxs[i], 2));
+   }
+}
+
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   vector<complex<double>> dxs(dim);
+   complex<double> det(1.0, 0.0);
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i < dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   // in the 2D case the coefficient is scalar 1/det(J)
+   if (dim == 2)
+   {
+      M = (1.0 / det).real();
+   }
+   else
+   {
+      M = 0.0;
+      for (int i = 0; i < dim; ++i)
+      {
+         M(i, i) = (pow(dxs[i], 2) / det).real();
+      }
+   }
+}
+
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+{
+   int dim = pml->dim;
+   double omega = pml->omega;
+   vector<complex<double>> dxs(dim);
+   complex<double> det = 1.0;
+   pml->StretchFunction(x, dxs, omega);
+
+   for (int i = 0; i < dim; ++i)
+   {
+      det *= dxs[i];
+   }
+
+   if (dim == 2)
+   {
+      M = (1.0 / det).imag();
+   }
+   else
+   {
+      M = 0.0;
+      for (int i = 0; i < dim; ++i)
+      {
+         M(i, i) = (pow(dxs[i], 2) / det).imag();
+      }
+   }
+}
@@ -0,0 +1,179 @@
+#pragma once
+#include "mfem.hpp"
+#include "complex_linalg.hpp"
+#include <fstream>
+#include <iostream>
+using namespace std;
+using namespace mfem;
+
+
+// Class for setting up a simple Cartesian PML region
+class CartesianPML
+{
+private:
+   Mesh *mesh;
+
+   // Length of the PML Region in each direction
+   Array2D<double> length;
+
+   // Computational Domain Boundary
+   Array2D<double> comp_dom_bdr;
+
+   // Domain Boundary
+   Array2D<double> dom_bdr;
+
+   // Integer Array identifying elements in the pml
+   // 0: in the pml, 1: not in the pml
+   Array<int> elems;
+
+   // Compute Domain and Computational Domain Boundaries
+   void SetBoundaries();
+
+public:
+   // Constructor
+   CartesianPML(Mesh *mesh_,Array2D<double> length_);
+
+   int dim;
+   double omega;
+   // Return Computational Domain Boundary
+   Array2D<double> GetCompDomainBdr() {return comp_dom_bdr;}
+
+   // Return Domain Boundary
+   Array2D<double> GetDomainBdr() {return dom_bdr;}
+
+   // Return Marker list for elements
+   Array<int> * GetMarkedPMLElements() {return &elems;}
+
+   // Mark element in the PML region
+   void SetAttributes(Mesh *mesh_);
+
+   void SetOmega(double omega_) {omega = omega_;}
+
+   // PML complex stretching function
+   void StretchFunction(const Vector &x, vector<complex<double>> &dxs, double omega);
+};
+
+class ToroidPML
+{
+private:
+   Mesh *mesh;
+
+   Vector zlim, zpml_thickness; // range in axial direction
+   Vector rlim, rpml_thickness; // range in radial direction
+   Vector alim, apml_thickness; // range in azimuthal direction
+
+   // Integer Array identifying elements in the pml
+   // 0: in the pml, 1: not in the pml
+   Array<int> elems;
+
+   double GetAngle(const double x, const double y);
+
+   // Compute Domain and Computational Domain Boundaries
+   void SetBoundaries();
+
+   bool zstretch = false;
+   bool rstretch = false;
+   bool astretch = false;
+
+public:
+   // Constructor
+   ToroidPML(Mesh *mesh_);
+
+   int dim;
+   double omega;
+   // Return Computational Domain Boundary
+
+   // Return Domain Boundary
+   void GetDomainBdrs(Vector & zlim_, Vector & rlim_, Vector & alim_)
+   {
+      zlim_.SetSize(2); zlim_ = zlim;
+      rlim_.SetSize(2); rlim_ = rlim;
+      alim_.SetSize(2); alim_ = alim;
+   }
+
+   void SetPmlWidth(const Vector & zpml, const Vector & rpml, const Vector & apml)
+   {
+      MFEM_VERIFY(zpml.Size() == 2 , "Check zpml size");
+      MFEM_VERIFY(rpml.Size() == 2 , "Check rpml size");
+      MFEM_VERIFY(apml.Size() == 2 , "Check apml size");
+      zpml_thickness = zpml;
+      rpml_thickness = rpml;
+      apml_thickness = apml;
+   }
+
+   void SetPmlAxes(const bool zstretch_, 
+                   const bool rstretch_, 
+                   const bool astretch_ )
+   {
+      zstretch = zstretch_;
+      rstretch = rstretch_;
+      astretch = astretch_;
+   }
+
+   // // Return Marker list for elements
+   Array<int> * GetMarkedPMLElements() {return &elems;}
+
+   // Mark element in the PML region
+   void SetAttributes(Mesh *mesh_);
+
+   void SetOmega(double omega_) {omega = omega_;}
+
+   // PML complex stretching function
+   // void StretchFunction(const Vector &X, vector<complex<double>> &dxs, double omega);
+   void StretchFunction(const Vector &X, ComplexDenseMatrix & J, double omega);
+};
+
+class PmlCoefficient : public Coefficient
+{
+private:
+   CartesianPML * pml = nullptr;
+   double (*Function)(const Vector &, CartesianPML * );
+public:
+   PmlCoefficient(double (*F)(const Vector &, CartesianPML *), CartesianPML * pml_)
+      : pml(pml_), Function(F)
+   {}
+   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   {
+      double x[3];
+      Vector transip(x, 3);
+      T.Transform(ip, transip);
+      return ((*Function)(transip, pml));
+   }
+};
+
+
+// This includes scalar coefficients
+class PmlMatrixCoefficient : public MatrixCoefficient
+{
+private:
+   CartesianPML * pml = nullptr;
+   void (*Function)(const Vector &, CartesianPML * , DenseMatrix &);
+public:
+   PmlMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
+                                          DenseMatrix &),
+                        CartesianPML * pml_)
+      : MatrixCoefficient(dim), pml(pml_), Function(F)
+   {}
+   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+                     const IntegrationPoint &ip)
+   {
+      double x[3];
+      Vector transip(x, 3);
+      T.Transform(ip, transip);
+      K.SetSize(height, width);
+      (*Function)(transip, pml, K);
+   }
+};
+
+// Helmholtz pml Functions
+double pml_detJ_Re(const Vector & x, CartesianPML * pml);
+double pml_detJ_Im(const Vector & x, CartesianPML * pml);
+void pml_detJ_JT_J_inv_Re(const Vector & x, CartesianPML * pml , DenseMatrix & M);
+void pml_detJ_JT_J_inv_Im(const Vector & x, CartesianPML * pml , DenseMatrix & M);
+
+// Maxwell Pml functions
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
@@ -0,0 +1,619 @@
+#include "Utilities.hpp"
+
+Sweep::Sweep(int dim_) : dim(dim_)
+{
+   nsweeps = pow(2,dim);
+   sweeps.resize(nsweeps);
+
+   for (int is = 0; is<nsweeps; is++)
+   {
+      sweeps[is].SetSize(dim);
+   }
+
+   switch(dim)
+   {
+      case 1: 
+         sweeps[0][0] =  1; 
+         sweeps[1][0] = -1; 
+         break;
+      case 2: 
+         sweeps[0][0] =  1; sweeps[0][1] =  1; 
+         sweeps[1][0] = -1; sweeps[1][1] =  1; 
+         sweeps[2][0] =  1; sweeps[2][1] = -1; 
+         sweeps[3][0] = -1; sweeps[3][1] = -1;
+         break;
+      default:
+         sweeps[0][0] =  1; sweeps[0][1] =  1; sweeps[0][2] =  1; 
+         sweeps[1][0] = -1; sweeps[1][1] =  1; sweeps[1][2] =  1; 
+         sweeps[2][0] =  1; sweeps[2][1] = -1; sweeps[2][2] =  1; 
+         sweeps[3][0] = -1; sweeps[3][1] = -1; sweeps[3][2] =  1;
+         sweeps[4][0] =  1; sweeps[4][1] =  1; sweeps[4][2] = -1; 
+         sweeps[5][0] = -1; sweeps[5][1] =  1; sweeps[5][2] = -1; 
+         sweeps[6][0] =  1; sweeps[6][1] = -1; sweeps[6][2] = -1; 
+         sweeps[7][0] = -1; sweeps[7][1] = -1; sweeps[7][2] = -1;
+         break;
+   }
+}
+
+Sweep::~Sweep()
+{
+   for (int i = 0; i<nsweeps; i++)
+   {
+      sweeps[i].DeleteAll();
+   }
+}
+
+
+double CutOffFncn(const Vector &x, const Vector & pmin, const Vector & pmax, const Array2D<double> & h_)
+{
+   int dim = pmin.Size();
+   Vector h0(dim);
+   Vector h1(dim);
+   for (int i=0; i<dim; i++)
+   {
+      h0(i) = h_[i][0];
+      h1(i) = h_[i][1];
+   }
+   Vector x0(dim);
+   Vector x1(dim);
+   x0 = pmin; x0+=h0;
+   x1 = pmax; x1-=h1;
+
+   double f = 1.0;
+   for (int i = 0; i<dim; i++)
+   {
+      double val = 1.0;
+      if( x(i) >= pmax(i) || x(i) <= pmin(i))
+      {
+         val = 0.0;
+      }  
+      else if (x(i) < pmax(i) && x(i) >= x1(i))
+      {
+         if(h1(i) != 0.0)
+            // val = (x(i)-pmax(i))/(x1(i)-pmax(i)); 
+            val = pow((x(i)-pmax(i))/(x1(i)-pmax(i)),1.0); 
+      }
+      else if (x(i) > pmin(i) && x(i) <= x0(i))
+      {
+         if (h0(i) != 0.0)
+            // val = (x(i)-pmin(i))/(x0(i)-pmin(i)); 
+            val = pow((x(i)-pmin(i))/(x0(i)-pmin(i)),1.0); 
+      }
+
+      if (h0(i) == 0 && x(i) <= x1(i))
+      {
+         val = 1.0;
+      }
+      if (h1(i) == 0 && x(i) >= x0(i))
+      {
+         val = 1.0;
+      }
+      f *= val;
+   }
+   return f;
+}
+
+double ChiFncn(const Vector &x, const Vector & pmin, const Vector & pmax, const Array2D<double> & h_)
+{
+   int dim = pmin.Size();
+   Vector h0(dim);
+   Vector h1(dim);
+   for (int i=0; i<dim; i++)
+   {
+      h0(i) = h_[i][0];
+      h1(i) = h_[i][1];
+   }
+   Vector x0(dim);
+   Vector x1(dim);
+   x0 = pmin; x0+=h0;
+   x1 = pmax; x1-=h1;
+
+   double f = 1.0;
+   for (int i = 0; i<dim; i++)
+   {
+      double val = 1.0;
+      if( x(i) >= pmax(i) || x(i) <= pmin(i))
+      {
+         val = 0.0;
+      }  
+      else if (x(i) < pmax(i) && x(i) >= x1(i))
+      {
+         if(h1(i) != 0.0)
+            val = (x(i)-pmax(i))/(x1(i)-pmax(i)); 
+            // This function has to be changed to smth more reasonable
+            // val = pow((x(i)-pmax(i))/(x1(i)-pmax(i)),100.0); 
+      }
+      else if (x(i) > pmin(i) && x(i) <= x0(i))
+      {
+         if (h0(i) != 0.0)
+            val = (x(i)-pmin(i))/(x0(i)-pmin(i)); 
+            // val = pow((x(i)-pmin(i))/(x0(i)-pmin(i)),100.0); 
+      }
+
+      if (h0(i) == 0 && x(i) <= x1(i))
+      {
+         val = 1.0;
+      }
+      if (h1(i) == 0 && x(i) >= x0(i))
+      {
+         val = 1.0;
+      }
+      f *= val;
+   }
+   return f;
+}
+
+
+DofMap::DofMap(FiniteElementSpace * fes , MeshPartition * partition) 
+{
+   const FiniteElementCollection * fec = fes->FEColl();
+   nrpatch = partition->nrpatch;
+
+   fespaces.SetSize(nrpatch);
+
+   Dof2GlobalDof.resize(nrpatch);
+
+   for (int ip=0; ip<nrpatch; ++ip)
+   {
+      // create finite element spaces for each patch 
+      fespaces[ip] = new FiniteElementSpace(partition->patch_mesh[ip],fec);
+
+      // construct the patch tdof to global tdof map
+      int nrdof = fespaces[ip]->GetTrueVSize();
+      Dof2GlobalDof[ip].SetSize(2*nrdof);
+
+      // loop through the elements in the patch
+      for (int iel = 0; iel<partition->element_map[ip].Size(); ++iel)
+      {
+         // index in the global mesh
+         int iel_idx = partition->element_map[ip][iel];
+         // get the dofs of this element
+         Array<int> ElemDofs;
+         Array<int> GlobalElemDofs;
+         fespaces[ip]->GetElementDofs(iel,ElemDofs);
+         fes->GetElementDofs(iel_idx,GlobalElemDofs);
+         // the sizes have to match
+         MFEM_VERIFY(ElemDofs.Size() == GlobalElemDofs.Size(),
+                     "Size inconsistency");
+         // loop through the dofs and take into account the signs;
+         int ndof = ElemDofs.Size();
+         for (int i = 0; i<ndof; ++i)
+         {
+            int pdof_ = ElemDofs[i];
+            int gdof_ = GlobalElemDofs[i];
+            int pdof = (pdof_ >= 0) ? pdof_ : abs(pdof_) - 1;
+            int gdof = (gdof_ >= 0) ? gdof_ : abs(gdof_) - 1;
+            Dof2GlobalDof[ip][pdof] = gdof;
+            Dof2GlobalDof[ip][pdof+nrdof] = gdof+fes->GetTrueVSize();
+         }
+      }
+   }
+}
+
+DofMap::DofMap(FiniteElementSpace * fes , MeshPartition * partition, int nrlayers) 
+{
+
+   nx = partition->nxyz[0];
+   ny = partition->nxyz[1];
+   nz = partition->nxyz[2];
+
+   int partition_kind = partition->partition_kind;
+   // Mesh * mesh = fespace->GetMesh();
+   const FiniteElementCollection * fec = fes->FEColl();
+   nrpatch = partition->nrpatch;
+
+   fespaces.SetSize(nrpatch);
+   PmlMeshes.SetSize(nrpatch);
+   // Extend patch meshes to include pml
+
+   for  (int ip = 0; ip<nrpatch; ip++)
+   {
+      int k = ip/(nx*ny);
+      int j = (ip-k*nx*ny)/nx;
+      int i = (ip-k*nx*ny)%nx;
+      
+      Array<int> directions;
+      if (i > 0)
+      {
+         for (int i=0; i<nrlayers; i++)
+         {
+            directions.Append(-1);
+         }
+      }
+      if (j > 0)
+      {
+         for (int i=0; i<nrlayers; i++)
+         {
+            directions.Append(-2);
+         }
+      }
+      if (k > 0)
+      {
+         for (int i=0; i<nrlayers; i++)
+         {
+            directions.Append(-3);
+         }
+      }
+      if (i < nx-1)
+      {
+         for (int i=0; i<nrlayers; i++)
+         {
+            if (partition_kind == 3 || partition_kind == 2) directions.Append(1);
+         }
+      }
+      if (j < ny-1)
+      {
+         for (int i=0; i<nrlayers; i++)
+         {
+            if (partition_kind == 3 || partition_kind == 2) directions.Append(2);
+         }
+      }
+      if (k < nz-1)
+      {
+         for (int i=0; i<nrlayers; i++)
+         {
+            if (partition_kind == 3 || partition_kind == 2) directions.Append(1);
+         }
+      }
+      PmlMeshes[ip] = ExtendMesh(partition->patch_mesh[ip],directions);
+   }
+
+   // Save PML_meshes
+   string meshpath;
+   string solpath;
+   if (partition_kind == 3 || partition_kind == 2) 
+   {
+      meshpath = "output/mesh_ovlp_pml.";
+      solpath = "output/sol_ovlp_pml.";
+   }
+   else if (partition_kind == 4)
+   {
+      meshpath = "output/mesh_novlp_pml.";
+      solpath = "output/sol_novlp_pml.";
+   }
+   else
+   {
+      MFEM_ABORT("This partition kind not supported yet");
+   }
+   
+   // SaveMeshPartition(PmlMeshes, meshpath, solpath);
+
+   PmlFespaces.SetSize(nrpatch);
+   Dof2GlobalDof.resize(nrpatch);
+   Dof2PmlDof.resize(nrpatch);
+
+   for (int ip=0; ip<nrpatch; ++ip)
+   {
+      // create finite element spaces for each patch 
+      fespaces[ip] = new FiniteElementSpace(partition->patch_mesh[ip],fec);
+      PmlFespaces[ip] = new FiniteElementSpace(PmlMeshes[ip],fec);
+
+      // construct the patch tdof to global tdof map
+      int nrdof = fespaces[ip]->GetTrueVSize();
+      Dof2GlobalDof[ip].SetSize(2*nrdof);
+      Dof2PmlDof[ip].SetSize(2*nrdof);
+
+      // build dof maps between patch and extended patch
+      // loop through the patch elements and constract the dof map
+      // The same elements in the extended mesh have the same ordering (but not the dofs)
+
+      // loop through the elements in the patch
+      for (int iel = 0; iel<partition->element_map[ip].Size(); ++iel)
+      {
+         // index in the global mesh
+         int iel_idx = partition->element_map[ip][iel];
+         // get the dofs of this element
+         Array<int> ElemDofs;
+         Array<int> PmlElemDofs;
+         Array<int> GlobalElemDofs;
+         fespaces[ip]->GetElementDofs(iel,ElemDofs);
+         PmlFespaces[ip]->GetElementDofs(iel,PmlElemDofs);
+         fes->GetElementDofs(iel_idx,GlobalElemDofs);
+         // the sizes have to match
+         MFEM_VERIFY(ElemDofs.Size() == GlobalElemDofs.Size(),
+                     "Size inconsistency");
+         MFEM_VERIFY(ElemDofs.Size() == PmlElemDofs.Size(),
+                     "Size inconsistency");            
+         // loop through the dofs and take into account the signs;
+         int ndof = ElemDofs.Size();
+         for (int i = 0; i<ndof; ++i)
+         {
+            int pdof_ = ElemDofs[i];
+            int gdof_ = GlobalElemDofs[i];
+            int pmldof_ = PmlElemDofs[i];
+            int pdof = (pdof_ >= 0) ? pdof_ : abs(pdof_) - 1;
+            int gdof = (gdof_ >= 0) ? gdof_ : abs(gdof_) - 1;
+            int pmldof = (pmldof_ >= 0) ? pmldof_ : abs(pmldof_) - 1;
+
+            Dof2GlobalDof[ip][pdof] = gdof;
+            Dof2GlobalDof[ip][pdof+nrdof] = gdof+fes->GetTrueVSize();
+            Dof2PmlDof[ip][pdof] = pmldof;
+            Dof2PmlDof[ip][pdof+nrdof] = pmldof+PmlFespaces[ip]->GetTrueVSize();
+         }
+      }
+   }
+}
+
+
+LocalDofMap::LocalDofMap(const FiniteElementCollection * fec_, MeshPartition * part1_, 
+               MeshPartition * part2_):fec(fec_), part1(part1_), part2(part2_)
+{
+   // Each overlapping patch has 2 non-overlapping subdomains
+   // Thre are n non-overlapping and and n-1 overlapping subdomains
+   int nrpatch = part2->nrpatch;
+   MFEM_VERIFY(part1->nrpatch-1 == part2->nrpatch, "Check number of subdomains");
+
+   cout << "Constructing local dof maps" << endl; 
+   map1.resize(nrpatch);
+   map2.resize(nrpatch);
+   for (int ip=0; ip<nrpatch; ip++)
+   {
+      // Get the 3 meshes involved
+      Mesh * mesh = part2->patch_mesh[ip];
+      Mesh * mesh1 = part1->patch_mesh[ip];
+      Mesh * mesh2 = part1->patch_mesh[ip+1];
+
+      // Define the fespaces
+      FiniteElementSpace fespace(mesh, fec);
+      FiniteElementSpace fespace1(mesh1, fec);
+      FiniteElementSpace fespace2(mesh2, fec);
+
+      int ndof1 = fespace1.GetTrueVSize();
+      int ndof2 = fespace2.GetTrueVSize();
+
+      map1[ip].SetSize(2*ndof1); // times 2 because it's complex
+      map2[ip].SetSize(2*ndof2); // times 2 because it's complex
+
+      // loop through the elements in the patches
+      // map 1 is constructed by the first half of elements
+      // map 2 is constructed by the second half of elements
+
+      for (int iel = 0; iel<part1->element_map[ip].Size(); ++iel)
+      {
+         // index in the overlapping mesh
+         int iel_idx = iel;
+         Array<int> ElemDofs;
+         Array<int> GlobalElemDofs;
+         fespace1.GetElementDofs(iel,ElemDofs);
+         fespace.GetElementDofs(iel_idx,GlobalElemDofs);
+         // the sizes have to match
+         MFEM_VERIFY(ElemDofs.Size() == GlobalElemDofs.Size(),
+                     "Size inconsistency");
+         // loop through the dofs and take into account the signs;
+         int ndof = ElemDofs.Size();
+         for (int i = 0; i<ndof; ++i)
+         {
+            int pdof_ = ElemDofs[i];
+            int gdof_ = GlobalElemDofs[i];
+            int pdof = (pdof_ >= 0) ? pdof_ : abs(pdof_) - 1;
+            int gdof = (gdof_ >= 0) ? gdof_ : abs(gdof_) - 1;
+            map1[ip][pdof] = gdof;
+            map1[ip][pdof+ndof1] = gdof+fespace.GetTrueVSize();
+         }
+      }
+      for (int iel = 0; iel<part1->element_map[ip+1].Size(); ++iel)
+      {
+         // index in the overlapping mesh
+         int k = part1->element_map[ip].Size();
+         int iel_idx = iel+k;
+         Array<int> ElemDofs;
+         Array<int> GlobalElemDofs;
+         fespace2.GetElementDofs(iel,ElemDofs);
+         fespace.GetElementDofs(iel_idx,GlobalElemDofs);
+         // the sizes have to match
+         MFEM_VERIFY(ElemDofs.Size() == GlobalElemDofs.Size(),
+                     "Size inconsistency");
+         // loop through the dofs and take into account the signs;
+         int ndof = ElemDofs.Size();
+         for (int i = 0; i<ndof; ++i)
+         {
+            int pdof_ = ElemDofs[i];
+            int gdof_ = GlobalElemDofs[i];
+            int pdof = (pdof_ >= 0) ? pdof_ : abs(pdof_) - 1;
+            int gdof = (gdof_ >= 0) ? gdof_ : abs(gdof_) - 1;
+            map2[ip][pdof] = gdof;
+            map2[ip][pdof+ndof2] = gdof+fespace.GetTrueVSize();
+         }
+      }
+   }
+};
+
+
+NeighborDofMaps::NeighborDofMaps(MeshPartition * part_, FiniteElementSpace * fes_,
+                                DofMap * dmap_, 
+                                int ovlp_layers_) : part(part_), fes(fes_), 
+                                dmap(dmap_),
+                                ovlp_layers(ovlp_layers_)
+{
+
+   nrsubdomains = part->nrpatch;
+   nxyz.SetSize(3);
+   mesh = fes->GetMesh();
+   dim = mesh->Dimension();
+   for (int d=0; d<3; d++)  nxyz[d] = part->nxyz[d];
+   MarkOvlpElements();
+   ComputeNeighborDofMaps();
+}
+
+void NeighborDofMaps::MarkOvlpElements()
+{
+   // Lists of elements
+   // x,y,z = +/- 1 ovlp 
+   OvlpElems.resize(nrsubdomains);
+
+   for (int ip = 0; ip<nrsubdomains; ip++)
+   {
+      int i0,j0,k0;
+      Getijk(ip,i0,j0,k0);
+      int ijk[dim]; ijk[0] = i0; ijk[1]=j0;
+      if (dim==3) ijk[2] = k0;
+
+      FiniteElementSpace * sub_fes = dmap->fespaces[ip];
+      Mesh * sub_mesh = sub_fes->GetMesh();
+      // OvlpElems[ip].resize(2*dim);
+      OvlpElems[ip].resize(pow(3,dim)); 
+
+      Vector pmin, pmax;
+      sub_mesh->GetBoundingBox(pmin,pmax);
+      double h = part->MeshSize;
+      // Loop through elements
+      for (int iel=0; iel<sub_mesh->GetNE(); iel++)
+      {
+         // Get element center
+         Vector center(dim);
+         int geom = sub_mesh->GetElementBaseGeometry(iel);
+         ElementTransformation * tr = sub_mesh->GetElementTransformation(iel);
+         tr->Transform(Geometries.GetCenter(geom),center);
+
+         // loop through dimensions   
+         Array<bool> pos(dim); pos = 0;
+         Array<bool> neg(dim); neg = 0;
+
+         for (int d=0;d<dim; d++)
+         {
+            if (ijk[d]>0 && center[d] < pmin[d]+2.0*h*ovlp_layers)
+            {
+               neg[d] = true;
+            }
+
+            if (ijk[d]<nxyz[d]-1 && center[d] > pmax[d]-2.0*h*ovlp_layers) 
+            {
+               pos[d] = true;
+            }
+         }
+         SetElementToOverlap(ip,iel,neg,pos);        
+      }   
+   }
+}
+
+void NeighborDofMaps::ComputeNeighborDofMaps()
+{
+   OvlpDofMaps.resize(nrsubdomains);
+
+   // Array<UniqueIndexGen * > Gen(nrsubdomains);
+   // // construct unique number generator for the elements of a patch
+   // for (int ip = 0; ip<nrsubdomains; ip++)
+   // {
+   //    Gen[ip] = new UniqueIndexGen;
+   //    // register the elements
+   //    int nel = part->element_map[ip].Size();
+   //    for (int iel=0; iel<nel; iel++)
+   //    {
+   //       int iel_idx = part->element_map[ip][iel];
+   //       Gen[ip]->Set(iel_idx);
+   //    }
+   // }
+
+   // construct dof maps
+   int nrneighbors = pow(3,dim); // including its self
+
+   for (int ip0 = 0; ip0<nrsubdomains; ip0++)
+   {
+      OvlpDofMaps[ip0].resize(nrneighbors);
+
+      FiniteElementSpace * fes0 = dmap->fespaces[ip0];
+      int tdofs0 = fes0->GetTrueVSize();
+      Array<int> marker0(tdofs0); marker0 = 0;
+      int i0, j0, k0;
+      Array<int> ijk(dim);
+      Getijk(ip0, i0,j0,k0);
+
+      int kbeg = (dim == 2) ? 0 : -1;
+      int kend = (dim == 2) ? 1 :  2;
+      for (int k=kbeg; k<kend; k++)
+      {
+         int k1 = k0 + k;
+         if (k1 <0 || k1>=nxyz[2]) continue;
+         int kk = (dim == 2) ? -1 : k;
+         for (int j=-1; j<2; j++)
+         {
+            int j1 = j0 + j;
+            if (j1 <0 || j1>=nxyz[1]) continue;
+            for (int i=-1; i<2; i++)
+            {
+               int i1 = i0 + i;
+               if (i1 <0 || i1>=nxyz[0]) continue;
+     
+               Array<int> ip0list;  marker0 = 0;
+               int directionId = GetDirectionId(i,j,kk);
+
+               Array<int> Elems = OvlpElems[ip0][directionId];
+               int nel = Elems.Size();
+
+               for (int iel = 0; iel<nel; ++iel)
+               {
+                  int iel0 = Elems[iel];   
+                  Array<int> ElemDofs0;
+
+                  fes0->GetElementDofs(iel0,ElemDofs0);
+                  int ndof = ElemDofs0.Size();
+                  // since the elements are added to the subdomain meshes 
+                  // in the same ordered fashion (as they come from the
+                  // original mesh) then the ordering of elements in each 
+                  // subdomain is the same. Hence the dof ovlp lists
+                  // can be computed for each subdomain independendly
+                  for (int l = 0; l<ndof; ++l)
+                  {
+                     int dof0_ = ElemDofs0[l];
+                     int dof0 = (dof0_ >= 0) ? dof0_ : abs(dof0_) - 1;
+                     if (!marker0[dof0])
+                     {
+                        ip0list.Append(dof0); // dofs of ip0 in ovlp
+                        marker0[dof0] = 1;
+                     }
+                  }
+               }
+               
+               OvlpDofMaps[ip0][directionId].Append(ip0list);
+               int tsize = fes0->GetTrueVSize();
+               // Imaginary part
+               for (int l=0;l<ip0list.Size(); l++) { ip0list[l] += tsize; }
+               OvlpDofMaps[ip0][directionId].Append(ip0list);
+            }
+         }
+      }
+   }
+}
+
+
+void NeighborDofMaps::GetNeighborDofMap(const int ip,
+                                        const Array<int> & directions, 
+                                        Array<int> & dofmap)
+{
+   int k = (dim == 2) ? -1 : directions[2];
+   int directionid = GetDirectionId(directions[0],directions[1],k);
+   dofmap = OvlpDofMaps[ip][directionid];
+}
+
+
+void NeighborDofMaps::SetElementToOverlap(int ip, int iel,
+                        const Array<bool> & neg, 
+                        const Array<bool> & pos)
+{
+   int kbeg = (dim == 2) ? 0 : -1;
+   int kend = (dim == 2) ? 0 :  1;
+   for (int k = kbeg; k<=kend; k++)
+   {
+      if (dim == 3)
+      {
+         if (k == -1 && !neg[2]) continue;   
+         if (k ==  1 && !pos[2]) continue;   
+      }   
+      for (int j = -1; j<=1; j++)
+      {
+         if (j== -1 && !neg[1]) continue;   
+         if (j==  1 && !pos[1]) continue;   
+         for (int i = -1; i<=1; i++)
+         {
+            // cases to skip 
+            if (i==-1 && !neg[0]) continue;   
+            if (i== 1 && !pos[0]) continue;   
+
+            if (i==0 && j==0 && k == 0) continue;
+            int kk  = (dim==2)?-1 : k;  
+            int DirId = GetDirectionId(i,j,kk);
+            OvlpElems[ip][DirId].Append(iel);
+         }
+      }
+   }
+}
@@ -0,0 +1,179 @@
+#pragma once
+#include "MeshPartition.hpp"
+#include "complex_linalg.hpp"
+
+struct UniqueIndexGen
+{
+   int counter = 0;
+   std::unordered_map<int,int> idx;
+
+   void Set(int i)
+   {
+      std::unordered_map<int,int>::iterator f = idx.find(i);
+      if (f == idx.end())
+      {
+         idx[i] = counter;
+         counter++;
+      }
+   }
+
+   int Get(int i)
+   {
+      std::unordered_map<int,int>::iterator f = idx.find(i);
+      if (f == idx.end())
+      {
+         return -1;
+      }
+      else
+      {
+         return (*f).second;
+      }
+   }
+   void Reset()
+   {
+      counter = 0;
+      idx.clear();
+   }
+};
+
+
+struct Sweep
+{
+private:
+   int dim;
+   std::vector<Array<int>> sweeps;
+public:   
+   int nsweeps;
+   Sweep(int dim_);
+   ~Sweep();
+   void GetSweep(const int i, Array<int> & sweep)
+   {
+      MFEM_VERIFY(i<nsweeps, "Sweep number out of bounds");
+      sweep.SetSize(dim);
+      sweep = sweeps[i];
+   }
+
+
+};
+
+
+
+// Function coefficient that takes the bounding box of the mesh as an input
+class CutOffFnCoefficient : public Coefficient
+{
+private:
+   double (*Function)(const Vector &, const Vector &, const Vector &, const Array2D<double> &);
+   Vector pmin, pmax;
+   Array2D<double> h; // specify the with of the cutoff function (h in each direction)
+   
+
+public:
+   CutOffFnCoefficient(double (*F)(const Vector &, const Vector &, const Vector &, const Array2D<double> &), 
+                             const Vector & pmin_, const Vector & pmax_, Array2D<double> & h_)
+      : Function(F), pmin(pmin_), pmax(pmax_), h(h_)
+   {}
+   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   {
+      double x[3];
+      Vector transip(x, 3);
+      T.Transform(ip, transip);
+      return ((*Function)(transip, pmin, pmax, h));
+   }
+};
+
+double CutOffFncn(const Vector &x, const Vector & pmin, 
+const Vector & pmax, const Array2D<double> & h_);
+double ChiFncn(const Vector &x, const Vector & pmin, 
+const Vector & pmax, const Array2D<double> & h_);
+
+class DofMap // Constructs dof maps for a given partition
+{
+public:
+   int nrpatch, nx, ny, nz;
+   vector<Array<int>> Dof2GlobalDof;
+   vector<Array<int>> Dof2PmlDof;
+   Array<Mesh *> PmlMeshes;
+   Array<FiniteElementSpace *> fespaces;
+   Array<FiniteElementSpace *> PmlFespaces;
+   // constructor
+   // Non PML constructor dof map
+   DofMap(FiniteElementSpace * fes, MeshPartition * partition);
+   // PML
+   DofMap(FiniteElementSpace * fes , MeshPartition * partition, int nrlayers);
+   ~DofMap(){};
+};
+
+
+
+class LocalDofMap // Constructs dof mapbetween two partitions
+{
+   const FiniteElementCollection *fec=nullptr;
+   MeshPartition * part1=nullptr;
+   MeshPartition * part2=nullptr;
+public:
+   int nrpatch, nx, ny, nz;
+   vector<Array<int>> map1;
+   vector<Array<int>> map2;
+   // constructor
+   LocalDofMap(const FiniteElementCollection * fec_, MeshPartition * part1_, 
+               MeshPartition * part2_);
+   ~LocalDofMap();
+};
+
+
+struct NeighborDofMaps
+{
+private:
+   int dim;
+   MeshPartition * part = nullptr;
+   FiniteElementSpace * fes = nullptr;
+   Mesh * mesh = nullptr;
+   std::vector<std::vector<Array<int>>> OvlpElems;
+   std::vector<std::vector<Array<int>>> OvlpDofMaps;
+
+   DofMap * dmap = nullptr;
+   int nrsubdomains = 0;
+   int ovlp_layers = 0;
+   Array<int> nxyz;
+   void SetElementToOverlap(int ip, int iel, 
+                           const Array<bool> & neg, 
+                           const Array<bool> & pos);
+
+   void MarkOvlpElements();
+   void ComputeNeighborDofMaps();
+
+   void Getijk(int ip, int & i, int & j, int & k) const
+   {
+      k = ip/(nxyz[0]*nxyz[1]);
+      j = (ip-k*nxyz[0]*nxyz[1])/nxyz[0];
+      i = (ip-k*nxyz[0]*nxyz[1])%nxyz[0];
+   }
+
+   int GetPatchId(const Array<int> & ijk) const
+   {
+      int d=ijk.Size();
+      int z = (d==2)? 0 : ijk[2];
+      return part->subdomains(ijk[0],ijk[1],z);
+   }
+      int GetDirectionId(int i, int j, int k=-1) 
+   {
+      int n = 3;
+      return (k+1)*n*n + (j+1)*n + i+1; 
+   }
+   void GetDirections(const int id, int & i, int & j, int & k) 
+   {
+      int n = 3;
+      k = id/(n*n) - 1;
+      j = (id-(k+1)*n*n)/n - 1;
+      i = (id-(k+1)*n*n)%n - 1;
+   }
+
+public:   
+   NeighborDofMaps(MeshPartition * part_, 
+                   FiniteElementSpace * fes_, 
+                   DofMap * dmap_,
+                   int ovlp_layers_);
+
+   void GetNeighborDofMap(const int ip, const Array<int> & directions,
+                          Array<int> & dofmap);
+};
@@ -0,0 +1,358 @@
+
+#include "../../../linalg/kernels.hpp"
+#include "complex_linalg.hpp"
+
+
+ComplexDenseMatrix::ComplexDenseMatrix(){}
+
+ComplexDenseMatrix::ComplexDenseMatrix(int s) 
+{
+   MFEM_ASSERT(s >= 0, "invalid ComplexDenseMatrix size: " << s);
+   height = s;
+   width  = s;
+   if (s > 0)
+   {
+      data = new complex<double>[s*s];
+      *this = 0.0; // init with zeroes
+   }
+}
+
+
+ComplexDenseMatrix::ComplexDenseMatrix(int m, int n) 
+{
+   MFEM_VERIFY(m >= 0 && n >= 0,
+               "invalid DenseMatrix size: " << m << " x " << n);
+   const int s = m*n;
+   height = m;
+   width  = n;
+   if (s > 0)
+   {
+      data = new complex<double>[s];
+      *this = 0.0; // init with zeroes
+   }
+}
+
+void ComplexDenseMatrix::SetSize(int h, int w)
+{
+   MFEM_VERIFY(h >= 0 && w >= 0,
+               "invalid ComplexDenseMatrix size: " << h << " x " << w);
+   if (Height() == h && Width() == w)
+   {
+      return;
+   }
+   height = h;
+   width = w;
+   const int hw = h*w;
+   delete data;
+   data = new complex<double>[hw];
+   *this = 0.0; // init with zeroes
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator=(double c)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] = c;
+   }
+   return *this;
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator=(complex<double> c)
+{
+   const int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] = c;
+   }
+   return *this;
+}
+
+
+std::complex<double> ComplexDenseMatrix::Det() const
+{
+   MFEM_ASSERT(Height() == Width() && Height() > 0,
+               "The matrix must be square and "
+               << "sized larger than zero to compute the determinant."
+               << "  Height() = " << Height()
+               << ", Width() = " << Width());
+
+   switch (Height())
+   {
+      case 1:
+         return data[0];
+
+      case 2:
+         return data[0] * data[3] - data[1] * data[2];
+
+      case 3:
+      {
+         const complex<double> *d = data;
+         return
+            d[0] * (d[4] * d[8] - d[5] * d[7]) +
+            d[3] * (d[2] * d[7] - d[1] * d[8]) +
+            d[6] * (d[1] * d[5] - d[2] * d[4]);
+      }
+      default:
+      {
+         MFEM_ABORT("dim>3 not supported yet");         
+         return 0;
+      }
+   }
+}
+
+DenseMatrix * ComplexDenseMatrix::real() const
+{
+   DenseMatrix * Ar = new DenseMatrix(height,width);
+   double * data = Ar->Data();
+   complex<double> * zdata = this->data;
+   for (int s = 0; s<height*width; s++)
+   {
+         data[s] = zdata[s].real();
+   }
+   return Ar;
+}
+DenseMatrix * ComplexDenseMatrix::imag() const
+{
+   DenseMatrix * Ai = new DenseMatrix(height,width);
+   double * data = Ai->Data();
+   complex<double> * zdata = this->data;
+   for (int s = 0; s<height*width; s++)
+   {
+         data[s] = zdata[s].imag();
+   }
+   return Ai;
+}
+
+void ComplexDenseMatrix::GetReal(DenseMatrix & Ar) 
+{
+   MFEM_ASSERT(Ar.Height() == height && Ar.Width() == width, "Incompatible dimensions");
+   double * data = Ar.Data();
+   complex<double> * zdata = this->data;
+   for (int s = 0; s<height*width; s++)
+   {
+         data[s] = zdata[s].real();
+   }
+}
+
+void ComplexDenseMatrix::GetImag(DenseMatrix & Ai) 
+{
+   double * data = Ai.Data();
+   complex<double> * zdata = this->data;
+   for (int s = 0; s<height*width; s++)
+   {
+         data[s] = zdata[s].imag();
+   }
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator=(const ComplexDenseMatrix &m)
+{
+   SetSize(m.height, m.width);
+
+   const int hw = height * width;
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] = m.data[i];
+   }
+   return *this;
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator+=(const complex<double> *m)
+{
+   const int hw = Height()*Width();
+   for (int i = 0; i < hw; i++)
+   {
+      data[i] += m[i];
+   }
+   return *this;
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator+=(const ComplexDenseMatrix &m)
+{
+   MFEM_ASSERT(Height() == m.Height() && Width() == m.Width(),
+               "incompatible matrix sizes.");
+   return *this += m.GetData();
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator-=(const ComplexDenseMatrix &m)
+{
+   int s = Height()*Width();
+   complex<double> * mdata = m.GetData();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] -= mdata[s];
+   }
+   return *this;
+}
+
+ComplexDenseMatrix &ComplexDenseMatrix::operator*=(complex<double> c)
+{
+   int s = Height()*Width();
+   for (int i = 0; i < s; i++)
+   {
+      data[i] *= c;
+   }
+   return *this;
+}
+
+
+void ComplexDenseMatrix::Print(std::ostream &out, int width_) const
+{
+   // save current output flags
+   ios::fmtflags old_flags = out.flags();
+   // output flags = scientific + show sign
+   out << setiosflags(ios::scientific | ios::showpos);
+   for (int i = 0; i < height; i++)
+   {
+      out << "[row " << i << "]\n";
+      for (int j = 0; j < width; j++)
+      {
+         out << (*this)(i,j);
+         if (j+1 == width || (j+1) % width_ == 0)
+         {
+            out << '\n';
+         }
+         else
+         {
+            out << ' ';
+         }
+      }
+   }
+   // reset output flags to original values
+   out.flags(old_flags);
+}
+
+void ComplexDenseMatrix::PrintMatlab(std::ostream &out) const
+{
+   // save current output flags
+   // ios::fmtflags old_flags = out.flags();
+   // output flags = scientific + show sign
+   // out << setiosflags(ios::scientific | ios::showpos);
+   for (int i = 0; i < height; i++)
+   {
+      for (int j = 0; j < width; j++)
+      {
+         out << (*this)(i,j);
+         out << ' ';
+      }
+      out << "\n";
+   }
+   // reset output flags to original values
+   // out.flags(old_flags);
+}
+
+ComplexDenseMatrixInverse::ComplexDenseMatrixInverse(const ComplexDenseMatrix & A) : ComplexDenseMatrix(A.Height())
+{
+   MFEM_VERIFY(A.Height() == A.Width(), "The matrix is not square");
+   MFEM_VERIFY(A.Height() < 4, "dim > 3 is not supported yet");
+
+   std::complex<double> detA = A.Det();
+   MFEM_VERIFY(abs(A.Det())>1e-14, "The given matrix is singular");
+
+   std::complex<double> * d = this->Data();
+   std::complex<double> *dA = A.GetData();
+   switch (A.Height())
+   {
+   case 1:
+      d[0] = 1.0/dA[0];
+      break;
+   case 2:
+      d[0] =  1.0/detA * dA[3];
+      d[1] = -1.0/detA * dA[1];
+      d[2] = -1.0/detA * dA[2];
+      d[3] =  1.0/detA * dA[0];
+      break;   
+   case 3:
+      d[0] =   1.0/detA*(dA[4]*dA[8] - dA[5]*dA[7]);
+      d[1] =  -1.0/detA*(dA[1]*dA[8] - dA[2]*dA[7]);
+      d[2] =   1.0/detA*(dA[1]*dA[5] - dA[2]*dA[4]);
+      d[3] =  -1.0/detA*(dA[3]*dA[8] - dA[5]*dA[6]);
+      d[4] =   1.0/detA*(dA[0]*dA[8] - dA[2]*dA[6]);
+      d[5] =  -1.0/detA*(dA[0]*dA[5] - dA[2]*dA[3]);
+      d[6] =   1.0/detA*(dA[3]*dA[7] - dA[4]*dA[6]);
+      d[7] =  -1.0/detA*(dA[0]*dA[7] - dA[1]*dA[6]);
+      d[8] =   1.0/detA*(dA[0]*dA[4] - dA[1]*dA[3]);
+      break;      
+   default:
+      // Should be unreachable 
+      break;
+   }
+}
+
+
+
+/// Matrix matrix multiplication.  A = B * C.
+void Mult(const ComplexDenseMatrix &b, const ComplexDenseMatrix &c, ComplexDenseMatrix &a)
+{
+   MFEM_ASSERT(a.Height() == b.Height() && a.Width() == c.Width() &&
+               b.Width() == c.Height(), "incompatible dimensions");
+
+   const int ah = a.Height();
+   const int aw = a.Width();
+   const int bw = b.Width();
+   complex<double> *ad = a.Data();
+   const complex<double> *bd = b.Data();
+   const complex<double> *cd = c.Data();
+   kernels::Mult(ah,aw,bw,bd,cd,ad);               
+}
+
+/// Multiply the transpose of a matrix A with a matrix B:   At*B
+void MultAtB(const ComplexDenseMatrix &A, const ComplexDenseMatrix &B, ComplexDenseMatrix &AtB)
+{
+   MFEM_ASSERT(A.Width() == AtB.Height() && B.Width() == AtB.Width() &&
+               A.Height() == B.Height(), "incompatible dimensions");
+   const int ah = A.Height();
+   const int aw = A.Width();
+   const int bw = B.Width();
+   const complex<double> *ad = A.Data();
+   const complex<double> *bd = B.Data();
+   complex<double> *cd = AtB.Data();
+
+   for (int j = 0; j < bw; j++)
+   {
+      const complex<double> *ap = ad;
+      for (int i = 0; i < aw; i++)
+      {
+         complex<double> d = 0.0;
+         for (int k = 0; k < ah; k++)
+         {
+            d += ap[k] * bd[k];
+         }
+         *(cd++) = d;
+         ap += ah;
+      }
+      bd += ah;
+   }            
+}
+
+/// Multiply the conjugate transpose of a matrix A with a matrix B:   At*B
+void MultAhB(const ComplexDenseMatrix &A, const ComplexDenseMatrix &B, ComplexDenseMatrix &AtB)
+{
+   MFEM_ASSERT(A.Width() == AtB.Height() && B.Width() == AtB.Width() &&
+               A.Height() == B.Height(), "incompatible dimensions");
+      MFEM_ASSERT(A.Width() == AtB.Height() && B.Width() == AtB.Width() &&
+               A.Height() == B.Height(), "incompatible dimensions");
+   const int ah = A.Height();
+   const int aw = A.Width();
+   const int bw = B.Width();
+   const complex<double> *ad = A.Data();
+   const complex<double> *bd = B.Data();
+   complex<double> *cd = AtB.Data();
+
+   for (int j = 0; j < bw; j++)
+   {
+      const complex<double> *ap = ad;
+      for (int i = 0; i < aw; i++)
+      {
+         complex<double> d = 0.0;
+         for (int k = 0; k < ah; k++)
+         {
+            d += conj(ap[k]) * bd[k];
+         }
+         *(cd++) = d;
+         ap += ah;
+      }
+      bd += ah;
+   }                    
+
+}
@@ -0,0 +1,98 @@
+#pragma once
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+class ComplexDenseMatrix 
+{
+private:
+   std::complex<double> * data = nullptr;
+   int height = 0;
+   int width  = 0;
+public:
+   ComplexDenseMatrix();
+   
+   /// Creates square matrix of size s.
+   explicit ComplexDenseMatrix(int s);
+
+   /// Creates rectangular matrix of size m x n.
+   ComplexDenseMatrix(int m, int n);
+
+   /// Change the size of the DenseMatrix to s x s.
+   void SetSize(int s) { SetSize(s, s); }
+
+   /// Change the size of the DenseMatrix to h x w.
+   void SetSize(int h, int w);
+
+   /// Returns the matrix data array.
+   inline complex<double> *Data() const
+   { return const_cast<complex<double>*>((const complex<double>*)data);}
+
+   /// Returns the matrix data array.
+   inline complex<double> *GetData() const { return Data(); }
+
+   /// Returns reference to a_{ij}.
+   inline complex<double> &operator()(int i, int j);
+   inline const complex<double> &operator()(int i, int j) const;
+
+   inline int Height() const { return height; }
+   inline int Width() const { return width; }
+
+   /// Sets the matrix elements equal to constant c
+   ComplexDenseMatrix &operator=(std::complex<double> c);
+   ComplexDenseMatrix &operator=(double c);
+
+   /// Sets the matrix size and elements equal to those of m
+   ComplexDenseMatrix &operator=(const ComplexDenseMatrix &m);
+   ComplexDenseMatrix &operator+=(const complex<double> *m);
+   ComplexDenseMatrix &operator+=(const ComplexDenseMatrix &m);
+   ComplexDenseMatrix &operator-=(const ComplexDenseMatrix &m);
+   ComplexDenseMatrix &operator*=(complex<double> c);
+
+   /// Calculates the determinant of the matrix
+   /// (for 2x2, 3x3)
+   std::complex<double> Det() const;
+
+   virtual void Print(std::ostream &out = mfem::out, int width_ = 4) const;
+   virtual void PrintMatlab(std::ostream &out = mfem::out) const;
+
+   DenseMatrix * real() const;
+   DenseMatrix * imag() const;
+
+   void GetReal(DenseMatrix & Ar);
+   void GetImag(DenseMatrix & Ai);
+};
+
+inline complex<double> &ComplexDenseMatrix::operator()(int i, int j)
+{
+   MFEM_VERIFY(data && i >= 0 && i < height && j >= 0 && j < width, "");
+   // return data[i*width+j];
+   return data[j*height+i];
+}
+
+inline const complex<double> &ComplexDenseMatrix::operator()(int i, int j) const
+{
+   MFEM_VERIFY(data && i >= 0 && i < height && j >= 0 && j < width, "");
+   // return data[i*width+j];
+   return data[j*height+i];
+}
+
+
+class ComplexDenseMatrixInverse : public ComplexDenseMatrix
+{
+private:
+public:
+   ComplexDenseMatrixInverse(const ComplexDenseMatrix & );   
+};
+
+/// Matrix matrix multiplication.  A = B * C.
+void Mult(const ComplexDenseMatrix &b, const ComplexDenseMatrix &c, ComplexDenseMatrix &a);
+
+/// Multiply the transpose of a matrix A with a matrix B:   At*B
+void MultAtB(const ComplexDenseMatrix &A, const ComplexDenseMatrix &B, ComplexDenseMatrix &AtB);
+
+/// Multiply the conjugate transpose of a matrix A with a matrix B:   At*B
+void MultAhB(const ComplexDenseMatrix &A, const ComplexDenseMatrix &B, ComplexDenseMatrix &AtB);
@@ -0,0 +1,404 @@
+//
+// Compile with: make helmholtzp
+//
+// Sample runs:   mpirun -np 4 ./helmholtzp -nd 2 -nx 4 -ny 4 -sr 3 -pr 3 -k 16.0 -o 2
+//                mpirun -np 4 ./helmholtzp -nd 3 -nx 2 -ny 2 -nz 2 -sr 3 -pr 1 -k 2.0 -o 2
+//
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include "ParDST/ParDST.hpp"
+
+using namespace std;
+using namespace mfem;
+
+// Exact solution and r.h.s., see below for implementation.
+double f_exact_Re(const Vector &x);
+double f_exact_Im(const Vector &x);
+
+double wavespeed(const Vector &x);
+
+double funccoeff_re(const Vector & x);
+double funccoeff_im(const Vector & x);
+
+
+int dim;
+double omega;
+int sol = 1;
+double length = 1.0;
+double pml_length = 0.25;
+Array2D<double>comp_bdr;
+
+int main(int argc, char *argv[])
+{
+   // 1. Initialize MPI.
+   int num_procs, myid;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+   // 2. Parse command-line options.
+   // finite element order of approximation
+   int order = 1;
+   bool visualization = 1;
+   // number of wavelengths
+   double k = 0.5;
+   // number of serial refinements
+   int ser_ref_levels = 1;
+   // number of parallel refinements
+   int par_ref_levels = 2;
+   // dimension
+   int nd = 2;
+   int nx=2;
+   int ny=2;
+   int nz=2;
+   bool herm_conv = true;
+
+   // optional command line inputs
+   OptionsParser args(argc, argv);
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree) or -1 for"
+                  " isoparametric space.");
+   args.AddOption(&nd, "-nd", "--dim","Problem space dimension");
+   args.AddOption(&nx, "-nx", "--nx","Number of subdomains in x direction");
+   args.AddOption(&ny, "-ny", "--ny","Number of subdomains in y direction");
+   args.AddOption(&nz, "-nz", "--nz","Number of subdomains in z direction");
+   args.AddOption(&sol, "-sol", "--exact",
+                  "Exact solution flag - 0:polynomial, 1: plane wave, -1: unknown exact");
+   args.AddOption(&k, "-k", "--wavelengths",
+                  "Number of wavelengths.");
+   args.AddOption(&pml_length, "-pml_length", "--pml_length",
+                  "Length of the PML region in each direction");
+   args.AddOption(&length, "-length", "--length",
+                  "length of the domain in each direction.");
+   args.AddOption(&ser_ref_levels, "-sr", "--ser_ref_levels",
+                  "Number of Serial Refinements.");
+   args.AddOption(&par_ref_levels, "-pr", "--par_ref_levels",
+                  "Number of Parallel Refinements.");                  
+   args.AddOption(&herm_conv, "-herm", "--hermitian", "-no-herm",
+                  "--no-hermitian", "Use convention for Hermitian operators.");                  
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   // check if the inputs are correct
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+   // Angular frequency
+   omega = 2.0 * M_PI * k;
+
+   // 3. Read the mesh from the given mesh file.
+   Mesh *mesh;
+
+   if (nd == 2)
+   {
+      mesh = new Mesh(1, 1, Element::QUADRILATERAL, true, length, length, false);
+   }
+   else
+   {
+      mesh = new Mesh(1, 1, 1, Element::HEXAHEDRON, true, length, length, length,false);
+   }
+
+   // 3. Executing uniform h-refinement
+   dim = mesh->Dimension();
+   for (int i = 0; i < ser_ref_levels; i++ )
+   {
+      mesh->UniformRefinement();
+   }
+
+   // 4. Define a parallel mesh by a partitioning of the serial mesh.
+   // ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   int nprocs;
+   int nprocsx;
+   int nprocsy;
+   int nprocsz;
+   if (dim == 2)
+   {
+      nprocs = sqrt(num_procs); 
+      // nprocsx = nprocs;
+      // nprocsy = nprocs;
+      nprocsx = 1;
+      nprocsy = num_procs;
+      nprocsz = 1;
+   }    
+   else
+   {
+      nprocs = cbrt(num_procs); 
+      // nprocsx = nprocs;
+      // nprocsy = nprocs;
+      // nprocsz = nprocs;
+      nprocsx = 1;
+      if (nz != 1)
+      {
+         nprocsy = sqrt(num_procs);
+         nprocsz = nprocsy;
+      }
+      else
+      {
+         nprocsy = num_procs;
+         nprocsz = 1;
+      }
+   }
+   // MFEM_VERIFY(nprocs*nprocs == num_procs, "Check MPI partitioning");
+   // int nxyz[3] = {num_procs,1,1};
+   // int nxyz[3] = {nprocs,nprocs,1};
+   // int nxyz[3] = {1,num_procs,1};
+   
+   int nxyz[3] = {nprocsx,nprocsy,nprocsz};
+   // int nxyz[3] = {num_procs,1,1};
+   int * part = mesh->CartesianPartitioning(nxyz);
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD,*mesh,part);
+   // ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD,*mesh);
+   delete [] part;
+   delete mesh;
+
+   for (int l = 0; l < par_ref_levels; l++)
+   {
+      pmesh->UniformRefinement();
+   }
+
+
+   double hl = GetUniformMeshElementSize(pmesh);
+   int nrlayers = 3;
+
+   Array2D<double> lengths(dim,2);
+   lengths = hl*nrlayers;
+   // lengths[0][1] = 0.0;
+   // lengths[1][1] = 0.0;
+   // lengths[1][0] = 0.0;
+   // lengths[0][0] = 0.0;
+   CartesianPML pml(pmesh,lengths);
+   pml.SetOmega(omega);
+   comp_bdr.SetSize(dim,2);
+   comp_bdr = pml.GetCompDomainBdr(); 
+
+   // 6. Define a finite element space on the mesh.
+   FiniteElementCollection *fec = new H1_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+
+   if (myid == 0)
+   {
+      cout << "Number of finite element unknowns: " << size << endl;
+   }
+   // 6. Set up the linear form (Real and Imaginary part)
+   FunctionCoefficient f_Re(f_exact_Re);
+   FunctionCoefficient f_Im(f_exact_Im);
+
+   // 8. Setup Complex Operator convention
+   ComplexOperator::Convention conv =
+      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;
+
+   // ParLinearForm *b_Re(new ParLinearForm);
+   ParComplexLinearForm b(fespace, conv);
+   b.AddDomainIntegrator(new DomainLFIntegrator(f_Re),
+                         new DomainLFIntegrator(f_Im));
+   b.real().Vector::operator=(0.0);
+   b.imag().Vector::operator=(0.0);
+   b.Assemble();
+
+   // 7. Set up the bilinear form (Real and Imaginary part)
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient sigma(-pow(omega, 2));
+
+   FunctionCoefficient ws(wavespeed);
+
+   PmlMatrixCoefficient c1_re(dim,pml_detJ_JT_J_inv_Re,&pml);
+   PmlMatrixCoefficient c1_im(dim,pml_detJ_JT_J_inv_Im,&pml);
+
+   PmlCoefficient detJ_re(pml_detJ_Re,&pml);
+   PmlCoefficient detJ_im(pml_detJ_Im,&pml);
+
+   ProductCoefficient c2_re0(sigma, detJ_re);
+   ProductCoefficient c2_im0(sigma, detJ_im);
+
+   ProductCoefficient c2_re(c2_re0, ws);
+   ProductCoefficient c2_im(c2_im0, ws);
+
+   ParSesquilinearForm a(fespace,conv);
+   a.AddDomainIntegrator(new DiffusionIntegrator(c1_re),
+                         new DiffusionIntegrator(c1_im));
+   a.AddDomainIntegrator(new MassIntegrator(c2_re),
+                         new MassIntegrator(c2_im));
+   a.Assemble();
+   a.Finalize();
+
+   Array<int> ess_tdof_list;
+   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
+   ess_bdr = 1;
+   fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+   // Solution grid function
+   ParComplexGridFunction p_gf(fespace); p_gf = 0.0;
+   OperatorHandle Ah;
+   Vector X, B;
+
+   a.FormLinearSystem(ess_tdof_list, p_gf, b, Ah, X, B);
+   {
+      StopWatch chrono;
+      chrono.Clear();
+      chrono.Start();
+      ParDST S(&a,lengths,omega, &ws,nrlayers,nx,ny,nz);
+      chrono.Stop();
+      double t1 = chrono.RealTime();
+
+      chrono.Clear();
+      chrono.Start();
+      // X = 0.0;
+      GMRESSolver gmres(MPI_COMM_WORLD);
+      gmres.SetPreconditioner(S);
+      gmres.SetOperator(*Ah);
+      gmres.SetRelTol(1e-6);
+      gmres.SetMaxIter(20);
+      gmres.SetPrintLevel(1);
+      gmres.Mult(B, X);
+      chrono.Stop();
+
+      double t2 = chrono.RealTime();
+      
+      MPI_Barrier(MPI_COMM_WORLD);
+
+
+      cout << " myid: " << myid 
+           << ", setup time: " << t1
+           << ", solution time: " << t2 << endl; 
+
+
+      a.RecoverFEMSolution(X,B,p_gf);
+      if (visualization)
+      {
+         char vishost[] = "localhost";
+         int  visport   = 19916;
+         string keys;
+         if (dim ==2 )
+         {
+            keys = "keys mrRljc\n";
+         }
+         else
+         {
+            keys = "keys mc\n";
+         }
+         socketstream sol_sock_re(vishost, visport);
+         sol_sock_re.precision(8);
+         sol_sock_re << "parallel " << num_procs << " " << myid << "\n"
+                     << "solution\n" << *pmesh << p_gf.real() << keys 
+                     << "window_title 'Numerical Pressure: Real Part' " << flush;                     
+
+         socketstream sol_sock_im(vishost, visport);
+         sol_sock_im.precision(8);
+         sol_sock_im << "parallel " << num_procs << " " << myid << "\n"
+                     << "solution\n" << *pmesh << p_gf.imag() << keys 
+                     << "window_title 'Numerical Pressure: Imag Part' " << flush;                     
+      }
+   }
+
+   delete fespace;
+   delete fec;
+	delete pmesh;
+   MPI_Finalize();
+   return 0;
+}
+
+
+double f_exact_Re(const Vector &x)
+{
+   
+   int nrsources = (dim == 2) ? 4 : 8;
+   Vector x0(nrsources);
+   Vector y0(nrsources);
+   Vector z0(nrsources);
+   x0(0) = 0.25; y0(0) = 0.25; z0(0) = 0.25;
+   x0(1) = 0.75; y0(1) = 0.25; z0(1) = 0.25;
+   x0(2) = 0.25; y0(2) = 0.75; z0(2) = 0.25;
+   x0(3) = 0.75; y0(3) = 0.75; z0(3) = 0.25;
+   if (dim == 3)
+   {
+      x0(4) = 0.25; y0(4) = 0.25; z0(4) = 0.75;
+      x0(5) = 0.75; y0(5) = 0.25; z0(5) = 0.75;
+      x0(6) = 0.25; y0(6) = 0.75; z0(6) = 0.75;
+      x0(7) = 0.75; y0(7) = 0.75; z0(7) = 0.75;
+   }
+  
+   double n = 4.0*omega/M_PI;
+   double coeff = 16.0*omega*omega/M_PI/M_PI/M_PI;
+
+   double f_re = 0.0;
+   // for (int i = 0; i<1; i++)
+   for (int i = 0; i<nrsources; i++)
+   {
+      double beta = pow(x0(i)-x(0),2) + pow(y0(i)-x(1),2);
+      if (dim == 3) { beta += pow(z0(i)-x(2),2); }
+      double alpha = -pow(n,2) * beta;
+      f_re += coeff*exp(alpha);
+   }
+
+   bool in_pml = false;
+   for (int i = 0; i<dim; i++)
+   {
+      if (x(i)<=comp_bdr(i,0) || x(i)>=comp_bdr(i,1))
+      {
+         in_pml = true;
+         break;
+      }
+   }
+   if (in_pml) f_re = 0.0;
+
+   return f_re;
+
+}
+double f_exact_Im(const Vector &x)
+{
+   double f_im;
+   f_im = 0.0;
+   return f_im;
+}
+
+double wavespeed(const Vector &x)
+{
+   double ws;
+   ws = 1.0;
+   return ws;
+}
+
+double funccoeff_re(const Vector & x)
+{
+   return sin(3*M_PI*(x.Sum()));
+}
+
+double funccoeff_im(const Vector & x)
+{
+   return cos(10*M_PI*(x.Sum()));
+}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
@@ -0,0 +1,67 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Use the MFEM build directory
+MFEM_DIR ?= ../..
+MFEM_BUILD_DIR ?= ../..
+SRC = $(if $(MFEM_DIR:../../..=),$(MFEM_DIR)/examples/maxwell-solver-dev/,)
+CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+SEQ_EXAMPLES = 
+PAR_EXAMPLES = helmholtzp maxwellp
+ifeq ($(MFEM_USE_MPI),NO)
+   EXAMPLES = $(SEQ_EXAMPLES)
+else
+   EXAMPLES = $(PAR_EXAMPLES) $(SEQ_EXAMPLES)
+endif
+
+.SUFFIXES:
+.SUFFIXES: .o .cpp .mk
+.PHONY: all clean
+.PRECIOUS: %.o
+
+COMMON_O= common/PML.o common/MeshPartition.o \
+			 common/Utilities.o common/complex_linalg.o\
+			 ParDST/ParDST.o ParDST/DofMapsDST.o
+
+# Remove built-in rules
+%: %.cpp
+%.o: %.cpp
+
+all: $(EXAMPLES)
+
+# Rules for building the EXAMPLES
+
+%: $(SRC)%.cpp $(COMMON_O) $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(COMMON_O) $(MFEM_LIBS)
+
+# Rules for compiling miniapp dependencies
+$(COMMON_O) $($(EXAMPLES)): \
+%.o: $(SRC)%.cpp $(SRC)%.hpp $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<) -o $(@)
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not built)
+
+clean:
+	rm -f *.o *~ $(SEQ_EXAMPLES) $(PAR_EXAMPLES)
+	rm -f DST/*.o
+	rm -f ParDST/*.o
+	rm -f common/*.o
+	rm -f DST2D/*.o
+	rm -rf *.dSYM *.TVD.*breakpoints
+	rm output/*
+
+
@@ -0,0 +1,535 @@
+//
+// Compile with: make maxwellp
+//
+// Sample runs:   mpirun -np 4 ./maxwellp -nd 2 -nx 4 -ny 4 -sr 3 -pr 3 -k 16.0 -o 2
+//                mpirun -np 4 ./maxwellp -nd 3 -nx 2 -ny 2 -nz 2 -sr 3 -pr 1 -k 2.0 -o 2
+//
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include "ParDST/ParDST.hpp"
+
+using namespace std;
+using namespace mfem;
+  
+void source_re(const Vector &x, Vector & f);
+void source_im(const Vector &x, Vector & f);
+void exact_re(const Vector & x, Vector & E);
+void exact_im(const Vector & x, Vector & E);
+void maxwell_solution(const Vector & x, double E[], double curl2E[]);
+double wavespeed(const Vector &x);
+void Mwavespeed(const Vector & x, DenseMatrix & M);
+
+void ess_data_func(const Vector & x, Vector & E);
+
+
+double mu = 1.0;
+double epsilon = 1.0;
+double omega;
+int dim;
+double length = 1.0;
+Array2D<double> comp_bdr;
+Array2D<double> domain_bdr;
+bool exact_known = false;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   int num_procs, myid;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+   int order = 1;
+   // number of serial refinements
+   int ser_ref_levels = 1;
+   // number of parallel refinements
+   int par_ref_levels = 2;
+   // number of wavelengths
+   double k = 5.0; // 
+   bool herm_conv = true;
+   bool visualization = 1;
+   int nd=2;
+   int nx=2;
+   int ny=2;
+   int nz=2;
+   OptionsParser args(argc, argv);
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&nd, "-nd", "--dim","Problem space dimension");
+   args.AddOption(&nx, "-nx", "--nx","Number of subdomains in x direction");
+   args.AddOption(&ny, "-ny", "--ny","Number of subdomains in y direction");
+   args.AddOption(&nz, "-nz", "--nz","Number of subdomains in z direction");               
+   args.AddOption(&ser_ref_levels, "-sr", "--ser_ref_levels",
+                  "Number of Serial Refinements.");
+   args.AddOption(&par_ref_levels, "-pr", "--par_ref_levels",
+                  "Number of Parallel Refinements."); 
+   args.AddOption(&mu, "-mu", "--permeability",
+                  "Permeability of free space (or 1/(spring constant)).");
+   args.AddOption(&epsilon, "-eps", "--permittivity",
+                  "Permittivity of free space (or mass constant).");
+   args.AddOption(&k, "-k", "--wavelengths",
+                  "Number of wavelengths.");
+   args.AddOption(&herm_conv, "-herm", "--hermitian", "-no-herm",
+                  "--no-hermitian", "Use convention for Hermitian operators.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+
+   // check if the inputs are correct
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // Angular frequency
+   omega = 2.0 * M_PI * k;
+
+   Mesh *mesh;
+
+
+   int nel = 1;
+   if (nd == 2)
+   {
+      mesh = new Mesh(nel, nel, Element::QUADRILATERAL, true, length, length, false);
+   }
+   else
+   {
+      mesh = new Mesh(nel, nel, nel, Element::HEXAHEDRON, true, length, length, length,false);
+   }
+
+   dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution.
+   for (int l = 0; l < ser_ref_levels; l++)
+   {
+      mesh->UniformRefinement();
+   }
+
+   // 4. Define a parallel mesh by a partitioning of the serial mesh.
+   // ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   int nprocs;
+   int nprocsx;
+   int nprocsy;
+   int nprocsz;
+   if (dim == 2)
+   {
+      nprocs = sqrt(num_procs); 
+      nprocsx = nprocs;
+      nprocsy = nprocs;
+      nprocsz = 1;
+   }    
+   else
+   {
+      nprocs = cbrt(num_procs); 
+      nprocsx = nprocs;
+      nprocsy = nprocs;
+      nprocsz = nprocs;
+   }
+   int nxyz[3] = {nprocsx,nprocsy,nprocsz};
+   int * part = mesh->CartesianPartitioning(nxyz);
+   // ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD,*mesh,part);
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD,*mesh);
+   delete [] part;
+
+   
+   delete mesh;
+
+   for (int l = 0; l < par_ref_levels; l++)
+   {
+      pmesh->UniformRefinement();
+   }
+
+
+   double hl = GetUniformMeshElementSize(pmesh);
+   int nrlayers = 3;
+   Array2D<double> lengths(dim,2);
+   lengths = hl*nrlayers;
+   // lengths[0][1] = 0.0;
+   // lengths[1][1] = 0.0;
+   // lengths[1][0] = 0.0;
+   // lengths[0][0] = 0.0;
+   if (exact_known) lengths = 0.0;
+   // CartesianPML pml(mesh,lengths);
+   CartesianPML pml(pmesh,lengths);
+   pml.SetOmega(omega);
+   comp_bdr.SetSize(dim,2);
+   comp_bdr = pml.GetCompDomainBdr(); 
+
+
+   // 6. Define a finite element space on the 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);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+
+   if (myid == 0)
+   {
+      cout << "Number of finite element unknowns: " << size << endl;
+   }
+
+   // 7. Determine the list of true essential boundary dofs. In this example,
+   //    the boundary conditions are defined based on the specific mesh and the
+   //    problem type.
+   Array<int> ess_tdof_list;
+   if (pmesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(pmesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   // 8. Setup Complex Operator convention
+   ComplexOperator::Convention conv =
+      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;
+
+   // 9. Set up the linear form b(.) which corresponds to the right-hand side of
+   //    the FEM linear system.
+   VectorFunctionCoefficient f_re(dim, source_re);
+   VectorFunctionCoefficient f_im(dim, source_re);
+   ParComplexLinearForm b(fespace, conv);
+   b.AddDomainIntegrator(new VectorFEDomainLFIntegrator(f_re),
+                         new VectorFEDomainLFIntegrator(f_im));
+   b.Vector::operator=(0.0);
+   b.Assemble();
+
+   // 10. Define the solution vector x as a complex finite element grid function
+   //     corresponding to fespace.
+   ParComplexGridFunction x(fespace);
+   x = 0.0;
+   // VectorFunctionCoefficient done(dim,ess_data_func);
+   // x.ProjectCoefficient(done,done);
+   VectorFunctionCoefficient E_re(dim,exact_re);
+   VectorFunctionCoefficient E_im(dim,exact_re);
+   if (exact_known)
+   {
+      x.ProjectCoefficient(E_re,E_re);
+   }
+   // 11. Set up the sesquilinear form a(.,.)
+   //
+   //       1/mu (1/det(J) J^T J Curl E, Curl F)
+   //        - omega^2 * epsilon (det(J) * (J^T J)^-1 * E, F)
+   //
+   FunctionCoefficient ws(wavespeed);
+
+   // MatrixFunctionCoefficient Mws(dim,Mwavespeed);
+
+   // DenseMatrix M(dim); M = 0.0;
+   // M(0,0) = -pow(omega, 2);
+   // M(1,1) = -pow(omega, 2);
+   // M(2,2) = -pow(omega, 2);
+   // MatrixConstantCoefficient Momeg(M);
+   MatrixFunctionCoefficient eps_func(dim,Mwavespeed);
+
+   ConstantCoefficient omeg(-pow(omega, 2));
+   int cdim = (dim == 2) ? 1 : dim;
+   PmlMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, &pml);
+   PmlMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, &pml);
+
+   PmlMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,&pml);
+   PmlMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,&pml);
+   ScalarMatrixProductCoefficient c2_Re0(omeg,pml_c2_Re);
+   ScalarMatrixProductCoefficient c2_Im0(omeg,pml_c2_Im);
+   // ScalarMatrixProductCoefficient c2_Re(ws,c2_Re0);
+   // ScalarMatrixProductCoefficient c2_Im(ws,c2_Im0);
+
+   MatrixMatrixProductCoefficient c2_Re(c2_Re0,eps_func);
+   MatrixMatrixProductCoefficient c2_Im(c2_Im0,eps_func);
+
+   // MatrixMatrixProductCoefficient c2_Re0(Momeg,pml_c2_Re);
+   // MatrixMatrixProductCoefficient c2_Im0(Momeg,pml_c2_Im);
+   // MatrixMatrixProductCoefficient c2_Re(Mws,c2_Re0);
+   // MatrixMatrixProductCoefficient c2_Im(Mws,c2_Im0);
+
+
+   ParSesquilinearForm a(fespace, conv);
+   a.AddDomainIntegrator(new CurlCurlIntegrator(pml_c1_Re),
+                         new CurlCurlIntegrator(pml_c1_Im));
+   a.AddDomainIntegrator(new VectorFEMassIntegrator(c2_Re),
+                         new VectorFEMassIntegrator(c2_Im));
+
+   a.Assemble(0);
+
+   OperatorHandle Ah;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, Ah, X, B);
+
+   ComplexSparseMatrix * Ac = Ah.As<ComplexSparseMatrix>();
+   StopWatch chrono;
+
+
+   chrono.Clear();
+   chrono.Start();
+   ParDST * S = new ParDST(&a,lengths, omega, &ws, nrlayers, nx, ny, nz);
+   chrono.Stop();
+   double t1 = chrono.RealTime();
+
+   chrono.Clear();
+   chrono.Start();
+   // X = 0.0;
+	GMRESSolver gmres(MPI_COMM_WORLD);
+	// gmres.iterative_mode = true;
+   gmres.SetPreconditioner(*S);
+	gmres.SetOperator(*Ac);
+	gmres.SetRelTol(1e-8);
+	gmres.SetMaxIter(100);
+	gmres.SetPrintLevel(1);
+	gmres.Mult(B, X);
+   delete S;
+   chrono.Stop();
+   double t2 = chrono.RealTime();
+
+   MPI_Barrier(MPI_COMM_WORLD);
+
+
+   cout << " myid: " << myid 
+         << ", setup time: " << t1
+         << ", solution time: " << t2 << endl; 
+
+   a.RecoverFEMSolution(X, b, x);
+
+
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      string keys;
+      if (dim ==2 )
+      {
+         keys = "keys mrRljc\n";
+      }
+      else
+      {
+         keys = "keys mc\n";
+      }
+      socketstream sol_sock_re(vishost, visport);
+      sol_sock_re.precision(8);
+      sol_sock_re << "parallel " << num_procs << " " << myid << "\n"
+                  << "solution\n" << *pmesh << x.real() << keys 
+                  << "window_title 'E: Real Part' " << flush;                     
+
+      socketstream sol_sock_im(vishost, visport);
+      sol_sock_im.precision(8);
+      sol_sock_im << "parallel " << num_procs << " " << myid << "\n"
+                  << "solution\n" << *pmesh << x.imag() << keys 
+                  << "window_title 'E: Imag Part' " << flush;   
+
+      {
+         ParGridFunction x_t(fespace);
+         x_t = x.real();
+
+         socketstream sol_sock(vishost, visport);
+         sol_sock.precision(8);
+         sol_sock << "parallel " << num_procs << " " << myid << "\n"
+                  << "solution\n" << *pmesh << x_t << keys << "autoscale off\n"
+                  << "window_title 'Harmonic Solution (t = 0.0 T)'"
+                  << "pause\n" << flush;
+
+         if (myid == 0)
+         {
+            cout << "GLVis visualization paused."
+                 << " Press space (in the GLVis window) to resume it.\n";
+         }
+
+         int num_frames = 32;
+         int i = 0;
+         while (sol_sock)
+         {
+            double t = (double)(i % num_frames) / num_frames;
+            ostringstream oss;
+            oss << "Harmonic Solution (t = " << t << " T)";
+
+            add(cos(2.0*M_PI*t), x.real(), sin(2.0*M_PI*t), x.imag(), x_t);
+            sol_sock << "parallel " << num_procs << " " << myid << "\n";
+            sol_sock << "solution\n" << *pmesh << x_t
+                     << "window_title '" << oss.str() << "'" << flush;
+            i++;
+         }
+      }
+   }
+
+   // 18. Free the used memory.
+   delete fespace;
+   delete fec;
+   delete pmesh;
+   MPI_Finalize();
+   return 0;
+}
+
+void source_re(const Vector &x, Vector &f)
+{
+   f = 0.0;
+   if (exact_known)
+   {
+      double E[3], curl2E[3];
+      maxwell_solution(x, E, curl2E);
+      // curl ( curl E) +/- omega^2 E = f
+      double coeff = -omega * omega;
+      f(0) = curl2E[0] + coeff * E[0];
+      f(1) = curl2E[1] + coeff * E[1];
+      if (dim == 2)
+      {
+         if (x.Size() == 3) {f(2)=0.0;}
+      }
+      else
+      {
+         f(2) = curl2E[2] + coeff * E[2];
+      }
+   }
+   else
+   {
+      int nrsources = (dim == 2) ? 4 : 8;
+      Vector x0(nrsources);
+      Vector y0(nrsources);
+      Vector z0(nrsources);
+      x0(0) = 0.25; y0(0) = 0.25; z0(0) = 0.25;
+      x0(1) = 0.75; y0(1) = 0.25; z0(1) = 0.25;
+      x0(2) = 0.25; y0(2) = 0.75; z0(2) = 0.25;
+      x0(3) = 0.75; y0(3) = 0.75; z0(3) = 0.25;
+      if (dim == 3)
+      {
+         x0(4) = 0.25; y0(4) = 0.25; z0(4) = 0.75;
+         x0(5) = 0.75; y0(5) = 0.25; z0(5) = 0.75;
+         x0(6) = 0.25; y0(6) = 0.75; z0(6) = 0.75;
+         x0(7) = 0.75; y0(7) = 0.75; z0(7) = 0.75;
+      }
+  
+      double n = 4.0*omega/M_PI;
+      double coeff = 16.0*omega*omega/M_PI/M_PI/M_PI;
+
+      for (int i = 0; i<nrsources; i++)
+      {
+         double beta = pow(x0(i)-x(0),2) + pow(y0(i)-x(1),2);
+         if (dim == 3) { beta += pow(z0(i)-x(2),2); }
+         double alpha = -pow(n,2) * beta;
+         f[0] += coeff*exp(alpha);
+      }
+
+      bool in_pml = false;
+      for (int i = 0; i<dim; i++)
+      {
+         if (x(i)<=comp_bdr(i,0) || x(i)>=comp_bdr(i,1))
+         {
+            in_pml = true;
+            break;
+         }
+      }
+      if (in_pml) f = 0.0;
+   }
+}
+
+void source_im(const Vector &x, Vector &f)
+{
+   f = 0.0;
+}
+
+double wavespeed(const Vector &x)
+{
+   double ws;
+   ws = 1.0;
+   return ws;
+}
+
+void Mwavespeed(const Vector & x, DenseMatrix & M)
+{
+   M = 0.0;
+   M(0,0) = 1.0;
+   M(1,1) = 1.0;
+   // M(2,2) = 4.0*x(0)-1.0;
+   if (dim == 3) M(2,2) = 1.0;
+}
+
+
+void exact_re(const Vector & x, Vector & E)
+{
+   double curl2E[3];
+   maxwell_solution(x, E, curl2E);
+}
+void exact_im(const Vector & x, Vector & E)
+{
+   // double curl2E[3];
+   // maxwell_solution(x, E, curl2E);
+   E = 0.0;
+}
+void maxwell_solution(const Vector & x, double E[], double curl2E[])
+{
+   // point source
+   if (dim == 2)
+   {
+      // shift to avoid singularity
+      double x0 = x(0) + 0.1;
+      double x1 = x(1) + 0.1;
+      //
+      double r = sqrt(x0 * x0 + x1 * x1);
+
+      E[0] = cos(omega * r);
+      E[1] = 0.0;
+
+      double r_x = x0 / r;
+      double r_y = x1 / r;
+      double r_xy = -(r_x / r) * r_y;
+      double r_yx = r_xy;
+      double r_yy = (1.0 / r) * (1.0 - r_y * r_y);
+
+      curl2E[0] = omega * ((r_yy ) * sin(omega * r) + (omega * r_y * r_y) * cos(omega * r));
+      curl2E[1] = -omega * (r_yx * sin(omega * r) + omega * r_y * r_x * cos(omega * r));
+      curl2E[2] = 0.0;
+   }
+   else
+   {
+   // shift to avoid singularity
+      double x0 = x(0) + 0.1;
+      double x1 = x(1) + 0.1;
+      double x2 = x(2) + 0.1;
+      //
+      double r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
+
+      E[0] = cos(omega * r);
+      E[1] = 0.0;
+      E[2] = 0.0;
+
+      double r_x = x0 / r;
+      double r_y = x1 / r;
+      double r_z = x2 / r;
+      double r_xy = -(r_x / r) * r_y;
+      double r_xz = -(r_x / r) * r_z;
+      double r_yx = r_xy;
+      double r_yy = (1.0 / r) * (1.0 - r_y * r_y);
+      double r_zx = r_xz;
+      double r_zz = (1.0 / r) * (1.0 - r_z * r_z);
+
+      curl2E[0] = omega * ((r_yy + r_zz) * sin(omega * r) +
+                           (omega * r_y * r_y + omega * r_z * r_z) * cos(omega * r));
+      curl2E[1] = -omega * (r_yx * sin(omega * r) + omega * r_y * r_x * cos(omega * r));
+      curl2E[2] = -omega * (r_zx * sin(omega * r) + omega * r_z * r_x * cos(omega * r));
+   }
+}
+
+
+void ess_data_func(const Vector & x, Vector & E)
+{
+   E = 0.0;
+   if (x(1)==0.0) E[0] = sin(x(0)+x(1));
+
+   bool in_pml = false;
+   for (int i = 0; i<dim; i++)
+   {
+      if (x(i)<comp_bdr(i,0) || x(i)>comp_bdr(i,1))
+      {
+         in_pml = true;
+         break;
+      }
+   }
+   if (in_pml) E = 0.0;
+
+}
@@ -121,7 +121,9 @@ 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.
+   //    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.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -131,6 +133,7 @@ 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.
@@ -122,7 +122,9 @@ 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.
+   //    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).
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
   delete mesh;
   {
@@ -132,6 +134,7 @@ 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.
@@ -282,10 +282,6 @@ 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.
@@ -39,7 +39,6 @@ set(SRCS
  complex_fem.cpp
  convergence.cpp
  datacollection.cpp
-  doftrans.cpp
  eltrans.cpp
  estimators.cpp
  fe.cpp
@@ -106,7 +105,6 @@ 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
@@ -120,7 +118,6 @@ set(HDRS
  complex_fem.hpp
  convergence.hpp
  datacollection.hpp
-  doftrans.hpp
  eltrans.hpp
  estimators.hpp
  fe.hpp
@@ -167,7 +164,6 @@ set(HDRS
  tmop.hpp
  tmop/tmop_pa.hpp
  tmop_tools.hpp
-  tmop_amr.hpp
  gslib.hpp
  transfer.hpp
  lor.hpp
@@ -188,11 +184,6 @@ 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 (interior_face_integs.Size() > 0)
+   if (fbfi.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
-   domain_integs = bf->domain_integs;
+   dbfi = bf->dbfi;

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

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

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

   AllocMat();
 }
@@ -234,47 +234,46 @@ void BilinearForm::Finalize (int skip_zeros)

 void BilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi)
 {
-   domain_integs.Append(bfi);
-   domain_integs_marker.Append(NULL); // NULL marker means apply everywhere
+   dbfi.Append(bfi);
+   dbfi_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);
+   dbfi.Append(bfi);
+   dbfi_marker.Append(&elem_marker);
 }

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

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

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

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

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

 void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
@@ -286,14 +285,14 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
      return;
   }

-   if (domain_integs.Size())
+   if (dbfi.Size())
   {
      const FiniteElement &fe = *fes->GetFE(i);
      ElementTransformation *eltrans = fes->GetElementTransformation(i);
-      domain_integs[0]->AssembleElementMatrix(fe, *eltrans, elmat);
-      for (int k = 1; k < domain_integs.Size(); k++)
+      dbfi[0]->AssembleElementMatrix(fe, *eltrans, elmat);
+      for (int k = 1; k < dbfi.Size(); k++)
      {
-         domain_integs[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
+         dbfi[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
         elmat += elemmat;
      }
   }
@@ -307,14 +306,14 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)

 void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
 {
-   if (boundary_integs.Size())
+   if (bbfi.Size())
   {
      const FiniteElement &be = *fes->GetBE(i);
      ElementTransformation *eltrans = fes->GetBdrElementTransformation(i);
-      boundary_integs[0]->AssembleElementMatrix(be, *eltrans, elmat);
-      for (int k = 1; k < boundary_integs.Size(); k++)
+      bbfi[0]->AssembleElementMatrix(be, *eltrans, elmat);
+      for (int k = 1; k < bbfi.Size(); k++)
      {
-         boundary_integs[k]->AssembleElementMatrix(be, *eltrans, elemmat);
+         bbfi[k]->AssembleElementMatrix(be, *eltrans, elemmat);
         elmat += elemmat;
      }
   }
@@ -391,7 +390,6 @@ void BilinearForm::Assemble(int skip_zeros)
   }

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

@@ -409,14 +407,13 @@ void BilinearForm::Assemble(int skip_zeros)
   }
 #endif

-   if (domain_integs.Size())
+   if (dbfi.Size())
   {
-      for (int k = 0; k < domain_integs.Size(); k++)
+      for (int k = 0; k < dbfi.Size(); k++)
      {
-         if (domain_integs_marker[k] != NULL)
+         if (dbfi_marker[k] != NULL)
         {
-            MFEM_VERIFY(mesh->attributes.Size() ==
-                        domain_integs_marker[k]->Size(),
+            MFEM_VERIFY(mesh->attributes.Size() == dbfi_marker[k]->Size(),
                        "invalid element marker for domain integrator #"
                        << k << ", counting from zero");
         }
@@ -425,7 +422,7 @@ void BilinearForm::Assemble(int skip_zeros)
      for (int i = 0; i < fes -> GetNE(); i++)
      {
         int elem_attr = fes->GetMesh()->GetAttribute(i);
-         doftrans = fes->GetElementVDofs(i, vdofs);
+         fes->GetElementVDofs(i, vdofs);
         if (element_matrices)
         {
            elmat_p = &(*element_matrices)(i);
@@ -433,14 +430,14 @@ void BilinearForm::Assemble(int skip_zeros)
         else
         {
            elmat.SetSize(0);
-            for (int k = 0; k < domain_integs.Size(); k++)
+            for (int k = 0; k < dbfi.Size(); k++)
            {
-               if ( domain_integs_marker[k] == NULL ||
-                    (*(domain_integs_marker[k]))[elem_attr-1] == 1)
+               if ( dbfi_marker[k] == NULL ||
+                    (*(dbfi_marker[k]))[elem_attr-1] == 1)
               {
                  const FiniteElement &fe = *fes->GetFE(i);
                  eltrans = fes->GetElementTransformation(i);
-                  domain_integs[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
+                  dbfi[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
                  if (elmat.Size() == 0)
                  {
                     elmat = elemmat;
@@ -459,11 +456,6 @@ void BilinearForm::Assemble(int skip_zeros)
            {
               elmat_p = &elmat;
            }
-            if (doftrans)
-            {
-               doftrans->TransformDual(elmat);
-            }
-            elmat_p = &elmat;
         }
         if (static_cond)
         {
@@ -480,20 +472,20 @@ void BilinearForm::Assemble(int skip_zeros)
      }
   }

-   if (boundary_integs.Size())
+   if (bbfi.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 < boundary_integs.Size(); k++)
+      for (int k = 0; k < bbfi.Size(); k++)
      {
-         if (boundary_integs_marker[k] == NULL)
+         if (bbfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *boundary_integs_marker[k];
+         Array<int> &bdr_marker = *bbfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary integrator #"
                     << k << ", counting from zero");
@@ -509,47 +501,42 @@ void BilinearForm::Assemble(int skip_zeros)
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }

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

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

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

-   if (interior_face_integs.Size())
+   if (fbfi.Size())
   {
      FaceElementTransformations *tr;
      Array<int> vdofs2;
@@ -563,19 +550,18 @@ void BilinearForm::Assemble(int skip_zeros)
            fes -> GetElementVDofs (tr -> Elem1No, vdofs);
            fes -> GetElementVDofs (tr -> Elem2No, vdofs2);
            vdofs.Append (vdofs2);
-            for (int k = 0; k < interior_face_integs.Size(); k++)
+            for (int k = 0; k < fbfi.Size(); k++)
            {
-               interior_face_integs[k]->
-               AssembleFaceMatrix(*fes->GetFE(tr->Elem1No),
-                                  *fes->GetFE(tr->Elem2No),
-                                  *tr, elemmat);
+               fbfi[k] -> AssembleFaceMatrix (*fes -> GetFE (tr -> Elem1No),
+                                              *fes -> GetFE (tr -> Elem2No),
+                                              *tr, elemmat);
               mat -> AddSubMatrix (vdofs, vdofs, elemmat, skip_zeros);
            }
         }
      }
   }

-   if (boundary_face_integs.Size())
+   if (bfbfi.Size())
   {
      FaceElementTransformations *tr;
      const FiniteElement *fe1, *fe2;
@@ -584,14 +570,14 @@ 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 < boundary_face_integs.Size(); k++)
+      for (int k = 0; k < bfbfi.Size(); k++)
      {
-         if (boundary_face_integs_marker[k] == NULL)
+         if (bfbfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *boundary_face_integs_marker[k];
+         Array<int> &bdr_marker = *bfbfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary face integrator #"
                     << k << ", counting from zero");
@@ -615,14 +601,12 @@ 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 < boundary_face_integs.Size(); k++)
+            for (int k = 0; k < bfbfi.Size(); k++)
            {
-               if (boundary_face_integs_marker[k] &&
-                   (*boundary_face_integs_marker[k])[bdr_attr-1] == 0)
-               { continue; }
+               if (bfbfi_marker[k] &&
+                   (*bfbfi_marker[k])[bdr_attr-1] == 0) { continue; }

-               boundary_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr,
-                                                              elemmat);
+               bfbfi[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elemmat);
               mat -> AddSubMatrix (vdofs, vdofs, elemmat, skip_zeros);
            }
         }
@@ -736,8 +720,8 @@ 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.MakeRef(x, 0, x.Size());
-         B.MakeRef(b, 0, b.Size());
+         X.NewMemoryAndSize(x.GetMemory(), x.Size(), false);
+         B.NewMemoryAndSize(b.GetMemory(), b.Size(), false);
         if (!copy_interior) { X.SetSubVectorComplement(ess_tdof_list, 0.0); }
      }
   }
@@ -873,7 +857,7 @@ void BilinearForm::RecoverFEMSolution(const Vector &X,

 void BilinearForm::ComputeElementMatrices()
 {
-   if (element_matrices || domain_integs.Size() == 0 || fes->GetNE() == 0)
+   if (element_matrices || dbfi.Size() == 0 || fes->GetNE() == 0)
   {
      return;
   }
@@ -902,11 +886,11 @@ void BilinearForm::ComputeElementMatrices()
 #endif
      fes->GetElementTransformation(i, &eltrans);

-      domain_integs[0]->AssembleElementMatrix(fe, eltrans, elmat);
-      for (int k = 1; k < domain_integs.Size(); k++)
+      dbfi[0]->AssembleElementMatrix(fe, eltrans, elmat);
+      for (int k = 1; k < dbfi.Size(); k++)
      {
         // note: some integrators may not be thread-safe
-         domain_integs[k]->AssembleElementMatrix(fe, eltrans, tmp);
+         dbfi[k]->AssembleElementMatrix(fe, eltrans, tmp);
         elmat += tmp;
      }
      elmat.ClearExternalData();
@@ -1121,12 +1105,10 @@ BilinearForm::~BilinearForm()
   if (!extern_bfs)
   {
      int 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]; }
+      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]; }
   }

   delete ext;
@@ -1159,13 +1141,13 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
   ext = NULL;

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

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

   assembly = AssemblyLevel::LEGACY;
   ext = NULL;
@@ -1254,8 +1236,7 @@ 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
@@ -1286,39 +1267,38 @@ void MixedBilinearForm::GetBlocks(Array2D<SparseMatrix *> &blocks) const

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

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

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

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

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

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

 void MixedBilinearForm::Assemble (int skip_zeros)
@@ -1329,10 +1309,9 @@ void MixedBilinearForm::Assemble (int skip_zeros)
      return;
   }

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

   Mesh *mesh = test_fes -> GetMesh();

@@ -1341,45 +1320,37 @@ void MixedBilinearForm::Assemble (int skip_zeros)
      mat = new SparseMatrix(height, width);
   }

-   if (domain_integs.Size())
+   if (dbfi.Size())
   {
      for (int i = 0; i < test_fes -> GetNE(); i++)
      {
-         dom_dof_trans = trial_fes -> GetElementVDofs (i, trial_vdofs);
-         ran_dof_trans = test_fes  -> GetElementVDofs (i, test_vdofs);
+         trial_fes -> GetElementVDofs (i, tr_vdofs);
+         test_fes  -> GetElementVDofs (i, te_vdofs);
         eltrans = test_fes -> GetElementTransformation (i);
-
-         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
-         elmat = 0.0;
-         for (int k = 0; k < domain_integs.Size(); k++)
+         for (int k = 0; k < dbfi.Size(); k++)
         {
-            domain_integs[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
-                                                        *test_fes  -> GetFE(i),
-                                                        *eltrans, elemmat);
-            elmat += elemmat;
+            dbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
+                                               *test_fes  -> GetFE(i),
+                                               *eltrans, elemmat);
+            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
         }
-         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 (boundary_integs.Size())
+   if (bbfi.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 < boundary_integs.Size(); k++)
+      for (int k = 0; k < bbfi.Size(); k++)
      {
-         if (boundary_integs_marker[k] == NULL)
+         if (bbfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *boundary_integs_marker[k];
+         Array<int> &bdr_marker = *bbfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary integrator #"
                     << k << ", counting from zero");
@@ -1394,48 +1365,40 @@ void MixedBilinearForm::Assemble (int skip_zeros)
         const int bdr_attr = mesh->GetBdrAttribute(i);
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }

-         dom_dof_trans = trial_fes -> GetBdrElementVDofs (i, trial_vdofs);
-         ran_dof_trans = test_fes  -> GetBdrElementVDofs (i, test_vdofs);
+         trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
+         test_fes  -> GetBdrElementVDofs (i, te_vdofs);
         eltrans = test_fes -> GetBdrElementTransformation (i);
-
-         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
-         elmat = 0.0;
-         for (int k = 0; k < boundary_integs.Size(); k++)
+         for (int k = 0; k < bbfi.Size(); k++)
         {
-            if (boundary_integs_marker[k] &&
-                (*boundary_integs_marker[k])[bdr_attr-1] == 0) { continue; }
+            if (bbfi_marker[k] &&
+                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }

-            boundary_integs[k]->AssembleElementMatrix2 (*trial_fes -> GetBE(i),
-                                                        *test_fes  -> GetBE(i),
-                                                        *eltrans, elemmat);
-            elmat += elemmat;
+            bbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetBE(i),
+                                               *test_fes  -> GetBE(i),
+                                               *eltrans, elemmat);
+            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
         }
-         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 (trace_face_integs.Size())
+   if (tfbfi.Size())
   {
      FaceElementTransformations *ftr;
-      Array<int> test_vdofs2;
+      Array<int> te_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, trial_vdofs);
-         test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
+         trial_fes->GetFaceVDofs(i, tr_vdofs);
+         test_fes->GetElementVDofs(ftr->Elem1No, te_vdofs);
         trial_face_fe = trial_fes->GetFaceElement(i);
         test_fe1 = test_fes->GetFE(ftr->Elem1No);
         if (ftr->Elem2No >= 0)
         {
-            test_fes->GetElementVDofs(ftr->Elem2No, test_vdofs2);
-            test_vdofs.Append(test_vdofs2);
+            test_fes->GetElementVDofs(ftr->Elem2No, te_vdofs2);
+            te_vdofs.Append(te_vdofs2);
            test_fe2 = test_fes->GetFE(ftr->Elem2No);
         }
         else
@@ -1445,16 +1408,16 @@ void MixedBilinearForm::Assemble (int skip_zeros)
            // want to actually make a fake element.
            test_fe2 = test_fe1;
         }
-         for (int k = 0; k < trace_face_integs.Size(); k++)
+         for (int k = 0; k < tfbfi.Size(); k++)
         {
-            trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
-                                                     *test_fe2, *ftr, elemmat);
-            mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
+            tfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                         *ftr, elemmat);
+            mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
         }
      }
   }

-   if (boundary_trace_face_integs.Size())
+   if (btfbfi.Size())
   {
      FaceElementTransformations *ftr;
      Array<int> te_vdofs2;
@@ -1464,17 +1427,17 @@ 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 < boundary_trace_face_integs.Size(); k++)
+      for (int k = 0; k < btfbfi.Size(); k++)
      {
-         if (boundary_trace_face_integs_marker[k] == NULL)
+         if (btfbfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *boundary_trace_face_integs_marker[k];
+         Array<int> &bdr_marker = *btfbfi_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];
@@ -1489,25 +1452,22 @@ void MixedBilinearForm::Assemble (int skip_zeros)
         ftr = mesh->GetBdrFaceTransformations(i);
         if (ftr)
         {
-            trial_fes->GetFaceVDofs(ftr->ElementNo, trial_vdofs);
-            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
+            trial_fes->GetFaceVDofs(ftr->ElementNo, tr_vdofs);
+            test_fes->GetElementVDofs(ftr->Elem1No, te_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 < boundary_trace_face_integs.Size(); k++)
+            for (int k = 0; k < btfbfi.Size(); k++)
            {
-               if (boundary_trace_face_integs_marker[k] &&
-                   (*boundary_trace_face_integs_marker[k])[bdr_attr-1] == 0)
-               { continue; }
+               if (btfbfi_marker[k] &&
+                   (*btfbfi_marker[k])[bdr_attr-1] == 0) { continue; }

-               boundary_trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe,
-                                                                 *test_fe1,
-                                                                 *test_fe2,
-                                                                 *ftr, elemmat);
-               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
+               btfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                             *ftr, elemmat);
+               mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
            }
         }
      }
@@ -1597,17 +1557,15 @@ void MixedBilinearForm::ConformingAssemble()

 void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
 {
-   if (domain_integs.Size())
+   if (dbfi.Size())
   {
      const FiniteElement &trial_fe = *trial_fes->GetFE(i);
      const FiniteElement &test_fe = *test_fes->GetFE(i);
      ElementTransformation *eltrans = test_fes->GetElementTransformation(i);
-      domain_integs[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans,
-                                               elmat);
-      for (int k = 1; k < domain_integs.Size(); k++)
+      dbfi[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans, elmat);
+      for (int k = 1; k < dbfi.Size(); k++)
      {
-         domain_integs[k]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans,
-                                                  elemmat);
+         dbfi[k]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans, elemmat);
         elmat += elemmat;
      }
   }
@@ -1622,17 +1580,15 @@ void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)

 void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
 {
-   if (boundary_integs.Size())
+   if (bbfi.Size())
   {
      const FiniteElement &trial_be = *trial_fes->GetBE(i);
      const FiniteElement &test_be = *test_fes->GetBE(i);
      ElementTransformation *eltrans = test_fes->GetBdrElementTransformation(i);
-      boundary_integs[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans,
-                                                 elmat);
-      for (int k = 1; k < boundary_integs.Size(); k++)
+      bbfi[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans, elmat);
+      for (int k = 1; k < bbfi.Size(); k++)
      {
-         boundary_integs[k]->AssembleElementMatrix2(trial_be, test_be, *eltrans,
-                                                    elemmat);
+         bbfi[k]->AssembleElementMatrix2(trial_be, test_be, *eltrans, elemmat);
         elmat += elemmat;
      }
   }
@@ -1732,10 +1688,10 @@ 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)
@@ -1773,17 +1729,17 @@ void MixedBilinearForm::FormRectangularSystemMatrix(
   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;
   }

@@ -1821,13 +1777,10 @@ MixedBilinearForm::~MixedBilinearForm()
   if (!extern_bfs)
   {
      int 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]; }
+      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]; }
   }
   delete ext;
 }
@@ -1869,8 +1822,6 @@ 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;

@@ -1879,33 +1830,27 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
      mat = new SparseMatrix(height, width);
   }

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

-         domain_integs[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                  totelmat);
-         for (int j = 1; j < domain_integs.Size(); j++)
+         dbfi[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
+         for (int j = 1; j < dbfi.Size(); j++)
         {
-            domain_integs[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                     elmat);
+            dbfi[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 (trace_face_integs.Size())
+   if (tfbfi.Size())
   {
      const int nfaces = test_fes->GetMesh()->GetNumFaces();
      for (int i = 0; i < nfaces; i++)
@@ -1916,12 +1861,10 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
         dom_fe = trial_fes->GetFaceElement(i);
         ran_fe = test_fes->GetFaceElement(i);

-         trace_face_integs[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                      totelmat);
-         for (int j = 1; j < trace_face_integs.Size(); j++)
+         tfbfi[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
+         for (int j = 1; j < tfbfi.Size(); j++)
         {
-            trace_face_integs[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                         elmat);
+            tfbfi[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
            totelmat += elmat;
         }
         mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
@@ -84,29 +84,28 @@ protected:
       the BilinearForm. */
   long sequence;

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

   /// Set of Domain Integrators to be applied.
-   Array<BilinearFormIntegrator*> domain_integs;
+   Array<BilinearFormIntegrator*> dbfi;
   /// 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;
+   Array<Array<int>*>             dbfi_marker;

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

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

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

   DenseMatrix elemmat;
   Array<int>  vdofs;
@@ -232,25 +231,24 @@ public:
   void AllocateMatrix() { if (mat == NULL) { AllocMat(); } }

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

   /// Access all the integrators added with AddBoundaryIntegrator().
-   Array<BilinearFormIntegrator*> *GetBBFI() { return &boundary_integs; }
+   Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
   /** @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 &boundary_integs_marker; }
+   Array<Array<int>*> *GetBBFI_Marker() { return &bbfi_marker; }

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

   /// Access all integrators added with AddBdrFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetBFBFI() { return &boundary_face_integs; }
+   Array<BilinearFormIntegrator*> *GetBFBFI() { return &bfbfi; }
   /** @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 &boundary_face_integs_marker; }
+   Array<Array<int>*> *GetBFBFI_Marker() { return &bfbfi_marker; }

   /// Returns a reference to: \f$ M_{ij} \f$
   const double &operator()(int i, int j) { return (*mat)(i,j); }
@@ -654,25 +652,23 @@ protected:
       Partial Assembly (PA), or Matrix Free assembly (MF). */
   MixedBilinearFormExtension *ext;

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

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

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

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

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

   DenseMatrix elemmat;
   Array<int>  trial_vdofs, test_vdofs;
@@ -766,26 +762,24 @@ public:
                                   Array<int> &bdr_marker);

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

   /// Access all integrators added with AddBoundaryIntegrator().
-   Array<BilinearFormIntegrator*> *GetBBFI() { return &boundary_integs; }
+   Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
   /** @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 &boundary_integs_marker; }
+   Array<Array<int>*> *GetBBFI_Marker() { return &bbfi_marker; }

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

   /// Access all integrators added with AddBdrTraceFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetBTFBFI()
-   { return &boundary_trace_face_integs; }
+   Array<BilinearFormIntegrator*> *GetBTFBFI() { return &btfbfi; }
   /** @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 &boundary_trace_face_integs_marker; }
+   Array<Array<int>*> *GetBTFBFI_Marker() { return &btfbfi_marker; }

   /// Sets all sparse values of \f$ M \f$ to @a a.
   void operator=(const double a) { *mat = a; }
@@ -1010,7 +1004,7 @@ public:
   { AddTraceFaceIntegrator(di); }

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

   /// 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->AddMultTranspose(faceIntY, y);
+         int_face_restrict_lex->MultTranspose(faceIntY, y);
      }
   }

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

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

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

@@ -490,7 +490,7 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultTransposePA(faceBdrX, faceBdrY);
         }
-         bdr_face_restrict_lex->AddMultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->MultTranspose(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->AddMultTranspose(faceIntY, y);
+         int_face_restrict_lex->MultTranspose(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->AddMultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->MultTranspose(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->AddMultTranspose(faceIntY, y);
+         int_face_restrict_lex->MultTranspose(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->AddMultTranspose(faceBdrY, y);
+         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
      }
   }
 }
@@ -72,8 +72,8 @@ protected:
   mutable Vector faceIntX, faceIntY;
   mutable Vector faceBdrX, faceBdrY;
   const Operator *elem_restrict; // Not owned
-   const FaceRestriction *int_face_restrict_lex; // Not owned
-   const FaceRestriction *bdr_face_restrict_lex; // Not owned
+   const Operator *int_face_restrict_lex; // Not owned
+   const Operator *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 FaceRestriction *int_face_restrict_lex; // Not owned
-   const FaceRestriction *bdr_face_restrict_lex; // Not owned
+   const Operator *int_face_restrict_lex; // Not owned
+   const Operator *bdr_face_restrict_lex; // Not owned

 public:
   MFBilinearFormExtension(BilinearForm *form);
@@ -175,11 +175,6 @@ 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)
@@ -207,12 +202,6 @@ 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)
 {
@@ -220,12 +209,6 @@ 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)
 {
@@ -233,15 +216,6 @@ 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)
 {
@@ -1777,16 +1751,15 @@ 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, spaceDim);
+   dshapedxt.SetSize(trial_nd,dim);
   dshapedxi.SetSize(trial_nd);
-   invdfdx.SetSize(dim, spaceDim);
+   invdfdx.SetSize(dim);
   shape.SetSize (test_nd);

   const IntegrationRule *ir = IntRule;
@@ -261,8 +261,6 @@ 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);
@@ -330,8 +328,6 @@ 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);
@@ -350,8 +346,6 @@ 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);
@@ -370,8 +364,6 @@ private:
 public:
   SumIntegrator(int own_integs = 1) { own_integrators = own_integs; }

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

@@ -711,7 +703,7 @@ protected:
   {
      return "MixedScalarDerivativeIntegrator:  "
             "Trial and test spaces must both be scalar fields in 1D "
-             "and the trial space must implement CalcDShape.";
+             "and the trial space must implement CaldDShape.";
   }

   inline virtual void CalcTrialShape(const FiniteElement & trial_fe,
@@ -2936,11 +2928,11 @@ 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>
-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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -69,14 +69,14 @@ void EAConvectionAssemble1D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -146,14 +146,14 @@ void EAConvectionAssemble2D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   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
-void PAConvectionSetup2D(const int NQ,
-                         const int NE,
-                         const Array<double> &w,
-                         const Vector &j,
-                         const Vector &vel,
-                         const double alpha,
-                         Vector &op)
+static 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 @@ void PAConvectionSetup2D(const int NQ,
 }

 // PA Convection Assemble 3D kernel
-void PAConvectionSetup3D(const int NQ,
-                         const int NE,
-                         const Array<double> &w,
-                         const Vector &j,
-                         const Vector &vel,
-                         const double alpha,
-                         Vector &op)
+static 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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 void SmemPAConvectionApply3D(const int ne,
                             const Array<double> &b,
                             const Array<double> &g,
@@ -16,12 +16,12 @@
 namespace mfem
 {

-void EADGTraceAssemble1DInt(const int NF,
-                            const Array<double> &basis,
-                            const Vector &padata,
-                            Vector &eadata_int,
-                            Vector &eadata_ext,
-                            const bool add)
+static 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 @@ void EADGTraceAssemble1DInt(const int NF,
   });
 }

-void EADGTraceAssemble1DBdr(const int NF,
-                            const Array<double> &basis,
-                            const Vector &padata,
-                            Vector &eadata_bdr,
-                            const bool add)
+static 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 @@ void EADGTraceAssemble1DBdr(const int NF,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -128,13 +128,13 @@ void EADGTraceAssemble2DInt(const int NF,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -170,14 +170,14 @@ void EADGTraceAssemble2DBdr(const int NF,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -268,13 +268,13 @@ void EADGTraceAssemble3DInt(const int NF,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   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
-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)
+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)
 {
   const int VDIM = 2;

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

-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)
+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)
 {
   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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0> static
 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>
+template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 0> static
 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>
-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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -68,14 +68,14 @@ void EADiffusionAssemble1D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -145,14 +145,14 @@ void EADiffusionAssemble2D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -496,14 +496,14 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -562,14 +562,14 @@ 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>
-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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -656,14 +656,14 @@ void SmemPADiffusionDiagonal2D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -757,14 +757,14 @@ void PADiffusionDiagonal3D(const int NE,

 // Shared memory PA Diffusion Diagonal 3D kernel
 template<int T_D1D = 0, int T_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)
+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)
 {
   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -1034,17 +1034,17 @@ static void OccaPADiffusionApply3D(const int D1D,

 // PA Diffusion Apply 2D kernel
 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1156,15 +1156,15 @@ 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>
-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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1314,16 +1314,16 @@ void SmemPADiffusionApply2D(const int NE,

 // PA Diffusion Apply 3D kernel
 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -1533,15 +1533,15 @@ static MFEM_HOST_DEVICE inline double sign(const int q, const int d)
 }

 template<int T_D1D = 0, int T_Q1D = 0>
-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)
+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)
 {
   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
-void PADivergenceSetup2D(const int Q1D,
-                         const int NE,
-                         const Array<double> &w,
-                         const Vector &j,
-                         const double COEFF,
-                         Vector &op)
+static 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 @@ void PADivergenceSetup2D(const int Q1D,
 }

 // PA Divergence Assemble 3D kernel
-void PADivergenceSetup3D(const int Q1D,
-                         const int NE,
-                         const Array<double> &w,
-                         const Vector &j,
-                         const double COEFF,
-                         Vector &op)
+static 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>
-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)
+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)
 {
   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 @@ 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>
-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)
+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)
 {
   // TODO
   MFEM_ASSERT(false, "SHARED MEM NOT PROGRAMMED YET");
@@ -298,16 +298,16 @@ 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>
-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)
+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)
 {
   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 @@ 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>
-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)
+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)
 {
   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 @@ 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>
-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)
+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)
 {
   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 @@ 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>
-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)
+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)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -70,12 +70,12 @@ namespace mfem
   the \b MFEM_SHARED keyword for local arrays. */

 // PA Gradient Assemble 2D kernel
-void PAGradientSetup2D(const int Q1D,
-                       const int NE,
-                       const Array<double> &w,
-                       const Vector &j,
-                       const Vector &c,
-                       Vector &op)
+static 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();
@@ -105,12 +105,12 @@ void PAGradientSetup2D(const int Q1D,
 }

 // PA Gradient Assemble 3D kernel
-void PAGradientSetup3D(const int Q1D,
-                       const int NE,
-                       const Array<double> &w,
-                       const Vector &j,
-                       const Vector &c,
-                       Vector &op)
+static 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();
@@ -254,16 +254,16 @@ void GradientIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,

 // PA Gradient Apply 2D kernel
 template<int T_TR_D1D = 0, int T_TE_D1D = 0, int T_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)
+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)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -384,16 +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>
-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)
+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)
 {
   const int TR_D1D = T_TR_D1D ? T_TR_D1D : tr_d1d;
   const int TE_D1D = T_TE_D1D ? T_TE_D1D : te_d1d;
@@ -579,16 +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>
-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)
+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)
 {
   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
-void PACurlCurlSetup2D(const int Q1D,
-                       const int NE,
-                       const Array<double> &w,
-                       const Vector &j,
-                       Vector &coeff,
-                       Vector &op)
+static 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 @@ void PACurlCurlSetup2D(const int Q1D,
 }

 // PA H(curl) curl-curl assemble 3D kernel
-void PACurlCurlSetup3D(const int Q1D,
-                       const int coeffDim,
-                       const int NE,
-                       const Array<double> &w,
-                       const Vector &j,
-                       Vector &coeff,
-                       Vector &op)
+static 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)
   }
 }

-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)
+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)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HCURL_MAX_D1D;
@@ -1166,19 +1166,19 @@ void PACurlCurlApply2D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-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)
+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)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -1677,19 +1677,19 @@ void PACurlCurlApply3D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-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)
+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)
 {
   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
   }
 }

-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)
+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)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
@@ -2087,16 +2087,16 @@ void PACurlCurlAssembleDiagonal2D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-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)
+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)
 {
   constexpr static int VDIM = 3;
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
@@ -2273,16 +2273,16 @@ void PACurlCurlAssembleDiagonal3D(const int D1D,
 }

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-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)
+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)
 {
   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>
-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)
+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)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -3297,16 +3297,16 @@ 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>
-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)
+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)
 {
   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
@@ -3585,18 +3585,18 @@ 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>
-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)
+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)
 {
   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>
-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)
+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)
 {
   // See PAHcurlL2Apply3D for comments.

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

 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
-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)
+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)
 {
   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.
-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_)
+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_)
 {
   auto B = Reshape(B_.Read(), c_dofs1D, c_dofs1D);
   auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
@@ -4753,12 +4753,12 @@ void PAHcurlApplyGradient2D(const int c_dofs1D,
 }

 // Specialization of PAHcurlApplyGradient2D to the case where B is identity
-void PAHcurlApplyGradient2DBId(const int c_dofs1D,
-                               const int o_dofs1D,
-                               const int NE,
-                               const Array<double> &G_,
-                               const Vector &x_,
-                               Vector &y_)
+static 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 @@ void PAHcurlApplyGradient2DBId(const int c_dofs1D,
   });
 }

-void PAHcurlApplyGradientTranspose2D(
+static 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 @@ void PAHcurlApplyGradientTranspose2D(

 // Specialization of PAHcurlApplyGradientTranspose2D to the case where
 // B is identity
-void PAHcurlApplyGradientTranspose2DBId(
+static 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 @@ void PAHcurlApplyGradientTranspose2DBId(
   });
 }

-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_)
+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_)
 {
   auto B = Reshape(B_.Read(), c_dofs1D, c_dofs1D);
   auto G = Reshape(G_.Read(), o_dofs1D, c_dofs1D);
@@ -5154,12 +5154,12 @@ void PAHcurlApplyGradient3D(const int c_dofs1D,
 }

 // Specialization of PAHcurlApplyGradient3D to the case where
-void PAHcurlApplyGradient3DBId(const int c_dofs1D,
-                               const int o_dofs1D,
-                               const int NE,
-                               const Array<double> &G_,
-                               const Vector &x_,
-                               Vector &y_)
+static 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 @@ void PAHcurlApplyGradient3DBId(const int c_dofs1D,
   });
 }

-void PAHcurlApplyGradientTranspose3D(
+static 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 @@ void PAHcurlApplyGradientTranspose3D(
 }

 // Specialization of PAHcurlApplyGradientTranspose3D to the case where
-void PAHcurlApplyGradientTranspose3DBId(
+static 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
   }
 }

-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_)
+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_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6002,14 +6002,14 @@ void PAHcurlVecH1IdentityApply3D(const int c_dofs1D,
   });
 }

-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_)
+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_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6228,14 +6228,14 @@ void PAHcurlVecH1IdentityApplyTranspose3D(const int c_dofs1D,
   });
 }

-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_)
+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_)
 {
   auto Bc = Reshape(Bclosed.Read(), c_dofs1D, c_dofs1D);
   auto Bo = Reshape(Bopen.Read(), o_dofs1D, c_dofs1D);
@@ -6327,14 +6327,14 @@ void PAHcurlVecH1IdentityApply2D(const int c_dofs1D,
   });
 }

-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_)
+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_)
 {
   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
-void PADivDivSetup2D(const int Q1D,
-                     const int NE,
-                     const Array<double> &w,
-                     const Vector &j,
-                     Vector &coeff_,
-                     Vector &op)
+static 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 @@ void PADivDivSetup2D(const int Q1D,
   });
 }

-void PADivDivSetup3D(const int Q1D,
-                     const int NE,
-                     const Array<double> &w,
-                     const Vector &j,
-                     Vector &coeff_,
-                     Vector &op)
+static 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 @@ void PADivDivSetup3D(const int Q1D,
   });
 }

-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_)
+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_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -718,16 +718,16 @@ void PADivDivApply2D(const int D1D,
   }); // end of element loop
 }

-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_)
+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_)
 {
   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
   }
 }

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

-void PADivDivAssembleDiagonal3D(const int D1D,
-                                const int Q1D,
-                                const int NE,
-                                const Array<double> &Bo_,
-                                const Array<double> &Gc_,
-                                const Vector &op_,
-                                Vector &diag_)
+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_)
 {
   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
-void PADivL2Setup2D(const int Q1D,
-                    const int NE,
-                    const Array<double> &w,
-                    Vector &coeff_,
-                    Vector &op)
+static 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 @@ void PADivL2Setup2D(const int Q1D,
   });
 }

-void PADivL2Setup3D(const int Q1D,
-                    const int NE,
-                    const Array<double> &w,
-                    Vector &coeff_,
-                    Vector &op)
+static 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.
-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_)
+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_)
 {
   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 @@ 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.
-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_)
+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_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -1494,16 +1494,16 @@ void PAHdivL2Apply2D(const int D1D,
   }); // end of element loop
 }

-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_)
+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_)
 {
   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 @@ void PAHdivL2ApplyTranspose3D(const int D1D,
   }); // end of element loop
 }

-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_)
+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_)
 {
   constexpr static int VDIM = 2;
   constexpr static int MAX_D1D = HDIV_MAX_D1D;
@@ -1791,16 +1791,16 @@ void VectorFEDivergenceIntegrator::AddMultTransposePA(const Vector &x,
   }
 }

-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_)
+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_)
 {
   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 @@ void PAHdivL2AssembleDiagonal_ADAt_3D(const int D1D,
   }); // end of element loop
 }

-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_)
+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_)
 {
   constexpr static int VDIM = 2;

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

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -67,13 +67,13 @@ void EAMassAssemble1D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -139,13 +139,13 @@ void EAMassAssemble2D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -155,12 +155,12 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 }

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

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

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

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

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -661,14 +661,14 @@ void PAMassApply2D(const int NE,
 }

 template<int T_D1D = 0, int T_Q1D = 0, int T_NBZ = 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)
+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)
 {
   MFEM_CONTRACT_VAR(bt_);
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -784,14 +784,14 @@ void SmemPAMassApply2D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -925,14 +925,14 @@ void PAMassApply3D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   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
-void PAVectorDiffusionSetup2D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              const Vector &c,
-                              Vector &op)
+static 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();
@@ -59,12 +59,12 @@ void PAVectorDiffusionSetup2D(const int Q1D,
 }

 // PA Diffusion Assemble 3D kernel
-void PAVectorDiffusionSetup3D(const int Q1D,
-                              const int NE,
-                              const Array<double> &w,
-                              const Vector &j,
-                              const Vector &c,
-                              Vector &op)
+static 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();
@@ -251,7 +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>
+template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0> static
 void PAVectorDiffusionApply2D(const int NE,
                              const Array<double> &b,
                              const Array<double> &g,
@@ -374,7 +374,7 @@ void PAVectorDiffusionApply2D(const int NE,

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

 template<int T_D1D = 0, int T_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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -673,13 +673,13 @@ void PAVectorDiffusionDiagonal2D(const int NE,
 }

 template<int T_D1D = 0, int T_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)
+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)
 {
   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>
-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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -201,14 +201,14 @@ void PAVectorMassApply2D(const int NE,

 template<const int T_D1D = 0,
         const int T_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)
+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)
 {
   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>
-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)
+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)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
@@ -431,13 +431,13 @@ void PAVectorMassAssembleDiagonal2D(const int NE,
 }

 template<const int T_D1D = 0, const int T_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)
+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)
 {
   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
   {
@@ -629,6 +629,27 @@ void MatrixVectorProductCoefficient::Eval(Vector &V, ElementTransformation &T,
   ma.Mult(vb, V);
 }

+
+MatrixMatrixProductCoefficient::MatrixMatrixProductCoefficient(MatrixCoefficient &A,
+                                           MatrixCoefficient &B)
+   : MatrixCoefficient(A.GetHeight(), A.GetWidth()),
+     a(&A), b(&B),
+     ma(A.GetHeight(), A.GetWidth()), 
+     mb(B.GetHeight(), B.GetWidth())
+{
+   MFEM_ASSERT(A.GetWidth() == B.GetHeight(),
+               "MatrixMatrixProductCoefficient:  "
+               "Arguments must have the same dimensions.");
+}
+
+void MatrixMatrixProductCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                          const IntegrationPoint &ip)
+{
+   a->Eval(ma, T, ip);
+   b->Eval(mb, T, ip);
+   Mult(ma, mb, M);
+}
+
 void IdentityMatrixCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
                                     const IntegrationPoint &ip)
 {
@@ -1470,6 +1470,42 @@ public:
                     const IntegrationPoint &ip);
 };

+/** @brief Matrix coefficient defined as a product of two 
+    matrix coefficients */
+class MatrixMatrixProductCoefficient : public MatrixCoefficient
+{
+private:
+   MatrixCoefficient * a;
+   MatrixCoefficient * b;
+
+   mutable DenseMatrix ma;
+   mutable DenseMatrix mb;
+
+public:
+   /// Constructor with two coefficients.  Result is A*B.
+   MatrixMatrixProductCoefficient(MatrixCoefficient &A, MatrixCoefficient &B);
+
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
+   /// Reset the vector coefficient
+   void SetBCoef(MatrixCoefficient &B) { b = &B; }
+   /// Return the vector coefficient
+   MatrixCoefficient * GetBCoef() const { return b; }
+
+   /// Evaluate the vector coefficient at @a ip.
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
+/// Convenient alias for the MatrixVectorProductCoefficient
+typedef MatrixMatrixProductCoefficient MatMatCoefficient;
+
+
+
+
 /// Matrix coefficient defined as the linear combination of two matrices
 class MatrixSumCoefficient : public MatrixCoefficient
 {
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
psocratis	39150a110c	Merge branch 'master' into DST-maxwell-solver-dev	2021-06-16 10:30:33 -07:00
psocratis	1bd031a948	ParDST first commit in new (clean) branch	2020-12-21 11:36:56 -08:00