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
105 changed files with 7688 additions and 2584 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
@@ -48,58 +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

 # 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 and setup_baseline phases to download content outside of mfem
-#   directory.
+# - 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
-  needs: []
-
-# 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.
-setup_baseline:
-  tags:
-    - shell
-    - quartz
-  stage: setup_baseline
  variables:
    GIT_STRATEGY: none
  script:
@@ -25,7 +25,7 @@
 .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:
@@ -94,7 +94,6 @@ q_report_failure:
 .build_and_test_on_quartz:
  extends: [.build_toss_3_x86_64_ib_script, .on_quartz]
  stage: q_build_and_test
-  needs: [setup]

 # Build MFEM
 debug_ser_gcc_4_9_3:
@@ -140,7 +139,7 @@ opt_par_gcc_6_1_0_pumi:
 # Baseline
 baselinecheck_mfem_intel_quartz:
  extends: [.baselinecheck_mfem, .on_quartz]
-  needs: [setup_baseline]
+  needs: [setup]

 update_autotest:
  extends: [.on_quartz]
@@ -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
@@ -173,11 +173,7 @@ Version 4.2.1 (development)
  mixed meshes. The LOR Transfer miniapp (miniapps/tools/lor-transfer.cpp) now
  supports meshes with any element geometry.

- Testing improvements:
-  * Transitioned from Travis to GitHub Action for testing/CI on GitHub.
-  * Effectively remove Travis from CI.
-  * Use Spack (and Uberenv) to automate TPL building in LLNL GitLab tests.
-  * Added a set of suggested git hooks for developers in config/githooks.
+- 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,
@@ -235,15 +231,6 @@ Version 4.2.1 (development)

 - Added makefile rule to generate TAGS table for vi or Emacs users.

-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`.
-
 libCEED integration improvements
 --------------------------------
 - Refactor the libCEED integration
@@ -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
@@ -96,9 +91,8 @@ The MFEM source code has the following structure:
 ```
  .
  ├── config
-  │   ├── cmake
-  │   │    └── ...
-  │   └── githooks
+  │   └── cmake
+  │       └── ...
  ├── data
  ├── doc
  ├── examples
@@ -369,10 +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.

@@ -380,20 +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.
@@ -413,7 +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.
@@ -530,7 +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
@@ -592,17 +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.
@@ -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
@@ -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);
@@ -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;
+
+}
@@ -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;
      }
   }
@@ -408,14 +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");
         }
@@ -432,14 +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;
@@ -474,20 +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");
@@ -506,21 +504,21 @@ void BilinearForm::Assemble(int skip_zeros)
         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 (!static_cond)
@@ -538,7 +536,7 @@ void BilinearForm::Assemble(int skip_zeros)
      }
   }

-   if (interior_face_integs.Size())
+   if (fbfi.Size())
   {
      FaceElementTransformations *tr;
      Array<int> vdofs2;
@@ -552,19 +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;
@@ -573,14 +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");
@@ -604,14 +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);
            }
         }
@@ -862,7 +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;
   }
@@ -891,11 +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();
@@ -1110,12 +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;
@@ -1148,13 +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;
@@ -1243,8 +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
@@ -1275,39 +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)
@@ -1329,37 +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++)
      {
         trial_fes -> GetElementVDofs (i, tr_vdofs);
         test_fes  -> GetElementVDofs (i, te_vdofs);
         eltrans = test_fes -> GetElementTransformation (i);
-         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);
+            dbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
+                                               *test_fes  -> GetFE(i),
+                                               *eltrans, elemmat);
            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, 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");
@@ -1377,20 +1368,20 @@ void MixedBilinearForm::Assemble (int skip_zeros)
         trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
         test_fes  -> GetBdrElementVDofs (i, te_vdofs);
         eltrans = test_fes -> GetBdrElementTransformation (i);
-         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);
+            bbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetBE(i),
+                                               *test_fes  -> GetBE(i),
+                                               *eltrans, elemmat);
            mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
         }
      }
   }

-   if (trace_face_integs.Size())
+   if (tfbfi.Size())
   {
      FaceElementTransformations *ftr;
      Array<int> te_vdofs2;
@@ -1417,16 +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);
+            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;
@@ -1436,17 +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];
@@ -1469,16 +1460,13 @@ void MixedBilinearForm::Assemble (int skip_zeros)
            // 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);
+               btfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                             *ftr, elemmat);
               mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
            }
         }
@@ -1569,17 +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;
      }
   }
@@ -1594,17 +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;
      }
   }
@@ -1704,10 +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)
@@ -1745,17 +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;
   }

@@ -1793,13 +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;
 }
@@ -1849,7 +1830,7 @@ 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++)
      {
@@ -1859,19 +1840,17 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
         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;
         }
         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++)
@@ -1882,12 +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); }

@@ -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
 {
@@ -17,7 +17,6 @@

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

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

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

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

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

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

-   /// Enable or disable restart mode. If restart is enabled, new writes will
-   /// preserve timestep metadata for any solutions prior to the currently
-   /// defined time.
-   void UseRestartMode(bool restart_mode_);
-
   /// Load the collection - not implemented in the ParaView writer
   virtual void Load(int cycle_ = 0) override;
 };
@@ -7948,27 +7948,7 @@ VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
                         p, M, FunctionSpace::Qk),
     TensorBasisElement(dims, p, VerifyNodal(cbtype), dmtype),
     cbasis1d(poly1d.GetBasis(p, VerifyClosed(cbtype))),
-     obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(obtype)))
-{
-   MFEM_VERIFY(dims > 1, "Constructor for VectorTensorFiniteElement with both "
-               "open and closed bases is not valid for 1D elements.");
-}
-
-VectorTensorFiniteElement::VectorTensorFiniteElement(const int dims,
-                                                     const int d,
-                                                     const int p,
-                                                     const int obtype,
-                                                     const int M,
-                                                     const DofMapType dmtype)
-   : VectorFiniteElement(dims, GetTensorProductGeometry(dims), d,
-                         p, M, FunctionSpace::Pk),
-     TensorBasisElement(dims, p, obtype, dmtype),
-     cbasis1d(poly1d.GetBasis(p, VerifyOpen(obtype))),
-     obasis1d(poly1d.GetBasis(p, VerifyOpen(obtype)))
-{
-   MFEM_VERIFY(dims == 1, "Constructor for VectorTensorFiniteElement without "
-               "closed basis is only valid for 1D elements.");
-}
+     obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(obtype))) { }

 H1_SegmentElement::H1_SegmentElement(const int p, const int btype)
   : NodalTensorFiniteElement(1, p, VerifyClosed(btype), H1_DOF_MAP)
@@ -13075,8 +13055,9 @@ void ND_TriangleElement::CalcCurlShape(const IntegrationPoint &ip,
 const double ND_SegmentElement::tk[1] = { 1. };

 ND_SegmentElement::ND_SegmentElement(const int p, const int ob_type)
-   : VectorTensorFiniteElement(1, p, p - 1, ob_type, H_CURL,
-                               DofMapType::L2_DOF_MAP),
+   : VectorFiniteElement(1, Geometry::SEGMENT, p, p - 1,
+                         H_CURL, FunctionSpace::Pk),
+     obasis1d(poly1d.GetBasis(p - 1, VerifyOpen(ob_type))),
     dof2tk(dof)
 {
   if (obasis1d.IsIntegratedType()) { is_nodal = false; }
@@ -2239,11 +2239,6 @@ public:
                             const int cbtype, const int obtype,
                             const int M, const DofMapType dmtype);

-   // For 1D elements: there is only an "open basis", no "closed basis"
-   VectorTensorFiniteElement(const int dims, const int d, const int p,
-                             const int obtype, const int M,
-                             const DofMapType dmtype);
-
   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
                                 DofToQuad::Mode mode) const;

@@ -3316,9 +3311,11 @@ public:


 /// Arbitrary order Nedelec elements in 1D on a segment
-class ND_SegmentElement : public VectorTensorFiniteElement
+class ND_SegmentElement : public VectorFiniteElement
 {
   static const double tk[1];
+
+   Poly_1D::Basis &obasis1d;
   Array<int> dof2tk;

 public:
@@ -1225,7 +1225,7 @@ const Operator *FiniteElementSpace::GetElementRestriction(
   return L2E_nat.Ptr();
 }

-const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
+const Operator *FiniteElementSpace::GetFaceRestriction(
   ElementDofOrdering e_ordering, FaceType type, L2FaceValues mul) const
 {
   const bool is_dg_space = IsDGSpace();
@@ -1239,7 +1239,7 @@ const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
   }
   else
   {
-      FaceRestriction *res;
+      Operator* res;
      if (is_dg_space)
      {
         res = new L2FaceRestriction(*this, e_ordering, type, m);
@@ -164,7 +164,7 @@ protected:
                + 8 * (int)std::get<3>(k);
      }
   };
-   using map_L2F = std::unordered_map<const key_face,FaceRestriction*,key_hash>;
+   using map_L2F = std::unordered_map<const key_face,Operator*,key_hash>;
   mutable map_L2F L2F;

   mutable Array<QuadratureInterpolator*> E2Q_array;
@@ -488,7 +488,7 @@ public:
   const Operator *GetElementRestriction(ElementDofOrdering e_ordering) const;

   /// Return an Operator that converts L-vectors to E-vectors on each face.
-   virtual const FaceRestriction *GetFaceRestriction(
+   virtual const Operator *GetFaceRestriction(
      ElementDofOrdering e_ordering, FaceType,
      L2FaceValues mul = L2FaceValues::DoubleValued) const;

@@ -34,7 +34,6 @@ IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry)
   nx = irx.GetNPoints();
   ny = iry.GetNPoints();
   SetSize(nx * ny);
-   SetPointIndices();

   for (j = 0; j < ny; j++)
   {
@@ -49,6 +48,8 @@ IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry)
         ip.weight = ipx.weight * ipy.weight;
      }
   }
+
+   SetPointIndices();
 }

 IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry,
@@ -58,7 +59,6 @@ IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry,
   const int ny = iry.GetNPoints();
   const int nz = irz.GetNPoints();
   SetSize(nx*ny*nz);
-   SetPointIndices();

   for (int iz = 0; iz < nz; ++iz)
   {
@@ -78,6 +78,8 @@ IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry,
         }
      }
   }
+
+   SetPointIndices();
 }

 const Array<double> &IntegrationRule::GetWeights() const
@@ -123,7 +125,6 @@ void IntegrationRule::GrundmannMollerSimplexRule(int s, int n)
   }
   np /= f;
   SetSize(np);
-   SetPointIndices();

   int pt = 0;
   for (int i = 0; i <= s; i++)
@@ -374,7 +375,6 @@ public:
 void QuadratureFunctions1D::GaussLegendre(const int np, IntegrationRule* ir)
 {
   ir->SetSize(np);
-   ir->SetPointIndices();

   switch (np)
   {
@@ -477,7 +477,6 @@ void QuadratureFunctions1D::GaussLobatto(const int np, IntegrationRule* ir)
   */

   ir->SetSize(np);
-   ir->SetPointIndices();
   if ( np == 1 )
   {
      ir->IntPoint(0).Set1w(0.5, 1.0);
@@ -577,7 +576,6 @@ void QuadratureFunctions1D::GaussLobatto(const int np, IntegrationRule* ir)
 void QuadratureFunctions1D::OpenUniform(const int np, IntegrationRule* ir)
 {
   ir->SetSize(np);
-   ir->SetPointIndices();

   // The Newton-Cotes quadrature is based on weights that integrate exactly the
   // interpolatory polynomial through the equally spaced quadrature points.
@@ -593,7 +591,6 @@ void QuadratureFunctions1D::ClosedUniform(const int np,
                                          IntegrationRule* ir)
 {
   ir->SetSize(np);
-   ir->SetPointIndices();
   if ( np == 1 ) // allow this case as "closed"
   {
      ir->IntPoint(0).Set1w(0.5, 1.0);
@@ -611,7 +608,6 @@ void QuadratureFunctions1D::ClosedUniform(const int np,
 void QuadratureFunctions1D::OpenHalfUniform(const int np, IntegrationRule* ir)
 {
   ir->SetSize(np);
-   ir->SetPointIndices();

   // Open half points: the centers of np uniform intervals
   for (int i = 0; i < np ; ++i)
@@ -625,7 +621,6 @@ void QuadratureFunctions1D::OpenHalfUniform(const int np, IntegrationRule* ir)
 void QuadratureFunctions1D::ClosedGL(const int np, IntegrationRule* ir)
 {
   ir->SetSize(np);
-   ir->SetPointIndices();
   ir->IntPoint(0).x = 0.0;
   ir->IntPoint(np-1).x = 1.0;

@@ -96,6 +96,9 @@ private:
       by request with the method GetWeights(). */
   mutable Array<double> weights;

+   /// Sets the indices of each quadrature point on initialization.
+   void SetPointIndices();
+
   /// Define n-simplex rule (triangle/tetrahedron for n=2/3) of order (2s+1)
   void GrundmannMollerSimplexRule(int s, int n = 3);

@@ -224,11 +227,6 @@ public:
      }
   }

-   /// Sets the indices of each quadrature point on initialization.
-   /** Note that most calls to IntegrationRule::SetSize should be paired with a
-       call to SetPointIndices in order for the indices to be set correctly. */
-   void SetPointIndices();
-
   /// Tensor product of two 1D integration rules
   IntegrationRule(IntegrationRule &irx, IntegrationRule &iry);

@@ -26,14 +26,14 @@ LinearForm::LinearForm(FiniteElementSpace *f, LinearForm *lf)
   extern_lfs = 1;

   // Copy the pointers to the integrators
-   domain_integs = lf->domain_integs;
+   dlfi = lf->dlfi;

-   domain_delta_integs = lf->domain_delta_integs;
+   dlfi_delta = lf->dlfi_delta;

-   boundary_integs = lf->boundary_integs;
+   blfi = lf->blfi;

-   boundary_face_integs = lf->boundary_face_integs;
-   boundary_face_integs_marker = lf->boundary_face_integs_marker;
+   flfi = lf->flfi;
+   flfi_marker = lf->flfi_marker;
 }

 void LinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi)
@@ -42,13 +42,13 @@ void LinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi)
      dynamic_cast<DeltaLFIntegrator *>(lfi);
   if (!maybe_delta || !maybe_delta->IsDelta())
   {
-      domain_integs.Append(lfi);
+      dlfi.Append(lfi);
   }
   else
   {
-      domain_delta_integs.Append(maybe_delta);
+      dlfi_delta.Append(maybe_delta);
   }
-   domain_integs_marker.Append(NULL);
+   dlfi_marker.Append(NULL);
 }

 void LinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi,
@@ -58,45 +58,44 @@ void LinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi,
      dynamic_cast<DeltaLFIntegrator *>(lfi);
   if (!maybe_delta || !maybe_delta->IsDelta())
   {
-      domain_integs.Append(lfi);
+      dlfi.Append(lfi);
   }
   else
   {
-      domain_delta_integs.Append(maybe_delta);
+      dlfi_delta.Append(maybe_delta);
   }
-   domain_integs_marker.Append(&elem_marker);
+   dlfi_marker.Append(&elem_marker);
 }

 void LinearForm::AddBoundaryIntegrator (LinearFormIntegrator * lfi)
 {
-   boundary_integs.Append (lfi);
-   boundary_integs_marker.Append(NULL); // NULL -> all attributes are active
+   blfi.Append (lfi);
+   blfi_marker.Append(NULL); // NULL -> all attributes are active
 }

 void LinearForm::AddBoundaryIntegrator (LinearFormIntegrator * lfi,
                                        Array<int> &bdr_attr_marker)
 {
-   boundary_integs.Append (lfi);
-   boundary_integs_marker.Append(&bdr_attr_marker);
+   blfi.Append (lfi);
+   blfi_marker.Append(&bdr_attr_marker);
 }

 void LinearForm::AddBdrFaceIntegrator (LinearFormIntegrator * lfi)
 {
-   boundary_face_integs.Append(lfi);
-   // NULL -> all attributes are active
-   boundary_face_integs_marker.Append(NULL);
+   flfi.Append(lfi);
+   flfi_marker.Append(NULL); // NULL -> all attributes are active
 }

 void LinearForm::AddBdrFaceIntegrator(LinearFormIntegrator *lfi,
                                      Array<int> &bdr_attr_marker)
 {
-   boundary_face_integs.Append(lfi);
-   boundary_face_integs_marker.Append(&bdr_attr_marker);
+   flfi.Append(lfi);
+   flfi_marker.Append(&bdr_attr_marker);
 }

 void LinearForm::AddInteriorFaceIntegrator(LinearFormIntegrator *lfi)
 {
-   interior_face_integs.Append(lfi);
+   iflfi.Append(lfi);
 }

 void LinearForm::Assemble()
@@ -113,14 +112,14 @@ void LinearForm::Assemble()
   // The first use of AddElementVector() below will move it back to host
   // because both 'vdofs' and 'elemvect' are on host.

-   if (domain_integs.Size())
+   if (dlfi.Size())
   {
-      for (int k = 0; k < domain_integs.Size(); k++)
+      for (int k = 0; k < dlfi.Size(); k++)
      {
-         if (domain_integs_marker[k] != NULL)
+         if (dlfi_marker[k] != NULL)
         {
            MFEM_VERIFY(fes->GetMesh()->attributes.Size() ==
-                        domain_integs_marker[k]->Size(),
+                        dlfi_marker[k]->Size(),
                        "invalid element marker for domain linear form "
                        "integrator #" << k << ", counting from zero");
         }
@@ -129,15 +128,14 @@ void LinearForm::Assemble()
      for (i = 0; i < fes -> GetNE(); i++)
      {
         int elem_attr = fes->GetMesh()->GetAttribute(i);
-         for (int k = 0; k < domain_integs.Size(); k++)
+         for (int k = 0; k < dlfi.Size(); k++)
         {
-            if ( domain_integs_marker[k] == NULL ||
-                 (*(domain_integs_marker[k]))[elem_attr-1] == 1 )
+            if ( dlfi_marker[k] == NULL ||
+                 (*(dlfi_marker[k]))[elem_attr-1] == 1 )
            {
               fes -> GetElementVDofs (i, vdofs);
               eltrans = fes -> GetElementTransformation (i);
-               domain_integs[k]->AssembleRHSElementVect(*fes->GetFE(i),
-                                                        *eltrans, elemvect);
+               dlfi[k]->AssembleRHSElementVect(*fes->GetFE(i), *eltrans, elemvect);
               AddElementVector (vdofs, elemvect);
            }
         }
@@ -145,7 +143,7 @@ void LinearForm::Assemble()
   }
   AssembleDelta();

-   if (boundary_integs.Size())
+   if (blfi.Size())
   {
      Mesh *mesh = fes->GetMesh();

@@ -153,14 +151,14 @@ void LinearForm::Assemble()
      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 < blfi.Size(); k++)
      {
-         if (boundary_integs_marker[k] == NULL)
+         if (blfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *boundary_integs_marker[k];
+         Array<int> &bdr_marker = *blfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary integrator #"
                     << k << ", counting from zero");
@@ -176,19 +174,18 @@ void LinearForm::Assemble()
         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
         fes -> GetBdrElementVDofs (i, vdofs);
         eltrans = fes -> GetBdrElementTransformation (i);
-         for (int k=0; k < boundary_integs.Size(); k++)
+         for (int k=0; k < blfi.Size(); k++)
         {
-            if (boundary_integs_marker[k] &&
-                (*boundary_integs_marker[k])[bdr_attr-1] == 0) { continue; }
+            if (blfi_marker[k] &&
+                (*blfi_marker[k])[bdr_attr-1] == 0) { continue; }

-            boundary_integs[k]->AssembleRHSElementVect(*fes->GetBE(i),
-                                                       *eltrans, elemvect);
+            blfi[k]->AssembleRHSElementVect(*fes->GetBE(i), *eltrans, elemvect);

            AddElementVector (vdofs, elemvect);
         }
      }
   }
-   if (boundary_face_integs.Size())
+   if (flfi.Size())
   {
      FaceElementTransformations *tr;
      Mesh *mesh = fes->GetMesh();
@@ -197,14 +194,14 @@ void LinearForm::Assemble()
      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 < flfi.Size(); k++)
      {
-         if (boundary_face_integs_marker[k] == NULL)
+         if (flfi_marker[k] == NULL)
         {
            bdr_attr_marker = 1;
            break;
         }
-         Array<int> &bdr_marker = *boundary_face_integs_marker[k];
+         Array<int> &bdr_marker = *flfi_marker[k];
         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
                     "invalid boundary marker for boundary face integrator #"
                     << k << ", counting from zero");
@@ -223,26 +220,24 @@ void LinearForm::Assemble()
         if (tr != NULL)
         {
            fes -> GetElementVDofs (tr -> Elem1No, vdofs);
-            for (int k = 0; k < boundary_face_integs.Size(); k++)
+            for (int k = 0; k < flfi.Size(); k++)
            {
-               if (boundary_face_integs_marker[k] &&
-                   (*boundary_face_integs_marker[k])[bdr_attr-1] == 0)
-               { continue; }
+               if (flfi_marker[k] &&
+                   (*flfi_marker[k])[bdr_attr-1] == 0) { continue; }

-               boundary_face_integs[k]->
-               AssembleRHSElementVect(*fes->GetFE(tr->Elem1No),
-                                      *tr, elemvect);
+               flfi[k] -> AssembleRHSElementVect (*fes->GetFE(tr -> Elem1No),
+                                                  *tr, elemvect);
               AddElementVector (vdofs, elemvect);
            }
         }
      }
   }

-   if (interior_face_integs.Size())
+   if (iflfi.Size())
   {
      Mesh *mesh = fes->GetMesh();

-      for (int k = 0; k < interior_face_integs.Size(); k++)
+      for (int k = 0; k < iflfi.Size(); k++)
      {
         for (i = 0; i < mesh->GetNumFaces(); i++)
         {
@@ -254,10 +249,9 @@ void LinearForm::Assemble()
               Array<int> vdofs2;
               fes -> GetElementVDofs (tr -> Elem2No, vdofs2);
               vdofs.Append(vdofs2);
-               interior_face_integs[k]->
-               AssembleRHSElementVect(*fes->GetFE(tr->Elem1No),
-                                      *fes->GetFE(tr->Elem2No),
-                                      *tr, elemvect);
+               iflfi[k] -> AssembleRHSElementVect (*fes->GetFE(tr -> Elem1No),
+                                                   *fes->GetFE(tr -> Elem2No),
+                                                   *tr, elemvect);
               AddElementVector (vdofs, elemvect);
            }
         }
@@ -283,41 +277,40 @@ void LinearForm::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)

 void LinearForm::AssembleDelta()
 {
-   if (domain_delta_integs.Size() == 0) { return; }
+   if (dlfi_delta.Size() == 0) { return; }

   if (!HaveDeltaLocations())
   {
      int sdim = fes->GetMesh()->SpaceDimension();
      Vector center;
-      DenseMatrix centers(sdim, domain_delta_integs.Size());
+      DenseMatrix centers(sdim, dlfi_delta.Size());
      for (int i = 0; i < centers.Width(); i++)
      {
         centers.GetColumnReference(i, center);
-         domain_delta_integs[i]->GetDeltaCenter(center);
+         dlfi_delta[i]->GetDeltaCenter(center);
         MFEM_VERIFY(center.Size() == sdim,
                     "Point dim " << center.Size() <<
                     " does not match space dim " << sdim);
      }
-      fes->GetMesh()->FindPoints(centers, domain_delta_integs_elem_id,
-                                 domain_delta_integs_ip);
+      fes->GetMesh()->FindPoints(centers, dlfi_delta_elem_id, dlfi_delta_ip);
   }

   Array<int> vdofs;
   Vector elemvect;
-   for (int i = 0; i < domain_delta_integs.Size(); i++)
+   for (int i = 0; i < dlfi_delta.Size(); i++)
   {
-      int elem_id = domain_delta_integs_elem_id[i];
+      int elem_id = dlfi_delta_elem_id[i];
      // The delta center may be outside of this sub-domain, or
      // (Par)Mesh::FindPoints() failed to find this point:
      if (elem_id < 0) { continue; }

-      const IntegrationPoint &ip = domain_delta_integs_ip[i];
+      const IntegrationPoint &ip = dlfi_delta_ip[i];
      ElementTransformation &Trans = *fes->GetElementTransformation(elem_id);
      Trans.SetIntPoint(&ip);

      fes->GetElementVDofs(elem_id, vdofs);
-      domain_delta_integs[i]->AssembleDeltaElementVect(*fes->GetFE(elem_id),
-                                                       Trans, elemvect);
+      dlfi_delta[i]->AssembleDeltaElementVect(*fes->GetFE(elem_id), Trans,
+                                              elemvect);
      AddElementVector(vdofs, elemvect);
   }
 }
@@ -340,14 +333,11 @@ LinearForm::~LinearForm()
   if (!extern_lfs)
   {
      int k;
-      for (k=0; k < domain_delta_integs.Size(); k++)
-      { delete domain_delta_integs[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 < boundary_face_integs.Size(); k++)
-      { delete boundary_face_integs[k]; }
-      for (k=0; k < interior_face_integs.Size(); k++)
-      { delete interior_face_integs[k]; }
+      for (k=0; k < dlfi_delta.Size(); k++) { delete dlfi_delta[k]; }
+      for (k=0; k < dlfi.Size(); k++) { delete dlfi[k]; }
+      for (k=0; k < blfi.Size(); k++) { delete blfi[k]; }
+      for (k=0; k < flfi.Size(); k++) { delete flfi[k]; }
+      for (k=0; k < iflfi.Size(); k++) { delete iflfi[k]; }
   }
 }

@@ -26,46 +26,43 @@ protected:
   /// FE space on which the LinearForm lives. Not owned.
   FiniteElementSpace *fes;

-   /** @brief Indicates the LinearFormIntegrator%s stored in #domain_integs,
-       #domain_delta_integs, #boundary_integs, and #boundary_face_integs are
-       owned by another LinearForm. */
+   /** @brief Indicates the LinearFormIntegrator%s stored in #dlfi, #dlfi_delta,
+       #blfi, and #flfi are owned by another LinearForm. */
   int extern_lfs;

   /// Set of Domain Integrators to be applied.
-   Array<LinearFormIntegrator*> domain_integs;
+   Array<LinearFormIntegrator*> dlfi;
   /// 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>*>           dlfi_marker;

   /// Separate array for integrators with delta function coefficients.
-   Array<DeltaLFIntegrator*>    domain_delta_integs;
+   Array<DeltaLFIntegrator*> dlfi_delta;

   /// Set of Boundary Integrators to be applied.
-   Array<LinearFormIntegrator*> boundary_integs;
-   /// Entries are not owned.
-   Array<Array<int>*>           boundary_integs_marker;
+   Array<LinearFormIntegrator*> blfi;
+   Array<Array<int>*>           blfi_marker; ///< Entries are not owned.

   /// Set of Boundary Face Integrators to be applied.
-   Array<LinearFormIntegrator*> boundary_face_integs;
-   Array<Array<int>*> boundary_face_integs_marker; ///< Entries not owned.
+   Array<LinearFormIntegrator*> flfi;
+   Array<Array<int>*>           flfi_marker; ///< Entries are not owned.

   /// Set of Internal Face Integrators to be applied.
-   Array<LinearFormIntegrator*> interior_face_integs;
+   Array<LinearFormIntegrator*> iflfi;

   /// The element ids where the centers of the delta functions lie
-   Array<int> domain_delta_integs_elem_id;
+   Array<int> dlfi_delta_elem_id;

   /// The reference coordinates where the centers of the delta functions lie
-   Array<IntegrationPoint> domain_delta_integs_ip;
+   Array<IntegrationPoint> dlfi_delta_ip;

   /// If true, the delta locations are not (re)computed during assembly.
-   bool HaveDeltaLocations()
-   { return (domain_delta_integs_elem_id.Size() != 0); }
+   bool HaveDeltaLocations() { return (dlfi_delta_elem_id.Size() != 0); }

   /// Force (re)computation of delta locations.
-   void ResetDeltaLocations() { domain_delta_integs_elem_id.SetSize(0); }
+   void ResetDeltaLocations() { dlfi_delta_elem_id.SetSize(0); }

 private:
   /// Copy construction is not supported; body is undefined.
@@ -153,25 +150,22 @@ public:
   /** @brief Access all integrators added with AddDomainIntegrator() which are
       not DeltaLFIntegrator%s or they are DeltaLFIntegrator%s with non-delta
       coefficients. */
-   Array<LinearFormIntegrator*> *GetDLFI() { return &domain_integs; }
+   Array<LinearFormIntegrator*> *GetDLFI() { return &dlfi; }

   /** @brief Access all integrators added with AddDomainIntegrator() which are
       DeltaLFIntegrator%s with delta coefficients. */
-   Array<DeltaLFIntegrator*> *GetDLFI_Delta() { return &domain_delta_integs; }
+   Array<DeltaLFIntegrator*> *GetDLFI_Delta() { return &dlfi_delta; }

   /// Access all integrators added with AddBoundaryIntegrator().
-   Array<LinearFormIntegrator*> *GetBLFI() { return &boundary_integs; }
+   Array<LinearFormIntegrator*> *GetBLFI() { return &blfi; }

   /// Access all integrators added with AddBdrFaceIntegrator().
-   Array<LinearFormIntegrator*> *GetFLFI() { return &boundary_face_integs; }
-
-   /// Access all integrators added with AddInteriorFaceIntegrator().
-   Array<LinearFormIntegrator*> *GetIFLFI() { return &interior_face_integs; }
+   Array<LinearFormIntegrator*> *GetFLFI() { return &flfi; }

   /** @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>*> *GetFLFI_Marker() { return &boundary_face_integs_marker; }
+   Array<Array<int>*> *GetFLFI_Marker() { return &flfi_marker; }

   /// Assembles the linear form i.e. sums over all domain/bdr integrators.
   void Assemble();
@@ -979,8 +979,6 @@ void BlockNonlinearForm::ComputeGradientBlocked(const BlockVector &bx) const

            for (int k = 0; k < bfnfi.Size(); ++k)
            {
-               if (bfnfi_marker[k] &&
-                   (*bfnfi_marker[k])[bdr_attr-1] == 0) { continue; }
               bfnfi[k]->AssembleFaceGrad(fe, fe2, *tr, el_x_const, elmats);
               for (int l=0; l<fes.Size(); ++l)
               {
@@ -40,10 +40,10 @@ protected:
 public:
   /** @brief Prescribe a fixed IntegrationRule to use (when @a ir != NULL) or
       let the integrator choose (when @a ir == NULL). */
-   virtual void SetIntRule(const IntegrationRule *ir) { IntRule = ir; }
+   void SetIntRule(const IntegrationRule *ir) { IntRule = ir; }

   /// Prescribe a fixed IntegrationRule to use.
-   void SetIntegrationRule(const IntegrationRule &ir) { SetIntRule(&ir); }
+   void SetIntegrationRule(const IntegrationRule &irule) { IntRule = &irule; }

   /// Set the memory type used for GeometricFactors and other large allocations
   /// in PA extensions.
@@ -130,7 +130,7 @@ void ParBilinearForm::ParallelAssemble(OperatorHandle &A, SparseMatrix *A_local)

   OperatorHandle dA(A.Type()), Ph(A.Type()), hdA;

-   if (interior_face_integs.Size() == 0)
+   if (fbfi.Size() == 0)
   {
      // construct a parallel block-diagonal matrix 'A' based on 'a'
      dA.MakeSquareBlockDiag(pfes->GetComm(), pfes->GlobalVSize(),
@@ -214,12 +214,11 @@ void ParBilinearForm::AssembleSharedFaces(int skip_zeros)
         }
      }
      vdofs_all.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(*pfes->GetFE(T->Elem1No),
-                            *pfes->GetFaceNbrFE(Elem2NbrNo),
-                            *T, elemmat);
+         fbfi[k]->AssembleFaceMatrix(*pfes->GetFE(T->Elem1No),
+                                     *pfes->GetFaceNbrFE(Elem2NbrNo),
+                                     *T, elemmat);
         if (keep_nbr_block)
         {
            mat->AddSubMatrix(vdofs_all, vdofs_all, elemmat, skip_zeros);
@@ -234,7 +233,7 @@ void ParBilinearForm::AssembleSharedFaces(int skip_zeros)

 void ParBilinearForm::Assemble(int skip_zeros)
 {
-   if (interior_face_integs.Size())
+   if (fbfi.Size())
   {
      pfes->ExchangeFaceNbrData();
      if (!ext && mat == NULL)
@@ -245,7 +244,7 @@ void ParBilinearForm::Assemble(int skip_zeros)

   BilinearForm::Assemble(skip_zeros);

-   if (!ext && interior_face_integs.Size() > 0)
+   if (!ext && fbfi.Size() > 0)
   {
      AssembleSharedFaces(skip_zeros);
   }
@@ -317,8 +316,7 @@ ParallelEliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
 void ParBilinearForm::TrueAddMult(const Vector &x, Vector &y, const double a)
 const
 {
-   MFEM_VERIFY(interior_face_integs.Size() == 0,
-               "the case of interior face integrators is not"
+   MFEM_VERIFY(fbfi.Size() == 0, "the case of interior face integrators is not"
               " implemented");

   if (X.ParFESpace() != pfes)
@@ -515,7 +515,7 @@ const FiniteElement *ParFiniteElementSpace::GetFE(int i) const
   else { return FiniteElementSpace::GetFE(i); }
 }

-const FaceRestriction *ParFiniteElementSpace::GetFaceRestriction(
+const Operator *ParFiniteElementSpace::GetFaceRestriction(
   ElementDofOrdering e_ordering, FaceType type, L2FaceValues mul) const
 {
   const bool is_dg_space = IsDGSpace();
@@ -529,7 +529,7 @@ const FaceRestriction *ParFiniteElementSpace::GetFaceRestriction(
   }
   else
   {
-      FaceRestriction *res;
+      Operator* res;
      if (is_dg_space)
      {
         res = new ParL2FaceRestriction(*this, e_ordering, type, m);
@@ -299,7 +299,7 @@ public:
       presence of shared faces. Shared faces are treated as interior faces,
       the returned operator handles the communication needed to get the
       shared face values from other MPI ranks */
-   virtual const FaceRestriction *GetFaceRestriction(
+   virtual const Operator *GetFaceRestriction(
      ElementDofOrdering e_ordering, FaceType type,
      L2FaceValues mul = L2FaceValues::DoubleValued) const;

@@ -47,7 +47,7 @@ void ParLinearForm::Assemble()
 {
   LinearForm::Assemble();

-   if (interior_face_integs.Size())
+   if (iflfi.Size())
   {
      pfes->ExchangeFaceNbrData();
      AssembleSharedFaces();
@@ -59,10 +59,10 @@ void ParLinearForm::AssembleSharedFaces()
   Array<int> vdofs;
   Vector elemvect;

-   if (interior_face_integs.Size())
+   if (iflfi.Size())
   {
      ParMesh *pmesh = pfes->GetParMesh();
-      for (int k = 0; k < interior_face_integs.Size(); k++)
+      for (int k = 0; k < iflfi.Size(); k++)
      {
         for (int i = 0; i < pmesh->GetNSharedFaces(); i++)
         {
@@ -73,10 +73,9 @@ void ParLinearForm::AssembleSharedFaces()
            {
               int Elem2Nbr = tr->Elem2No - pmesh->GetNE();
               fes -> GetElementVDofs (tr -> Elem1No, vdofs);
-               interior_face_integs[k]->
-               AssembleRHSElementVect(*fes->GetFE(tr->Elem1No),
-                                      *pfes->GetFaceNbrFE(Elem2Nbr),
-                                      *tr, elemvect);
+               iflfi[0] -> AssembleRHSElementVect (*fes->GetFE(tr -> Elem1No),
+                                                   *pfes->GetFaceNbrFE(Elem2Nbr),
+                                                   *tr, elemvect);
               AddElementVector (vdofs, elemvect);
            }
         }
@@ -847,7 +847,7 @@ void H1FaceRestriction::Mult(const Vector& x, Vector& y) const
   });
 }

-void H1FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
+void H1FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
 {
   // Assumes all elements have the same number of dofs
   const int nd = dof;
@@ -856,7 +856,7 @@ void H1FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
   auto d_offsets = offsets.Read();
   auto d_indices = gather_indices.Read();
   auto d_x = Reshape(x.Read(), nd, vd, nf);
-   auto d_y = Reshape(y.ReadWrite(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
   MFEM_FORALL(i, ndofs,
   {
      const int offset = d_offsets[i];
@@ -1267,7 +1267,7 @@ void L2FaceRestriction::Mult(const Vector& x, Vector& y) const
   }
 }

-void L2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
+void L2FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
 {
   // Assumes all elements have the same number of dofs
   const int nd = dof;
@@ -1280,7 +1280,7 @@ void L2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
   if (m == L2FaceValues::DoubleValued)
   {
      auto d_x = Reshape(x.Read(), nd, vd, 2, nf);
-      auto d_y = Reshape(y.ReadWrite(), t?vd:ndofs, t?ndofs:vd);
+      auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
      MFEM_FORALL(i, ndofs,
      {
         const int offset = d_offsets[i];
@@ -1304,7 +1304,7 @@ void L2FaceRestriction::AddMultTranspose(const Vector& x, Vector& y) const
   else
   {
      auto d_x = Reshape(x.Read(), nd, vd, nf);
-      auto d_y = Reshape(y.ReadWrite(), t?vd:ndofs, t?ndofs:vd);
+      auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
      MFEM_FORALL(i, ndofs,
      {
         const int offset = d_offsets[i];
@@ -21,6 +21,10 @@ namespace mfem
 class FiniteElementSpace;
 enum class ElementDofOrdering;

+/** An enum type to specify if only e1 value is requested (SingleValued) or both
+    e1 and e2 (DoubleValued). */
+enum class L2FaceValues : bool {SingleValued, DoubleValued};
+
 /// Operator that converts FiniteElementSpace L-vectors to E-vectors.
 /** Objects of this type are typically created and owned by FiniteElementSpace
    objects, see FiniteElementSpace::GetElementRestriction(). */
@@ -100,75 +104,10 @@ public:
   void FillJAndData(const Vector &ea_data, SparseMatrix &mat) const;
 };

-/** An enum type to specify if only e1 value is requested (SingleValued) or both
-    e1 and e2 (DoubleValued). */
-enum class L2FaceValues : bool {SingleValued, DoubleValued};
-
-/** @brief Base class for operators that extracts Face degrees of freedom.
-
-    In order to compute quantities on the faces of a mesh, it is often useful to
-    extract the degrees of freedom on the faces of the elements. This class
-    provides an interface for such operations.
-
-    If the FiniteElementSpace is ordered by Ordering::byVDIM, then the expected
-    format for the L-vector is (vdim x ndofs), otherwise if Ordering::byNODES
-    the expected format is (ndofs x vdim), where ndofs is the total number of
-    degrees of freedom.
-    Since FiniteElementSpace can either be continuous or discontinuous, the
-    degrees of freedom on a face can either be single valued or double valued,
-    this is what we refer to as the multiplicity and is represented by the
-    L2FaceValues enum type.
-    The format of the output face E-vector of degrees of freedom is
-    (face_dofs x vdim x multiplicity x nfaces), where face_dofs is the number of
-    degrees of freedom on each face, and nfaces the number of faces of the
-    requested FaceType (see FiniteElementSpace::GetNFbyType).
-
-    @note Objects of this type are typically created and owned by
-    FiniteElementSpace objects, see FiniteElementSpace::GetFaceRestriction(). */
-class FaceRestriction : public Operator
-{
-public:
-   FaceRestriction(): Operator() { }
-
-   FaceRestriction(int h, int w): Operator(h, w) { }
-
-   virtual ~FaceRestriction() { }
-
-   /** @brief Extract the face degrees of freedom from @a x into @a y.
-
-       @param[in]  x The L-vector of degrees of freedom.
-       @param[out] y The degrees of freedom on the face, corresponding to a face
-                     E-vector.
-   */
-   void Mult(const Vector &x, Vector &y) const override = 0;
-
-   /** @brief Add the face degrees of freedom @a x to the element degrees of
-       freedom @a y.
-
-       @param[in]     x The face degrees of freedom on the face.
-       @param[in,out] y The L-vector of degrees of freedom to which we add the
-                        face degrees of freedom.
-   */
-   virtual void AddMultTranspose(const Vector &x, Vector &y) const = 0;
-
-   /** @brief Set the face degrees of freedom in the element degrees of freedom
-       @a y to the values given in @a x.
-
-       @param[in]     x The face degrees of freedom on the face.
-       @param[in,out] y The L-vector of degrees of freedom to which we add the
-                        face degrees of freedom.
-   */
-   void MultTranspose(const Vector &x, Vector &y) const override
-   {
-      y = 0.0;
-      AddMultTranspose(x, y);
-   }
-};
-
-/// Operator that extracts Face degrees of freedom for H1 FiniteElementSpaces.
+/// Operator that extracts Face degrees of freedom.
 /** Objects of this type are typically created and owned by FiniteElementSpace
    objects, see FiniteElementSpace::GetFaceRestriction(). */
-class H1FaceRestriction : public FaceRestriction
+class H1FaceRestriction : public Operator
 {
 protected:
   const FiniteElementSpace &fes;
@@ -183,42 +122,16 @@ protected:
   Array<int> gather_indices;

 public:
-   /** @brief Constructor for a H1FaceRestriction.
-
-       @param[in] fes The FiniteElementSpace on which this H1FaceRestriction
-                      operates.
-       @param[in] ordering The requested output ordering of the
-                           H1FaceRestriction, either Native or Lexicographic.
-       @param[in] type The requested type of faces on which this operator
-                       extracts the degrees of freedom, either Interior or
-                       Boundary.
-   */
-   H1FaceRestriction(const FiniteElementSpace& fes,
-                     const ElementDofOrdering ordering,
-                     const FaceType type);
-
-   /** @brief Extract the face degrees of freedom from @a x into @a y.
-
-       @param[in]  x The L-vector of degrees of freedom.
-       @param[out] y The degrees of freedom on the face, corresponding to a face
-                     E-vector.
-   */
-   void Mult(const Vector &x, Vector &y) const override;
-
-   /** @brief Add the face degrees of freedom @a x to the element degrees of
-       freedom @a y.
-
-       @param[in]     x The face degrees of freedom on the face.
-       @param[in,out] y The L-vector of degrees of freedom to which we add the
-                        face degrees of freedom.
-   */
-   void AddMultTranspose(const Vector &x, Vector &y) const override;
+   H1FaceRestriction(const FiniteElementSpace&, const ElementDofOrdering,
+                     const FaceType);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
 };

-/// Operator that extracts Face degrees of freedom on L2 FiniteElementSpaces.
+/// Operator that extracts Face degrees of freedom.
 /** Objects of this type are typically created and owned by FiniteElementSpace
    objects, see FiniteElementSpace::GetFaceRestriction(). */
-class L2FaceRestriction : public FaceRestriction
+class L2FaceRestriction : public Operator
 {
 protected:
   const FiniteElementSpace &fes;
@@ -241,38 +154,19 @@ protected:
                     const L2FaceValues m = L2FaceValues::DoubleValued);

 public:
-   L2FaceRestriction(const FiniteElementSpace&,
-                     const ElementDofOrdering,
+   L2FaceRestriction(const FiniteElementSpace&, const ElementDofOrdering,
                     const FaceType,
                     const L2FaceValues m = L2FaceValues::DoubleValued);
-
-   /** @brief Extract the face degrees of freedom from @a x into @a y.
-
-       @param[in]  x The L-vector of degrees of freedom.
-       @param[out] y The degrees of freedom on the face, corresponding to a face
-                     E-vector.
-   */
-   void Mult(const Vector &x, Vector &y) const override;
-
-   /** @brief Add the face degrees of freedom @a x to the element degrees of
-       freedom @a y.
-
-       @param[in]     x The face degrees of freedom on the face.
-       @param[in,out] y The L-vector of degrees of freedom to which we add the
-                        face degrees of freedom.
-   */
-   void AddMultTranspose(const Vector &x, Vector &y) const override;
-
+   virtual void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
       given by this L2FaceRestriction. */
   virtual void FillI(SparseMatrix &mat, const bool keep_nbr_block = false) const;
-
   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
       pattern given by this L2FaceRestriction, and the values of ea_data. */
   virtual void FillJAndData(const Vector &ea_data,
                             SparseMatrix &mat,
                             const bool keep_nbr_block = false) const;
-
   /// This methods adds the DG face matrices to the element matrices.
   void AddFaceMatricesToElementMatrices(Vector &fea_data,
                                         Vector &ea_data) const;
@@ -34,7 +34,6 @@ void TMOP_Combo_QualityMetric::EvalP(const DenseMatrix &Jpt,
                                     DenseMatrix &P) const
 {
   DenseMatrix Pt(P.Size());
-   P = 0.0;
   for (int i = 0; i < tmop_q_arr.Size(); i++)
   {
      tmop_q_arr[i]->EvalP(Jpt, Pt);
@@ -51,7 +50,6 @@ void TMOP_Combo_QualityMetric::AssembleH(const DenseMatrix &Jpt,
   DenseMatrix At(A.Size());
   for (int i = 0; i < tmop_q_arr.Size(); i++)
   {
-      At = 0.0;
      tmop_q_arr[i]->AssembleH(Jpt, DS, weight, At);
      At *= wt_arr[i];
      A += At;
@@ -371,8 +371,6 @@ public:
      AddQualityMetric(sh_metric, 1.-gamma_);
      AddQualityMetric(sz_metric, gamma_);
   }
-   virtual int Id() const { return 80; }
-   double GetGamma() const { return gamma; }

   virtual ~TMOP_Metric_080() { delete sh_metric; delete sz_metric; }
 };
@@ -592,52 +590,6 @@ public:
   virtual int Id() const { return 321; }
 };

-/// 3D barrier Shape+Size (VS) metric (polyconvex).
-class TMOP_Metric_332 : public TMOP_Combo_QualityMetric
-{
-protected:
-   double gamma;
-   TMOP_QualityMetric *sh_metric, *sz_metric;
-
-public:
-   TMOP_Metric_332(double gamma_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_302),
-      sz_metric(new TMOP_Metric_315)
-   {
-      // (1-gamma) mu_302 + gamma mu_315
-      AddQualityMetric(sh_metric, 1.-gamma_);
-      AddQualityMetric(sz_metric, gamma_);
-   }
-
-   virtual int Id() const { return 332; }
-   double GetGamma() const { return gamma; }
-
-   virtual ~TMOP_Metric_332() { delete sh_metric; delete sz_metric; }
-};
-
-/// 3D barrier Shape+Size (VS) metric (polyconvex).
-class TMOP_Metric_333 : public TMOP_Combo_QualityMetric
-{
-protected:
-   double gamma;
-   TMOP_QualityMetric *sh_metric, *sz_metric;
-
-public:
-   TMOP_Metric_333(double gamma_) : gamma(gamma_),
-      sh_metric(new TMOP_Metric_302),
-      sz_metric(new TMOP_Metric_316)
-   {
-      // (1-gamma) mu_302 + gamma mu_316
-      AddQualityMetric(sh_metric, 1.-gamma_);
-      AddQualityMetric(sz_metric, gamma_);
-   }
-
-   virtual int Id() const { return 333; }
-   double GetGamma() const { return gamma; }
-
-   virtual ~TMOP_Metric_333() { delete sh_metric; delete sz_metric; }
-};
-
 /// Shifted barrier form of 3D metric 16 (volume, ideal barrier metric), 3D
 class TMOP_Metric_352 : public TMOP_QualityMetric
 {
@@ -150,49 +150,9 @@ void EvalH_077(const int e, const int qx, const int qy,
   }
 }

-static MFEM_HOST_DEVICE inline
-void EvalH_080(const int e, const int qx, const int qy,
-               const double weight, const double gamma, const double *Jpt,
-               DeviceTensor<7,double> H)
-{
-   // h_80 = (1-gamma) h_2 + gamma h_77.
-
-   constexpr int DIM = 2;
-   double ddI1[4], ddI1b[4], dI2[4], dI2b[4], ddI2[4];
-   kernels::InvariantsEvaluator2D ie(Args()
-                                     .J(Jpt)
-                                     .dI2(dI2)
-                                     .ddI1(ddI1)
-                                     .ddI1b(ddI1b)
-                                     .dI2b(dI2b)
-                                     .ddI2(ddI2));
-
-   const double I2 = ie.Get_I2(), I2inv_sq = 1.0 / (I2 * I2);
-   ConstDeviceMatrix di2(ie.Get_dI2(),DIM,DIM);
-   for (int i = 0; i < DIM; i++)
-   {
-      for (int j = 0; j < DIM; j++)
-      {
-         ConstDeviceMatrix ddi1b(ie.Get_ddI1b(i,j),DIM,DIM);
-         ConstDeviceMatrix ddi2(ie.Get_ddI2(i,j),DIM,DIM);
-         for (int r = 0; r < DIM; r++)
-         {
-            for (int c = 0; c < DIM; c++)
-            {
-               H(r,c,i,j,qx,qy,e) =
-                  (1.0 - gamma) * 0.5 * weight * ddi1b(r,c) +
-                  gamma * ( weight * 0.5 * (1.0 - I2inv_sq) * ddi2(r,c) +
-                            weight * (I2inv_sq / I2) * di2(r,c) * di2(i,j) );
-            }
-         }
-      }
-   }
-}
-
 MFEM_REGISTER_TMOP_KERNELS(void, SetupGradPA_2D,
                           const Vector &x_,
                           const double metric_normal,
-                           const double metric_param,
                           const int mid,
                           const int NE,
                           const Array<double> &w_,
@@ -203,7 +163,7 @@ MFEM_REGISTER_TMOP_KERNELS(void, SetupGradPA_2D,
                           const int d1d,
                           const int q1d)
 {
-   MFEM_VERIFY(mid == 1 || mid == 2 || mid == 7 || mid == 77 || mid == 80,
+   MFEM_VERIFY(mid == 1 || mid == 2 || mid == 7 || mid == 77,
               "Metric not yet implemented!");

   constexpr int DIM = 2;
@@ -262,7 +222,6 @@ MFEM_REGISTER_TMOP_KERNELS(void, SetupGradPA_2D,
            if (mid ==  2) { EvalH_002(e,qx,qy,weight,Jpt,H); }
            if (mid ==  7) { EvalH_007(e,qx,qy,weight,Jpt,H); }
            if (mid == 77) { EvalH_077(e,qx,qy,weight,Jpt,H); }
-            if (mid == 80) { EvalH_080(e,qx,qy,weight,metric_param,Jpt,H); }
         } // qx
      } // qy
   });
@@ -282,10 +241,7 @@ void TMOP_Integrator::AssembleGradPA_2D(const Vector &X) const
   const Array<double> &G = PA.maps->G;
   Vector &H = PA.H;

-   double mp = 0.0;
-   if (auto m = dynamic_cast<TMOP_Metric_080 *>(metric)) { mp = m->GetGamma(); }
-
-   MFEM_LAUNCH_TMOP_KERNEL(SetupGradPA_2D,id,X,mn,mp,M,N,W,B,G,J,H);
+   MFEM_LAUNCH_TMOP_KERNEL(SetupGradPA_2D,id,X,mn,M,N,W,B,G,J,H);
 }

 } // namespace mfem
@@ -181,58 +181,8 @@ void EvalH_321(const int e, const int qx, const int qy, const int qz,
   }
 }

-// H_332 = (1-gamma) H_302 + gamma H_315
-static MFEM_HOST_DEVICE inline
-void EvalH_332(const int e, const int qx, const int qy, const int qz,
-               const double weight, const double gamma,
-               const double *J, DeviceTensor<8,double> dP)
-{
-   double B[9];
-   double         dI1b[9],          ddI1b[9];
-   double dI2[9], dI2b[9], ddI2[9], ddI2b[9];
-   double         dI3b[9],          ddI3b[9];
-   constexpr int DIM = 3;
-   kernels::InvariantsEvaluator3D ie(Args()
-                                     .J(J).B(B)
-                                     .dI1b(dI1b).ddI1b(ddI1b)
-                                     .dI2(dI2).dI2b(dI2b).ddI2(ddI2).ddI2b(ddI2b)
-                                     .dI3b(dI3b).ddI3b(ddI3b));
-   double sign_detJ;
-   const double c1 = weight/9.;
-   const double I1b = ie.Get_I1b();
-   const double I2b = ie.Get_I2b();
-   const double I3b = ie.Get_I3b(sign_detJ);
-   ConstDeviceMatrix di1b(ie.Get_dI1b(),DIM,DIM);
-   ConstDeviceMatrix di2b(ie.Get_dI2b(),DIM,DIM);
-   ConstDeviceMatrix di3b(ie.Get_dI3b(sign_detJ),DIM,DIM);
-   for (int i = 0; i < DIM; i++)
-   {
-      for (int j = 0; j < DIM; j++)
-      {
-         ConstDeviceMatrix ddi1b(ie.Get_ddI1b(i,j),DIM,DIM);
-         ConstDeviceMatrix ddi2b(ie.Get_ddI2b(i,j),DIM,DIM);
-         ConstDeviceMatrix ddi3b(ie.Get_ddI3b(i,j),DIM,DIM);
-         for (int r = 0; r < DIM; r++)
-         {
-            for (int c = 0; c < DIM; c++)
-            {
-               const double dp_302 =
-                  (di2b(r,c)*di1b(i,j) + di1b(r,c)*di2b(i,j))
-                  + ddi2b(r,c)*I1b
-                  + ddi1b(r,c)*I2b;
-               const double dp_315 = 2.0 * weight * (I3b - 1.0) * ddi3b(r,c) +
-                                     2.0 * weight * di3b(r,c) * di3b(i,j);
-               dP(r,c,i,j,qx,qy,qz,e) = (1.0 - gamma) * c1 * dp_302 +
-                                        gamma * dp_315;
-            }
-         }
-      }
-   }
-}
-
 MFEM_REGISTER_TMOP_KERNELS(void, SetupGradPA_3D,
                           const double metric_normal,
-                           const double metric_param,
                           const int mid,
                           const Vector &x_,
                           const int NE,
@@ -244,8 +194,8 @@ MFEM_REGISTER_TMOP_KERNELS(void, SetupGradPA_3D,
                           const int d1d,
                           const int q1d)
 {
-   MFEM_VERIFY(mid == 302 || mid == 303 || mid == 315 ||
-               mid == 321 || mid == 332, "3D metric not yet implemented!");
+   MFEM_VERIFY(mid == 302 || mid == 303 || mid == 315 || mid == 321 ,
+               "3D metric not yet implemented!");

   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -305,7 +255,6 @@ MFEM_REGISTER_TMOP_KERNELS(void, SetupGradPA_3D,
               if (mid == 303) { EvalH_303(e,qx,qy,qz,weight,Jpt,H); }
               if (mid == 315) { EvalH_315(e,qx,qy,qz,weight,Jpt,H); }
               if (mid == 321) { EvalH_321(e,qx,qy,qz,weight,Jpt,H); }
-               if (mid == 332) { EvalH_332(e,qx,qy,qz,weight,metric_param,Jpt,H); }
            } // qx
         } // qy
      } // qz
@@ -326,10 +275,7 @@ void TMOP_Integrator::AssembleGradPA_3D(const Vector &X) const
   const Array<double> &G = PA.maps->G;
   Vector &H = PA.H;

-   double mp = 0.0;
-   if (auto m = dynamic_cast<TMOP_Metric_332 *>(metric)) { mp = m->GetGamma(); }
-
-   MFEM_LAUNCH_TMOP_KERNEL(SetupGradPA_3D,id,mn,mp,M,X,N,W,B,G,J,H);
+   MFEM_LAUNCH_TMOP_KERNEL(SetupGradPA_3D,id,mn,M,X,N,W,B,G,J,H);
 }

 } // namespace mfem
@@ -58,24 +58,8 @@ void EvalP_077(const double *Jpt, double *P)
   kernels::Set(2,2, 0.5 * (1.0 - 1.0 / (I2 * I2)), ie.Get_dI2(), P);
 }

-static MFEM_HOST_DEVICE inline
-void EvalP_080(const double *Jpt, double gamma, double *P)
-{
-   // p_80 = (1-gamma) p_2 + gamma p_77.
-
-   double dI1b[4], dI2[4], dI2b[4];
-   kernels::InvariantsEvaluator2D ie(Args().J(Jpt).
-                                     dI1b(dI1b).dI2(dI2).dI2b(dI2b));
-
-   kernels::Set(2,2, (1.0 - gamma) * 1./2., ie.Get_dI1b(), P);
-
-   const double I2 = ie.Get_I2();
-   kernels::Add(2,2, gamma * 0.5 * (1.0 - 1.0 / (I2 * I2)), ie.Get_dI2(), P);
-}
-
 MFEM_REGISTER_TMOP_KERNELS(void, AddMultPA_Kernel_2D,
                           const double metric_normal,
-                           const double metric_param,
                           const int mid,
                           const int NE,
                           const DenseTensor &j_,
@@ -87,7 +71,7 @@ MFEM_REGISTER_TMOP_KERNELS(void, AddMultPA_Kernel_2D,
                           const int d1d,
                           const int q1d)
 {
-   MFEM_VERIFY(mid == 1 || mid == 2 || mid == 7 || mid == 77 || mid == 80,
+   MFEM_VERIFY(mid == 1 || mid == 2 || mid == 7 || mid == 77,
               "Metric not yet implemented!");

   constexpr int DIM = 2;
@@ -148,7 +132,6 @@ MFEM_REGISTER_TMOP_KERNELS(void, AddMultPA_Kernel_2D,
            if (mid ==  2) { EvalP_002(Jpt, P); }
            if (mid ==  7) { EvalP_007(Jpt, P); }
            if (mid == 77) { EvalP_077(Jpt, P); }
-            if (mid == 80) { EvalP_080(Jpt, metric_param, P); }
            for (int i = 0; i < 4; i++) { P[i] *= weight; }

            // PMatO += DS . P^t += DSh . (Jrt . P^t)
@@ -177,10 +160,7 @@ void TMOP_Integrator::AddMultPA_2D(const Vector &X, Vector &Y) const
   const Array<double> &G = PA.maps->G;
   const double mn = metric_normal;

-   double mp = 0.0;
-   if (auto m = dynamic_cast<TMOP_Metric_080 *>(metric)) { mp = m->GetGamma(); }
-
-   MFEM_LAUNCH_TMOP_KERNEL(AddMultPA_Kernel_2D,id,mn,mp,M,N,J,W,B,G,X,Y);
+   MFEM_LAUNCH_TMOP_KERNEL(AddMultPA_Kernel_2D,id,mn,M,N,J,W,B,G,X,Y);
 }

 } // namespace mfem
@@ -75,29 +75,8 @@ void EvalP_321(const double *J, double *P)
   kernels::Add(3,3, ie.Get_dI1(), P);
 }

-// P_332 = (1-gamma) P_302 + gamma P_315.
-static MFEM_HOST_DEVICE inline
-void EvalP_332(const double *J, double gamma, double *P)
-{
-   double B[9];
-   double dI1b[9], dI2[9], dI2b[9], dI3b[9];
-   kernels::InvariantsEvaluator3D ie(Args()
-                                     .J(J).B(B)
-                                     .dI1b(dI1b)
-                                     .dI2(dI2).dI2b(dI2b)
-                                     .dI3b(dI3b));
-   const double alpha = (1.0 - gamma) * ie.Get_I1b()/9.;
-   const double beta = (1.0 - gamma) * ie.Get_I2b()/9.;
-   kernels::Add(3,3, alpha, ie.Get_dI2b(), beta, ie.Get_dI1b(), P);
-
-   double sign_detJ;
-   const double I3b = ie.Get_I3b(sign_detJ);
-   kernels::Add(3,3, gamma * 2.0 * (I3b - 1.0), ie.Get_dI3b(sign_detJ), P);
-}
-
 MFEM_REGISTER_TMOP_KERNELS(void, AddMultPA_Kernel_3D,
                           const double metric_normal,
-                           double metric_param,
                           const int mid,
                           const int NE,
                           const DenseTensor &j_,
@@ -109,8 +88,8 @@ MFEM_REGISTER_TMOP_KERNELS(void, AddMultPA_Kernel_3D,
                           const int d1d,
                           const int q1d)
 {
-   MFEM_VERIFY(mid == 302 || mid == 303 || mid == 315 ||
-               mid == 321 || mid == 332, "3D metric not yet implemented!");
+   MFEM_VERIFY(mid == 302 || mid == 303 || mid == 315 || mid == 321 ,
+               "3D metric not yet implemented!");

   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -167,11 +146,10 @@ MFEM_REGISTER_TMOP_KERNELS(void, AddMultPA_Kernel_3D,

               // metric->EvalP(Jpt, P);
               double P[9];
-               if (mid == 302) { EvalP_302(Jpt, P); }
-               if (mid == 303) { EvalP_303(Jpt, P); }
-               if (mid == 315) { EvalP_315(Jpt, P); }
-               if (mid == 321) { EvalP_321(Jpt, P); }
-               if (mid == 332) { EvalP_332(Jpt, metric_param, P); }
+               if (mid == 302) { EvalP_302(Jpt,P); }
+               if (mid == 303) { EvalP_303(Jpt,P); }
+               if (mid == 315) { EvalP_315(Jpt,P); }
+               if (mid == 321) { EvalP_321(Jpt,P); }
               for (int i = 0; i < 9; i++) { P[i] *= weight; }

               // Y += DS . P^t += DSh . (Jrt . P^t)
@@ -202,10 +180,7 @@ void TMOP_Integrator::AddMultPA_3D(const Vector &X, Vector &Y) const
   const Array<double> &G = PA.maps->G;
   const double mn = metric_normal;

-   double mp = 0.0;
-   if (auto m = dynamic_cast<TMOP_Metric_332 *>(metric)) { mp = m->GetGamma(); }
-
-   MFEM_LAUNCH_TMOP_KERNEL(AddMultPA_Kernel_3D,id,mn,mp,M,N,J,W,B,G,X,Y);
+   MFEM_LAUNCH_TMOP_KERNEL(AddMultPA_Kernel_3D,id,mn,M,N,J,W,B,G,X,Y);
 }

 } // namespace mfem
@@ -50,15 +50,8 @@ double EvalW_077(const double *Jpt)
   return 0.5*(I2b*I2b + 1./(I2b*I2b) - 2.);
 }

-static MFEM_HOST_DEVICE inline
-double EvalW_080(const double *Jpt, double gamma)
-{
-   return (1.0 - gamma) * EvalW_002(Jpt) + gamma * EvalW_077(Jpt);
-}
-
 MFEM_REGISTER_TMOP_KERNELS(double, EnergyPA_2D,
                           const double metric_normal,
-                           const double metric_param,
                           const int mid,
                           const int NE,
                           const DenseTensor &j_,
@@ -71,7 +64,7 @@ MFEM_REGISTER_TMOP_KERNELS(double, EnergyPA_2D,
                           const int d1d,
                           const int q1d)
 {
-   MFEM_VERIFY(mid == 1 || mid == 2 || mid == 7 || mid == 77 || mid == 80,
+   MFEM_VERIFY(mid == 1 || mid == 2 || mid == 7 || mid == 77,
               "2D metric not yet implemented!");

   constexpr int DIM = 2;
@@ -132,8 +125,7 @@ MFEM_REGISTER_TMOP_KERNELS(double, EnergyPA_2D,
            mid ==  1 ? EvalW_001(Jpt) :
            mid ==  2 ? EvalW_002(Jpt) :
            mid ==  7 ? EvalW_007(Jpt) :
-            mid == 77 ? EvalW_077(Jpt) :
-            mid == 80 ? EvalW_080(Jpt, metric_param) : 0.0;
+            mid == 77 ? EvalW_077(Jpt) : 0.0;

            E(qx,qy,e) = weight * EvalW;
         }
@@ -149,7 +141,7 @@ double TMOP_Integrator::GetLocalStateEnergyPA_2D(const Vector &X) const
   const int D1D = PA.maps->ndof;
   const int Q1D = PA.maps->nqpt;
   const int id = (D1D << 4 ) | Q1D;
-   const double mn = metric_normal;
+   const double m = metric_normal;
   const DenseTensor &J = PA.Jtr;
   const Array<double> &W = PA.ir->GetWeights();
   const Array<double> &B = PA.maps->B;
@@ -157,10 +149,7 @@ double TMOP_Integrator::GetLocalStateEnergyPA_2D(const Vector &X) const
   const Vector &O = PA.O;
   Vector &E = PA.E;

-   double mp = 0.0;
-   if (auto m = dynamic_cast<TMOP_Metric_080 *>(metric)) { mp = m->GetGamma(); }
-
-   MFEM_LAUNCH_TMOP_KERNEL(EnergyPA_2D,id,mn,mp,M,N,J,W,B,G,X,O,E);
+   MFEM_LAUNCH_TMOP_KERNEL(EnergyPA_2D,id,m,M,N,J,W,B,G,X,O,E);
 }

 } // namespace mfem
@@ -58,15 +58,8 @@ double EvalW_321(const double *J)
   return ie.Get_I1() + ie.Get_I2()/ie.Get_I3() - 6.0;
 }

-static MFEM_HOST_DEVICE inline
-double EvalW_332(const double *J, double gamma)
-{
-   return (1.0 - gamma) * EvalW_302(J) + gamma * EvalW_315(J);
-}
-
 MFEM_REGISTER_TMOP_KERNELS(double, EnergyPA_3D,
                           const double metric_normal,
-                           const double metric_param,
                           const int mid,
                           const int NE,
                           const DenseTensor &j_,
@@ -79,8 +72,8 @@ MFEM_REGISTER_TMOP_KERNELS(double, EnergyPA_3D,
                           const int d1d,
                           const int q1d)
 {
-   MFEM_VERIFY(mid == 302 || mid == 303 || mid == 315 ||
-               mid == 321 || mid == 332, "3D metric not yet implemented!");
+   MFEM_VERIFY(mid == 302 || mid == 303 || mid == 315 || mid == 321 ,
+               "3D metric not yet implemented!");

   constexpr int DIM = 3;
   const int D1D = T_D1D ? T_D1D : d1d;
@@ -141,8 +134,7 @@ MFEM_REGISTER_TMOP_KERNELS(double, EnergyPA_3D,
               mid == 302 ? EvalW_302(Jpt) :
               mid == 303 ? EvalW_303(Jpt) :
               mid == 315 ? EvalW_315(Jpt) :
-               mid == 321 ? EvalW_321(Jpt) :
-               mid == 332 ? EvalW_332(Jpt, metric_param) : 0.0;
+               mid == 321 ? EvalW_321(Jpt) : 0.0;

               E(qx,qy,qz,e) = weight * EvalW;
            }
@@ -167,10 +159,7 @@ double TMOP_Integrator::GetLocalStateEnergyPA_3D(const Vector &X) const
   const Vector &O = PA.O;
   Vector &E = PA.E;

-   double mp = 0.0;
-   if (auto m = dynamic_cast<TMOP_Metric_332 *>(metric)) { mp = m->GetGamma(); }
-
-   MFEM_LAUNCH_TMOP_KERNEL(EnergyPA_3D,id,mn,mp,M,N,J,W,B,G,O,X,E);
+   MFEM_LAUNCH_TMOP_KERNEL(EnergyPA_3D,id,mn,M,N,J,W,B,G,O,X,E);
 }

 } // namespace mfem
@@ -71,7 +71,7 @@ static const unsigned char b64table[] =
   255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255
 };

-void DecodeBase64(const char *src, size_t len, std::vector<char> &buf)
+void DecodeBase64(const char *src, size_t len, std::vector<unsigned char> &buf)
 {
   const unsigned char *in = (const unsigned char *)src;
   buf.clear();
@@ -79,7 +79,7 @@ void DecodeBase64(const char *src, size_t len, std::vector<char> &buf)
   for (size_t i=0; i<len; ++i) { if (b64table[in[i]] != 255) { ++count; } }
   if (count % 4 != 0) { return; }
   buf.resize(3*len/4);
-   unsigned char *out = (unsigned char *)buf.data();
+   unsigned char *out = buf.data();
   count = 0;
   int pad = 0;
   unsigned char c[4];
@@ -97,10 +97,8 @@ void DecodeBase64(const char *src, size_t len, std::vector<char> &buf)
         count = pad = 0;
      }
   }
-   buf.resize(out - (unsigned char *)buf.data());
+   buf.resize(out - buf.data());
 }

-size_t NumBase64Chars(size_t nbytes) { return ((4*nbytes/3) + 3) & ~3; }
-
 } // namespace mfem::bin_io
 } // namespace mfem
@@ -50,7 +50,6 @@ inline T read(const char *buf)
   return value;
 }

-/// Append the binary representation of @a val to the byte buffer @a vec.
 template <typename T>
 void AppendBytes(std::vector<char> &vec, const T &val)
 {
@@ -58,17 +57,9 @@ void AppendBytes(std::vector<char> &vec, const T &val)
   vec.insert(vec.end(), ptr, ptr + sizeof(T));
 }

-/// Given a buffer @a buf of length @a nbytes, encode the data in base-64
-/// format, and write the encoded data to the output stream @a out.
-void WriteBase64(std::ostream &out, const void *bytes, size_t nbytes);
+void WriteBase64(std::ostream &out, const void *bytes, size_t length);

-/// Decode @a len base-64 encoded characters in the buffer @a src, and store the
-/// resulting decoded data in @a buf. @a buf will be resized as needed.
-void DecodeBase64(const char *src, size_t len, std::vector<char> &buf);
-
-/// Return the number of characters needed to encode @a nbytes in base-64. This
-/// is equal to 4*nbytes/3, rounded up to the nearest multiple of 4.
-size_t NumBase64Chars(size_t nbytes);
+void DecodeBase64(const char *src, size_t len, std::vector<unsigned char> &buf);

 } // namespace mfem::bin_io

@@ -17,7 +17,6 @@ list(APPEND SRCS
  complex_operator.cpp
  constraints.cpp
  densemat.cpp
-  fdsolver.cpp
  symmat.cpp
  handle.cpp
  matrix.cpp
@@ -40,7 +39,6 @@ list(APPEND HDRS
  dinvariants.hpp
  symmat.hpp
  dtensor.hpp
-  fdsolver.hpp
  handle.hpp
  invariants.hpp
  kernels.hpp
@@ -208,14 +208,11 @@ void AmgXSolver::DefaultParameters(const AMGX_MODE amgxMode_,
                    " \"config_version\": 2, \n"
                    " \"solver\": { \n"
                    "   \"solver\": \"AMG\", \n"
-                    "   \"scope\": \"main\", \n"
-                    "   \"smoother\": \"JACOBI_L1\", \n"
                    "   \"presweeps\": 1, \n"
-                    "   \"interpolator\": \"D2\", \n"
-                    "   \"max_row_sum\" : 0.9, \n"
-                    "   \"strength_threshold\" : 0.25, \n"
                    "   \"postsweeps\": 1, \n"
-                    "   \"max_iters\": 1, \n"
+                    "   \"interpolator\": \"D2\", \n"
+                    "   \"max_iters\": 2, \n"
+                    "   \"convergence\": \"ABSOLUTE\", \n"
                    "   \"cycle\": \"V\"";
      if (verbose)
      {
@@ -242,21 +239,22 @@ void AmgXSolver::DefaultParameters(const AMGX_MODE amgxMode_,
                    "     \"solver\": \"AMG\", \n"
                    "     \"smoother\": { \n"
                    "     \"scope\": \"jacobi\", \n"
-                    "     \"solver\": \"JACOBI_L1\" \n"
+                    "     \"solver\": \"BLOCK_JACOBI\", \n"
+                    "     \"relaxation_factor\": 0.7 \n"
                    "       }, \n"
                    "     \"presweeps\": 1, \n"
                    "     \"interpolator\": \"D2\", \n"
                    "     \"max_row_sum\" : 0.9, \n"
                    "     \"strength_threshold\" : 0.25, \n"
-                    "     \"max_iters\": 1, \n"
+                    "     \"max_iters\": 2, \n"
                    "     \"scope\": \"amg\", \n"
                    "     \"max_levels\": 100, \n"
                    "     \"cycle\": \"V\", \n"
                    "     \"postsweeps\": 1 \n"
                    "    }, \n"
                    "  \"solver\": \"PCG\", \n"
-                    "  \"max_iters\": 150, \n"
-                    "  \"convergence\": \"RELATIVE_INI_CORE\", \n"
+                    "  \"max_iters\": 100, \n"
+                    "  \"convergence\": \"RELATIVE_MAX\", \n"
                    "  \"scope\": \"main\", \n"
                    "  \"tolerance\": 1e-12, \n"
                    "  \"monitor_residual\": 1, \n"
@@ -50,10 +50,6 @@ dsyevr_(char *JOBZ, char *RANGE, char *UPLO, int *N, double *A, int *LDA,
        double *W, double *Z, int *LDZ, int *ISUPPZ, double *WORK, int *LWORK,
        int *IWORK, int *LIWORK, int *INFO);
 extern "C" void
-dgeev_(const char * jobvl, const char * jobvr, int *n, double * A, int * lda,
-       double * wr, double * wl, double * vl, int * ldvl, double * vr, int * ldvr,
-       double * work, int * lwork, int * info);
-extern "C" void
 dsyev_(char *JOBZ, char *UPLO, int *N, double *A, int *LDA, double *W,
       double *WORK, int *LWORK, int *INFO);
 extern "C" void
@@ -178,14 +174,7 @@ const double &DenseMatrix::Elem(int i, int j) const

 void DenseMatrix::Mult(const double *x, double *y) const
 {
-   const double *data = Read();
-   const int h = height;
-   const int w = width;
-
-   MFEM_FORALL(i, 1,
-   {
-      kernels::Mult(h, w, data, x, y);
-   });
+   kernels::Mult(height, width, Data(), x, y);
 }

 void DenseMatrix::Mult(const Vector &x, Vector &y) const
@@ -193,9 +182,7 @@ void DenseMatrix::Mult(const Vector &x, Vector &y) const
   MFEM_ASSERT(height == y.Size() && width == x.Size(),
               "incompatible dimensions");

-   const double *dx = x.Read();
-   double *dy = y.ReadWrite();
-   Mult(dx, dy);
+   Mult((const double *)x, (double *)y);
 }

 double DenseMatrix::operator *(const DenseMatrix &m) const
@@ -2016,7 +2003,7 @@ void Mult(const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
   MFEM_ASSERT(a.Height() == b.Height() && a.Width() == c.Width() &&
               b.Width() == c.Height(), "incompatible dimensions");

-#if defined(MFEM_USE_LAPACK) && !defined(MFEM_USE_CUDA) && !defined(MFEM_USE_HIP)
+#ifdef MFEM_USE_LAPACK
   static char transa = 'N', transb = 'N';
   static double alpha = 1.0, beta = 0.0;
   int m = b.Height(), n = c.Width(), k = b.Width();
@@ -2027,13 +2014,10 @@ void Mult(const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
   const int ah = a.Height();
   const int aw = a.Width();
   const int bw = b.Width();
-   double *ad = a.ReadWrite();
-   const double *bd = b.Read();
-   const double *cd = c.Read();
-   MFEM_FORALL(i, 1,
-   {
-      kernels::Mult(ah, aw, bw, bd, cd, ad);
-   });
+   double *ad = a.Data();
+   const double *bd = b.Data();
+   const double *cd = c.Data();
+   kernels::Mult(ah,aw,bw,bd,cd,ad);
 #endif
 }

@@ -2875,155 +2859,6 @@ void AddMult_a_VVt(const double a, const Vector &v, DenseMatrix &VVt)
   }
 }

-void KronProd(const DenseMatrix & A, const DenseMatrix & B, DenseMatrix & C)
-{
-   const int ah = A.Height();
-   const int aw = A.Width();
-   const int bh = B.Height();
-   const int bw = B.Width();
-
-   C.SetSize(ah*bh,aw*bw);
-   const double * ad = A.Read();
-   const double * bd = B.Read();
-   double * cd = C.ReadWrite();
-
-   MFEM_FORALL(i, 1,
-   {
-      for (int ja = 0; ja<aw; ++ja)
-         for (int jb = 0; jb<bw; ++jb)
-            for (int ia = 0; ia<ah; ++ia)
-               for (int ib = 0; ib<bh; ++ib)
-                  cd[bh*ia + ib + ah*bh*(bw*ja + jb)]
-                     = ad[ia + ja * ah] * bd[ib + jb*bh];
-   });
-}
-
-#if 0 // this is a finer level parallel KronProd
-void KronProd2(const DenseMatrix & A, const DenseMatrix & B, DenseMatrix & C)
-{
-   const int ah = A.Height();
-   const int aw = A.Width();
-   const int bh = B.Height();
-   const int bw = B.Width();
-   const int ch = ah * bh;
-   const int cw = aw * bw;
-
-   C.SetSize(ch, cw);
-   const double *ad = A.Read();
-   const double *bd = B.Read();
-   double *cd = C.ReadWrite();
-
-   MFEM_FORALL(i, ch * cw,
-   {
-      const int jc = i / ch;
-      const int ic = i - jc * ch;
-      const int ja = jc / bw;
-      const int jb = jc - ja * bw;
-      const int ia = ic / bh;
-      const int ib = ic - ia * bh;
-      cd[jc * ch + ic] = ad[ja * ah + ia] * bd[jb * bh + ib];
-   });
-}
-#endif
-
-void KronMult(const DenseMatrix &A, const DenseMatrix &B, const Vector &r,
-              Vector &z)
-{
-   const int nA = A.Height();
-   const int mA = A.Width();
-   const int nB = B.Height();
-   const int mB = B.Width();
-   const int nr = r.Size();
-   MFEM_VERIFY(nr == mA*mB, "Wrong size of Vector r");
-   z.SetSize(nA*nB);
-#if !defined(MFEM_USE_CUDA)
-   DenseMatrix R(r.GetData(),mB,mA);
-   DenseMatrix X(nB,mA);
-   DenseMatrix Y(z.GetData(),nB,nA);
-   Mult(B,R,X);
-   MultABt(X,A,Y);
-#else
-   const double *ad = A.Read();
-   const double *bd = B.Read();
-   const double *rd = r.Read();
-   double *zd = z.Write();
-   MFEM_FORALL(i, 1,
-   {
-      kernels::KronMult(nA, mA, ad, nB, mB, bd, rd, zd);
-   });
-#endif
-}
-
-void KronMult(const DenseMatrix &A, const DenseMatrix &B, const DenseMatrix &R,
-              DenseMatrix & Z)
-{
-   const int nA = A.Height();
-   const int nB = B.Height();
-   const int nR = R.Height();
-   const int mR = R.Width();
-   Z.SetSize(nA*nB,mR);
-
-   Vector r,z;
-   double * dataR = R.Data();
-   for (int i = 0; i<mR; i++)
-   {
-      r.SetDataAndSize(&dataR[i*nR],nR);
-      KronMult(A,B,r,z);
-      Z.SetCol(i,z);
-   }
-}
-
-void KronMult(const DenseMatrix &A, const DenseMatrix &B, const DenseMatrix &C,
-              const Vector &r, Vector &z)
-{
-   const int nA = A.Height();
-   const int mA = A.Width();
-   const int nB = B.Height();
-   const int mB = B.Width();
-   const int nC = C.Height();
-   const int mC = C.Width();
-   const int nr = r.Size();
-   MFEM_VERIFY(nr == mA*mB*mC, "Wrong size of Vector r");
-   z.SetSize(nA*nB*nC);
-
-#if !defined(MFEM_USE_CUDA)
-   double * dataR = r.GetData();
-   DenseMatrix R(dataR,mC,mA*mB);
-   DenseMatrix X(nC,mA*mB);
-   Mult(C,R,X);
-   X.Transpose();
-   DenseMatrix Z(z.GetData(),mA*mB,nC);
-   KronMult(A,B,X,Z);
-   Z.Transpose();
-#else
-   const double *ad = A.Read();
-   const double *bd = B.Read();
-   const double *cd = C.Read();
-   const double *rd = r.Read();
-   double *zd = z.Write();
-   MFEM_FORALL(i, 1,
-   {
-      kernels::KronMult(nA, mA, ad, nB, mB, bd, nC, mC, cd, rd, zd);
-   });
-#endif
-}
-
-void KronMult(const Array<DenseMatrix *> & A, const Vector & r, Vector & z)
-{
-   int dim = A.Size();
-   if (dim == 2)
-   {
-      KronMult(*A[0],*A[1],r,z);
-   }
-   else if (dim == 3)
-   {
-      KronMult(*A[0],*A[1],*A[2], r,z);
-   }
-   else
-   {
-      MFEM_ABORT("KronMult::Wrong dimension");
-   }
-}

 bool LUFactors::Factor(int m, double TOL)
 {
@@ -3475,105 +3310,23 @@ DenseMatrixInverse::~DenseMatrixInverse()
   delete [] lu.ipiv;
 }

-void KronMult(const DenseMatrixInverse &A, const DenseMatrixInverse &B,
-              const Vector &r, Vector & z)
-{
-   // A and B are square matrices
-   z.SetSize(r.Size());
-   int nA = A.Height();
-   int nB = B.Height();
-   DenseMatrix R(r.GetData(),nB,nA);
-   DenseMatrix X(nB,nA);
-   B.Mult(R,X);
-   X.Transpose();
-   DenseMatrix Y(z.GetData(),nA,nB);
-   A.Mult(X,Y);
-   Y.Transpose();
-}

-void KronMult(const DenseMatrixInverse &A, const DenseMatrixInverse &B,
-              const DenseMatrix &R, DenseMatrix & Z)
-{
-   // A and B are square matrices
-   int nR = R.Height();
-   int mR = R.Width();
-   Z.SetSize(nR,mR);
-   Vector r(nR);
-   Vector z(nR);
-   double * dataR = R.GetData();
-   double * dataZ = Z.GetData();
-   for (int i = 0; i<mR; i++)
-   {
-      r.SetData(&dataR[i*nR]);
-      z.SetData(&dataZ[i*nR]);
-      KronMult(A,B,r,z);
-   }
-}
-
-void KronMult(const DenseMatrixInverse &A, const DenseMatrixInverse &B,
-              const DenseMatrixInverse &C, const Vector &r, Vector & z)
-{
-   // A, B and C are square matrices
-   int n = r.Size();
-   z.SetSize(n);
-   int nA = A.Height();
-   int nB = B.Height();
-   int nC = C.Height();
-   double * dataR = r.GetData();
-   DenseMatrix R(dataR,nC,nA*nB);
-   DenseMatrix X(nC,nA*nB);
-   C.Mult(R,X);
-   X.Transpose();
-   DenseMatrix Z(z.GetData(),nC,nA*nB);
-   KronMult(A,B,X,Z);
-   Z.Transpose();
-}
-
-void KronMult(const Array<DenseMatrixInverse *> & A, const Vector & r,
-              Vector & z)
-{
-   int dim = A.Size();
-   if (dim == 2)
-   {
-      KronMult(*A[0],*A[1],r,z);
-   }
-   else if (dim == 3)
-   {
-      KronMult(*A[0],*A[1],*A[2], r,z);
-   }
-   else
-   {
-      MFEM_ABORT("KronMult::Wrong dimension");
-   }
-}
-
-DenseMatrixEigensystem::DenseMatrixEigensystem(DenseMatrix &m, bool sym_)
+DenseMatrixEigensystem::DenseMatrixEigensystem(DenseMatrix &m)
   : mat(m)
 {
   n = mat.Width();
   EVal.SetSize(n);
-   EVali.SetSize(n);
   EVect.SetSize(n);
   ev.SetDataAndSize(NULL, n);

 #ifdef MFEM_USE_LAPACK
-   sym = sym_;
   jobz = 'V';
+   uplo = 'U';
   lwork = -1;
   double qwork;
-   if (sym)
-   {
-      uplo = 'U';
-      dsyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
-             &qwork, &lwork, &info);
-   }
-   else
-   {
-      char jobvl = 'N';
-      int ldvl = 1;
-      dgeev_(&jobvl,&jobz,&n, mat.GetData(), &n, EVal.GetData(), EVali.GetData(),
-             nullptr, &ldvl, EVect.GetData(), &n, &qwork, &lwork, &info);
-   }
+   dsyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
+          &qwork, &lwork, &info);
+
   lwork = (int) qwork;
   work = new double[lwork];
 #endif
@@ -3585,7 +3338,6 @@ DenseMatrixEigensystem::DenseMatrixEigensystem(
     n(other.n)
 {
 #ifdef MFEM_USE_LAPACK
-   sym = other.sym;
   jobz = other.jobz;
   uplo = other.uplo;
   lwork = other.lwork;
@@ -3604,24 +3356,13 @@ void DenseMatrixEigensystem::Eval()
 #endif

 #ifdef MFEM_USE_LAPACK
-   if (sym)
-   {
-      EVect = mat;
-      dsyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
-             work, &lwork, &info);
-   }
-   else
-   {
-      char jobvl = 'N';
-      int ldvl = 1;
-      DenseMatrix T = mat; // mat is overwritten by dgeev
-      dgeev_(&jobvl,&jobz,&n, T.GetData(), &n, EVal.GetData(), EVali.GetData(),
-             nullptr, &ldvl, EVect.GetData(), &n, work, &lwork, &info);
-   }
+   EVect = mat;
+   dsyev_(&jobz, &uplo, &n, EVect.Data(), &n, EVal.GetData(),
+          work, &lwork, &info);
+
   if (info != 0)
   {
-      string lpck = (sym) ? "DSYEV" : "DGEEV";
-      mfem::err << "DenseMatrixEigensystem::Eval(): " << lpck << "error code: "
+      mfem::err << "DenseMatrixEigensystem::Eval(): DSYEV error code: "
                << info << endl;
      mfem_error();
   }
@@ -523,23 +523,6 @@ void AddMult_a_VWt(const double a, const Vector &v, const Vector &w,
 /// VVt += a * v v^t
 void AddMult_a_VVt(const double a, const Vector &v, DenseMatrix &VVt);

-/// C = A ⊗ B
-void KronProd(const DenseMatrix & A, const DenseMatrix & B, DenseMatrix & C);
-void KronProd2(const DenseMatrix & A, const DenseMatrix & B, DenseMatrix & C);
-
-/// z = (A ⊗ B) r  = vec(B R A^T), where R := vec^-1 (r)
-void KronMult(const DenseMatrix &A, const DenseMatrix &B, const Vector &r,
-              Vector & z);
-
-/// z = (A ⊗ B) R
-void KronMult(const DenseMatrix &A, const DenseMatrix &B, const DenseMatrix &R,
-              DenseMatrix & Z);
-
-/// z = ( A ⊗ B ⊗ C ) r
-void KronMult(const DenseMatrix &A, const DenseMatrix &B, const DenseMatrix &C,
-              const Vector &r, Vector & z);
-
-void KronMult(const Array<DenseMatrix *> & A, const Vector & r, Vector & z);

 /** Class that can compute LU factorization of external data and perform various
    operations with the factored data. */
@@ -702,33 +685,16 @@ public:
   virtual ~DenseMatrixInverse();
 };

-/// z = (A^-1 ⊗ B^-1) r  = vec(B^-1 R A^-T), where R := vec^-1 (r)
-void KronMult(const DenseMatrixInverse &Ainv, const DenseMatrixInverse &Binv,
-              const Vector &r, Vector & z);
-
-/// z = (A^-1 ⊗ B^-1) R
-void KronMult(const DenseMatrixInverse &Ainv, const DenseMatrixInverse &Binv,
-              const DenseMatrix &R, DenseMatrix & Z);
-
-/// z = ( A^-1 ⊗ B^-1 ⊗ C^-1 ) r
-void KronMult(const DenseMatrixInverse &Ainv, const DenseMatrixInverse &Binv,
-              const DenseMatrixInverse &Cinv, const Vector &r, Vector & z);
-
-void KronMult(const Array<DenseMatrixInverse *> & A, const Vector & r,
-              Vector & z);

 class DenseMatrixEigensystem
 {
   DenseMatrix &mat;
   Vector      EVal;
-   // Possible non zero imaginary part of Eigenvalues
-   Vector      EVali;
   DenseMatrix EVect;
   Vector ev;
   int n;

 #ifdef MFEM_USE_LAPACK
-   bool sym;
   double *work;
   char jobz, uplo;
   int lwork, info;
@@ -736,10 +702,10 @@ class DenseMatrixEigensystem

 public:

-   DenseMatrixEigensystem(DenseMatrix &m, bool sym_ = false);
+   DenseMatrixEigensystem(DenseMatrix &m);
   DenseMatrixEigensystem(const DenseMatrixEigensystem &other);
   void Eval();
-   Vector &Eigenvalues(bool imag = false) { return imag ? EVali : EVal; }
+   Vector &Eigenvalues() { return EVal; }
   DenseMatrix &Eigenvectors() { return EVect; }
   double Eigenvalue(int i) { return EVal(i); }
   const Vector &Eigenvector(int i)
@@ -1,143 +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.
-
-#include "linalg.hpp"
-
-namespace mfem
-{
-
-void KronProdInvDiag(const Vector & a, const Vector & b, Vector & dinv)
-{
-   int n = a.Size(), m = b.Size();
-   dinv.SetSize(n*m);
-
-   for (int j = 0; j<m; j++)
-      for (int i = 0; i<n; i++)
-      {
-         dinv(i*m+j) = 1./(a(i) + b(j));
-      }
-}
-
-void KronProdInvDiag(const Vector & a, const Vector & b,
-                     const Vector & c, Vector & dinv)
-{
-   int n = a.Size(), m = b.Size(), l = c.Size();
-   dinv.SetSize(n*m*l);
-
-   for (int k = 0; k<l; k++)
-      for (int j = 0; j<m; j++)
-         for (int i = 0; i<n; i++)
-         {
-            dinv(i*m*l+j*l+k) = 1./(a(i) + b(j) + c(k));
-         }
-}
-
-void KronProdInvDiag(const Array<Vector *> & X, Vector & dinv)
-{
-   int dim = X.Size();
-   if (dim == 1)
-   {
-      int n = X[0]->Size();
-      dinv.SetSize(n);
-      for (int i = 0; i<n; i++) { dinv(i) = 1./(*X[0])(i); }
-   }
-   else if (dim == 2)
-   {
-      KronProdInvDiag(*X[0], *X[1], dinv);
-   }
-   else if (dim == 3)
-   {
-      KronProdInvDiag(*X[0], *X[1], *X[2], dinv);
-   }
-   else
-   {
-      MFEM_ABORT("KronProdInvDiag::Wrong dimension");
-   }
-}
-
-#ifdef MFEM_USE_LAPACK
-
-FDSolver::FDSolver(const Array<DenseMatrix *> & A,
-                   const Array<DenseMatrix *> & B)
-{
-   MFEM_ASSERT(A.Size() == B.Size(), "DenseFDSolver: Incompatible Dimensions");
-   dim = A.Size();
-
-   int solver_size = 1;
-   for (int i = 0; i<dim; i++)
-   {
-      MFEM_ASSERT(A[i]->Height() == A[i]->Width(),
-                  "DenseFDSolver: Matrix is not square");
-      MFEM_ASSERT(B[i]->Height() == B[i]->Width(),
-                  "DenseFDSolver: Matrix is not square");
-      MFEM_ASSERT(A[i]->Height() == B[i]->Height(),
-                  "DenseFDSolver: Matrices A and B have incompatible size");
-      solver_size *= A[i]->Height();
-   }
-   this->height = solver_size;
-   this->width  = solver_size;
-   if (solver_size) { Setup(A,B); }
-}
-
-void FDSolver::Setup(const Array<DenseMatrix *> & A,
-                     const Array<DenseMatrix *> & B)
-{
-   EigSystem.SetSize(dim);
-   eigv.SetSize(dim);
-   Array<Vector *> evalues(dim);
-   SQ.SetSize(dim);
-   DenseMatrix D;
-   for (int i = 0; i<dim; i++)
-   {
-      DenseMatrixInverse Minv(*B[i]);
-      Minv.Mult(*A[i],D);
-      EigSystem[i] = new DenseMatrixEigensystem(D);
-      EigSystem[i]->Eval();
-      evalues[i] = &EigSystem[i]->Eigenvalues();
-      eigv[i] = &EigSystem[i]->Eigenvectors();
-      DenseMatrixInverse Qinv(*eigv[i]);
-      DenseMatrix Sdinv;
-      Minv.GetInverseMatrix(Sdinv);
-      SQ[i] = new DenseMatrix;
-      Qinv.Mult(Sdinv,*SQ[i]);
-   }
-   KronProdInvDiag(evalues,dinv);
-}
-
-
-void FDSolver::Mult(const Vector & r,Vector & z) const
-{
-   MFEM_ASSERT(height == r.Size(),
-               "DenseFDSolver::Mult: Inconsistent vector size");
-   if (r.Size() == 0) { return; }
-   Vector rtemp;
-   KronMult(SQ,r,rtemp);
-   // 2. Diagonal solve;
-   rtemp *= dinv;
-   // 3. Modify RHS; z <-- (Q1 x Q2) rtemp
-   KronMult(eigv,rtemp,z);
-}
-
-FDSolver::~FDSolver()
-{
-   if (height)
-   {
-      for (int i=0; i<dim; i++)
-      {
-         delete SQ[i];
-         delete EigSystem[i];
-      }
-   }
-}
-
-#endif // MFEM_USE_LAPACK
-
-} // namespace mfem
@@ -1,60 +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.
-
-#ifndef MFEM_FDSOLVER
-#define MFEM_FDSOLVER
-
-#include "../config/config.hpp"
-#include "densemat.hpp"
-
-namespace mfem
-{
-
-/// Computes the inverse diagonal dinv = (a⊗I + I⊗b)^-1
-/// where a, b are diagonal matrices and I is the identity of the
-/// appropriate size
-void KronProdInvDiag(const Vector & a, const Vector & b, Vector & dinv);
-
-/// Computes the inverse diagonal dinv = (a⊗I⊗I + I⊗b⊗I + I⊗I⊗c)^-1
-/// where a, b, c are diagonal matrices and I is the identity of the
-/// appropriate size
-void KronProdInvDiag(const Vector & a, const Vector & b,
-                     const Vector & c, Vector & dinv);
-
-void KronProdInvDiag(const Array<Vector *> & X, Vector & dinv);
-
-#ifdef MFEM_USE_LAPACK
-
-/// In 2D it solves the system (A_0 ⊗ B_1 + B_0 ⊗ A_1) z = r
-/// In 3D it solves the system
-///     (A_0 ⊗ B_1 ⊗ B_2 + B_0 ⊗ A_1 ⊗ B_2 + B_0 ⊗ B_1 ⊗ A_2) z = r
-class FDSolver: public Solver
-{
-private:
-   int dim = 2;
-   Array<DenseMatrixEigensystem *> EigSystem;
-   Array<DenseMatrix *> eigv; // eigenvectors
-   Array<DenseMatrix *> SQ;
-   mutable Vector dinv;
-   void Setup(const Array<DenseMatrix *> & A, const Array<DenseMatrix *> & B);
-public:
-   FDSolver(const Array<DenseMatrix *> & A, const Array<DenseMatrix *> & B);
-   virtual void SetOperator(const Operator &op) {}
-   virtual void Mult(const Vector &r, Vector &z) const;
-   virtual ~FDSolver();
-};
-
-#endif // MFEM_USE_LAPACK
-
-} // mfem name space
-
-
-#endif // MFEM_FDSOLVER
@@ -516,14 +516,7 @@ public:

   /// Initialize all entries with value.
   HypreParMatrix &operator=(double value)
-   {
-#if MFEM_HYPRE_VERSION < 22200
-      internal::hypre_ParCSRMatrixSetConstantValues(A, value);
-#else
-      hypre_ParCSRMatrixSetConstantValues(A, value);
-#endif
-      return *this;
-   }
+   { internal::hypre_ParCSRMatrixSetConstantValues(A, value); return *this; }

   /** Perform the operation `*this += B`, assuming that both matrices use the
       same row and column partitions and the same col_map_offd arrays, or B has
@@ -1942,8 +1942,8 @@ HYPRE_Int
 hypre_ParCSRMatrixSetConstantValues(hypre_ParCSRMatrix *A,
                                    HYPRE_Complex       value)
 {
-   internal::hypre_CSRMatrixSetConstantValues(hypre_ParCSRMatrixDiag(A), value);
-   internal::hypre_CSRMatrixSetConstantValues(hypre_ParCSRMatrixOffd(A), value);
+   hypre_CSRMatrixSetConstantValues(hypre_ParCSRMatrixDiag(A), value);
+   hypre_CSRMatrixSetConstantValues(hypre_ParCSRMatrixOffd(A), value);

   return 0;
 }
@@ -198,16 +198,6 @@ hypre_CSRMatrixSum(hypre_CSRMatrix *A,
                   HYPRE_Complex    beta,
                   hypre_CSRMatrix *B);

-#if MFEM_HYPRE_VERSION >= 22200
-/** Provide an overloaded function for code consistency between HYPRE API
-    versions. */
-inline hypre_CSRMatrix *hypre_CSRMatrixAdd(hypre_CSRMatrix *A,
-                                           hypre_CSRMatrix *B)
-{
-   return ::hypre_CSRMatrixAdd(1.0, A, 1.0, B);
-}
-#endif
-
 /** Return a new matrix containing the sum of A and B, assuming that both
    matrices use the same row and column partitions. The col_map_offd do not
    need to be the same, but a more efficient algorithm is used if that's the
@@ -160,7 +160,7 @@ double Norml2(const int size, const T *data)
    data of the input and output vectors. */
 template<typename TA, typename TX, typename TY>
 MFEM_HOST_DEVICE inline
-void Mult(const int height, const int width, const TA *data, const TX *x, TY *y)
+void Mult(const int height, const int width, TA *data, const TX *x, TY *y)
 {
   if (width == 0)
   {
@@ -170,8 +170,7 @@ void Mult(const int height, const int width, const TA *data, const TX *x, TY *y)
      }
      return;
   }
-
-   TA *d_col = (TA *) data;
+   TA *d_col = data;
   TX x_col = x[0];
   for (int row = 0; row < height; row++)
   {
@@ -189,52 +188,6 @@ void Mult(const int height, const int width, const TA *data, const TX *x, TY *y)
   }
 }

-template<typename TA, typename TB, typename TR, typename TZ>
-MFEM_HOST_DEVICE inline
-void KronMult(const int ah, const int aw, const TA *ad, const int bh, const int bw, const TB *bd, TR *r, TZ *z)
-{
-   for (int i = 0; i < bh; i++)
-   {
-      for (int l = 0; l < ah; l++)
-      {
-         TZ t1 = 0.0;
-         for (int j = 0; j < bw; j++)
-         {
-            const TB t2 = bd[i + j * bh];
-            for (int k = 0; k < aw; k++)
-            {
-               t1 += t2 * r[j + k * bw] * ad[l + k * ah];
-            }
-         }
-         z[i + l * bh] = t1;
-      }
-   }
-}
-
-template<typename TA, typename TB, typename TC, typename TR, typename TZ>
-MFEM_HOST_DEVICE inline
-void KronMult(const int ah, const int aw, const TA *ad, const int bh, const int bw, const TB *bd, const int ch, const int cw, const TC *cd, TR *r, TZ *z)
-{
-   for (int i = 0; i < ch; i++)
-   {
-      for (int l = 0; l < ah * bh; l++)
-      {
-         TZ t1 = 0.0;
-         for (int j = 0; j < cw; j++)
-         {
-            const TB t2 = cd[i + j * ch];
-            for (int k = 0; k < aw * bw; k++)
-            {
-               const TA ta = ad[(l / bh) + (k / bw) * ah];
-               const TB tb = bd[(l % bh) + (k % bw) * bh];
-               t1 += t2 * r[j + k * cw] * ta * tb;
-            }
-         }
-         z[i + l * ch] = t1;
-      }
-   }
-}
-
 /// Symmetrize a square matrix with given @a size and @a data: A -> (A+A^T)/2.
 template<typename T>
 MFEM_HOST_DEVICE inline
@@ -323,20 +276,6 @@ void Add(const int height, const int width, const TA *Adata, TB *Bdata)
   }
 }

-/** @brief Compute B +=alpha*A, where the matrices A and B are of size
-    @a height x @a width with data @a Adata and @a Bdata. */
-template<typename TA, typename TB>
-MFEM_HOST_DEVICE inline
-void Add(const int height, const int width,
-         const double alpha, const TA *Adata, TB *Bdata)
-{
-   const int m = height * width;
-   for (int i = 0; i < m; i++)
-   {
-      Bdata[i] += alpha * Adata[i];
-   }
-}
-
 /** @brief Compute B = alpha*A, where the matrices A and B are of size
    @a height x @a width with data @a Adata and @a Bdata. */
 template<typename TA, typename TB>
@@ -351,6 +290,7 @@ void Set(const int height, const int width,
   }
 }

+
 /** @brief Matrix-matrix multiplication: A = B * C, where the matrices A, B and
    C are of sizes @a Aheight x @a Awidth, @a Aheight x @a Bwidth and @a Bwidth
    x @a Awidth, respectively. */
@@ -31,7 +31,6 @@
 #include "invariants.hpp"
 #include "constraints.hpp"
 #include "auxiliary.hpp"
-#include "fdsolver.hpp"

 #ifdef MFEM_USE_AMGX
 #include "amgxsolver.hpp"
@@ -232,7 +232,7 @@ void OperatorJacobiSmoother::Mult(const Vector &x, Vector &y) const
   MFEM_FORALL(i, height, Y[i] += DI[i] * R[i]; );
 }

-OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator &oper_,
+OperatorChebyshevSmoother::OperatorChebyshevSmoother(Operator* oper_,
                                                     const Vector &d,
                                                     const Array<int>& ess_tdofs,
                                                     int order_, double max_eig_estimate_)
@@ -246,15 +246,15 @@ OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator &oper_,
   coeffs(order),
   ess_tdof_list(ess_tdofs),
   residual(N),
-   oper(&oper_) { Setup(); }
+   oper(oper_) { Setup(); }

 #ifdef MFEM_USE_MPI
-OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator &oper_,
+OperatorChebyshevSmoother::OperatorChebyshevSmoother(Operator* oper_,
                                                     const Vector &d,
                                                     const Array<int>& ess_tdofs,
                                                     int order_, MPI_Comm comm, int power_iterations, double power_tolerance)
 #else
-OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator &oper_,
+OperatorChebyshevSmoother::OperatorChebyshevSmoother(Operator* oper_,
                                                     const Vector &d,
                                                     const Array<int>& ess_tdofs,
                                                     int order_, int power_iterations, double power_tolerance)
@@ -267,7 +267,7 @@ OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator &oper_,
     coeffs(order),
     ess_tdof_list(ess_tdofs),
     residual(N),
-     oper(&oper_)
+     oper(oper_)
 {
   OperatorJacobiSmoother invDiagOperator(diag, ess_tdofs, 1.0);
   ProductOperator diagPrecond(&invDiagOperator, oper, false, false);
@@ -284,28 +284,6 @@ OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator &oper_,
   Setup();
 }

-OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator* oper_,
-                                                     const Vector &d,
-                                                     const Array<int>& ess_tdofs,
-                                                     int order_, double max_eig_estimate_)
-   : OperatorChebyshevSmoother(*oper_, d, ess_tdofs, order_, max_eig_estimate_) { }
-
-#ifdef MFEM_USE_MPI
-OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator* oper_,
-                                                     const Vector &d,
-                                                     const Array<int>& ess_tdofs,
-                                                     int order_, MPI_Comm comm, int power_iterations, double power_tolerance)
-   : OperatorChebyshevSmoother(*oper_, d, ess_tdofs, order_, comm,
-                               power_iterations, power_tolerance) { }
-#else
-OperatorChebyshevSmoother::OperatorChebyshevSmoother(const Operator* oper_,
-                                                     const Vector &d,
-                                                     const Array<int>& ess_tdofs,
-                                                     int order_, int power_iterations, double power_tolerance)
-   : OperatorChebyshevSmoother(*oper_, d, ess_tdofs, order_, power_iterations,
-                               power_tolerance) { }
-#endif
-
 void OperatorChebyshevSmoother::Setup()
 {
   // Invert diagonal
@@ -2555,7 +2533,7 @@ BlockILU::BlockILU(int block_size_,
     reordering(reordering_)
 { }

-BlockILU::BlockILU(const Operator &op,
+BlockILU::BlockILU(Operator &op,
                   int block_size_,
                   Reordering reordering_,
                   int k_fill_)
@@ -208,13 +208,7 @@ public:
       the matrix-free setting. The estimated largest eigenvalue of the
       diagonally preconditoned operator must be provided via
       max_eig_estimate. */
-   OperatorChebyshevSmoother(const Operator &oper_, const Vector &d,
-                             const Array<int>& ess_tdof_list,
-                             int order, double max_eig_estimate);
-
-   /// Deprecated: see pass-by-reference version above
-   MFEM_DEPRECATED
-   OperatorChebyshevSmoother(const Operator* oper_, const Vector &d,
+   OperatorChebyshevSmoother(Operator* oper_, const Vector &d,
                             const Array<int>& ess_tdof_list,
                             int order, double max_eig_estimate);

@@ -226,28 +220,13 @@ public:
       accuracy of the estimated eigenvalue may be controlled via
       power_iterations and power_tolerance. */
 #ifdef MFEM_USE_MPI
-   OperatorChebyshevSmoother(const Operator &oper_, const Vector &d,
-                             const Array<int>& ess_tdof_list,
-                             int order, MPI_Comm comm = MPI_COMM_NULL,
-                             int power_iterations = 10,
-                             double power_tolerance = 1e-8);
-
-   /// Deprecated: see pass-by-reference version above
-   MFEM_DEPRECATED
-   OperatorChebyshevSmoother(const Operator* oper_, const Vector &d,
+   OperatorChebyshevSmoother(Operator* oper_, const Vector &d,
                             const Array<int>& ess_tdof_list,
                             int order, MPI_Comm comm = MPI_COMM_NULL,
                             int power_iterations = 10,
                             double power_tolerance = 1e-8);
 #else
-   OperatorChebyshevSmoother(const Operator &oper_, const Vector &d,
-                             const Array<int>& ess_tdof_list,
-                             int order, int power_iterations = 10,
-                             double power_tolerance = 1e-8);
-
-   /// Deprecated: see pass-by-reference version above
-   MFEM_DEPRECATED
-   OperatorChebyshevSmoother(const Operator* oper_, const Vector &d,
+   OperatorChebyshevSmoother(Operator* oper_, const Vector &d,
                             const Array<int>& ess_tdof_list,
                             int order, int power_iterations = 10,
                             double power_tolerance = 1e-8);
@@ -752,7 +731,7 @@ public:
    *  case that @a op is a HypreParMatrix, the ILU factorization is performed
    *  on the diagonal blocks of the parallel decomposition.
    */
-   BlockILU(const Operator &op, int block_size_ = 1,
+   BlockILU(Operator &op, int block_size_ = 1,
            Reordering reordering_ = Reordering::MINIMUM_DISCARDED_FILL,
            int k_fill_ = 0);

@@ -37,7 +37,6 @@ MFEM makefile targets:
   make distclean
   make style
   make tags
-   make hooks

 Examples:

@@ -97,8 +96,6 @@ make style
 make tags
   Generate a vi or Emacs compatible TAGS file in ${MFEM_DIR}/TAGS. Requires
   functional "etags" and "egrep" in the user ${PATH}.
-make hooks
-   Creates symlinks to the hooks in the `.git/hooks` directory.
 endef

 # Save the MAKEOVERRIDES for cases where we explicitly want to pass the command
@@ -762,15 +759,6 @@ endif
 	@cd $(MFEM_REAL_DIR) && $(ETAGS_BIN) --class-qualify \
 	--declarations -o $(MFEM_REAL_DIR)/TAGS $(MFEM_TRACKED_SOURCE)

-# Creates symlinks to the hooks in the `.git/hooks` directory. Individual
-# hooks can be enabled by manually creating symlinks. Hooks can be customized
-# using hard copies (trading off with automated updates).
-.PHONY: hooks
-hooks:
-	@cd $(MFEM_DIR)/.git/hooks && \
-	ln -s ../../config/githooks/pre-commit pre-commit; \
-	ln -s ../../config/githooks/pre-push pre-push;
-
 # Print the contents of a makefile variable, e.g.: 'make print-MFEM_LIBS'.
 print-%:
 	$(info [ variable name]: $*)
@@ -11478,10 +11478,10 @@ FaceGeometricFactors::FaceGeometricFactors(const Mesh *mesh,
   const int NF   = fespace->GetNFbyType(type);
   const int NQ   = ir.GetNPoints();

-   const FaceRestriction *face_restr = fespace->GetFaceRestriction(
-                                          ElementDofOrdering::LEXICOGRAPHIC,
-                                          type,
-                                          L2FaceValues::SingleValued );
+   const Operator *face_restr = fespace->GetFaceRestriction(
+                                   ElementDofOrdering::LEXICOGRAPHIC,
+                                   type,
+                                   L2FaceValues::SingleValued );
   Vector Fnodes(face_restr->Height());
   face_restr->Mult(*nodes, Fnodes);

@@ -691,31 +691,16 @@ struct BufferReader : BufferReaderBase
   BufferReader(bool compressed_, HeaderType header_type_)
      : compressed(compressed_), header_type(header_type_) { }

-   /// Return the number of bytes of each header entry.
-   size_t HeaderEntrySize() const
-   {
-      return header_type == UINT64_HEADER ? sizeof(uint64_t) : sizeof(uint32_t);
-   }
-
-   /// Return the value of the header entry pointer to by @a header_buf. The
-   /// value is stored as either uint32_t or uint64_t, according to the @a
-   /// header_type, and is returned as uint64_t.
-   uint64_t ReadHeaderEntry(const char *header_buf) const
-   {
-      return (header_type == UINT64_HEADER) ? bin_io::read<uint64_t>(header_buf)
-             : bin_io::read<uint32_t>(header_buf);
-   }
-
   /// Return the number of bytes in the header. The header consists of one
-   /// integer if the data is uncompressed, and @a N + 3 integers if the data is
-   /// compressed, where @a N is the number of blocks. The integers are either
-   /// 32 or 64 bytes depending on the value of @a header_type. The number of
-   /// blocks is determined by reading the first integer (of type @a
-   /// header_type) pointed to by @a header_buf.
-   int NumHeaderBytes(const char *header_buf) const
+   /// integer if the data is uncompressed, and four integers if the data is
+   /// compressed. The integers are either 32 or 64 bytes depending on the value
+   /// of @a header_type.
+   int NumHeaderBytes() const
   {
-      if (!compressed) { return HeaderEntrySize(); }
-      return (3 + ReadHeaderEntry(header_buf))*HeaderEntrySize();
+      int num_entries = compressed ? 4 : 1;
+      int entry_size = (header_type == UINT64_HEADER)
+                       ? sizeof(uint64_t) : sizeof(uint32_t);
+      return num_entries*entry_size;
   }

   /// Read @a n elements of type @a F from the source buffer @a buf into the
@@ -726,42 +711,32 @@ struct BufferReader : BufferReaderBase
   void ReadBinaryWithHeader(const char *header_buf, const char *buf,
                             void *dest_void, int n) const
   {
-      std::vector<char> uncompressed_data;
+      std::vector<unsigned char> uncompressed_data;
      T *dest = static_cast<T*>(dest_void);

      if (compressed)
      {
 #ifdef MFEM_USE_ZLIB
-         // The header has format (where header_t is uint32_t or uint64_t):
-         //    header_t number_of_blocks;
-         //    header_t uncompressed_block_size;
-         //    header_t uncompressed_last_block_size;
-         //    header_t compressed_size[number_of_blocks];
-         int header_entry_size = HeaderEntrySize();
-         int nblocks = ReadHeaderEntry(header_buf);
-         header_buf += header_entry_size;
-         std::vector<int> header(nblocks + 2);
-         for (int i=0; i<nblocks+2; ++i)
+         uint64_t header[4];
+         if (header_type == UINT32_HEADER)
         {
-            header[i] = ReadHeaderEntry(header_buf);
-            header_buf += header_entry_size;
+            uint32_t *header_32 = (uint32_t *)header_buf;
+            for (int i=0; i<4; ++i) { header[i] = header_32[i]; }
         }
-         uncompressed_data.resize((nblocks-1)*header[0] + header[1]);
-         Bytef *dest_ptr = (Bytef *)uncompressed_data.data();
-         Bytef *dest_start = dest_ptr;
-         const Bytef *source_ptr = (const Bytef *)buf;
-         for (int i=0; i<nblocks; ++i)
+         else
         {
-            uLongf source_len = header[i+2];
-            uLong dest_len = (i == nblocks-1) ? header[1] : header[0];
-            int res = uncompress(dest_ptr, &dest_len, source_ptr, source_len);
-            MFEM_VERIFY(res == Z_OK, "Error uncompressing");
-            dest_ptr += dest_len;
-            source_ptr += source_len;
+            uint64_t *header_64 = (uint64_t *)header_buf;
+            for (int i=0; i<4; ++i) { header[i] = header_64[i]; }
         }
-         MFEM_VERIFY(int(sizeof(F)*n) == (dest_ptr - dest_start),
-                     "AppendedData: wrong data size");
-         buf = uncompressed_data.data();
+
+         MFEM_VERIFY(header[0] == 1, "Multiple compressed blocks not supported");
+         uLongf dest_len = header[1];
+         uncompressed_data.resize(dest_len);
+         int res = uncompress(uncompressed_data.data(), &dest_len,
+                              (const Bytef *)buf, header[3]);
+         MFEM_VERIFY(res == Z_OK, "Error uncompressing");
+         MFEM_VERIFY(sizeof(F)*n == dest_len, "AppendedData: wrong data size");
+         buf = (const char *)uncompressed_data.data();
 #else
         MFEM_ABORT("MFEM must be compiled with zlib enabled to uncompress.")
 #endif
@@ -804,7 +779,7 @@ struct BufferReader : BufferReaderBase
   /// buffer @a dest. The input buffer contains both the header and the data.
   void ReadBinary(const char *buf, void *dest, int n) const override
   {
-      ReadBinaryWithHeader(buf, buf + NumHeaderBytes(buf), dest, n);
+      ReadBinaryWithHeader(buf, buf + NumHeaderBytes(), dest, n);
   }

   /// Read @a n elements of type @a F from base-64 encoded source buffer into
@@ -821,25 +796,21 @@ struct BufferReader : BufferReaderBase
      }
      if (compressed)
      {
-         // Decode the first entry of the header, which we need to determine
-         // how long the rest of the header is.
-         std::vector<char> nblocks_buf;
-         int nblocks_b64 = bin_io::NumBase64Chars(HeaderEntrySize());
-         bin_io::DecodeBase64(txt, nblocks_b64, nblocks_buf);
-         std::vector<char> data, header;
+         std::vector<unsigned char> data, header;
         // Compute number of characters needed to encode header in base 64,
         // then round to nearest multiple of 4 to take padding into account.
-         int header_b64 = bin_io::NumBase64Chars(NumHeaderBytes(nblocks_buf.data()));
+         int b64_header = ((4*NumHeaderBytes()/3) + 3) & ~3;
         // If data is compressed, header is encoded separately
-         bin_io::DecodeBase64(txt, header_b64, header);
-         bin_io::DecodeBase64(txt + header_b64, strlen(txt)-header_b64, data);
-         ReadBinaryWithHeader(header.data(), data.data(), dest, n);
+         bin_io::DecodeBase64(txt, b64_header, header);
+         bin_io::DecodeBase64(txt + b64_header, strlen(txt)-b64_header, data);
+         ReadBinaryWithHeader((const char *)header.data(),
+                              (const char *)data.data(), dest, n);
      }
      else
      {
-         std::vector<char> data;
+         std::vector<unsigned char> data;
         bin_io::DecodeBase64(txt, strlen(txt), data);
-         ReadBinary(data.data(), dest, n);
+         ReadBinary((const char *)data.data(), dest, n);
      }
   }
 };
@@ -4321,7 +4321,7 @@ const CoarseFineTransformations& NCMesh::GetRefinementTransforms()
   if (!transforms.embeddings.Size())
   {
      transforms.Clear();
-      transforms.embeddings.SetSize(NElements);
+      transforms.embeddings.SetSize(leaf_elements.Size());

      std::string ref_path;
      ref_path.reserve(100);
@@ -4455,8 +4455,7 @@ struct RefType
 void CoarseFineTransformations::GetCoarseToFineMap(
   const mfem::Mesh &fine_mesh, Table &coarse_to_fine,
   Array<int> &coarse_to_ref_type, Table &ref_type_to_matrix,
-   Array<mfem::Geometry::Type> &ref_type_to_geom,
-   bool get_coarse_to_fine_only) const
+   Array<mfem::Geometry::Type> &ref_type_to_geom) const
 {
   const int fine_ne = embeddings.Size();
   int coarse_ne = -1;
@@ -4496,11 +4495,6 @@ void CoarseFineTransformations::GetCoarseToFineMap(
      coarse_to_fine.GetJ()[i] = cf_j[i].two;
   }

-   if (get_coarse_to_fine_only) { return; }
-   MFEM_VERIFY(fine_mesh.GetLastOperation() != Mesh::Operation::DEREFINE,
-               "GetCoarseToFineMap is not fully supported for derefined meshes."
-               " Set 'get_coarse_to_fine_only=true'.")
-
   using internal::RefType;
   using std::map;
   using std::pair;
@@ -4542,18 +4536,6 @@ void CoarseFineTransformations::GetCoarseToFineMap(
   ref_type_to_matrix.ShiftUpI();
 }

-void CoarseFineTransformations::GetCoarseToFineMap(const Mesh &fine_mesh,
-                                                   Table &coarse_to_fine) const
-{
-   Array<int> coarse_to_ref_type;
-   Table ref_type_to_matrix;
-   Array<mfem::Geometry::Type> ref_type_to_geom;
-   bool get_coarse_to_fine_only = true;
-   GetCoarseToFineMap(fine_mesh, coarse_to_fine, coarse_to_ref_type,
-                      ref_type_to_matrix, ref_type_to_geom,
-                      get_coarse_to_fine_only);
-}
-
 void NCMesh::ClearTransforms()
 {
   coarse_elements.DeleteAll();
@@ -68,11 +68,7 @@ struct CoarseFineTransformations
                           Table &coarse_to_fine,
                           Array<int> &coarse_to_ref_type,
                           Table &ref_type_to_matrix,
-                           Array<Geometry::Type> &ref_type_to_geom,
-                           bool get_coarse_to_fine_only = false) const;
-
-   void GetCoarseToFineMap(const Mesh &fine_mesh,
-                           Table &coarse_to_fine) const;
+                           Array<Geometry::Type> &ref_type_to_geom) const;

   void Clear();
   bool IsInitialized() const;
@@ -297,6 +297,9 @@ protected: // implementation

   virtual void Update();

+   virtual int GetNumGhostElements() const { return NGhostElements; }
+   virtual int GetNumGhostVertices() const { return NGhostVertices; }
+
   /// Return the processor number for a global element number.
   int Partition(long index, long total_elements) const
   { return index * NRanks / total_elements; }
@@ -109,19 +109,15 @@ int main(int argc, char *argv[])
   args.Parse();
   if (!args.Good())
   {
-      if (myid == 0)
-      {
-         args.PrintUsage(cout);
-      }
-      MPI_Finalize();
+      args.PrintUsage(cout);
      return 1;
   }
-   if (myid == 0) { args.PrintOptions(cout); }
+   args.PrintOptions(cout);

   // Enable hardware devices such as GPUs, and programming models such as CUDA,
   // OCCA, RAJA and OpenMP based on command line options.
   Device device("cpu");
-   if (myid == 0) { device.Print(); }
+   device.Print();

   // Refine the mesh.
   Mesh mesh(mesh_file, 1, 1);
@@ -96,7 +96,7 @@ SparseMatrix* AggToInteriorDof(const Array<int>& bdr_truedofs,
                               const SparseMatrix& agg_elem,
                               const SparseMatrix& elem_dof,
                               const HypreParMatrix& dof_truedof,
-                               Array<HYPRE_Int>& agg_starts)
+                               Array<int>& agg_starts)
 {
   OperatorPtr agg_dof(Mult(agg_elem, elem_dof));
   SparseMatrix& agg_dof_ref = *agg_dof.As<SparseMatrix>();
@@ -131,7 +131,7 @@ SparseMatrix* AggToInteriorDof(const Array<int>& bdr_truedofs,

 void DFSSpaces::MakeDofRelationTables(int level)
 {
-   Array<HYPRE_Int> agg_starts(Array<HYPRE_Int>(l2_0_fes_->GetDofOffsets(), 2));
+   Array<int> agg_starts(Array<int>(l2_0_fes_->GetDofOffsets(), 2));
   auto& elem_agg = (const SparseMatrix&)*l2_0_fes_->GetUpdateOperator();
   OperatorPtr agg_elem(Transpose(elem_agg));
   SparseMatrix& agg_el = *agg_elem.As<SparseMatrix>();
@@ -110,7 +110,6 @@ then
    echo "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"

    cp ${hostconfig_path} ${project_dir}/config/
-    ln -sf ${build_root}/data ${project_dir}/../

    make all -j ${threads}
 fi
@@ -28,7 +28,6 @@ set(UNIT_TESTS_SRCS
  linalg/test_complex_operator.cpp
  linalg/test_constrainedsolver.cpp
  linalg/test_direct_solvers.cpp
-  linalg/test_fdsolver.cpp
  linalg/test_hypre_ilu.cpp
  linalg/test_ilu.cpp
  linalg/test_matrix_block.cpp
@@ -11,14 +11,48 @@

 #define CATCH_CONFIG_RUNNER
 #include "mfem.hpp"
-#include "run_unit_tests.hpp"
+#include "unit_tests.hpp"

 bool launch_all_non_regression_tests = false;
-std::string mfem_data_dir;

 int main(int argc, char *argv[])
 {
   mfem::Device device("cuda");
-   // Include only tests labeled with CUDA. Exclude parallel tests.
-   return RunCatchSession(argc, argv, {"[CUDA]", "~[Parallel]"});
+
+   // There must be exactly one instance.
+   Catch::Session session;
+
+   // Build a new command line parser on top of Catch's
+   using namespace Catch::clara;
+   auto cli = session.cli() |
+              Opt(launch_all_non_regression_tests) ["--all"] ("all tests");
+   session.cli(cli);
+
+   // For floating point comparisons, print 8 digits for single precision
+   // values, and 16 digits for double precision values.
+   Catch::StringMaker<float>::precision = 8;
+   Catch::StringMaker<double>::precision = 16;
+
+   // Apply provided command line arguments.
+   int r = session.applyCommandLine(argc, argv);
+   if (r != 0) { return r; }
+
+   auto cfg = session.configData();
+
+   cfg.testsOrTags.push_back("[CUDA]");
+
+#ifdef MFEM_USE_MPI
+   // Exclude tests marked as Parallel in a serial run, even when compiled with
+   // MPI. This is done because there is no MPI session initialized.
+   cfg.testsOrTags.push_back("~[Parallel]");
+#endif
+
+   std::cout << "INFO: Test filter: [CUDA] ~[Parallel]" << std::endl;
+   device.Print();
+
+   session.useConfigData(cfg);
+
+   int result = session.run();
+
+   return result;
 }
@@ -11,7 +11,6 @@

 #include "mfem.hpp"
 #include "unit_tests.hpp"
-#include "general/tinyxml2.h"
 #include <stdio.h>

 #ifndef _WIN32
@@ -236,86 +235,3 @@ TEST_CASE("Save and load from collections", "[DataCollection]")
   }

 }
-
-void SaveDataCollection(DataCollection &dc, int cycle, double t)
-{
-   dc.SetCycle(cycle);
-   dc.SetTime(t);
-   dc.Save();
-}
-
-TEST_CASE("ParaView restart mode", "[ParaView]")
-{
-   Mesh mesh = Mesh::MakeCartesian2D(2, 3, Element::QUADRILATERAL);
-   H1_FECollection fec(1, mesh.Dimension());
-   FiniteElementSpace fes(&mesh, &fec);
-   GridFunction u(&fes);
-   u = 0.0;
-
-   // Write initial dataset with three timesteps: 0, 1, 2.
-   {
-      ParaViewDataCollection dc("ParaView", &mesh);
-      dc.RegisterField("u", &u);
-      SaveDataCollection(dc, 0, 0);
-      SaveDataCollection(dc, 1, 1);
-      SaveDataCollection(dc, 2, 2);
-   }
-
-   // Using restart mode, append to the existing dataset, overwriting timesteps
-   // 1 and 2 with 1 and 1.5.
-   {
-      ParaViewDataCollection dc("ParaView", &mesh);
-      dc.UseRestartMode(true);
-      dc.RegisterField("u", &u);
-      SaveDataCollection(dc, 1, 1.0);
-      SaveDataCollection(dc, 2, 1.5);
-   }
-
-   // Parse the resulting PVD file, and verify that the structure is correct,
-   // and that it contains three timesteps: 0, 1, and 1.5.
-   using namespace tinyxml2;
-   auto StringCompare = [](const char *s1, const char *s2)
-   {
-      if (s1 == NULL || s2 == NULL) { return false; }
-      return strcmp(s1, s2) == 0;
-   };
-   auto VerifyDataset = [StringCompare](const XMLElement *ds, double t_ref)
-   {
-      REQUIRE(ds);
-      REQUIRE(StringCompare(ds->Name(), "DataSet"));
-      const char *timestep = ds->Attribute("timestep");
-      REQUIRE(timestep);
-      double t = std::stod(timestep);
-      REQUIRE(t == MFEM_Approx(t_ref));
-   };
-
-   XMLDocument xml;
-   xml.LoadFile("ParaView/ParaView.pvd");
-   REQUIRE(xml.ErrorID() == XML_SUCCESS);
-
-   const XMLElement *vtkfile = xml.FirstChildElement();
-   REQUIRE(vtkfile);
-   REQUIRE(StringCompare(vtkfile->Name(), "VTKFile"));
-   const XMLElement *collection = vtkfile->FirstChildElement();
-   REQUIRE(collection);
-   REQUIRE(StringCompare(collection->Name(), "Collection"));
-
-   const XMLElement *dataset = collection->FirstChildElement();
-   VerifyDataset(dataset, 0.0);
-   dataset = dataset->NextSiblingElement();
-   VerifyDataset(dataset, 1.0);
-   dataset = dataset->NextSiblingElement();
-   VerifyDataset(dataset, 1.5);
-   REQUIRE(dataset->NextSiblingElement() == NULL);
-
-   // Clean up
-   for (int c=0; c<=2; ++c)
-   {
-      std::string prefix = "ParaView/Cycle00000" + std::to_string(c);
-      REQUIRE(remove((prefix + "/data.pvtu").c_str()) == 0);
-      REQUIRE(remove((prefix + "/proc000000.vtu").c_str()) == 0);
-      REQUIRE(rmdir(prefix.c_str()) == 0);
-   }
-   REQUIRE(remove("ParaView/ParaView.pvd") == 0);
-   REQUIRE(rmdir("ParaView") == 0);
-}
@@ -167,9 +167,9 @@ TEST_CASE("DG SumIntegrator", "[SumIntegrator][PartialAssembly]")
   integ2.AssemblePAInteriorFaces(fes);
   integ_sum.AssemblePAInteriorFaces(fes);

-   const FaceRestriction *R_int = fes.GetFaceRestriction(
-                                     ElementDofOrdering::LEXICOGRAPHIC,
-                                     FaceType::Interior);
+   const Operator *R_int = fes.GetFaceRestriction(
+                              ElementDofOrdering::LEXICOGRAPHIC,
+                              FaceType::Interior);

   int n_int = R_int->Height();
   Vector x(n_int), y1(n_int), y2(n_int);
@@ -198,10 +198,10 @@ TEST_CASE("DG SumIntegrator", "[SumIntegrator][PartialAssembly]")
   integ2.AssemblePABoundaryFaces(fes);
   integ_sum.AssemblePABoundaryFaces(fes);

-   const FaceRestriction *R_bdr = fes.GetFaceRestriction(
-                                     ElementDofOrdering::LEXICOGRAPHIC,
-                                     FaceType::Boundary,
-                                     L2FaceValues::DoubleValued);
+   const Operator *R_bdr = fes.GetFaceRestriction(
+                              ElementDofOrdering::LEXICOGRAPHIC,
+                              FaceType::Boundary,
+                              L2FaceValues::DoubleValued);

   int n_bdr = R_bdr->Height();
   x.SetSize(n_bdr);
@@ -38,7 +38,7 @@ TEST_CASE("OperatorChebyshevSmoother", "[Chebyshev symmetry]")
      Vector diag(fespace.GetTrueVSize());
      aform.AssembleDiagonal(diag);

-      Solver* smoother = new OperatorChebyshevSmoother(*opr, diag, ess_tdof_list,
+      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), diag, ess_tdof_list,
                                                       cheb_order);

      int n = smoother->Width();
@@ -1,126 +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.
-
-#include "mfem.hpp"
-#include "unit_tests.hpp"
-
-using namespace mfem;
-
-#ifdef MFEM_USE_LAPACK
-
-TEST_CASE("FDSolver",
-          "[FDSolver]")
-{
-   double tol = 1e-10;
-
-   // SPD matrices
-   DenseMatrix A0(
-   {
-      {
-         1.29919, 0.61256, 0.82545
-      },
-      {0.61256, 0.57891, 0.39662},
-      {0.82545, 0.39662, 0.57541}
-   });
-
-   DenseMatrix A1(
-   {
-      {0.748236, 0.701663, 0.607517, 0.236740},
-      {0.701663, 0.809316, 0.713186, 0.256070},
-      {0.607517, 0.713186, 0.794221, 0.233943},
-      {0.236740, 0.256070, 0.233943, 0.083129}
-   });
-
-   DenseMatrix B0(
-   {
-      {0.13483, 0.51389, 0.43052},
-      {0.51389, 2.26750, 1.86331},
-      {0.43052, 1.86331, 1.59869}
-   });
-
-   DenseMatrix B1(
-   {
-      {0.94177, 1.02400, 1.14743, 0.35723},
-      {1.02400, 1.79087, 1.78708, 0.78304},
-      {1.14743, 1.78708, 2.06259, 0.80837},
-      {0.35723, 0.78304, 0.80837, 1.01798}
-   });
-
-
-   SECTION("2D")
-   {
-      Array<DenseMatrix *> A(2), B(2);
-      A[0] = &A0;  A[1] = &A1;
-      B[0] = &B0;  B[1] = &B1;
-
-      Vector y(12); y.Randomize(1);
-      Vector x(12), diff(12);
-
-      FDSolver S(A,B);
-      S.Mult(y,x);
-
-      DenseMatrix C1, C;
-      KronProd(A0, B1, C1);
-      KronProd(B0, A1, C);
-
-      C.Add(1., C1);
-
-      DenseMatrixInverse Cinv(C);
-      Cinv.Mult(y,diff);
-
-      diff-=x;
-      REQUIRE(diff.Norml2() < tol);
-   }
-
-
-   SECTION("3D")
-   {
-      DenseMatrix A2(
-      {
-         {1.14593, 0.76119},
-         {0.76119, 0.78993}
-      });
-      DenseMatrix B2(
-      {
-         {0.88088, 0.37899},
-         {0.37899, 0.45096}
-      });
-      Array<DenseMatrix *> A(3), B(3);
-      A[0] = &A0;  A[1] = &A1; A[2] = &A2;
-      B[0] = &B0;  B[1] = &B1; B[2] = &B2;
-
-      Vector y(24); y.Randomize(1);
-      Vector x(24), diff(24);
-
-      FDSolver S(A,B);
-      S.Mult(y,x);
-
-      DenseMatrix Temp, C0, C1, C;
-
-      KronProd(A0, B1, Temp);
-      KronProd(Temp, B2, C0);
-      KronProd(B0, A1, Temp);
-      KronProd(Temp, B2, C1);
-      KronProd(B0, B1, Temp);
-      KronProd(Temp, A2, C);
-
-      C.Add(1.,C0);
-      C.Add(1.,C1);
-
-      DenseMatrixInverse Cinv(C);
-      Cinv.Mult(y,diff);
-
-      diff-=x;
-      REQUIRE(diff.Norml2() < tol);
-   }
-}
-
-#endif // if MFEM_USE_LAPACK
@@ -12,8 +12,6 @@
 #include "mfem.hpp"
 #include "unit_tests.hpp"
 #include "linalg/dtensor.hpp"
-#include "nvToolsExt.h"
-#include "nvToolsExtCudaRt.h"

 using namespace mfem;

@@ -241,212 +239,6 @@ TEST_CASE("DenseMatrix A*B^T methods",
   }
 }

-TEST_CASE("KronMult methods",
-          "[DenseMatrix], [CUDA]")
-{
-   double tol = 1e-12;
-   int nA = 3, mA = 4;
-   int nB = 5, mB = 6;
-   DenseMatrix A(nA,mA);
-   DenseMatrix B(nB,mB);
-
-   for (int i = 0; i<nA; i++)
-      for (int j = 0; j<mA; j++)
-      {
-         A(i,j) = ((double)rand()/(double)RAND_MAX);
-      }
-
-   for (int i = 0; i<nB; i++)
-      for (int j = 0; j<mB; j++)
-      {
-         B(i,j) = ((double)rand()/(double)RAND_MAX);
-      }
-
-   DenseMatrix AB;
-   KronProd(A,B,AB);
-   AB.HostRead();
-
-   // (A ⊗ B) r
-   SECTION("KronMultABr")
-   {
-      nvtxRangePush("KronMultABr");
-      Vector r(mA*mB);
-      MFEM_VERIFY(r.Size() == AB.Width(), "Check r size");
-
-      r.HostReadWrite();
-      r.Randomize();
-
-      Vector z0(AB.Height());
-      AB.Mult(r,z0);
-      //z0.HostRead();
-      Vector z1;
-      KronMult(A,B,r,z1);
-      MFEM_VERIFY(z0.Size() == z1.Size(), "Check z1 size");
-      z0-=z1;
-      REQUIRE(z0.Norml2() < tol);
-      nvtxRangePop();
-   }
-
-
-   // (A ⊗ B) R
-   SECTION("KronMultABR")
-   {
-      nvtxRangePush("KronMultABR");
-      int nR = mA*mB;
-      int mR = 7;
-      DenseMatrix R(nR, mR);
-      R.HostReadWrite();
-
-      for (int i = 0; i<nR; i++)
-         for (int j = 0; j<mR; j++)
-         {
-            R(i,j) = ((double)rand()/(double)RAND_MAX);
-         }
-
-      DenseMatrix Z0(nA*nB,mR);
-      Mult(AB,R,Z0);
-
-      DenseMatrix Z1;
-      KronMult(A,B,R,Z1);
-      MFEM_VERIFY(Z0.Height() == Z1.Height() &&
-                  Z0.Width() == Z1.Width(), "Check z1 size");
-      Z0-=Z1;
-
-      REQUIRE(Z0.MaxMaxNorm() < tol);
-
-      nvtxRangePop();
-   }
-
-   // (A ⊗ B ⊗ C) r
-   SECTION("KronMultABCr")
-   {
-      nvtxRangePush("KronMultABCr");
-
-      int nC = 7, mC = 2;
-      DenseMatrix C(nC, mC);
-
-      C.HostReadWrite();
-
-      for (int i = 0; i<nC; i++)
-         for (int j = 0; j<mC; j++)
-         {
-            C(i,j) = ((double)rand()/(double)RAND_MAX);
-         }
-
-      DenseMatrix ABC;
-      KronProd(AB,C,ABC);
-
-      Vector r(mA*mB*mC);
-      r.HostReadWrite();
-      r.Randomize();
-
-      MFEM_VERIFY(r.Size() == ABC.Width(), "Check r size");
-      Vector z0(nA*nB*nC);
-      ABC.Mult(r,z0);
-
-      Vector z1;
-      KronMult(A,B,C,r,z1);
-      MFEM_VERIFY(z0.Size() == z1.Size(), "Check z1 size");
-      z0-=z1;
-      REQUIRE(z0.Norml2() < tol);
-
-      nvtxRangePop();
-   }
-}
-
-TEST_CASE("KronMultInv methods",
-          "[DenseMatrixInverse]")
-{
-   double tol = 1e-12;
-   int nA = 3;
-   int nB = 2;
-   DenseMatrix A(
-   {
-      { 1.0,  0.2, 3.4},
-      {-2.0, -1.0, 3.1},
-      { 0.7,  1.4,-0.9}
-   });
-   DenseMatrix B(
-   {
-      {-10.1, 5.7},
-      {-3.0,  4.2}
-   });
-
-   DenseMatrixInverse Ainv(A);
-   DenseMatrixInverse Binv(B);
-
-   DenseMatrix AB;
-   KronProd(A,B,AB);
-
-   // (A^-1 ⊗ B^-1) r
-   SECTION("KronMultInvABr")
-   {
-
-      Vector r(nA*nB); r.Randomize();
-      MFEM_VERIFY(r.Size() == AB.Width(), "Check r size");
-      Vector z0(AB.Height());
-      DenseMatrixInverse ABinv(AB);
-      ABinv.Mult(r,z0);
-
-      Vector z1;
-      KronMult(Ainv,Binv,r,z1);
-      MFEM_VERIFY(z0.Size() == z1.Size(), "Check z1 size");
-      z0-=z1;
-      REQUIRE(z0.Norml2() < tol);
-   }
-
-   // (A^-1 ⊗ B^-1) R
-   SECTION("KronMultInvABR")
-   {
-      int nR = nA*nB;
-      int mR = 7;
-      DenseMatrix R(nR, mR);
-      for (int i = 0; i<nR; i++)
-         for (int j = 0; j<mR; j++)
-         {
-            R(i,j) = ((double)rand()/(double)RAND_MAX);
-         }
-
-      DenseMatrixInverse ABinv(AB);
-      DenseMatrix Z0(nA*nB,mR);
-      ABinv.Mult(R,Z0);
-
-      DenseMatrix Z1;
-      KronMult(Ainv,Binv,R,Z1);
-      MFEM_VERIFY(Z0.Height() == Z1.Height() &&
-                  Z0.Width() == Z1.Width(), "Check z1 size");
-      Z0-=Z1;
-
-      REQUIRE(Z0.MaxMaxNorm() < tol);
-   }
-
-   // (A^-1 ⊗ B^-1 ⊗ C^-1) r
-   SECTION("KronMultInvABCr")
-   {
-      int nC = 4;
-      DenseMatrix C(
-      {
-         {-2.1, 1.6, -3.4,  17.5},
-         {-7.1, 1.3, -7.5, -12.5},
-         { 0.5, 5.7, -6.0, -0.5},
-         { 9.2, 0.3, -1.4, -14.9}
-      });
-      DenseMatrix ABC;
-      KronProd(AB,C,ABC);
-      DenseMatrixInverse ABCInv(ABC);
-      Vector r(nA*nB*nC); r.Randomize();
-      MFEM_VERIFY(r.Size() == ABC.Width(), "Check r size");
-      Vector z0(nA*nB*nC);
-      ABCInv.Mult(r,z0);
-
-      DenseMatrixInverse Cinv(C);
-      Vector z1;
-      KronMult(Ainv,Binv,Cinv,r,z1);
-      MFEM_VERIFY(z0.Size() == z1.Size(), "Check z1 size");
-      z0-=z1;
-      REQUIRE(z0.Norml2() < tol);
-   }
-}

 TEST_CASE("LUFactors RightSolve", "[DenseMatrix]")
 {
@@ -522,88 +314,6 @@ TEST_CASE("DenseTensor LinearSolve methods",
   }
 }

-#ifdef MFEM_USE_LAPACK
-
-TEST_CASE("EigenSystem methods",
-          "[DenseMatrix]")
-{
-   double tol = 1e-12;
-   SECTION("SPD Matrix")
-   {
-      DenseMatrix A({{0.56806, 0.29211, 0.48315, 0.70024},
-         {0.29211, 0.85147, 0.68123, 0.70689},
-         {0.48315, 0.68123, 1.07229, 1.02681},
-         {0.70024, 0.70689, 1.02681, 1.15468}
-      });
-      DenseMatrix V, AV(4);
-      Vector Lambda;
-      for (bool sym: { false, true })
-      {
-         DenseMatrixEigensystem  EigA(A,sym);
-         EigA.Eval();
-         V = EigA.Eigenvectors();
-         Lambda = EigA.Eigenvalues();
-         Mult(A,V,AV);
-         V.RightScaling(Lambda);
-         AV -= V;
-         REQUIRE(AV.MaxMaxNorm() < tol);
-      }
-   }
-
-   SECTION("Indefinite Matrix")
-   {
-      DenseMatrix A({{0.486278, 0.041135, 0.480727, 0.616026},
-         {0.523599, 0.119827, 0.087808, 0.415241},
-         {0.214454, 0.661631, 0.909626, 0.744259},
-         {0.107007, 0.630604, 0.077862, 0.221006}
-      });
-      DenseMatrixEigensystem  EigA(A);
-      EigA.Eval();
-
-      Vector Lambda_r, Lambda_i;
-      // Real part of eigenvalues
-      Lambda_r = EigA.Eigenvalues();
-      // Imag part of eigenvalues
-      Lambda_i = EigA.Eigenvalues(true);
-
-      DenseMatrix V;
-      V = EigA.Eigenvectors();
-      // Real part of eigenvectors
-      DenseMatrix Vr(4), Vi(4);
-      Vr.SetCol(0,V.GetColumn(0));
-      Vr.SetCol(1,V.GetColumn(1));
-      Vr.SetCol(2,V.GetColumn(1));
-      Vr.SetCol(3,V.GetColumn(3));
-
-      // Imag part of eigenvectors
-      Vector vi(4); V.GetColumn(2,vi);
-      Vi.SetCol(0,0.);
-      Vi.SetCol(1,vi); vi *= -1.;
-      Vi.SetCol(2,vi);
-      Vi.SetCol(3,0.);
-
-      // Check that A*V = V * Lambda
-      // or A * (V_r + i V_i ) = (V_r + i V_i)*(Lamda_r + i Lambda_i)
-      // or  A * V_r = V_r * Lambda_r -  V_i * Lambda_i
-      // and A * V_i = V_r ( Lambda_i +  V_i * Lambda_r
-      DenseMatrix AVr(4), AVi(4);
-      Mult(A,Vr, AVr);
-      Mult(A,Vi, AVi);
-
-      DenseMatrix Vrlr = Vr; Vrlr.RightScaling(Lambda_r);
-      DenseMatrix Vrli = Vr; Vrli.RightScaling(Lambda_i);
-      DenseMatrix Vilr = Vi; Vilr.RightScaling(Lambda_r);
-      DenseMatrix Vili = Vi; Vili.RightScaling(Lambda_i);
-
-      AVr -= Vrlr; AVr+= Vili;
-      AVi -= Vrli; AVi-= Vilr;
-
-      REQUIRE(AVr.MaxMaxNorm() < tol);
-      REQUIRE(AVi.MaxMaxNorm() < tol);
-   }
-}
-
-#endif // if MFEM_USE_LAPACK
 TEST_CASE("DenseTensor copy", "[DenseMatrix][DenseTensor]")
 {
   DenseTensor t1(2,3,4);
@@ -214,27 +214,21 @@ $(DATA_DIR):
 MFEM_TESTS = UNIT_TESTS
 include $(MFEM_TEST_MK)

-ifeq (,$(wildcard $(MFEM_DIR)/../data))
-   MFEM_DATA_FLAG =
-else
-   MFEM_DATA_FLAG = --data $(MFEM_DIR)/../data
-endif
-
 %-test-seq: %
-	@$(call mfem-test,$<,, Unit tests,$(MFEM_DATA_FLAG),SKIP-NO-VIS)
+	@$(call mfem-test,$<,, Unit tests,,SKIP-NO-VIS)

 ceed_tests-test-seq: ceed_tests
-	@$(call mfem-test,$<,, CEED Unit tests (cpu),--device ceed-cpu $(MFEM_DATA_FLAG),SKIP-NO-VIS)
+	@$(call mfem-test,$<,, CEED Unit tests (cpu),--device ceed-cpu,SKIP-NO-VIS)
 ifeq ($(MFEM_USE_CUDA),YES)
-	@$(call mfem-test,$<,, CEED Unit tests (cuda-ref),--device ceed-cuda:/gpu/cuda/ref $(MFEM_DATA_FLAG),SKIP-NO-VIS)
-	@$(call mfem-test,$<,, CEED Unit tests (cuda-shared),--device ceed-cuda:/gpu/cuda/shared $(MFEM_DATA_FLAG),SKIP-NO-VIS)
-	@$(call mfem-test,$<,, CEED Unit tests (cuda-gen),--device ceed-cuda:/gpu/cuda/gen $(MFEM_DATA_FLAG),SKIP-NO-VIS)
+	@$(call mfem-test,$<,, CEED Unit tests (cuda-ref),--device ceed-cuda:/gpu/cuda/ref,SKIP-NO-VIS)
+	@$(call mfem-test,$<,, CEED Unit tests (cuda-shared),--device ceed-cuda:/gpu/cuda/shared,SKIP-NO-VIS)
+	@$(call mfem-test,$<,, CEED Unit tests (cuda-gen),--device ceed-cuda:/gpu/cuda/gen,SKIP-NO-VIS)
 endif

 RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP)
 %-test-par: %
-	@$(call mfem-test,$<, $(RUN_MPI) 1, Parallel unit tests,$(MFEM_DATA_FLAG),SKIP-NO-VIS)
-	@$(call mfem-test,$<, $(RUN_MPI) $(MFEM_MPI_NP), Parallel unit tests,$(MFEM_DATA_FLAG),SKIP-NO-VIS)
+	@$(call mfem-test,$<, $(RUN_MPI) 1, Parallel unit tests,,SKIP-NO-VIS)
+	@$(call mfem-test,$<, $(RUN_MPI) $(MFEM_MPI_NP), Parallel unit tests,,SKIP-NO-VIS)

 # Generate an error message if the MFEM library is not built and exit
 $(MFEM_LIB_FILE):
@@ -243,3 +237,4 @@ $(MFEM_LIB_FILE):
 clean:
 	rm -f $(SEQ_UNIT_TESTS) $(PAR_UNIT_TESTS) *.o */*.o */*~ *~
 	rm -rf *.dSYM output_meshes
+
@@ -41,21 +41,3 @@ TEST_CASE("VTU XML Reader", "[Mesh][VTU][XML]")
      REQUIRE(mesh.GetNumGeometries(2) == 1);
   }
 }
-
-TEST_CASE("VTU XML Compressed Blocks", "[VTU][XML][MFEMData]")
-{
-   auto filename = GENERATE(
-                      "bracket_appended_compressed.vtu",
-                      "bracket_appended_encoded_compressed.vtu",
-                      "bracket_inline_compressed.vtu"
-                   );
-
-   std::string mesh_path = mfem_data_dir + "/vtk/" + filename;
-   Mesh mesh = Mesh::LoadFromFile(mesh_path.c_str());
-
-   REQUIRE(mesh.Dimension() == 3);
-   REQUIRE(mesh.GetNE() == 206208);
-   REQUIRE(mesh.GetNV() == 50000);
-   REQUIRE(mesh.HasGeometry(Geometry::TETRAHEDRON));
-   REQUIRE(mesh.GetNumGeometries(3) == 1);
-}
@@ -186,12 +186,10 @@ int tmop(int id, Req &res, int argc, char *argv[])
      case   2: metric = new TMOP_Metric_002; break;
      case   7: metric = new TMOP_Metric_007; break;
      case  77: metric = new TMOP_Metric_077; break;
-      case  80: metric = new TMOP_Metric_080(0.5); break;
      case 302: metric = new TMOP_Metric_302; break;
      case 303: metric = new TMOP_Metric_303; break;
      case 315: metric = new TMOP_Metric_315; break;
      case 321: metric = new TMOP_Metric_321; break;
-      case 332: metric = new TMOP_Metric_332(0.5); break;
      default:
      {
         if (id == 0) { cout << "Unknown metric_id: " << metric_id << endl; }
@@ -742,13 +740,6 @@ static void tmop_tests(int id = 0, bool all = false)
          POR({1,2}).QOR({2,4}).
          TID({4}).MID({1,2})).Run(id,all);

-   Launch(Launch::Args("Square01 + Adapted discrete size").
-          MESH("../../miniapps/meshing/square01.mesh").REFINE(1).
-          NORMALIZATION(true).
-          POR({1,2}).QOR({4,6}).
-          LINEAR_ITERATIONS(150).
-          TID({5}).MID({80}).LS({3})).Run(id,all);
-
   Launch(Launch::Args("Blade").
          MESH("../../miniapps/meshing/blade.mesh").
          POR({1,2}).QOR({2,4}).
@@ -777,12 +768,6 @@ static void tmop_tests(int id = 0, bool all = false)
          POR({1,2}).QOR({4,2}).
          TID({7}).MID({302,321})).Run(id,all);

-   Launch(Launch::Args("Cube + Discrete size + normalization").
-          MESH("../../miniapps/meshing/cube.mesh").
-          NORMALIZATION(true).
-          POR({1,2}).QOR({4,2}).
-          TID({5}).MID({332})).Run(id,all);
-
   // Note: order 1 has no interior nodes, so all residuals are zero and the
   // Newton iteration exits immediately.
   Launch(Launch::Args("Toroid-Hex").
--- 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