Adding coef-fact etc to .gitignore

Disable testing for coef-fact
make style
2020-09-29 10:39:00 -07:00 · 2020-09-29 09:49:32 -07:00 · 2020-09-28 20:08:37 -07:00 · 2020-09-28 20:08:08 -07:00 · 2020-09-27 12:01:56 -07:00 · 2020-09-27 11:58:13 -07:00
174 changed files with 30395 additions and 12559 deletions
@@ -15,7 +15,9 @@ install:
 - msmpisdk.msi /passive
 - set PATH=C:\Program Files\Microsoft MPI\Bin;%PATH%

-# Install METIS
+# Install METIS, use a mirror because the original source server is not always
+# up. Original url:
+#    http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/metis-5.1.0.tar.gz
 - ps: Start-FileDownload 'https://mfem.github.io/tpls/metis-5.1.0.tar.gz'
 - 7z x metis-5.1.0.tar.gz -so | 7z x -si -ttar > nul
 - cd metis-5.1.0
@@ -175,6 +175,7 @@ miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
 miniapps/meshing/minimal-surface
 miniapps/meshing/pminimal-surface
+miniapps/meshing/polar-nc

 miniapps/meshing/mobius-strip.mesh
 miniapps/meshing/klein-bottle.mesh
@@ -187,6 +188,7 @@ miniapps/meshing/extruder.mesh
 miniapps/meshing/trimmer.mesh
 miniapps/meshing/optimized*
 miniapps/meshing/perturbed*
+miniapps/meshing/polar-nc.mesh

 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -197,10 +199,13 @@ miniapps/performance/sol.*

 miniapps/tools/display-basis
 miniapps/tools/load-dc
+miniapps/tools/coef-fact
 miniapps/tools/convert-dc
 miniapps/tools/lor-transfer
 miniapps/tools/get-values

+miniapps/tools/coef-fact.inp
+
 miniapps/toys/automata
 miniapps/toys/life
 miniapps/toys/mandel
@@ -233,6 +238,7 @@ miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*

 miniapps/gslib/field-diff
+miniapps/gslib/field-interp
 miniapps/gslib/findpts
 miniapps/gslib/pfindpts

@@ -259,5 +265,10 @@ tests/scripts/*.err
 tests/scripts/*.out
 tests/scripts/*.msg

+# Other tests
+tests/convergence/rates
+tests/convergence/prates
+tests/par-mesh-format/ex1p
+
 # VPATH builds
 build-*/*
@@ -71,6 +71,8 @@ stages:
  - build
  - test
  - deallocate
+  - lassen_build
+  - lassen_test
  - baseline_check
  - baseline_publish

@@ -79,7 +81,11 @@ stages:
 # 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
+setup:
+  tags:
+    - shell
+    - quartz
  stage: setup
  variables:
    GIT_STRATEGY: none
@@ -100,6 +106,15 @@ stages:
  before_script:
    - module load gcc/6.1.0

+# On lassen
+.with_gcc_8_3_1:
+  variables:
+    TOOLCHAIN: gcc_8_3_1
+    CXX: g++
+    CC: gcc
+  before_script:
+    - module load gcc/8.3.1
+
 .with_gcc_4_9_3:
  variables:
    TOOLCHAIN: gcc_4_9_3
@@ -290,3 +305,4 @@ stages:
 # The list on jobs is defined in machine-specific files.
 include:
  - local: .gitlab/quartz.yml
+  - local: .gitlab/lassen.yml
@@ -0,0 +1,57 @@
+# Copyright (c) 2010-2020, 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.
+
+# GitLab pipelines configurations for the Lassen machine at LLNL
+
+.on_lassen:
+  tags:
+    - shell
+    - lassen
+  variables:
+    PLAT: lassen
+
+# Build MFEM
+build_mfem_ser_lassen:
+  extends: [.with_gcc_8_3_1, .on_lassen]
+  needs: [setup]
+  stage: lassen_build
+  script:
+    - mkdir -p ${BUILD_PATH}
+    - cp -r ${CI_PROJECT_DIR} ${BUILD_PATH}/${CI_PROJECT_NAME}_lassen_ser
+    - cd ${BUILD_PATH}/${CI_PROJECT_NAME}_lassen_ser
+    - lalloc 1 -W 5 -q pdebug make -j cuda CUDA_ARCH=sm_70
+
+build_mfem_debug_ser_lassen:
+  extends: [.with_gcc_8_3_1, .on_lassen]
+  needs: [setup]
+  stage: lassen_build
+  script:
+    - mkdir -p ${BUILD_PATH}
+    - cp -r ${CI_PROJECT_DIR} ${BUILD_PATH}/${CI_PROJECT_NAME}_lassen_ser_debug
+    - cd ${BUILD_PATH}/${CI_PROJECT_NAME}_lassen_ser_debug
+    - lalloc 1 -W 5 -q pdebug make -j cuda MFEM_DEBUG="YES" CUDA_ARCH=sm_70
+
+# Sanity check
+sanitycheck_mfem_ser_lassen:
+  extends: [.with_gcc_8_3_1, .on_lassen]
+  stage: lassen_test
+  needs: [build_mfem_ser_lassen]
+  script:
+    - cd ${BUILD_PATH}/${CI_PROJECT_NAME}_lassen_ser
+    - lalloc 1 -W 15 -q pdebug make -j test
+
+sanitycheck_mfem_debug_ser_lassen:
+  extends: [.with_gcc_8_3_1, .on_lassen]
+  stage: lassen_test
+  needs: [build_mfem_debug_ser_lassen]
+  script:
+    - cd ${BUILD_PATH}/${CI_PROJECT_NAME}_lassen_ser_debug
+    - lalloc 1 -W 30 -q pdebug make -j test
@@ -22,10 +22,6 @@
    MAKE_PAR: 6
    BASELINE_PAR: 18

-# Setup
-setup_quartz:
-  extends: [.setup, .on_quartz]
-
 # Allocate
 allocate_quartz:
  variables:
@@ -11,6 +11,9 @@

 language: cpp

+os: linux
+dist: bionic
+
 stages:
  - checks
  - tests
@@ -34,6 +37,7 @@ jobs:

    - stage: checks
      os: linux
+      dist: xenial
      name: "code-style"
      addons:
        apt:
@@ -52,9 +56,6 @@ jobs:
          packages:
            - doxygen
            - graphviz
-            - mpich
-            - libmpich-dev
-      env: MPI=YES
      script:
        - cd ${TRAVIS_BUILD_DIR}
        - cd tests/scripts
@@ -69,13 +70,24 @@ jobs:
            - mpich
            - libmpich-dev
      env: MPI=YES
-      script:
+      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
@@ -84,6 +96,7 @@ jobs:

    - stage: optional
      name: "branch-history"
+      if: branch != next
      # need full git history for the binary/big files check
      git:
        depth: false
@@ -112,6 +125,8 @@ jobs:
           MPI=NO
           CODECOV=NO
           MFEM_TEST_TARGET=check
+      cache:
+        ccache: true

    - os: linux
      compiler: gcc
@@ -120,6 +135,8 @@ jobs:
           MPI=NO
           CODECOV=NO
           MFEM_TEST_TARGET=test
+      cache:
+        ccache: true

    - os: linux
      compiler: gcc
@@ -143,6 +160,7 @@ jobs:
           MFEM_TEST_TARGET=check
           NPROCS=2
      cache:
+        ccache: true
        directories:
          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
@@ -173,6 +191,7 @@ jobs:
           MFEM_TEST_TARGET=test
           NPROCS=2
      cache:
+        ccache: true
        directories:
          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
@@ -204,6 +223,7 @@ jobs:
        - make -j3
        - ctest --output-on-failure
      cache:
+        ccache: true
        directories:
          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
@@ -221,27 +241,43 @@ jobs:
    # - parallel

    - os: osx
-      # osx_image: xcode7.3
+      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: xcode7.3
+      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: xcode7.3
+      osx_image: xcode11.2
      compiler: clang
      name: "Mac: Parallel + Debug"
+      addons:
+        homebrew:
+          packages:
+            - ccache
      env: DEBUG=YES
           MPI=YES
           CODECOV=NO
@@ -249,6 +285,7 @@ jobs:
           NPROCS=4
           TMPDIR=/tmp
      cache:
+        ccache: true
        directories:
          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
@@ -259,9 +296,13 @@ jobs:
          rm -f Lib/*.{c,o}

    - os: osx
-      # osx_image: xcode7.3
+      osx_image: xcode11.2
      compiler: clang
      name: "Mac: Parallel"
+      addons:
+        homebrew:
+          packages:
+            - ccache
      env: DEBUG=NO
           MPI=YES
           CODECOV=YES
@@ -269,6 +310,7 @@ jobs:
           NPROCS=4
           TMPDIR=/tmp
      cache:
+        ccache: true
        directories:
          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
          - $TRAVIS_BUILD_DIR/../metis-4.0
@@ -284,14 +326,19 @@ before_install:
   #      brew install open-mpi;
   #   fi

-   # On Mac OS X, build and cache OpenMPI 2.1.1:
+   # 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 $HOME/builds &&
-           wget https://www.open-mpi.org/software/ompi/v2.1/downloads/openmpi-2.1.1.tar.bz2 &&
-           tar jxf openmpi-2.1.1.tar.bz2 &&
+           wget https://download.open-mpi.org/release/open-mpi/v2.1/openmpi-2.1.6.tar.bz2 &&
+           tar jxf openmpi-2.1.6.tar.bz2 &&
           mkdir openmpi-build && cd openmpi-build &&
-           ../openmpi-2.1.1/configure --prefix=$HOME/local-cached &&
+           ../openmpi-2.1.6/configure --prefix=$HOME/local-cached &&
           make -j3 all && make install;
        fi;
        PATH=$HOME/local-cached/bin:$PATH;
@@ -352,7 +399,9 @@ install:
        echo "Serial build, not using hypre";
     fi

-   # METIS
+   # 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;
@@ -365,6 +414,18 @@ install:
        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 [ $MPI == "YES" ]; then
@@ -385,6 +446,9 @@ script:
     if [ "$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
@@ -16,7 +16,12 @@ Meshing improvements
 - The graph linear ordering library Gecko, previously an external dependency, is
  now included directly in MFEM. As a result, Mesh::GetGeckoElementOrdering is
  always available. The interface has also been improved, see for example the
-  mesh-explorer miniapp.
+  Mesh Explorer miniapp.
+
+- Improved Gmsh reader (version 2.2), which now supports both high-order and
+  periodic meshes. Segments, triangles, quadrilaterals, and tetrahedra are
+  supported up to order 10. Wedges and hexahedra are supported up to order 9.
+  For sample periodic meshes, see the periodic*.msh files in the data directory.

 - Added support for finite difference-based gradient and Hessian approximation
  in the TMOP mesh optimization algorithms. This improves the accuracy of the
@@ -27,15 +32,17 @@ Meshing improvements
  the user to specify different discrete functions for controlling the
  size, aspect-ratio, orientation, and skew of elements in the mesh.

- Added TMOP capability for approximate tangential mesh relaxation.
-
- Added support for reading periodic meshes in Gmsh format (version 2.2). See
-  for example the periodic-annulus-sector and periodic-torus-sector files in
-  the data directory.
+- Added TMOP capability for approximate tangential mesh relaxation. Added
+  support and examples for using TMOP on mixed meshes.

 - Added complete action of the TMOP Integrator to account for the spatial
  derivatives of discrete and analytic targets.

+- Added support for initialization of (serial) non-conforming meshes. Hanging
+  nodes can be marked with Mesh::AddVertexParents when building the mesh with
+  the "init" constructor. The usage is demonstrated in a new meshing miniapp
+  (polar-nc) which generates meshes that are non-conforming from the start.
+
 Performance improvements
 ------------------------
 - Added support for explicit vectorization in the high-performance templated
@@ -44,7 +51,7 @@ Performance improvements
    - x86 (SSE/AVX/AVX2/AVX512),
    - Power8 & Power9 (VSX),
    - BG/Q (QPX).
-  These are now enabled by default, and can be disabled with MFEM_USE_SIMD=NO.
+  These are disabled by default, and can be enabled with MFEM_USE_SIMD=YES.
  See the new file linalg/simd.hpp and the new directory linalg/simd.

 Improved GPU capabilities
@@ -58,8 +65,14 @@ Improved GPU capabilities
  compute a global sparse matrix. All integrators supported by element assembly
  are also supported by full assembly. See the '-fa' option in Example 9.

+- Added CUDA support for sparse matrix-vector multiplication with cuSPARSE.
+
 - Added support for BlockOperator on GPU. See the updated Example 5.

+- Added partial assembly and GPU support for complex operators, including the
+  classes ComplexOperator, [Par]ComplexGridFunction, [Par]ComplexLinearForm, and
+  [Par]SesquilinearForm. See the updated Example 22.
+
 Discretization improvements
 ---------------------------
 - Added support for matrix-free interpolation and restriction operators between
@@ -88,6 +101,14 @@ Discretization improvements

 - Added support face integrals on the boundaries of NURBS meshes.

+- Added support for interpolation of functions in L2, H(div) and H(curl)
+  spaces using GSLIB-FindPoints.
+
+- Added support for computing asymptotic error estimates and convergence rates
+  for the whole de Rham sequence based on the new class ConvergenceStudy and new
+  member methods in GridFunction and ParGridFunction. See the rates.cpp file in
+  the tests/convergence directory for sample usage.
+
 Linear and nonlinear solvers
 ----------------------------
 - Added power method to iteratively estimate the largest eigenvalue and the
@@ -113,6 +134,9 @@ Linear and nonlinear solvers

 - Added support for the SLEPc eigensolver package.

+- Added partially assembled convergent diagonal preconditioner for adaptively
+  refined meshes (i.e. non-conforming finite element spaces), see Example 6/6p.
+
 New and updated examples and miniapps
 -------------------------------------
 - Added a new example, Example 25/25p, to demonstrate the use of a Perfectly
@@ -149,6 +173,9 @@ New and updated examples and miniapps
 - Added a new meshing miniapp, Minimal Surface, which solves Plateau's problem:
  the Dirichlet problem for the minimal surface equation.

+- Added a new meshing miniapp, Polar NC, which demonstrates the construction of
+  polar non-conforming meshes.
+
 - Added partial assembly support to Example 4/4p and Example 5/5p, with diagonal
  preconditioning.

@@ -163,28 +190,47 @@ New and updated examples and miniapps
  mesh based on element attributes. Any newly exposed boundary elements are
  assigned attribute numbers related to the trimmed element attributes.

+- Added a new miniapp (field-interp) that demonstrates transfer of grid function
+  between different meshes using GSLIB-FindPoints.
+
+- Added diagonal preconditioner in Example 6/6p for partial assembly with AMR.
+
 - Added device support in Example 5/5p.

+- Added partial assembly and device support to Example 22/22p, with diagonal
+  preconditioning.
+
+- Added the option to plot a function in Mesh Explorer.
+
 Improved testing
 ----------------
+- Upgraded the Catch unit test framework from version 1.6.1 to version 2.13.0.
+
 - Added a GitLab pipeline that automates PR testing on supercomputing systems
  and Linux clusters at Lawrence Livermore National Lab (LLNL). This can be
  triggered only by LLNL developers, see .gitlab-ci.yml, the .gitlab directory
  and the updated CONTRIBUTING.md file.

+- Added testing of the parallel mesh format in tests/par-mesh-format.
+
 Miscellaneous
 -------------
 - Added support for ADIOS2 for parallel I/O with ParaView visualization. The
  classes adios2stream and ADIOS2DataCollection are introduced in mfem as the
  interfaces to generate ADIOS2 Binary Pack (BP4) directory datasets for the
-  entire spatial and temporal data. In addition, ADIOS2 allows for setting a
-  user-defined number of data substreams/subfiles. See examples 5, 9, 12, 16.
+  entire spatial and temporal node data. Cell centered data is accessible by
+  ADIOS2 data readers (e.g. Python), but currently not yet implement as of
+  ParaView v5.8.1. In addition, ADIOS2 allows for setting a user-defined number
+  of data substreams/subfiles at scale. See examples 5, 9, 12, 16.

 - The integration order used in the ComputeLpError and ComputeElementLpError
  methods of class GridFunction has been increased.

 - Various other simplifications, extensions, and bugfixes in the code.

+- Renamed "Backend::DEBUG" to "Backend::DEBUG_DEVICE" to avoid conflicts,
+  as DEBUG is sometimes used as a macro.
+

 Version 4.1, released on March 10, 2020
 =======================================
@@ -89,8 +89,38 @@ enable_language(CXX)
 if (MFEM_USE_CUDA)
   # MFEM_USE_CUDA requires CMake 3.8 or newer (for direct CUDA support)
   cmake_minimum_required(VERSION 3.8 FATAL_ERROR)
+   # Use ${CMAKE_CXX_COMPILER} as the cuda host compiler.
+   if (NOT CMAKE_CUDA_HOST_COMPILER)
+      set(CMAKE_CUDA_HOST_COMPILER ${CMAKE_CXX_COMPILER})
+   endif()
   enable_language(CUDA)
+   set(CMAKE_CUDA_STANDARD 11)
+   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
+   set(CMAKE_CUDA_EXTENSIONS OFF)
+   set(CUDA_FLAGS "--expt-extended-lambda")
+   if (CMAKE_VERSION VERSION_LESS 3.18.0)
+      set(CUDA_FLAGS "-arch=${CUDA_ARCH} ${CUDA_FLAGS}")
+   elseif (NOT CMAKE_CUDA_ARCHITECTURES)
+      string(REGEX REPLACE "^sm_" "" ARCH_NUMBER "${CUDA_ARCH}")
+      if ("${CUDA_ARCH}" STREQUAL "sm_${ARCH_NUMBER}")
+         set(CMAKE_CUDA_ARCHITECTURES "${ARCH_NUMBER}")
+      else()
+         message(FATAL_ERROR "Unknown CUDA_ARCH: ${CUDA_ARCH}")
+      endif()
+   else()
+      set(CUDA_ARCH "CMAKE_CUDA_ARCHITECTURES: ${CMAKE_CUDA_ARCHITECTURES}")
+   endif()
   message(STATUS "Using CUDA architecture: ${CUDA_ARCH}")
+   if (CMAKE_VERSION VERSION_LESS 3.12.0)
+      # CMake versions 3.8 and 3.9 require this to work; 3.10 and 3.11 are not
+      # tested and may not actually need this (but should be ok to keep).
+      set(CUDA_FLAGS "-ccbin=${CMAKE_CXX_COMPILER} ${CUDA_FLAGS}")
+      set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CMAKE_CXX_COMPILER})
+   endif()
+   set(CMAKE_CUDA_FLAGS "${CUDA_FLAGS}" CACHE STRING
+       "CUDA flags set for MFEM" FORCE)
+   set(CUSPARSE_FOUND TRUE)
+   set(CUSPARSE_LIBRARIES "cusparse")
 endif()

 if (XSDK_ENABLE_C)
@@ -296,22 +326,6 @@ if (MFEM_USE_HIOP)
  # find_package updates HIOP_FOUND, HIOP_INCLUDE_DIRS, HIOP_LIBRARIES
 endif()

-# CUDA
-if (MFEM_USE_CUDA)
-   set(CMAKE_CUDA_STANDARD 11)
-   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
-   set(CMAKE_CUDA_EXTENSIONS OFF)
-   set(CMAKE_CUDA_FLAGS "-arch=${CUDA_ARCH} --expt-extended-lambda"
-       CACHE STRING "CUDA flags set for MFEM" FORCE)
-   if (MFEM_USE_MPI)
-      set(CUDA_CCBIN_COMPILER ${MPI_CXX_COMPILER})
-   else()
-      set(CUDA_CCBIN_COMPILER ${CMAKE_CXX_COMPILER})
-   endif()
-   string(APPEND CMAKE_CUDA_FLAGS " -ccbin ${CUDA_CCBIN_COMPILER}")
-   set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CUDA_CCBIN_COMPILER})
-endif()
-
 # OCCA
 if (MFEM_USE_OCCA)
   find_package(OCCA REQUIRED)
@@ -357,7 +371,8 @@ endif()
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP BLAS LAPACK METIS HYPRE SuiteSparse SUNDIALS PETSC
    SLEPC MESQUITE SuperLUDist STRUMPACK AXOM CONDUIT Ginkgo GNUTLS GSLIB NETCDF
-    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE ADIOS2)
+    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE ADIOS2
+    CUSPARSE)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")
@@ -663,7 +663,7 @@ The specific libraries and their options are:
  URL: https://github.com/CEED/libCEED
       https://ceed.exascaleproject.org/libceed
  Options: CEED_DIR, CEED_OPT, CEED_LIB.
-  Versions: libCEED >= 0.6, git-hash a970f63.
+  Versions: libCEED > 0.6, git-hash bdfed75.

 - RAJA (optional), used when MFEM_USE_RAJA = YES.
  Beginning with MFEM v4.1, only RAJA v0.10.0+ is supported.
@@ -38,7 +38,19 @@ if(NOT ADIOS2_FOUND)
  endif()

  find_path(ADIOS2_INCLUDE_DIR adios2.h ${ADIOS2_INCLUDE_OPTS})
-  find_library(ADIOS2_LIBRARY NAMES adios2 ${ADIOS2_LIBRARY_OPTS}) 
+  
+  # adios2 version 2.5.0 
+  find_library(ADIOS2_LIBRARY NAMES adios2 ${ADIOS2_LIBRARY_OPTS})
+  
+  # adios2 version 2.6.0 and onwards
+  if(NOT ADIOS2_LIBRARY)
+  	find_library(ADIOS2_CXX11_MPI_LIBRARY NAMES adios2_cxx11_mpi ${ADIOS2_LIBRARY_OPTS})
+  	find_library(ADIOS2_CXX11_LIBRARY NAMES adios2_cxx11 ${ADIOS2_LIBRARY_OPTS})
+  	set(ADIOS2_LIBRARY ${ADIOS2_CXX11_MPI_LIBRARY} ${ADIOS2_CXX11_LIBRARY})
+  	if(MFEM_USE_MPI)
+  	  add_definitions(-DADIOS2_USE_MPI)
+  	endif()
+  endif() 

  include(FindPackageHandleStandardArgs)
  find_package_handle_standard_args(ADIOS2
@@ -128,7 +128,15 @@ function(add_mfem_miniapp MFEM_EXE_NAME)
  if (MFEM_USE_CUDA)
    set_property(SOURCE ${MAIN_LIST} ${EXTRA_SOURCES_LIST}
      PROPERTY LANGUAGE CUDA)
-    list(TRANSFORM EXTRA_OPTIONS_LIST PREPEND "-Xcompiler=")
+    if (CMAKE_VERSION VERSION_GREATER_EQUAL 3.12.0)
+      list(TRANSFORM EXTRA_OPTIONS_LIST PREPEND "-Xcompiler=")
+    else()
+      set(LIST_)
+      foreach(item IN LISTS EXTRA_OPTIONS_LIST)
+        list(APPEND LIST_ "-Xcompiler=${item}")
+      endforeach()
+      set(EXTRA_OPTIONS_LIST ${LIST_})
+    endif()
  endif()

  # Actually add the executable
@@ -50,7 +50,7 @@ option(MFEM_USE_OCCA "Enable OCCA" OFF)
 option(MFEM_USE_RAJA "Enable RAJA" OFF)
 option(MFEM_USE_CEED "Enable CEED" OFF)
 option(MFEM_USE_UMPIRE "Enable Umpire" OFF)
-option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" ON)
+option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" OFF)
 option(MFEM_USE_ADIOS2 "Enable ADIOS2" OFF)

 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")
@@ -138,7 +138,7 @@ MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
 MFEM_USE_CEED          = NO
 MFEM_USE_UMPIRE        = NO
-MFEM_USE_SIMD          = YES
+MFEM_USE_SIMD          = NO
 MFEM_USE_ADIOS2        = NO

 # Compile and link options for zlib.
@@ -341,9 +341,9 @@ GSLIB_DIR = @MFEM_DIR@/../gslib/build
 GSLIB_OPT = -I$(GSLIB_DIR)/include
 GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs

-# CUDA library configuration (currently not needed)
+# CUDA library configuration
 CUDA_OPT =
-CUDA_LIB =
+CUDA_LIB = -lcusparse

 # HIP library configuration (currently not needed)
 HIP_OPT =
@@ -78,6 +78,14 @@ groups_parallel=(
   "miniapps/electromagnetics"
   "joule.cpp"'
 #   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+'"convergence"
+   "Convergence tests:"
+   "tests/convergence"
+   "diffusion.cpp"'
+'"par-mesh-format"
+   "Parallel mesh tests:"
+   "tests/par-mesh-format"
+   "ex1p.cpp"'
 )
 # All groups serial + parallel runs mixed in the same group:
 groups_all=(
@@ -107,6 +115,14 @@ groups_all=(
   "miniapps/electromagnetics"
   "joule.cpp"'
 #   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+'"convergence"
+   "Convergence tests:"
+   "tests/convergence"
+   "diffusion.cpp"'
+'"par-mesh-format"
+   "Parallel mesh tests:"
+   "tests/par-mesh-format"
+   "ex1p.cpp"'
 )
 make_all="all"
 base_timeformat=$'real: %3Rs  user: %3Us  sys: %3Ss  %%cpu: %P'
@@ -380,10 +396,15 @@ function timed_run()
 # This function is used to execute the sample runs
 function go()
 {
-   local cmd=("$@")
+   # Strip leading and trailing spaces from $1 and store the result in cmd_line
+   shopt -s extglob
+   local cmd_line="${1##+( )}"
+   cmd_line="${cmd_line%%+( )}"
+   shopt -u extglob
+   eval local cmd=(${cmd_line})
   local res=""
   echo $sep
-   echo "<${group}>" "${cmd[@]}"
+   echo "<${group}>" "${cmd_line}"
   echo $sep
   if [ "${timing}" == "yes" ]; then
      timed_run "${cmd[@]}"
@@ -395,15 +416,15 @@ function go()
   else
      res="${red}FAILED${none}"
   fi
-   printf "[${res}] <${group}> ${cmd[*]}\n"
+   printf "[${res}] <${group}> ${cmd_line}\n"
   if [ "${timing}" == "yes" ]; then
      printf "Run time: %s\n" "${timer}"
      timer=(${timer})
      timer="${timer[1]}"
-      printf -v line "[$res](%8s) ${cmd[*]}" "$timer"
+      printf -v line "[$res](%8s) ${cmd_line}" "$timer"
      summary=("${summary[@]}" "$line")
   else
-      summary=("${summary[@]}" "[${res}] ${cmd[*]}")
+      summary=("${summary[@]}" "[${res}] ${cmd_line}")
   fi
   echo $sep
 }
@@ -438,7 +459,7 @@ function go_group()
      fi
      for run in "${runs[@]}"; do
         if [ "${run}" == "" ]; then continue; fi
-         eval go \${run_prefix} \${run} \${run_suffix} $output
+         eval go \"\${run_prefix} \${run} \${run_suffix}\" $output
      done
   done
   ${make} clean-exec
@@ -504,7 +525,7 @@ function echo_run()
 {
   echo "   $@"
   { echo "   $@"; echo "$sep";
-     "$@"
+     eval "$@"
     echo "$sep"; } >> "$echo_log" 2>&1
 }

@@ -524,6 +545,28 @@ function build_all()
   echo_run ${make} config ${mfem_config} || exit 1
   echo_run ${make} ${make_j} || exit 1
   echo_run ${make} ${make_all} ${make_j} || exit 1
+   # Build groups in directories other than the directories built by 'make all':
+   for group_params in "${groups[@]}"; do
+      eval params=(${group_params})
+      group_dir="${params[2]}"
+      case "$group_dir" in
+         (examples*|miniapps*)
+            # Built by 'make all'
+            ;;
+         (*)
+            if [ "${mfem_dir}" != "${mfem_build_dir}" ]; then
+               echo_run mkdir -p "${group_dir}" || exit 1
+               echo_run cd "${group_dir}" || exit 1
+               echo_run cp -af "${mfem_dir}/${group_dir}/makefile" . || exit 1
+            else
+               echo_run cd "${group_dir}" || exit 1
+            fi
+            echo_run ${make} clean || exit 1
+            echo_run ${make} MFEM_DIR="${mfem_dir}" ${make_j} || exit 1
+            echo_run cd "${mfem_build_dir}" || exit 1
+            ;;
+      esac
+   done
 }

 # Function that runs all sample runs, given by the array variable "groups".
@@ -1,13 +1,38 @@
 SetFactory("OpenCASCADE");

+// Select periodic mesh by setting this to either 0 - standard, 1 - periodic
+periodic = 1;
+
+// Set the geometry order (1, 2, ..., 9)
+order = 3;
+
+// Set the element type (3 - triangles, 4 - quadrilaterals)
+type = 3;
+
+// Number of radial elements
+nrad = 2;
+
+// Number of azimuthal elements on inner arc
+nazm1 = 3;
+
+// Number of azimuthal elements on outer arc
+nazm2 = 5;
+
+// Note: Using type = 4 with nazm1 != nazm2 can lead to mixed meshes
+//       containing both triangles and quadrilaterals.
+
+// Inner and outer radii
 R1 = 1.0;
 R2 = 2.0;

+// Angular size of the sector
+Phi = Pi/3.0;
+
 Point(1) = {0.0, 0, 0, 1.0};
 Point(2) = {R1, 0, 0, 1.0};
 Point(3) = {R2, 0, 0, 1.0};
-Point(4) = {R1*Cos(Pi/3), R1*Sin(Pi/3), 0, 1.0};
-Point(5) = {R2*Cos(Pi/3), R2*Sin(Pi/3), 0, 1.0};
+Point(4) = {R1*Cos(Phi), R1*Sin(Phi), 0, 1.0};
+Point(5) = {R2*Cos(Phi), R2*Sin(Phi), 0, 1.0};
 Line(1) = {2, 3};
 Line(2) = {4, 5};
 Circle(3) = {2, 1, 4};
@@ -15,13 +40,23 @@ Circle(4) = {3, 1, 5};
 Curve Loop(5) = {1, 4, -2, -3};
 Plane Surface(1) = {5};

-Transfinite Curve{1} = 7;
-Transfinite Curve{2} = 7;
-Transfinite Curve{3} = 4;
-Transfinite Curve{4} = 10;
+Transfinite Curve{1} = nrad+1;
+Transfinite Curve{2} = nrad+1;
+Transfinite Curve{3} = nazm1+1;
+Transfinite Curve{4} = nazm2+1;
+
+If (nazm1 == nazm2)
+   Transfinite Surface{1};
+EndIf
+
+If (type == 4)
+   Recombine Surface {1};
+EndIf

 // Set a rotation periodicity constraint:
-Periodic Line{1} = {2} Rotate{{0,0,1}, {0,0,0}, -Pi/3};
+If (periodic)
+   Periodic Line{1} = {2} Rotate{{0,0,1}, {0,0,0}, -Phi};
+EndIf

 // Tag surfaces and volumes with positive integers
 Physical Curve(1) = {3};
@@ -30,8 +65,22 @@ Physical Curve(3) = {1};
 Physical Curve(4) = {2};
 Physical Surface(1) = {1};

+// Optimize the high-order mesh
+// See https://gmsh.info/doc/texinfo/gmsh.html#index-Mesh_002eHighOrderOptimize
+// Mesh.ElementOrder = order;
+// Mesh.HighOrderOptimize = 1;
+
 // Generate 2D mesh
 Mesh 2;
+SetOrder order;
 Mesh.MshFileVersion = 2.2;

-Save "periodic-annulus-sector.msh";
+// Check the element quality (the Plugin may be called AnalyseCurvedMesh)
+// Plugin(AnalyseMeshQuality).JacobianDeterminant = 1;
+// Plugin(AnalyseMeshQuality).Run;
+
+If (periodic)
+   Save Sprintf("periodic-annulus-sector-t%01g-o%01g.msh", type, order);
+Else
+   Save Sprintf("annulus-sector-t%01g-o%01g.msh", type, order);
+EndIf
@@ -2,184 +2,191 @@ $MeshFormat
 2.2 0 8
 $EndMeshFormat
 $Nodes
-55
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 $EndNodes
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-74 2 2 1 1 39 52 38
-75 2 2 1 1 6 40 5
-76 2 2 1 1 34 52 50
-77 2 2 1 1 12 45 13
-78 2 2 1 1 30 55 46
-79 2 2 1 1 10 47 11
-80 2 2 1 1 8 39 38
-81 2 2 1 1 28 49 21
-82 2 2 1 1 7 38 25
-83 2 2 1 1 41 49 28
-84 2 2 1 1 20 49 27
-85 2 2 1 1 11 26 12
-86 2 2 1 1 27 49 41
-87 2 2 1 1 31 52 39
-88 2 2 1 1 25 40 6
-89 2 2 1 1 2 54 9
-90 2 2 1 1 14 55 4
-91 2 2 1 1 45 53 46
-92 2 2 1 1 45 46 13
-93 2 2 1 1 5 44 1
-94 2 2 1 1 21 49 20
-95 2 2 1 1 46 53 30
-96 2 2 1 1 3 48 10
-97 2 2 1 1 34 50 33
-98 2 2 1 1 36 51 37
-99 2 2 1 1 26 45 12
-100 2 2 1 1 11 47 26
-101 2 2 1 1 27 50 42
-102 2 2 1 1 40 44 5
-103 2 2 1 1 43 51 28
-104 2 2 1 1 10 48 47
-105 2 2 1 1 9 54 39
-106 2 2 1 1 46 55 14
-107 2 2 1 1 1 44 15
-108 2 2 1 1 16 48 3
+38
+1 26 2 3 1 1 5 6 7
+2 26 2 3 1 5 2 8 9
+3 26 2 4 2 3 10 11 12
+4 26 2 4 2 10 4 13 14
+5 26 2 1 3 1 15 17 18
+6 26 2 1 3 15 16 19 20
+7 26 2 1 3 16 3 21 22
+8 26 2 2 4 2 23 27 28
+9 26 2 2 4 23 24 29 30
+10 26 2 2 4 24 25 31 32
+11 26 2 2 4 25 26 33 34
+12 26 2 2 4 26 4 35 36
+13 21 2 1 1 3 41 10 45 46 47 48 12 11 49
+14 21 2 1 1 5 42 1 50 51 52 53 6 7 54
+15 21 2 1 1 16 41 3 55 56 46 45 22 21 57
+16 21 2 1 1 1 42 15 53 52 58 59 18 17 60
+17 21 2 1 1 37 40 38 61 62 63 64 65 66 67
+18 21 2 1 1 39 40 37 68 69 62 61 70 71 72
+19 21 2 1 1 38 41 37 73 74 75 76 66 65 77
+20 21 2 1 1 37 42 39 78 79 80 81 71 70 82
+21 21 2 1 1 24 39 23 83 84 85 86 29 30 87
+22 21 2 1 1 26 38 25 88 89 90 91 33 34 92
+23 21 2 1 1 15 37 16 93 94 95 96 20 19 97
+24 21 2 1 1 42 44 39 98 99 100 101 81 80 102
+25 21 2 1 1 38 43 41 103 104 105 106 74 73 107
+26 21 2 1 1 2 44 5 108 109 110 111 8 9 112
+27 21 2 1 1 10 43 4 113 114 115 116 14 13 117
+28 21 2 1 1 24 40 39 118 119 69 68 84 83 120
+29 21 2 1 1 38 40 25 64 63 121 122 91 90 123
+30 21 2 1 1 41 43 10 106 105 114 113 48 47 124
+31 21 2 1 1 5 44 42 111 110 99 98 51 50 125
+32 21 2 1 1 25 40 24 122 121 119 118 31 32 126
+33 21 2 1 1 37 41 16 76 75 56 55 96 95 127
+34 21 2 1 1 15 42 37 59 58 79 78 94 93 128
+35 21 2 1 1 4 43 26 116 115 129 130 35 36 131
+36 21 2 1 1 23 44 2 132 133 109 108 27 28 134
+37 21 2 1 1 26 43 38 130 129 104 103 89 88 135
+38 21 2 1 1 39 44 23 101 100 133 132 86 85 136
 $EndElements
 $Periodic
 1
 1 1 2
 Affine 0.5000000000000001 0.8660254037844386 0 0 -0.8660254037844386 0.5000000000000001 0 0 0 0 1 0 0 0 0 1
-7
-9 14
-6 11
-8 13
+3
 5 10
-7 12
-2 4
 1 3
+2 4
 $EndPeriodic
@@ -1,25 +1,141 @@
-SetFactory("OpenCASCADE");
+// Select periodic mesh by setting this to either 0 - standard, 1 - periodic
+periodic = 1;

-R = 1.5;
-r = 0.5;
+// Set the geometry order (1, 2, ..., 10 for tetrahedra or 9 for other types)
+order = 3;

-Torus(1) = {0,0,0, R, r, Pi/3};
+// Set the element type (4 - tetrahedra, 6 - wedges, 8 - hexahedra)
+type = 8;

-pts() = PointsOf{ Volume{1}; };
+// Minor and major radii
+R1 = 1.0;
+R2 = 2.0;

-Characteristic Length{ pts() } = 0.25;
+// Side length of interior square
+A1 = 0.8;
+
+// Angular size of the sector
+Phi = Pi/3.0;
+
+// Number of azimuthal elements
+nazm = 3;
+
+// Number of elements around a quarter of the circle
+narc = 2;
+
+// Number of elements between surface and interior square
+nshl = 1;
+
+lc = 0.5;
+a1 = A1 / Sqrt(2.0);
+
+Point(1) = {R2+R1, 0, 0, lc};
+Point(2) = {R2, 0, R1, lc};
+Point(3) = {R2-R1, 0, 0, lc};
+Point(4) = {R2, 0, -R1, lc};
+Point(5) = {R2, 0, 0, lc};
+Point(6) = {R2+a1, 0, 0, lc};
+Point(7) = {R2, 0, a1, lc};
+Point(8) = {R2-a1, 0, 0, lc};
+Point(9) = {R2, 0, -a1, lc};
+
+Circle(1) = {1,5,2};
+Circle(2) = {2,5,3};
+Circle(3) = {3,5,4};
+Circle(4) = {4,5,1};
+
+Line(5) = {6,1};
+Line(6) = {7,2};
+Line(7) = {8,3};
+Line(8) = {9,4};
+
+Line(9) = {6, 7};
+Line(10) = {7, 8};
+Line(11) = {8, 9};
+Line(12) = {9, 6};
+
+Line Loop(101) = {1, -6, -9, 5};
+Line Loop(102) = {2, -7, -10, 6};
+Line Loop(103) = {3, -8, -11, 7};
+Line Loop(104) = {4, -5, -12, 8};
+Line Loop(105) = {9, 10, 11, 12};
+
+Plane Surface(201) = {101};
+Plane Surface(202) = {102};
+Plane Surface(203) = {103};
+Plane Surface(204) = {104};
+Plane Surface(205) = {105};
+
+Transfinite Curve{1} = narc+1;
+Transfinite Curve{2} = narc+1;
+Transfinite Curve{3} = narc+1;
+Transfinite Curve{4} = narc+1;
+
+Transfinite Curve{5} = nshl+1;
+Transfinite Curve{6} = nshl+1;
+Transfinite Curve{7} = nshl+1;
+Transfinite Curve{8} = nshl+1;
+
+Transfinite Curve{9} = narc+1;
+Transfinite Curve{10} = narc+1;
+Transfinite Curve{11} = narc+1;
+Transfinite Curve{12} = narc+1;
+
+If (type == 8)
+   Recombine Surface {201};
+   Recombine Surface {202};
+   Recombine Surface {203};
+   Recombine Surface {204};
+   Recombine Surface {205};
+
+   Transfinite Surface {201} = {1,2,7,6};
+   Transfinite Surface {202} = {2,3,8,7};
+   Transfinite Surface {203} = {3,4,9,8};
+   Transfinite Surface {204} = {4,1,6,9};
+   Transfinite Surface {205} = {6,7,8,9};
+EndIf
+
+If (type == 4)
+   Extrude { {0,0,1} , {0,0,0} , Phi} {
+      Surface{201,202,203,204,205}; Layers{nazm};
+}
+Else
+   Extrude { {0,0,1} , {0,0,0} , Phi} {
+      Surface{201,202,203,204,205}; Layers{nazm}; Recombine;
+}
+EndIf

 // Set a rotation periodicity constraint:
-Periodic Surface{3} = {2} Rotate{{0,0,1}, {0,0,0}, Pi/3};
+If (periodic)
+   Periodic Surface{227} = {201} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{249} = {202} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{271} = {203} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{293} = {204} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{315} = {205} Rotate{{0,0,1}, {0,0,0}, Phi};
+EndIf

 // Tag surfaces and volumes with positive integers
-Physical Surface(1) = {1};
-Physical Surface(2) = {2};
-Physical Surface(3) = {3};
-Physical Volume(1) = {1};
+Physical Surface(1) = {201,202,203,204,205};
+Physical Surface(2) = {227,249,271,293,315};
+Physical Surface(3) = {214,236,258,280};
+Physical Volume(1) = {1,2,3,4,5};
+
+// Optimize the high-order mesh
+// See https://gmsh.info/doc/texinfo/gmsh.html#index-Mesh_002eHighOrderOptimize
+// Mesh.ElementOrder = order;
+// Mesh.HighOrderOptimize = 1;

 // Generate 3D mesh
 Mesh 3;
-
+SetOrder order;
 Mesh.MshFileVersion = 2.2;
-Save "periodic-torus-sector.msh";
+
+// Check the element quality (the Plugin may be called AnalyseCurvedMesh)
+// Plugin(AnalyseMeshQuality).JacobianDeterminant = 1;
+// Plugin(AnalyseMeshQuality).Run;
+
+If (periodic)
+   Save Sprintf("periodic-torus-sector-t%01g-o%01g.msh", type, order);
+Else
+   Save Sprintf("torus-sector-t%01g-o%01g.msh", type, order);
+EndIf
@@ -0,0 +1,118 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+#
+
+dimension
+2
+
+elements
+20
+1 3 0 1 6 5
+1 3 1 2 7 6
+1 3 2 3 8 7
+1 3 3 4 9 8
+1 3 5 6 11 10
+1 2 6 7 11
+1 2 7 12 11
+1 2 7 8 13
+1 2 7 13 12
+1 3 8 9 14 13
+1 3 10 11 16 15
+1 2 11 12 17
+1 2 11 17 16
+1 2 12 13 17
+1 2 13 18 17
+1 3 13 14 19 18
+1 3 15 16 21 20
+1 3 16 17 22 21
+1 3 17 18 23 22
+1 3 18 19 24 23
+
+boundary
+16
+2 1 0 1
+2 1 1 2
+2 1 2 3
+2 1 3 4
+2 1 21 20
+2 1 22 21
+2 1 23 22
+2 1 24 23
+1 1 5 0
+1 1 10 5
+1 1 15 10
+1 1 20 15
+1 1 4 9
+1 1 9 14
+1 1 14 19
+1 1 19 24
+
+vertices
+25
+
+nodes
+FiniteElementSpace
+FiniteElementCollection: H1_2D_P1
+VDim: 2
+Ordering: 0
+
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0
+0
+0
+0
+0.25
+0.25
+0.25
+0.25
+0.25
+0.5
+0.5
+0.5
+0.5
+0.5
+0.75
+0.75
+0.75
+0.75
+0.75
+1
+1
+1
+1
+1
@@ -144,12 +144,12 @@ namespace mfem {
 * - <a class="el" href="maxwell_8cpp_source.html">Maxwell</a>: simple transient full-wave electromagnetics simulation code
 * - <a class="el" href="joule_8cpp_source.html">Joule</a>: transient magnetics and Joule heating miniapp
 * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
-
-* - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
+ * - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
 * - <a class="el" href="klein-bottle_8cpp_source.html">Klein Bottle</a>: generate three types of Klein bottle surfaces
 * - <a class="el" href="toroid_8cpp_source.html">Toroid</a>: generate simple toroidal meshes
 * - <a class="el" href="twist_8cpp_source.html">Twist</a>: generate simple periodic meshes
 * - <a class="el" href="minimal-surface_8cpp_source.html">Minimal Surface</a>: compute minimal surfaces, <a class="el" href="minimal-surface_8cpp_source.html">serial</a> and <a class="el" href="pminimal-surface_8cpp_source.html">parallel</a> versions
+ * - <a class="el" href="polar-nc_8cpp_source.html">Polar NC</a>: generate polar non-conforming meshes
 * - <a class="el" href="shaper_8cpp_source.html">Shaper</a>: resolve material interfaces by mesh refinement
 * - <a class="el" href="extruder_8cpp_source.html">Extruder</a>: extrude a low-dimensional mesh into a higher dimension
 * - <a class="el" href="mesh-explorer_8cpp_source.html">Mesh Explorer</a>: visualize and manipulate meshes
@@ -162,6 +162,7 @@ namespace mfem {
 * - <a class="el" href="lor-transfer_8cpp_source.html">LOR Transfer</a>: map functions between high-order and low-order refined spaces
 * - <a class="el" href="findpts_8cpp_source.html">Find Points</a>: evaluate grid function in physical space, <a class="el" href="findpts_8cpp_source.html">serial</a> and <a class="el" href="pfindpts_8cpp_source.html">parallel</a> versions
 * - <a class="el" href="field-diff_8cpp_source.html">Field Diff</a>: compare grid functions on different meshes
+ * - <a class="el" href="field-interp_8cpp_source.html">Field Interp</a>: transfer a grid functions betwen meshes
 * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Laplace problem
 * - <a class="el" href="miniapps_2performance_2ex1p_8cpp_source.html">HPC Example 1p</a>: high-performance parallel nodal H1 FEM for the Laplace problem
 *
@@ -19,7 +19,7 @@ html: $(DOXYGEN_CONF)
 	@# Generate the html documentation
 	@doxygen $(DOXYGEN_CONF)
 	@echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > CodeDocumentation.html
-	@cat warnings.log
+	@cat warnings.log 1>&2
 	@# Generate the log of undocumented methods
 	@( cat $(DOXYGEN_CONF) ; echo "GENERATE_HTML=NO" ; echo "EXTRACT_ALL=NO" ; echo "WARN_LOGFILE=undoc.log" ; echo "QUIET=YES" ) | doxygen - &> /dev/null

@@ -6,17 +6,19 @@
 //               ex22 -m ../data/inline-tri.mesh -o 3
 //               ex22 -m ../data/inline-quad.mesh -o 3
 //               ex22 -m ../data/inline-quad.mesh -o 3 -p 1
+//               ex22 -m ../data/inline-quad.mesh -o 3 -p 1 -pa
 //               ex22 -m ../data/inline-quad.mesh -o 3 -p 2
 //               ex22 -m ../data/inline-tet.mesh -o 2
 //               ex22 -m ../data/inline-hex.mesh -o 2
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 1
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2
+//               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa
 //               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0
 //
-// With partial assembly:
-//               ex22 -m ../data/inline-quad.mesh -o 3 -p 1 -pa
-//               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa
-//               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0 -pa
+// Device sample runs:
+//               ex22 -m ../data/inline-quad.mesh -o 3 -p 1 -pa -d cuda
+//               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa -d cuda
+//               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0 -pa -d cuda
 //
 // Description:  This example code demonstrates the use of MFEM to define and
 //               solve simple complex-valued linear systems. It implements three
@@ -82,6 +84,7 @@ int main(int argc, char *argv[])
   bool herm_conv = true;
   bool exact_sol = true;
   bool pa = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -114,6 +117,8 @@ int main(int argc, char *argv[])
                  "Enable or disable GLVis visualization.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -143,13 +148,18 @@ int main(int argc, char *argv[])
   ComplexOperator::Convention conv =
      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;

-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes
   //    with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 3. Refine the mesh to increase resolution. In this example we do
+   // 4. Refine the mesh to increase resolution. In this example we do
   //    'ref_levels' of uniform refinement where the user specifies
   //    the number of levels with the '-r' option.
   for (int l = 0; l < ref_levels; l++)
@@ -157,7 +167,7 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 4. Define a finite element space on the mesh. Here we use continuous
+   // 5. Define a finite element space on the mesh. Here we use continuous
   //    Lagrange, Nedelec, or Raviart-Thomas finite elements of the specified
   //    order.
   if (dim == 1 && prob != 0 )
@@ -179,7 +189,7 @@ int main(int argc, char *argv[])
   cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
        << endl;

-   // 5. Determine the list of true (i.e. conforming) essential boundary dofs.
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
   //    In this example, the boundary conditions are defined based on the type
   //    of mesh and the problem type.
   Array<int> ess_tdof_list;
@@ -191,12 +201,12 @@ int main(int argc, char *argv[])
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

-   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
   //    the FEM linear system.
   ComplexLinearForm b(fespace, conv);
   b.Vector::operator=(0.0);

-   // 7. Define the solution vector u as a complex finite element grid function
+   // 8. Define the solution vector u as a complex finite element grid function
   //    corresponding to fespace. Initialize u with initial guess of 1+0i or
   //    the exact solution if it is known.
   ComplexGridFunction u(fespace);
@@ -218,7 +228,6 @@ int main(int argc, char *argv[])
   VectorConstantCoefficient zeroVecCoef(zeroVec);
   VectorConstantCoefficient oneVecCoef(oneVec);

-   u = 0.0;
   switch (prob)
   {
      case 0:
@@ -271,7 +280,7 @@ int main(int argc, char *argv[])
                 << "window_title 'Exact: Imaginary Part'" << flush;
   }

-   // 8. Set up the sesquilinear form a(.,.) on the finite element space
+   // 9. Set up the sesquilinear form a(.,.) on the finite element space
   //    corresponding to the damped harmonic oscillator operator of the
   //    appropriate type:
   //
@@ -314,7 +323,7 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 8a. Set up the bilinear form for the preconditioner corresponding to the
+   // 9a. Set up the bilinear form for the preconditioner corresponding to the
   //     appropriate operator
   //
   //      0) A scalar H1 field
@@ -349,9 +358,9 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 9. Assemble the form and the corresponding linear system, applying any
-   //    necessary transformations such as: assembly, eliminating boundary
-   //    conditions, conforming constraints for non-conforming AMR, etc.
+   // 10. Assemble the form and the corresponding linear system, applying any
+   //     necessary transformations such as: assembly, eliminating boundary
+   //     conditions, conforming constraints for non-conforming AMR, etc.
   a->Assemble();
   pcOp->Assemble();

@@ -362,7 +371,7 @@ int main(int argc, char *argv[])

   cout << "Size of linear system: " << A->Width() << endl << endl;

-   // 10. Define and apply a GMRES solver for AU=B with a block diagonal
+   // 11. Define and apply a GMRES solver for AU=B with a block diagonal
   //     preconditioner based on the appropriate sparse smoother.
   {
      Array<int> blockOffsets;
@@ -419,7 +428,7 @@ int main(int argc, char *argv[])
      gmres.Mult(B, U);
   }

-   // 11. Recover the solution as a finite element grid function and compute the
+   // 12. Recover the solution as a finite element grid function and compute the
   //     errors if the exact solution is known.
   a->RecoverFEMSolution(U, b, u);

@@ -451,7 +460,7 @@ int main(int argc, char *argv[])
      cout << endl;
   }

-   // 12. Save the refined mesh and the solution. This output can be viewed
+   // 13. Save the refined mesh and the solution. This output can be viewed
   //     later using GLVis: "glvis -m mesh -g sol".
   {
      ofstream mesh_ofs("refined.mesh");
@@ -466,7 +475,7 @@ int main(int argc, char *argv[])
      u.imag().Save(sol_i_ofs);
   }

-   // 13. Send the solution by socket to a GLVis server.
+   // 14. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -525,7 +534,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 14. Free the used memory.
+   // 15. Free the used memory.
   delete a;
   delete u_exact;
   delete pcOp;
@@ -7,16 +7,18 @@
 //               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 3
 //               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 3 -p 1
 //               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 3 -p 2
+//               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 1 -p 1 -pa
 //               mpirun -np 4 ex22p -m ../data/inline-tet.mesh -o 2
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 1
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 2
+//               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa
 //               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0
 //
-// With partial assembly:
-//               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 1 -p 1 -pa
-//               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa
-//               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0 -pa
+// Device sample runs:
+//               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 1 -p 1 -pa -d cuda
+//               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa -d cuda
+//               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0 -pa -d cuda
 //
 // Description:  This example code demonstrates the use of MFEM to define and
 //               solve simple complex-valued linear systems. It implements three
@@ -46,7 +48,6 @@
 //               We recommend viewing examples 1, 3 and 4 before viewing this
 //               example.

-
 #include "mfem.hpp"
 #include <fstream>
 #include <iostream>
@@ -90,6 +91,7 @@ int main(int argc, char *argv[])
   bool herm_conv = true;
   bool exact_sol = true;
   bool pa = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -124,6 +126,8 @@ int main(int argc, char *argv[])
                  "Enable or disable GLVis visualization.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -160,19 +164,24 @@ int main(int argc, char *argv[])
   ComplexOperator::Convention conv =
      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;

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

-   // 4. Refine the serial mesh on all processors to increase the resolution.
+   // 5. Refine the serial mesh on all processors to increase the resolution.
   for (int l = 0; l < ser_ref_levels; l++)
   {
      mesh->UniformRefinement();
   }

-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
   //    this mesh further in parallel to increase the resolution. Once the
   //    parallel mesh is defined, the serial mesh can be deleted.
   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
@@ -182,7 +191,7 @@ int main(int argc, char *argv[])
      pmesh->UniformRefinement();
   }

-   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
   //    use continuous Lagrange, Nedelec, or Raviart-Thomas finite elements of
   //    the specified order.
   if (dim == 1 && prob != 0 )
@@ -210,7 +219,7 @@ int main(int argc, char *argv[])
      cout << "Number of finite element unknowns: " << size << endl;
   }

-   // 7. Determine the list of true (i.e. parallel conforming) essential
+   // 8. Determine the list of true (i.e. parallel conforming) essential
   //    boundary dofs. In this example, the boundary conditions are defined
   //    based on the type of mesh and the problem type.
   Array<int> ess_tdof_list;
@@ -222,14 +231,14 @@ int main(int argc, char *argv[])
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

-   // 8. Set up the parallel linear form b(.) which corresponds to the
+   // 9. Set up the parallel linear form b(.) which corresponds to the
   //    right-hand side of the FEM linear system.
   ParComplexLinearForm b(fespace, conv);
   b.Vector::operator=(0.0);

-   // 9. Define the solution vector u as a parallel complex finite element grid
-   //    function corresponding to fespace. Initialize u with initial guess of
-   //    1+0i or the exact solution if it is known.
+   // 10. Define the solution vector u as a parallel complex finite element grid
+   //     function corresponding to fespace. Initialize u with initial guess of
+   //     1+0i or the exact solution if it is known.
   ParComplexGridFunction u(fespace);
   ParComplexGridFunction * u_exact = NULL;
   if (exact_sol) { u_exact = new ParComplexGridFunction(fespace); }
@@ -249,7 +258,6 @@ int main(int argc, char *argv[])
   VectorConstantCoefficient zeroVecCoef(zeroVec);
   VectorConstantCoefficient oneVecCoef(oneVec);

-   u = 0.0;
   switch (prob)
   {
      case 0:
@@ -304,7 +312,7 @@ int main(int argc, char *argv[])
                 << "window_title 'Exact: Imaginary Part'" << flush;
   }

-   // 10. Set up the parallel sesquilinear form a(.,.) on the finite element
+   // 11. Set up the parallel sesquilinear form a(.,.) on the finite element
   //     space corresponding to the damped harmonic oscillator operator of the
   //     appropriate type:
   //
@@ -347,7 +355,7 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 10a. Set up the parallel bilinear form for the preconditioner
+   // 11a. Set up the parallel bilinear form for the preconditioner
   //      corresponding to the appropriate operator
   //
   //      0) A scalar H1 field
@@ -381,7 +389,7 @@ int main(int argc, char *argv[])
      default: break; // This should be unreachable
   }

-   // 11. Assemble the parallel bilinear form and the corresponding linear
+   // 12. Assemble the parallel bilinear form and the corresponding linear
   //     system, applying any necessary transformations such as: parallel
   //     assembly, eliminating boundary conditions, applying conforming
   //     constraints for non-conforming AMR, etc.
@@ -399,7 +407,7 @@ int main(int argc, char *argv[])
           << 2 * fespace->GlobalTrueVSize() << endl << endl;
   }

-   // 12. Define and apply a parallel FGMRES solver for AU=B with a block
+   // 13. Define and apply a parallel FGMRES solver for AU=B with a block
   //     diagonal preconditioner based on the appropriate multigrid
   //     preconditioner from hypre.
   {
@@ -460,7 +468,7 @@ int main(int argc, char *argv[])
      fgmres.SetPrintLevel(1);
      fgmres.Mult(B, U);
   }
-   // 13. Recover the parallel grid function corresponding to U. This is the
+   // 14. Recover the parallel grid function corresponding to U. This is the
   //     local finite element solution on each processor.
   a->RecoverFEMSolution(U, b, u);

@@ -495,7 +503,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 14. Save the refined mesh and the solution in parallel. This output can be
+   // 15. Save the refined mesh and the solution in parallel. This output can be
   //     viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
   {
      ostringstream mesh_name, sol_r_name, sol_i_name;
@@ -515,7 +523,7 @@ int main(int argc, char *argv[])
      u.imag().Save(sol_i_ofs);
   }

-   // 15. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -580,7 +588,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 16. Free the used memory.
+   // 17. Free the used memory.
   delete a;
   delete u_exact;
   delete pcOp;
@@ -60,6 +60,7 @@ int main(int argc, char *argv[])
   bool static_cond = false;
   bool visualization = 1;
   bool amg_elast = 0;
+   bool reorder_space = false;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -75,6 +76,8 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
+   args.AddOption(&reorder_space, "-nodes", "--by-nodes", "-vdim", "--by-vdim",
+                  "Use byNODES ordering of vector space instead of byVDIM");
   args.Parse();
   if (!args.Good())
   {
@@ -156,7 +159,14 @@ int main(int argc, char *argv[])
   else
   {
      fec = new H1_FECollection(order, dim);
-      fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM);
+      if (reorder_space)
+      {
+         fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byNODES);
+      }
+      else
+      {
+         fespace = new ParFiniteElementSpace(pmesh, fec, dim, Ordering::byVDIM);
+      }
   }
   HYPRE_Int size = fespace->GlobalTrueVSize();
   if (myid == 0)
@@ -249,7 +259,7 @@ int main(int argc, char *argv[])
   }
   else
   {
-      amg->SetSystemsOptions(dim);
+      amg->SetSystemsOptions(dim, reorder_space);
   }
   HyprePCG *pcg = new HyprePCG(A);
   pcg->SetTol(1e-8);
@@ -108,7 +108,11 @@ int main(int argc, char *argv[])
   //    the Laplace problem -\Delta u = 1. We don't assemble the discrete
   //    problem yet, this will be done in the main loop.
   BilinearForm a(&fespace);
-   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   if (pa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a.SetDiagonalPolicy(Operator::DIAG_ONE);
+   }
   LinearForm b(&fespace);

   ConstantCoefficient one(1.0);
@@ -199,9 +203,10 @@ int main(int argc, char *argv[])
         umf_solver.Mult(B, X);
 #endif
      }
-      else // No preconditioning for now in partial assembly mode.
+      else // Diagonal preconditioning in partial assembly mode.
      {
-         CG(*A, B, X, 3, 2000, 1e-12, 0.0);
+         OperatorJacobiSmoother M(a, ess_tdof_list);
+         PCG(*A, M, B, X, 3, 2000, 1e-12, 0.0);
      }

      // 18. After solving the linear system, reconstruct the solution as a
@@ -129,7 +129,11 @@ int main(int argc, char *argv[])
   //    the Laplace problem -\Delta u = 1. We don't assemble the discrete
   //    problem yet, this will be done in the main loop.
   ParBilinearForm a(&fespace);
-   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   if (pa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a.SetDiagonalPolicy(Operator::DIAG_ONE);
+   }
   ParLinearForm b(&fespace);

   ConstantCoefficient one(1.0);
@@ -220,17 +224,26 @@ int main(int argc, char *argv[])

      // 17. Solve the linear system A X = B.
      //     * With full assembly, use the BoomerAMG preconditioner from hypre.
-      //     * With partial assembly, use no preconditioner, for now.
-      HypreBoomerAMG *amg = NULL;
-      if (!pa) { amg = new HypreBoomerAMG; amg->SetPrintLevel(0); }
+      //     * With partial assembly, use a diagonal preconditioner.
+      Solver *M = NULL;
+      if (pa)
+      {
+         M = new OperatorJacobiSmoother(a, ess_tdof_list);
+      }
+      else
+      {
+         HypreBoomerAMG *amg = new HypreBoomerAMG;
+         amg->SetPrintLevel(0);
+         M = amg;
+      }
      CGSolver cg(MPI_COMM_WORLD);
      cg.SetRelTol(1e-6);
      cg.SetMaxIter(2000);
      cg.SetPrintLevel(3); // print the first and the last iterations only
-      if (amg) { cg.SetPreconditioner(*amg); }
+      cg.SetPreconditioner(*M);
      cg.SetOperator(*A);
      cg.Mult(B, X);
-      delete amg;
+      delete M;

      // 18. Switch back to the host and extract the parallel grid function
      //     corresponding to the finite element approximation X. This is the
@@ -31,6 +31,7 @@ set(SRCS
  bilininteg_vecmass.cpp
  coefficient.cpp
  complex_fem.cpp
+  convergence.cpp
  datacollection.cpp
  eltrans.cpp
  estimators.cpp
@@ -65,6 +66,7 @@ set(HDRS
  bilininteg.hpp
  coefficient.hpp
  complex_fem.hpp
+  convergence.hpp
  datacollection.hpp
  eltrans.hpp
  estimators.hpp
@@ -627,6 +627,33 @@ void BilinearForm::AssembleDiagonal(Vector &diag) const
      MFEM_ASSERT(diag.Size() == fes->GetTrueVSize(),
                  "Vector for holding diagonal has wrong size!");
      const Operator *P = fes->GetProlongationMatrix();
+      // For an AMR mesh, a convergent diagonal is assembled with |P^T| d_e,
+      // where |P^T| has the entry-wise absolute values of the conforming
+      // prolongation transpose operator.
+      if (P && !fes->Conforming())
+      {
+         Vector local_diag(P->Height());
+         ext->AssembleDiagonal(local_diag);
+         const SparseMatrix *SP = dynamic_cast<const SparseMatrix*>(P);
+#ifdef MFEM_USE_MPI
+         const HypreParMatrix *HP = dynamic_cast<const HypreParMatrix*>(P);
+#endif
+         if (SP)
+         {
+            SP->AbsMultTranspose(local_diag, diag);
+         }
+#ifdef MFEM_USE_MPI
+         else if (HP)
+         {
+            HP->AbsMultTranspose(1.0, local_diag, 0.0, diag);
+         }
+#endif
+         else
+         {
+            MFEM_ABORT("Prolongation matrix has unexpected type.");
+         }
+         return;
+      }
      if (!IsIdentityProlongation(P))
      {
         Vector local_diag(P->Height());
@@ -96,6 +96,9 @@ void PABilinearFormExtension::Assemble()
      integrators[i]->AssemblePA(*a->FESpace());
   }

+   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
+               "Partial assembly does not support AddBoundaryIntegrator yet.");
+
   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
   const int intFaceIntegratorCount = intFaceIntegrators.Size();
   for (int i = 0; i < intFaceIntegratorCount; ++i)
@@ -116,7 +119,7 @@ void PABilinearFormExtension::AssembleDiagonal(Vector &y) const
   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();

   const int iSz = integrators.Size();
-   if (elem_restrict)
+   if (elem_restrict && !DeviceCanUseCeed())
   {
      localY = 0.0;
      for (int i = 0; i < iSz; ++i)
@@ -307,19 +310,21 @@ void EABilinearFormExtension::Assemble()

   ea_data.SetSize(ne*elemDofs*elemDofs, Device::GetMemoryType());
   ea_data.UseDevice(true);
-   ea_data = 0.0;

   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
   const int integratorCount = integrators.Size();
   for (int i = 0; i < integratorCount; ++i)
   {
-      integrators[i]->AssembleEA(*a->FESpace(), ea_data);
+      integrators[i]->AssembleEA(*a->FESpace(), ea_data, i);
   }

   faceDofs = trialFes ->
              GetTraceElement(0, trialFes->GetMesh()->GetFaceBaseGeometry(0)) ->
              GetDof();

+   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
+               "Element assembly does not support AddBoundaryIntegrator yet.");
+
   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
   const int intFaceIntegratorCount = intFaceIntegrators.Size();
   if (intFaceIntegratorCount>0)
@@ -327,14 +332,13 @@ void EABilinearFormExtension::Assemble()
      nf_int = trialFes->GetNFbyType(FaceType::Interior);
      ea_data_int.SetSize(2*nf_int*faceDofs*faceDofs, Device::GetMemoryType());
      ea_data_ext.SetSize(2*nf_int*faceDofs*faceDofs, Device::GetMemoryType());
-      ea_data_int = 0.0;
-      ea_data_ext = 0.0;
   }
   for (int i = 0; i < intFaceIntegratorCount; ++i)
   {
      intFaceIntegrators[i]->AssembleEAInteriorFaces(*a->FESpace(),
                                                     ea_data_int,
-                                                     ea_data_ext);
+                                                     ea_data_ext,
+                                                     i);
   }

   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
@@ -347,7 +351,7 @@ void EABilinearFormExtension::Assemble()
   }
   for (int i = 0; i < boundFaceIntegratorCount; ++i)
   {
-      bdrFaceIntegrators[i]->AssembleEABoundaryFaces(*a->FESpace(),ea_data_bdr);
+      bdrFaceIntegrators[i]->AssembleEABoundaryFaces(*a->FESpace(),ea_data_bdr,i);
   }

   if (factorize_face_terms && int_face_restrict_lex)
@@ -794,6 +798,12 @@ void PAMixedBilinearFormExtension::Assemble()
   {
      integrators[i]->AssemblePA(*trialFes, *testFes);
   }
+   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
+               "Partial assembly does not support AddBoundaryIntegrator yet.");
+   MFEM_VERIFY(a->GetTFBFI()->Size() == 0,
+               "Partial assembly does not support AddTraceFaceIntegrator yet.");
+   MFEM_VERIFY(a->GetBTFBFI()->Size() == 0,
+               "Partial assembly does not support AddBdrTraceFaceIntegrator yet.");
 }

 void PAMixedBilinearFormExtension::Update()
@@ -52,7 +52,8 @@ void BilinearFormIntegrator::AssembleDiagonalPA(Vector &)
 }

 void BilinearFormIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                        Vector &emat)
+                                        Vector &emat,
+                                        const bool add)
 {
   mfem_error ("BilinearFormIntegrator::AssembleEA(...)\n"
               "   is not implemented for this class.");
@@ -61,7 +62,8 @@ void BilinearFormIntegrator::AssembleEA(const FiniteElementSpace &fes,
 void BilinearFormIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace
                                                     &fes,
                                                     Vector &ea_data_int,
-                                                     Vector &ea_data_ext)
+                                                     Vector &ea_data_ext,
+                                                     const bool add)
 {
   mfem_error ("BilinearFormIntegrator::AssembleEAInteriorFaces(...)\n"
               "   is not implemented for this class.");
@@ -69,7 +71,8 @@ void BilinearFormIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace

 void BilinearFormIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace
                                                     &fes,
-                                                     Vector &ea_data_bdr)
+                                                     Vector &ea_data_bdr,
+                                                     const bool add)
 {
   mfem_error ("BilinearFormIntegrator::AssembleEABoundaryFaces(...)\n"
               "   is not implemented for this class.");
@@ -86,9 +86,10 @@ public:
   virtual void AddMultTransposePA(const Vector &x, Vector &y) const;

   /// Method defining element assembly.
-   /** The result of the element assembly is added and stored in the @a emat
-       Vector. */
-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+   /** The result of the element assembly is added to the @a emat Vector if
+       @a add is true. Otherwise, if @a add is false, we set @a emat. */
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat,
+                           const bool add = true);
   /** Used with BilinearFormIntegrators that have different spaces. */
   // virtual void AssembleEA(const FiniteElementSpace &trial_fes,
   //                         const FiniteElementSpace &test_fes,
@@ -96,10 +97,12 @@ public:

   virtual void AssembleEAInteriorFaces(const FiniteElementSpace &fes,
                                        Vector &ea_data_int,
-                                        Vector &ea_data_ext);
+                                        Vector &ea_data_ext,
+                                        const bool add = true);

   virtual void AssembleEABoundaryFaces(const FiniteElementSpace &fes,
-                                        Vector &ea_data_bdr);
+                                        Vector &ea_data_bdr,
+                                        const bool add = true);

   /// Given a particular Finite Element computes the element matrix elmat.
   virtual void AssembleElementMatrix(const FiniteElement &el,
@@ -262,14 +265,17 @@ public:
      bfi->AddMultTransposePA(x, y);
   }

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat,
+                           const bool add);

   virtual void AssembleEAInteriorFaces(const FiniteElementSpace &fes,
                                        Vector &ea_data_int,
-                                        Vector &ea_data_ext);
+                                        Vector &ea_data_ext,
+                                        const bool add);

   virtual void AssembleEABoundaryFaces(const FiniteElementSpace &fes,
-                                        Vector &ea_data_bdr);
+                                        Vector &ea_data_bdr,
+                                        const bool add);

   virtual ~TransposeIntegrator() { if (own_bfi) { delete bfi; } }
 };
@@ -1952,7 +1958,8 @@ public:

   virtual void AssemblePA(const FiniteElementSpace &fes);

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat,
+                           const bool add);

   virtual void AssembleDiagonalPA(Vector &diag);

@@ -1961,7 +1968,7 @@ public:
   static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
                                         const FiniteElement &test_fe);

-   void SetupPA(const FiniteElementSpace &fes, const bool force = false);
+   void SetupPA(const FiniteElementSpace &fes);
 };

 /** Class for local mass matrix assembling a(u,v) := (Q u, v) */
@@ -2027,7 +2034,8 @@ public:

   virtual void AssemblePA(const FiniteElementSpace &fes);

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat,
+                           const bool add);

   virtual void AssembleDiagonalPA(Vector &diag);

@@ -2037,7 +2045,7 @@ public:
                                         const FiniteElement &test_fe,
                                         ElementTransformation &Trans);

-   void SetupPA(const FiniteElementSpace &fes, const bool force = false);
+   void SetupPA(const FiniteElementSpace &fes);
 };

 /** Mass integrator (u, v) restricted to the boundary of a domain */
@@ -2083,7 +2091,8 @@ public:

   virtual void AssemblePA(const FiniteElementSpace&);

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
+   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat,
+                           const bool add);

   virtual void AddMultPA(const Vector&, Vector&) const;

@@ -2660,10 +2669,12 @@ public:

   virtual void AssembleEAInteriorFaces(const FiniteElementSpace& fes,
                                        Vector &ea_data_int,
-                                        Vector &ea_data_ext);
+                                        Vector &ea_data_ext,
+                                        const bool add);

   virtual void AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                        Vector &ea_data_bdr);
+                                        Vector &ea_data_bdr,
+                                        const bool add);

   static const IntegrationRule &GetRule(Geometry::Type geom, int order,
                                         FaceElementTransformations &T);
@@ -22,6 +22,7 @@ static void EAConvectionAssemble1D(const int NE,
                                   const Array<double> &g,
                                   const Vector &padata,
                                   Vector &eadata,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -54,7 +55,14 @@ static void EAConvectionAssemble1D(const int NE,
            {
               val += r_Bj[k1] * D(k1, e) * r_Gi[k1];
            }
-            A(i1, j1, e) += val;
+            if (add)
+            {
+               A(i1, j1, e) += val;
+            }
+            else
+            {
+               A(i1, j1, e) = val;
+            }
         }
      }
   });
@@ -66,6 +74,7 @@ static void EAConvectionAssemble2D(const int NE,
                                   const Array<double> &g,
                                   const Vector &padata,
                                   Vector &eadata,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -121,7 +130,14 @@ static void EAConvectionAssemble2D(const int NE,
                               * r_B[k1][j1]* r_B[k2][j2];
                     }
                  }
-                  A(i1, i2, j1, j2, e) += val;
+                  if (add)
+                  {
+                     A(i1, i2, j1, j2, e) += val;
+                  }
+                  else
+                  {
+                     A(i1, i2, j1, j2, e) = val;
+                  }
               }
            }
         }
@@ -135,6 +151,7 @@ static void EAConvectionAssemble3D(const int NE,
                                   const Array<double> &g,
                                   const Vector &padata,
                                   Vector &eadata,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -191,7 +208,14 @@ static void EAConvectionAssemble3D(const int NE,
                              }
                           }
                        }
-                        A(i1, i2, i3, j1, j2, j3, e) += val;
+                        if (add)
+                        {
+                           A(i1, i2, i3, j1, j2, j3, e) += val;
+                        }
+                        else
+                        {
+                           A(i1, i2, i3, j1, j2, j3, e) = val;
+                        }
                     }
                  }
               }
@@ -202,7 +226,8 @@ static void EAConvectionAssemble3D(const int NE,
 }

 void ConvectionIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                      Vector &ea_data)
+                                      Vector &ea_data,
+                                      const bool add)
 {
   AssemblePA(fes);
   const int ne = fes.GetMesh()->GetNE();
@@ -212,44 +237,47 @@ void ConvectionIntegrator::AssembleEA(const FiniteElementSpace &fes,
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EAConvectionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EAConvectionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EAConvectionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EAConvectionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EAConvectionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EAConvectionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EAConvectionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EAConvectionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EAConvectionAssemble1D<2,2>(ne,B,G,pa_data,ea_data,add);
+         case 0x33: return EAConvectionAssemble1D<3,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x44: return EAConvectionAssemble1D<4,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x55: return EAConvectionAssemble1D<5,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x66: return EAConvectionAssemble1D<6,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x77: return EAConvectionAssemble1D<7,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x88: return EAConvectionAssemble1D<8,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x99: return EAConvectionAssemble1D<9,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EAConvectionAssemble1D(ne,B,G,pa_data,ea_data,add,
+                                                     dofs1D,quad1D);
      }
   }
   else if (dim == 2)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EAConvectionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EAConvectionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EAConvectionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EAConvectionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EAConvectionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EAConvectionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EAConvectionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EAConvectionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EAConvectionAssemble2D<2,2>(ne,B,G,pa_data,ea_data,add);
+         case 0x33: return EAConvectionAssemble2D<3,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x44: return EAConvectionAssemble2D<4,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x55: return EAConvectionAssemble2D<5,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x66: return EAConvectionAssemble2D<6,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x77: return EAConvectionAssemble2D<7,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x88: return EAConvectionAssemble2D<8,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x99: return EAConvectionAssemble2D<9,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EAConvectionAssemble2D(ne,B,G,pa_data,ea_data,add,
+                                                     dofs1D,quad1D);
      }
   }
   else if (dim == 3)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x23: return EAConvectionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
-         case 0x34: return EAConvectionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
-         case 0x45: return EAConvectionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
-         case 0x56: return EAConvectionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
-         case 0x67: return EAConvectionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
-         case 0x78: return EAConvectionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
-         case 0x89: return EAConvectionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x23: return EAConvectionAssemble3D<2,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x34: return EAConvectionAssemble3D<3,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x45: return EAConvectionAssemble3D<4,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x56: return EAConvectionAssemble3D<5,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x67: return EAConvectionAssemble3D<6,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x78: return EAConvectionAssemble3D<7,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x89: return EAConvectionAssemble3D<8,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EAConvectionAssemble3D(ne,B,G,pa_data,ea_data,add,
+                                                     dofs1D,quad1D);
      }
   }
   MFEM_ABORT("Unknown kernel.");
@@ -806,16 +806,16 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   {
      vel.SetSize(dim * nq * ne);
      auto C = Reshape(vel.HostWrite(), dim, nq, ne);
-      Vector Vq(dim);
+      DenseMatrix Q_ir;
      for (int e = 0; e < ne; ++e)
      {
         ElementTransformation& T = *fes.GetElementTransformation(e);
+         Q->Eval(Q_ir, T, *ir);
         for (int q = 0; q < nq; ++q)
         {
-            Q->Eval(Vq, T, ir->IntPoint(q));
            for (int i = 0; i < dim; ++i)
            {
-               C(i,q,e) = Vq(i);
+               C(i,q,e) = Q_ir(i,q);
            }
         }
      }
@@ -20,7 +20,8 @@ static void EADGTraceAssemble1DInt(const int NF,
                                   const Array<double> &basis,
                                   const Vector &padata,
                                   Vector &eadata_int,
-                                   Vector &eadata_ext)
+                                   Vector &eadata_ext,
+                                   const bool add)
 {
   auto D = Reshape(padata.Read(), 2, 2, NF);
   auto A_int = Reshape(eadata_int.ReadWrite(), 2, NF);
@@ -32,23 +33,41 @@ static void EADGTraceAssemble1DInt(const int NF,
      val_ext10 = D(1, 0, f);
      val_ext01 = D(0, 1, f);
      val_int1  = D(1, 1, f);
-      A_int(0, f) += val_int0;
-      A_int(1, f) += val_int1;
-      A_ext(0, f) += val_ext01;
-      A_ext(1, f) += val_ext10;
+      if (add)
+      {
+         A_int(0, f) += val_int0;
+         A_int(1, f) += val_int1;
+         A_ext(0, f) += val_ext01;
+         A_ext(1, f) += val_ext10;
+      }
+      else
+      {
+         A_int(0, f) = val_int0;
+         A_int(1, f) = val_int1;
+         A_ext(0, f) = val_ext01;
+         A_ext(1, f) = val_ext10;
+      }
   });
 }

 static void EADGTraceAssemble1DBdr(const int NF,
                                   const Array<double> &basis,
                                   const Vector &padata,
-                                   Vector &eadata_bdr)
+                                   Vector &eadata_bdr,
+                                   const bool add)
 {
   auto D = Reshape(padata.Read(), 2, 2, NF);
   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), NF);
   MFEM_FORALL(f, NF,
   {
-      A_bdr(f) += D(0, 0, f);
+      if (add)
+      {
+         A_bdr(f) += D(0, 0, f);
+      }
+      else
+      {
+         A_bdr(f) = D(0, 0, f);
+      }
   });
 }

@@ -58,6 +77,7 @@ static void EADGTraceAssemble2DInt(const int NF,
                                   const Vector &padata,
                                   Vector &eadata_int,
                                   Vector &eadata_ext,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -88,10 +108,20 @@ static void EADGTraceAssemble2DInt(const int NF,
               val_ext10 += B(k1,i1) * B(k1,j1) * D(k1, 1, 0, f);
               val_int1  += B(k1,i1) * B(k1,j1) * D(k1, 1, 1, f);
            }
-            A_int(i1, j1, 0, f) += val_int0;
-            A_int(i1, j1, 1, f) += val_int1;
-            A_ext(i1, j1, 0, f) += val_ext01;
-            A_ext(i1, j1, 1, f) += val_ext10;
+            if (add)
+            {
+               A_int(i1, j1, 0, f) += val_int0;
+               A_int(i1, j1, 1, f) += val_int1;
+               A_ext(i1, j1, 0, f) += val_ext01;
+               A_ext(i1, j1, 1, f) += val_ext10;
+            }
+            else
+            {
+               A_int(i1, j1, 0, f) = val_int0;
+               A_int(i1, j1, 1, f) = val_int1;
+               A_ext(i1, j1, 0, f) = val_ext01;
+               A_ext(i1, j1, 1, f) = val_ext10;
+            }
         }
      }
   });
@@ -102,6 +132,7 @@ static void EADGTraceAssemble2DBdr(const int NF,
                                   const Array<double> &basis,
                                   const Vector &padata,
                                   Vector &eadata_bdr,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -125,7 +156,14 @@ static void EADGTraceAssemble2DBdr(const int NF,
            {
               val_bdr  += B(k1,i1) * B(k1,j1) * D(k1, 0, 0, f);
            }
-            A_bdr(i1, j1, f) += val_bdr;
+            if (add)
+            {
+               A_bdr(i1, j1, f) += val_bdr;
+            }
+            else
+            {
+               A_bdr(i1, j1, f) = val_bdr;
+            }
         }
      }
   });
@@ -137,6 +175,7 @@ static void EADGTraceAssemble3DInt(const int NF,
                                   const Vector &padata,
                                   Vector &eadata_int,
                                   Vector &eadata_ext,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -207,10 +246,20 @@ static void EADGTraceAssemble3DInt(const int NF,
                                    * s_D[k1][k2][1][0];
                     }
                  }
-                  A_int(i1, i2, j1, j2, 0, f) += val_int0;
-                  A_int(i1, i2, j1, j2, 1, f) += val_int1;
-                  A_ext(i1, i2, j1, j2, 0, f) += val_ext01;
-                  A_ext(i1, i2, j1, j2, 1, f) += val_ext10;
+                  if (add)
+                  {
+                     A_int(i1, i2, j1, j2, 0, f) += val_int0;
+                     A_int(i1, i2, j1, j2, 1, f) += val_int1;
+                     A_ext(i1, i2, j1, j2, 0, f) += val_ext01;
+                     A_ext(i1, i2, j1, j2, 1, f) += val_ext10;
+                  }
+                  else
+                  {
+                     A_int(i1, i2, j1, j2, 0, f) = val_int0;
+                     A_int(i1, i2, j1, j2, 1, f) = val_int1;
+                     A_ext(i1, i2, j1, j2, 0, f) = val_ext01;
+                     A_ext(i1, i2, j1, j2, 1, f) = val_ext10;
+                  }
               }
            }
         }
@@ -223,6 +272,7 @@ static void EADGTraceAssemble3DBdr(const int NF,
                                   const Array<double> &basis,
                                   const Vector &padata,
                                   Vector &eadata_bdr,
+                                   const bool add,
                                   const int d1d = 0,
                                   const int q1d = 0)
 {
@@ -280,7 +330,14 @@ static void EADGTraceAssemble3DBdr(const int NF,
                                   * s_D[k1][k2][0][0];
                     }
                  }
-                  A_bdr(i1, i2, j1, j2, f) += val_bdr;
+                  if (add)
+                  {
+                     A_bdr(i1, i2, j1, j2, f) += val_bdr;
+                  }
+                  else
+                  {
+                     A_bdr(i1, i2, j1, j2, f) = val_bdr;
+                  }
               }
            }
         }
@@ -290,7 +347,8 @@ static void EADGTraceAssemble3DBdr(const int NF,

 void DGTraceIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
                                                Vector &ea_data_int,
-                                                Vector &ea_data_ext)
+                                                Vector &ea_data_ext,
+                                                const bool add)
 {
   SetupPA(fes, FaceType::Interior);
   nf = fes.GetNFbyType(FaceType::Interior);
@@ -298,7 +356,7 @@ void DGTraceIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
   const Array<double> &B = maps->B;
   if (dim == 1)
   {
-      return EADGTraceAssemble1DInt(nf,B,pa_data,ea_data_int,ea_data_ext);
+      return EADGTraceAssemble1DInt(nf,B,pa_data,ea_data_int,ea_data_ext,add);
   }
   else if (dim == 2)
   {
@@ -306,31 +364,31 @@ void DGTraceIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
      {
         case 0x22:
            return EADGTraceAssemble2DInt<2,2>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x33:
            return EADGTraceAssemble2DInt<3,3>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x44:
            return EADGTraceAssemble2DInt<4,4>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x55:
            return EADGTraceAssemble2DInt<5,5>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x66:
            return EADGTraceAssemble2DInt<6,6>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x77:
            return EADGTraceAssemble2DInt<7,7>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x88:
            return EADGTraceAssemble2DInt<8,8>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x99:
            return EADGTraceAssemble2DInt<9,9>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         default:
            return EADGTraceAssemble2DInt(nf,B,pa_data,ea_data_int,
-                                          ea_data_ext,dofs1D,quad1D);
+                                          ea_data_ext,add,dofs1D,quad1D);
      }
   }
   else if (dim == 3)
@@ -339,35 +397,36 @@ void DGTraceIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
      {
         case 0x23:
            return EADGTraceAssemble3DInt<2,3>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x34:
            return EADGTraceAssemble3DInt<3,4>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x45:
            return EADGTraceAssemble3DInt<4,5>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x56:
            return EADGTraceAssemble3DInt<5,6>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x67:
            return EADGTraceAssemble3DInt<6,7>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x78:
            return EADGTraceAssemble3DInt<7,8>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         case 0x89:
            return EADGTraceAssemble3DInt<8,9>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
+                                               ea_data_ext,add);
         default:
            return EADGTraceAssemble3DInt(nf,B,pa_data,ea_data_int,
-                                          ea_data_ext,dofs1D,quad1D);
+                                          ea_data_ext,add,dofs1D,quad1D);
      }
   }
   MFEM_ABORT("Unknown kernel.");
 }

 void DGTraceIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                                Vector &ea_data_bdr)
+                                                Vector &ea_data_bdr,
+                                                const bool add)
 {
   SetupPA(fes, FaceType::Boundary);
   nf = fes.GetNFbyType(FaceType::Boundary);
@@ -375,37 +434,37 @@ void DGTraceIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
   const Array<double> &B = maps->B;
   if (dim == 1)
   {
-      return EADGTraceAssemble1DBdr(nf,B,pa_data,ea_data_bdr);
+      return EADGTraceAssemble1DBdr(nf,B,pa_data,ea_data_bdr,add);
   }
   else if (dim == 2)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EADGTraceAssemble2DBdr<2,2>(nf,B,pa_data,ea_data_bdr);
-         case 0x33: return EADGTraceAssemble2DBdr<3,3>(nf,B,pa_data,ea_data_bdr);
-         case 0x44: return EADGTraceAssemble2DBdr<4,4>(nf,B,pa_data,ea_data_bdr);
-         case 0x55: return EADGTraceAssemble2DBdr<5,5>(nf,B,pa_data,ea_data_bdr);
-         case 0x66: return EADGTraceAssemble2DBdr<6,6>(nf,B,pa_data,ea_data_bdr);
-         case 0x77: return EADGTraceAssemble2DBdr<7,7>(nf,B,pa_data,ea_data_bdr);
-         case 0x88: return EADGTraceAssemble2DBdr<8,8>(nf,B,pa_data,ea_data_bdr);
-         case 0x99: return EADGTraceAssemble2DBdr<9,9>(nf,B,pa_data,ea_data_bdr);
+         case 0x22: return EADGTraceAssemble2DBdr<2,2>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x33: return EADGTraceAssemble2DBdr<3,3>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x44: return EADGTraceAssemble2DBdr<4,4>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x55: return EADGTraceAssemble2DBdr<5,5>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x66: return EADGTraceAssemble2DBdr<6,6>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x77: return EADGTraceAssemble2DBdr<7,7>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x88: return EADGTraceAssemble2DBdr<8,8>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x99: return EADGTraceAssemble2DBdr<9,9>(nf,B,pa_data,ea_data_bdr,add);
         default:
-            return EADGTraceAssemble2DBdr(nf,B,pa_data,ea_data_bdr,dofs1D,quad1D);
+            return EADGTraceAssemble2DBdr(nf,B,pa_data,ea_data_bdr,add,dofs1D,quad1D);
      }
   }
   else if (dim == 3)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x23: return EADGTraceAssemble3DBdr<2,3>(nf,B,pa_data,ea_data_bdr);
-         case 0x34: return EADGTraceAssemble3DBdr<3,4>(nf,B,pa_data,ea_data_bdr);
-         case 0x45: return EADGTraceAssemble3DBdr<4,5>(nf,B,pa_data,ea_data_bdr);
-         case 0x56: return EADGTraceAssemble3DBdr<5,6>(nf,B,pa_data,ea_data_bdr);
-         case 0x67: return EADGTraceAssemble3DBdr<6,7>(nf,B,pa_data,ea_data_bdr);
-         case 0x78: return EADGTraceAssemble3DBdr<7,8>(nf,B,pa_data,ea_data_bdr);
-         case 0x89: return EADGTraceAssemble3DBdr<8,9>(nf,B,pa_data,ea_data_bdr);
+         case 0x23: return EADGTraceAssemble3DBdr<2,3>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x34: return EADGTraceAssemble3DBdr<3,4>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x45: return EADGTraceAssemble3DBdr<4,5>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x56: return EADGTraceAssemble3DBdr<5,6>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x67: return EADGTraceAssemble3DBdr<6,7>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x78: return EADGTraceAssemble3DBdr<7,8>(nf,B,pa_data,ea_data_bdr,add);
+         case 0x89: return EADGTraceAssemble3DBdr<8,9>(nf,B,pa_data,ea_data_bdr,add);
         default:
-            return EADGTraceAssemble3DBdr(nf,B,pa_data,ea_data_bdr,dofs1D,quad1D);
+            return EADGTraceAssemble3DBdr(nf,B,pa_data,ea_data_bdr,add,dofs1D,quad1D);
      }
   }
   MFEM_ABORT("Unknown kernel.");
@@ -43,7 +43,7 @@ static void PADGTraceSetup2D(const int Q1D,
   auto W = w.Read();
   auto qd = Reshape(op.Write(), Q1D, 2, 2, NF);

-   MFEM_FORALL(f, NF,//can be optimized with Q1D thread for NF blocks
+   MFEM_FORALL(f, NF, // can be optimized with Q1D thread for NF blocks
   {
      for (int q = 0; q < Q1D; ++q)
      {
@@ -85,7 +85,7 @@ static void PADGTraceSetup3D(const int Q1D,
   auto W = w.Read();
   auto qd = Reshape(op.Write(), Q1D, Q1D, 2, 2, NF);

-   MFEM_FORALL(f, NF,//can be optimized with Q1D*Q1D threads for NF blocks
+   MFEM_FORALL(f, NF, // can be optimized with Q1D*Q1D threads for NF blocks
   {
      for (int q1 = 0; q1 < Q1D; ++q1)
      {
@@ -156,57 +156,6 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
   pa_data.SetSize(symmDims * nq * nf, Device::GetMemoryType());
-   Vector r;
-   if (rho==nullptr)
-   {
-      r.SetSize(1);
-      r(0) = 1.0;
-   }
-   else if (ConstantCoefficient *c_rho = dynamic_cast<ConstantCoefficient*>(rho))
-   {
-      r.SetSize(1);
-      r(0) = c_rho->constant;
-   }
-   else if (QuadratureFunctionCoefficient* c_rho =
-               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
-   {
-      const QuadratureFunction &qFun = c_rho->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == nq * nf,
-                  "Incompatible QuadratureFunction dimension \n");
-
-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      r.SetSize(nq * nf);
-      auto C = Reshape(r.HostWrite(), nq, nf);
-      int f_ind = 0;
-      for (int f = 0; f < fes.GetNF(); ++f)
-      {
-         int e1, e2;
-         int inf1, inf2;
-         fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-         fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
-         int face_id = inf1 / 64;
-         if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
-             (type==FaceType::Boundary && e2<0 && inf2<0) )
-         {
-            ElementTransformation& T = *fes.GetMesh()->GetFaceTransformation(f);
-            for (int q = 0; q < nq; ++q)
-            {
-               // Convert to lexicographic ordering
-               int iq = ToLexOrdering(dim, face_id, quad1D, q);
-               C(iq,f_ind) = rho->Eval(T, ir->IntPoint(q));
-            }
-            f_ind++;
-         }
-      }
-      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
-   }
   Vector vel;
   if (VectorConstantCoefficient *c_u = dynamic_cast<VectorConstantCoefficient*>
                                        (u))
@@ -243,12 +192,15 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
         if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
             (type==FaceType::Boundary && e2<0 && inf2<0) )
         {
-            ElementTransformation& T = *fes.GetMesh()->GetFaceTransformation(f);
+            FaceElementTransformations &T =
+               *fes.GetMesh()->GetFaceElementTransformations(f);
            for (int q = 0; q < nq; ++q)
            {
               // Convert to lexicographic ordering
               int iq = ToLexOrdering(dim, face_id, quad1D, q);
-               u->Eval(Vq, T, ir->IntPoint(q));
+               T.SetAllIntPoints(&ir->IntPoint(q));
+               const IntegrationPoint &eip1 = T.GetElement1IntPoint();
+               u->Eval(Vq, *T.Elem1, eip1);
               for (int i = 0; i < dim; ++i)
               {
                  C(i,iq,f_ind) = Vq(i);
@@ -259,6 +211,80 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
      }
      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
   }
+   Vector r;
+   if (rho==nullptr)
+   {
+      r.SetSize(1);
+      r(0) = 1.0;
+   }
+   else if (ConstantCoefficient *c_rho = dynamic_cast<ConstantCoefficient*>(rho))
+   {
+      r.SetSize(1);
+      r(0) = c_rho->constant;
+   }
+   else if (QuadratureFunctionCoefficient* c_rho =
+               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
+   {
+      const QuadratureFunction &qFun = c_rho->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == nq * nf,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
+   else
+   {
+      r.SetSize(nq * nf);
+      auto C_vel = Reshape(vel.HostRead(), dim, nq, nf);
+      auto n = Reshape(geom->normal.HostRead(), nq, dim, nf);
+      auto C = Reshape(r.HostWrite(), nq, nf);
+      int f_ind = 0;
+      for (int f = 0; f < fes.GetNF(); ++f)
+      {
+         int e1, e2;
+         int inf1, inf2;
+         fes.GetMesh()->GetFaceElements(f, &e1, &e2);
+         fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+         int face_id = inf1 / 64;
+         if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
+             (type==FaceType::Boundary && e2<0 && inf2<0) )
+         {
+            FaceElementTransformations &T =
+               *fes.GetMesh()->GetFaceElementTransformations(f);
+            for (int q = 0; q < nq; ++q)
+            {
+               // Convert to lexicographic ordering
+               int iq = ToLexOrdering(dim, face_id, quad1D, q);
+
+               T.SetAllIntPoints(&ir->IntPoint(q));
+               const IntegrationPoint &eip1 = T.GetElement1IntPoint();
+               const IntegrationPoint &eip2 = T.GetElement2IntPoint();
+               double r;
+
+               if (inf2 < 0)
+               {
+                  r = rho->Eval(*T.Elem1, eip1);
+               }
+               else
+               {
+                  double udotn = 0.0;
+                  for (int d=0; d<dim; ++d)
+                  {
+                     udotn += C_vel(d,iq,f_ind)*n(iq,d,f_ind);
+                  }
+                  if (udotn >= 0.0) { r = rho->Eval(*T.Elem2, eip2); }
+                  else { r = rho->Eval(*T.Elem1, eip1); }
+               }
+               C(iq,f_ind) = r;
+            }
+            f_ind++;
+         }
+      }
+      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
+   }
   PADGTraceSetup(dim, dofs1D, quad1D, nf, ir->GetWeights(),
                  geom->detJ, geom->normal, r, vel,
                  alpha, beta, pa_data);
@@ -22,6 +22,7 @@ static void EADiffusionAssemble1D(const int NE,
                                  const Array<double> &g,
                                  const Vector &padata,
                                  Vector &eadata,
+                                  const bool add,
                                  const int d1d = 0,
                                  const int q1d = 0)
 {
@@ -53,7 +54,14 @@ static void EADiffusionAssemble1D(const int NE,
            {
               val += r_Gj[k1] * D(k1, e) * r_Gi[k1];
            }
-            A(i1, j1, e) += val;
+            if (add)
+            {
+               A(i1, j1, e) += val;
+            }
+            else
+            {
+               A(i1, j1, e) = val;
+            }
         }
      }
   });
@@ -65,6 +73,7 @@ static void EADiffusionAssemble2D(const int NE,
                                  const Array<double> &g,
                                  const Vector &padata,
                                  Vector &eadata,
+                                  const bool add,
                                  const int d1d = 0,
                                  const int q1d = 0)
 {
@@ -120,7 +129,14 @@ static void EADiffusionAssemble2D(const int NE,
                               + gbi * D11 * gbj;
                     }
                  }
-                  A(i1, i2, j1, j2, e) += val;
+                  if (add)
+                  {
+                     A(i1, i2, j1, j2, e) += val;
+                  }
+                  else
+                  {
+                     A(i1, i2, j1, j2, e) = val;
+                  }
               }
            }
         }
@@ -130,10 +146,11 @@ static void EADiffusionAssemble2D(const int NE,

 template<int T_D1D = 0, int T_Q1D = 0>
 static void EADiffusionAssemble3D(const int NE,
-                                  const Array<double> &g,
                                  const Array<double> &b,
+                                  const Array<double> &g,
                                  const Vector &padata,
                                  Vector &eadata,
+                                  const bool add,
                                  const int d1d = 0,
                                  const int q1d = 0)
 {
@@ -208,7 +225,14 @@ static void EADiffusionAssemble3D(const int NE,
                              }
                           }
                        }
-                        A(i1, i2, i3, j1, j2, j3, e) += val;
+                        if (add)
+                        {
+                           A(i1, i2, i3, j1, j2, j3, e) += val;
+                        }
+                        else
+                        {
+                           A(i1, i2, i3, j1, j2, j3, e) = val;
+                        }
                     }
                  }
               }
@@ -219,7 +243,8 @@ static void EADiffusionAssemble3D(const int NE,
 }

 void DiffusionIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                     Vector &ea_data)
+                                     Vector &ea_data,
+                                     const bool add)
 {
   AssemblePA(fes);
   const int ne = fes.GetMesh()->GetNE();
@@ -229,44 +254,47 @@ void DiffusionIntegrator::AssembleEA(const FiniteElementSpace &fes,
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EADiffusionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EADiffusionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EADiffusionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EADiffusionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EADiffusionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EADiffusionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EADiffusionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EADiffusionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EADiffusionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EADiffusionAssemble1D<2,2>(ne,B,G,pa_data,ea_data,add);
+         case 0x33: return EADiffusionAssemble1D<3,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x44: return EADiffusionAssemble1D<4,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x55: return EADiffusionAssemble1D<5,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x66: return EADiffusionAssemble1D<6,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x77: return EADiffusionAssemble1D<7,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x88: return EADiffusionAssemble1D<8,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x99: return EADiffusionAssemble1D<9,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EADiffusionAssemble1D(ne,B,G,pa_data,ea_data,add,
+                                                    dofs1D,quad1D);
      }
   }
   else if (dim == 2)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EADiffusionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EADiffusionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EADiffusionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EADiffusionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EADiffusionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EADiffusionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EADiffusionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EADiffusionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EADiffusionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EADiffusionAssemble2D<2,2>(ne,B,G,pa_data,ea_data,add);
+         case 0x33: return EADiffusionAssemble2D<3,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x44: return EADiffusionAssemble2D<4,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x55: return EADiffusionAssemble2D<5,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x66: return EADiffusionAssemble2D<6,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x77: return EADiffusionAssemble2D<7,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x88: return EADiffusionAssemble2D<8,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x99: return EADiffusionAssemble2D<9,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EADiffusionAssemble2D(ne,B,G,pa_data,ea_data,add,
+                                                    dofs1D,quad1D);
      }
   }
   else if (dim == 3)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x23: return EADiffusionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
-         case 0x34: return EADiffusionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
-         case 0x45: return EADiffusionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
-         case 0x56: return EADiffusionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
-         case 0x67: return EADiffusionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
-         case 0x78: return EADiffusionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
-         case 0x89: return EADiffusionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
-         default:   return EADiffusionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x23: return EADiffusionAssemble3D<2,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x34: return EADiffusionAssemble3D<3,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x45: return EADiffusionAssemble3D<4,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x56: return EADiffusionAssemble3D<5,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x67: return EADiffusionAssemble3D<6,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x78: return EADiffusionAssemble3D<7,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x89: return EADiffusionAssemble3D<8,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EADiffusionAssemble3D(ne,B,G,pa_data,ea_data,add,
+                                                    dofs1D,quad1D);
      }
   }
   MFEM_ABORT("Unknown kernel.");
@@ -96,26 +96,28 @@ void PADiffusionSetup2D<2>(const int Q1D,
                           const Vector &c,
                           Vector &d)
 {
-   const int NQ = Q1D*Q1D;
   const bool const_c = c.Size() == 1;
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 3, NE);
-
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,2,2,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D, 3, NE);
+   MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
   {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
      {
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double c_detJ = W[q] * coeff / ((J11*J22)-(J21*J12));
-         D(q,0,e) =  c_detJ * (J12*J12 + J22*J22); // 1,1
-         D(q,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
-         D(q,2,e) =  c_detJ * (J11*J11 + J21*J21); // 2,2
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            const double J11 = J(qx,qy,0,0,e);
+            const double J21 = J(qx,qy,1,0,e);
+            const double J12 = J(qx,qy,0,1,e);
+            const double J22 = J(qx,qy,1,1,e);
+            const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+            const double c_detJ = W(qx,qy) * coeff / ((J11*J22)-(J21*J12));
+            D(qx,qy,0,e) =  c_detJ * (J12*J12 + J22*J22); // 1,1
+            D(qx,qy,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
+            D(qx,qy,2,e) =  c_detJ * (J11*J11 + J21*J21); // 2,2
+         }
      }
   });
 }
@@ -131,33 +133,35 @@ void PADiffusionSetup2D<3>(const int Q1D,
 {
   constexpr int DIM = 2;
   constexpr int SDIM = 3;
-   const int NQ = Q1D*Q1D;
   const bool const_c = c.Size() == 1;
-
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, SDIM, DIM, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 3, NE);
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,SDIM,DIM,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D, 3, NE);
+   MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
   {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
      {
-         const double wq = W[q];
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J31 = J(q,2,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double J32 = J(q,2,1,e);
-         const double E = J11*J11 + J21*J21 + J31*J31;
-         const double G = J12*J12 + J22*J22 + J32*J32;
-         const double F = J11*J12 + J21*J22 + J31*J32;
-         const double iw = 1.0 / sqrt(E*G - F*F);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double alpha = wq * coeff * iw;
-         D(q,0,e) =  alpha * G; // 1,1
-         D(q,1,e) = -alpha * F; // 1,2
-         D(q,2,e) =  alpha * E; // 2,2
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            const double wq = W(qx,qy);
+            const double J11 = J(qx,qy,0,0,e);
+            const double J21 = J(qx,qy,1,0,e);
+            const double J31 = J(qx,qy,2,0,e);
+            const double J12 = J(qx,qy,0,1,e);
+            const double J22 = J(qx,qy,1,1,e);
+            const double J32 = J(qx,qy,2,1,e);
+            const double E = J11*J11 + J21*J21 + J31*J31;
+            const double G = J12*J12 + J22*J22 + J32*J32;
+            const double F = J11*J12 + J21*J22 + J31*J32;
+            const double iw = 1.0 / sqrt(E*G - F*F);
+            const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+            const double alpha = wq * coeff * iw;
+            D(qx,qy,0,e) =  alpha * G; // 1,1
+            D(qx,qy,1,e) = -alpha * F; // 1,2
+            D(qx,qy,2,e) =  alpha * E; // 2,2
+         }
      }
   });
 }
@@ -170,47 +174,53 @@ static void PADiffusionSetup3D(const int Q1D,
                               const Vector &c,
                               Vector &d)
 {
-   const int NQ = Q1D*Q1D*Q1D;
   const bool const_c = c.Size() == 1;
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 6, NE);
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,Q1D,3,3,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D,Q1D, 6, NE);
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
   {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
      {
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J31 = J(q,2,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double J32 = J(q,2,1,e);
-         const double J13 = J(q,0,2,e);
-         const double J23 = J(q,1,2,e);
-         const double J33 = J(q,2,2,e);
-         const double detJ = J11 * (J22 * J33 - J32 * J23) -
-         /* */               J21 * (J12 * J33 - J32 * J13) +
-         /* */               J31 * (J12 * J23 - J22 * J13);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double c_detJ = W[q] * coeff / detJ;
-         // adj(J)
-         const double A11 = (J22 * J33) - (J23 * J32);
-         const double A12 = (J32 * J13) - (J12 * J33);
-         const double A13 = (J12 * J23) - (J22 * J13);
-         const double A21 = (J31 * J23) - (J21 * J33);
-         const double A22 = (J11 * J33) - (J13 * J31);
-         const double A23 = (J21 * J13) - (J11 * J23);
-         const double A31 = (J21 * J32) - (J31 * J22);
-         const double A32 = (J31 * J12) - (J11 * J32);
-         const double A33 = (J11 * J22) - (J12 * J21);
-         // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
-         D(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
-         D(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
-         D(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
-         D(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
-         D(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
-         D(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qz,z,Q1D)
+            {
+               const double J11 = J(qx,qy,qz,0,0,e);
+               const double J21 = J(qx,qy,qz,1,0,e);
+               const double J31 = J(qx,qy,qz,2,0,e);
+               const double J12 = J(qx,qy,qz,0,1,e);
+               const double J22 = J(qx,qy,qz,1,1,e);
+               const double J32 = J(qx,qy,qz,2,1,e);
+               const double J13 = J(qx,qy,qz,0,2,e);
+               const double J23 = J(qx,qy,qz,1,2,e);
+               const double J33 = J(qx,qy,qz,2,2,e);
+               const double detJ = J11 * (J22 * J33 - J32 * J23) -
+               /* */               J21 * (J12 * J33 - J32 * J13) +
+               /* */               J31 * (J12 * J23 - J22 * J13);
+               const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
+               const double c_detJ = W(qx,qy,qz) * coeff / detJ;
+               // adj(J)
+               const double A11 = (J22 * J33) - (J23 * J32);
+               const double A12 = (J32 * J13) - (J12 * J33);
+               const double A13 = (J12 * J23) - (J22 * J13);
+               const double A21 = (J31 * J23) - (J21 * J33);
+               const double A22 = (J11 * J33) - (J13 * J31);
+               const double A23 = (J21 * J13) - (J11 * J23);
+               const double A31 = (J21 * J32) - (J31 * J22);
+               const double A32 = (J31 * J12) - (J11 * J32);
+               const double A33 = (J11 * J22) - (J12 * J21);
+               // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
+               D(qx,qy,qz,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
+               D(qx,qy,qz,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
+               D(qx,qy,qz,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
+               D(qx,qy,qz,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
+               D(qx,qy,qz,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
+               D(qx,qy,qz,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+            }
+         }
      }
   });
 }
@@ -253,8 +263,7 @@ static void PADiffusionSetup(const int dim,
   }
 }

-void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
-                                  const bool force)
+void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes)
 {
   // Assuming the same element type
   fespace = &fes;
@@ -263,7 +272,7 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
   const FiniteElement &el = *fes.GetFE(0);
   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
 #ifdef MFEM_USE_CEED
-   if (DeviceCanUseCeed() && !force)
+   if (DeviceCanUseCeed())
   {
      if (ceedDataPtr) { delete ceedDataPtr; }
      CeedData* ptr = new CeedData();
@@ -271,8 +280,6 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
      InitCeedCoeff(Q, ptr);
      return CeedPADiffusionAssemble(fes, *ir, *ptr);
   }
-#else
-   MFEM_CONTRACT_VAR(force);
 #endif
   const int dims = el.GetDim();
   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
@@ -749,9 +756,17 @@ static void PADiffusionAssembleDiagonal(const int dim,

 void DiffusionIntegrator::AssembleDiagonalPA(Vector &diag)
 {
-   if (pa_data.Size()==0) { SetupPA(*fespace, true); }
-   PADiffusionAssembleDiagonal(dim, dofs1D, quad1D, ne,
-                               maps->B, maps->G, pa_data, diag);
+#ifdef MFEM_USE_CEED
+   if (DeviceCanUseCeed())
+   {
+      CeedAssembleDiagonalPA(ceedDataPtr, diag);
+   }
+   else
+#endif
+   {
+      PADiffusionAssembleDiagonal(dim, dofs1D, quad1D, ne,
+                                  maps->B, maps->G, pa_data, diag);
+   }
 }


@@ -1665,7 +1680,7 @@ static void PADiffusionApply(const int dim,
      MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
   }
 #endif // MFEM_USE_OCCA
-   const int ID = (D1D << 4 ) | Q1D;
+   const int ID = (D1D << 4) | Q1D;

   if (dim == 2)
   {
@@ -1708,29 +1723,7 @@ void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
 #ifdef MFEM_USE_CEED
   if (DeviceCanUseCeed())
   {
-      const CeedScalar *x_ptr;
-      CeedScalar *y_ptr;
-      CeedMemType mem;
-      CeedGetPreferredMemType(internal::ceed, &mem);
-      if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
-      {
-         x_ptr = x.Read();
-         y_ptr = y.ReadWrite();
-      }
-      else
-      {
-         x_ptr = x.HostRead();
-         y_ptr = y.HostReadWrite();
-         mem = CEED_MEM_HOST;
-      }
-      CeedVectorSetArray(ceedDataPtr->u, mem, CEED_USE_POINTER,
-                         const_cast<CeedScalar*>(x_ptr));
-      CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, y_ptr);
-
-      CeedOperatorApplyAdd(ceedDataPtr->oper, ceedDataPtr->u, ceedDataPtr->v,
-                           CEED_REQUEST_IMMEDIATE);
-
-      CeedVectorSyncArray(ceedDataPtr->v, mem);
+      CeedAddMultPA(ceedDataPtr, x, y);
   }
   else
 #endif
@@ -21,6 +21,7 @@ static void EAMassAssemble1D(const int NE,
                             const Array<double> &basis,
                             const Vector &padata,
                             Vector &eadata,
+                             const bool add,
                             const int d1d = 0,
                             const int q1d = 0)
 {
@@ -52,7 +53,14 @@ static void EAMassAssemble1D(const int NE,
            {
               val += r_Bi[k1] * r_Bj[k1] * D(k1, e);
            }
-            M(i1, j1, e) += val;
+            if (add)
+            {
+               M(i1, j1, e) += val;
+            }
+            else
+            {
+               M(i1, j1, e) = val;
+            }
         }
      }
   });
@@ -63,6 +71,7 @@ static void EAMassAssemble2D(const int NE,
                             const Array<double> &basis,
                             const Vector &padata,
                             Vector &eadata,
+                             const bool add,
                             const int d1d = 0,
                             const int q1d = 0)
 {
@@ -114,7 +123,14 @@ static void EAMassAssemble2D(const int NE,
                               * s_D[k1][k2];
                     }
                  }
-                  M(i1, i2, j1, j2, e) += val;
+                  if (add)
+                  {
+                     M(i1, i2, j1, j2, e) += val;
+                  }
+                  else
+                  {
+                     M(i1, i2, j1, j2, e) = val;
+                  }
               }
            }
         }
@@ -127,6 +143,7 @@ static void EAMassAssemble3D(const int NE,
                             const Array<double> &basis,
                             const Vector &padata,
                             Vector &eadata,
+                             const bool add,
                             const int d1d = 0,
                             const int q1d = 0)
 {
@@ -189,7 +206,14 @@ static void EAMassAssemble3D(const int NE,
                              }
                           }
                        }
-                        M(i1, i2, i3, j1, j2, j3, e) += val;
+                        if (add)
+                        {
+                           M(i1, i2, i3, j1, j2, j3, e) += val;
+                        }
+                        else
+                        {
+                           M(i1, i2, i3, j1, j2, j3, e) = val;
+                        }
                     }
                  }
               }
@@ -200,7 +224,8 @@ static void EAMassAssemble3D(const int NE,
 }

 void MassIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                Vector &ea_data)
+                                Vector &ea_data,
+                                const bool add)
 {
   AssemblePA(fes);
   const int ne = fes.GetMesh()->GetNE();
@@ -209,44 +234,47 @@ void MassIntegrator::AssembleEA(const FiniteElementSpace &fes,
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EAMassAssemble1D<2,2>(ne,B,pa_data,ea_data);
-         case 0x33: return EAMassAssemble1D<3,3>(ne,B,pa_data,ea_data);
-         case 0x44: return EAMassAssemble1D<4,4>(ne,B,pa_data,ea_data);
-         case 0x55: return EAMassAssemble1D<5,5>(ne,B,pa_data,ea_data);
-         case 0x66: return EAMassAssemble1D<6,6>(ne,B,pa_data,ea_data);
-         case 0x77: return EAMassAssemble1D<7,7>(ne,B,pa_data,ea_data);
-         case 0x88: return EAMassAssemble1D<8,8>(ne,B,pa_data,ea_data);
-         case 0x99: return EAMassAssemble1D<9,9>(ne,B,pa_data,ea_data);
-         default:   return EAMassAssemble1D(ne,B,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EAMassAssemble1D<2,2>(ne,B,pa_data,ea_data,add);
+         case 0x33: return EAMassAssemble1D<3,3>(ne,B,pa_data,ea_data,add);
+         case 0x44: return EAMassAssemble1D<4,4>(ne,B,pa_data,ea_data,add);
+         case 0x55: return EAMassAssemble1D<5,5>(ne,B,pa_data,ea_data,add);
+         case 0x66: return EAMassAssemble1D<6,6>(ne,B,pa_data,ea_data,add);
+         case 0x77: return EAMassAssemble1D<7,7>(ne,B,pa_data,ea_data,add);
+         case 0x88: return EAMassAssemble1D<8,8>(ne,B,pa_data,ea_data,add);
+         case 0x99: return EAMassAssemble1D<9,9>(ne,B,pa_data,ea_data,add);
+         default:   return EAMassAssemble1D(ne,B,pa_data,ea_data,add,
+                                               dofs1D,quad1D);
      }
   }
   else if (dim == 2)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x22: return EAMassAssemble2D<2,2>(ne,B,pa_data,ea_data);
-         case 0x33: return EAMassAssemble2D<3,3>(ne,B,pa_data,ea_data);
-         case 0x44: return EAMassAssemble2D<4,4>(ne,B,pa_data,ea_data);
-         case 0x55: return EAMassAssemble2D<5,5>(ne,B,pa_data,ea_data);
-         case 0x66: return EAMassAssemble2D<6,6>(ne,B,pa_data,ea_data);
-         case 0x77: return EAMassAssemble2D<7,7>(ne,B,pa_data,ea_data);
-         case 0x88: return EAMassAssemble2D<8,8>(ne,B,pa_data,ea_data);
-         case 0x99: return EAMassAssemble2D<9,9>(ne,B,pa_data,ea_data);
-         default:   return EAMassAssemble2D(ne,B,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EAMassAssemble2D<2,2>(ne,B,pa_data,ea_data,add);
+         case 0x33: return EAMassAssemble2D<3,3>(ne,B,pa_data,ea_data,add);
+         case 0x44: return EAMassAssemble2D<4,4>(ne,B,pa_data,ea_data,add);
+         case 0x55: return EAMassAssemble2D<5,5>(ne,B,pa_data,ea_data,add);
+         case 0x66: return EAMassAssemble2D<6,6>(ne,B,pa_data,ea_data,add);
+         case 0x77: return EAMassAssemble2D<7,7>(ne,B,pa_data,ea_data,add);
+         case 0x88: return EAMassAssemble2D<8,8>(ne,B,pa_data,ea_data,add);
+         case 0x99: return EAMassAssemble2D<9,9>(ne,B,pa_data,ea_data,add);
+         default:   return EAMassAssemble2D(ne,B,pa_data,ea_data,add,
+                                               dofs1D,quad1D);
      }
   }
   else if (dim == 3)
   {
      switch ((dofs1D << 4 ) | quad1D)
      {
-         case 0x23: return EAMassAssemble3D<2,3>(ne,B,pa_data,ea_data);
-         case 0x34: return EAMassAssemble3D<3,4>(ne,B,pa_data,ea_data);
-         case 0x45: return EAMassAssemble3D<4,5>(ne,B,pa_data,ea_data);
-         case 0x56: return EAMassAssemble3D<5,6>(ne,B,pa_data,ea_data);
-         case 0x67: return EAMassAssemble3D<6,7>(ne,B,pa_data,ea_data);
-         case 0x78: return EAMassAssemble3D<7,8>(ne,B,pa_data,ea_data);
-         case 0x89: return EAMassAssemble3D<8,9>(ne,B,pa_data,ea_data);
-         default:   return EAMassAssemble3D(ne,B,pa_data,ea_data,dofs1D,quad1D);
+         case 0x23: return EAMassAssemble3D<2,3>(ne,B,pa_data,ea_data,add);
+         case 0x34: return EAMassAssemble3D<3,4>(ne,B,pa_data,ea_data,add);
+         case 0x45: return EAMassAssemble3D<4,5>(ne,B,pa_data,ea_data,add);
+         case 0x56: return EAMassAssemble3D<5,6>(ne,B,pa_data,ea_data,add);
+         case 0x67: return EAMassAssemble3D<6,7>(ne,B,pa_data,ea_data,add);
+         case 0x78: return EAMassAssemble3D<7,8>(ne,B,pa_data,ea_data,add);
+         case 0x89: return EAMassAssemble3D<8,9>(ne,B,pa_data,ea_data,add);
+         default:   return EAMassAssemble3D(ne,B,pa_data,ea_data,add,
+                                               dofs1D,quad1D);
      }
   }
   MFEM_ABORT("Unknown kernel.");
@@ -23,7 +23,7 @@ namespace mfem

 // PA Mass Assemble kernel

-void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
+void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
 {
   // Assuming the same element type
   fespace = &fes;
@@ -33,7 +33,7 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
   ElementTransformation *T = mesh->GetElementTransformation(0);
   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, *T);
 #ifdef MFEM_USE_CEED
-   if (DeviceCanUseCeed() && !force)
+   if (DeviceCanUseCeed())
   {
      if (ceedDataPtr) { delete ceedDataPtr; }
      CeedData* ptr = new CeedData();
@@ -41,8 +41,6 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
      InitCeedCoeff(Q, ptr);
      return CeedPAMassAssemble(fes, *ir, *ptr);
   }
-#else
-   MFEM_CONTRACT_VAR(force);
 #endif
   dim = mesh->Dimension();
   ne = fes.GetMesh()->GetNE();
@@ -94,49 +92,64 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
   if (dim==2)
   {
      const int NE = ne;
-      const int NQ = nq;
+      const int Q1D = quad1D;
      const bool const_c = coeff.Size() == 1;
-      auto w = ir->GetWeights().Read();
-      auto J = Reshape(geom->J.Read(), NQ,2,2,NE);
-      auto C =
-         const_c ? Reshape(coeff.Read(), 1,1) : Reshape(coeff.Read(), NQ,NE);
-      auto v = Reshape(pa_data.Write(), NQ, NE);
-      MFEM_FORALL(e, NE,
+      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,2,2,NE);
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1) :
+                     Reshape(coeff.Read(), Q1D,Q1D,NE);
+      auto v = Reshape(pa_data.Write(), Q1D,Q1D, NE);
+      MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
      {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
         {
-            const double J11 = J(q,0,0,e);
-            const double J12 = J(q,1,0,e);
-            const double J21 = J(q,0,1,e);
-            const double J22 = J(q,1,1,e);
-            const double detJ = (J11*J22)-(J21*J12);
-            const double coeff = const_c ? C(0,0) : C(q,e);
-            v(q,e) =  w[q] * coeff * detJ;
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               const double J11 = J(qx,qy,0,0,e);
+               const double J12 = J(qx,qy,1,0,e);
+               const double J21 = J(qx,qy,0,1,e);
+               const double J22 = J(qx,qy,1,1,e);
+               const double detJ = (J11*J22)-(J21*J12);
+               const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+               v(qx,qy,e) =  W(qx,qy) * coeff * detJ;
+            }
         }
      });
   }
   if (dim==3)
   {
      const int NE = ne;
-      const int NQ = nq;
+      const int Q1D = quad1D;
      const bool const_c = coeff.Size() == 1;
-      auto W = ir->GetWeights().Read();
-      auto J = Reshape(geom->J.Read(), NQ,3,3,NE);
-      auto C =
-         const_c ? Reshape(coeff.Read(), 1,1) : Reshape(coeff.Read(), NQ,NE);
-      auto v = Reshape(pa_data.Write(), NQ,NE);
-      MFEM_FORALL(e, NE,
+      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D,Q1D);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,Q1D,3,3,NE);
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1,1) :
+                     Reshape(coeff.Read(), Q1D,Q1D,Q1D,NE);
+      auto v = Reshape(pa_data.Write(), Q1D,Q1D,Q1D,NE);
+      MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
      {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
         {
-            const double J11 = J(q,0,0,e), J12 = J(q,0,1,e), J13 = J(q,0,2,e);
-            const double J21 = J(q,1,0,e), J22 = J(q,1,1,e), J23 = J(q,1,2,e);
-            const double J31 = J(q,2,0,e), J32 = J(q,2,1,e), J33 = J(q,2,2,e);
-            const double detJ = J11 * (J22 * J33 - J32 * J23) -
-            /* */               J21 * (J12 * J33 - J32 * J13) +
-            /* */               J31 * (J12 * J23 - J22 * J13);
-            const double coeff = const_c ? C(0,0) : C(q,e);
-            v(q,e) = W[q] * coeff * detJ;
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qz,z,Q1D)
+               {
+                  const double J11 = J(qx,qy,qz,0,0,e);
+                  const double J21 = J(qx,qy,qz,1,0,e);
+                  const double J31 = J(qx,qy,qz,2,0,e);
+                  const double J12 = J(qx,qy,qz,0,1,e);
+                  const double J22 = J(qx,qy,qz,1,1,e);
+                  const double J32 = J(qx,qy,qz,2,1,e);
+                  const double J13 = J(qx,qy,qz,0,2,e);
+                  const double J23 = J(qx,qy,qz,1,2,e);
+                  const double J33 = J(qx,qy,qz,2,2,e);
+                  const double detJ = J11 * (J22 * J33 - J32 * J23) -
+                  /* */               J21 * (J12 * J33 - J32 * J13) +
+                  /* */               J31 * (J12 * J23 - J22 * J13);
+                  const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
+                  v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * detJ;
+               }
+            }
         }
      });
   }
@@ -455,8 +468,16 @@ static void PAMassAssembleDiagonal(const int dim, const int D1D,

 void MassIntegrator::AssembleDiagonalPA(Vector &diag)
 {
-   if (pa_data.Size()==0) { SetupPA(*fespace, true); }
-   PAMassAssembleDiagonal(dim, dofs1D, quad1D, ne, maps->B, pa_data, diag);
+#ifdef MFEM_USE_CEED
+   if (DeviceCanUseCeed())
+   {
+      CeedAssembleDiagonalPA(ceedDataPtr, diag);
+   }
+   else
+#endif
+   {
+      PAMassAssembleDiagonal(dim, dofs1D, quad1D, ne, maps->B, pa_data, diag);
+   }
 }


@@ -1209,29 +1230,7 @@ void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 #ifdef MFEM_USE_CEED
   if (DeviceCanUseCeed())
   {
-      const CeedScalar *x_ptr;
-      CeedScalar *y_ptr;
-      CeedMemType mem;
-      CeedGetPreferredMemType(internal::ceed, &mem);
-      if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
-      {
-         x_ptr = x.Read();
-         y_ptr = y.ReadWrite();
-      }
-      else
-      {
-         x_ptr = x.HostRead();
-         y_ptr = y.HostReadWrite();
-         mem = CEED_MEM_HOST;
-      }
-      CeedVectorSetArray(ceedDataPtr->u, mem, CEED_USE_POINTER,
-                         const_cast<CeedScalar*>(x_ptr));
-      CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, y_ptr);
-
-      CeedOperatorApplyAdd(ceedDataPtr->oper, ceedDataPtr->u, ceedDataPtr->v,
-                           CEED_REQUEST_IMMEDIATE);
-
-      CeedVectorSyncArray(ceedDataPtr->v, mem);
+      CeedAddMultPA(ceedDataPtr, x, y);
   }
   else
 #endif
@@ -16,88 +16,171 @@ namespace mfem
 {

 void TransposeIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                     Vector &ea_data)
+                                     Vector &ea_data, const bool add)
 {
-   Vector ea_data_tmp(ea_data.Size());
-   ea_data_tmp = 0.0;
-   bfi->AssembleEA(fes, ea_data_tmp);
-   const int ne = fes.GetNE();
-   if (ne == 0) { return; }
-   const int dofs = fes.GetFE(0)->GetDof();
-   auto A = Reshape(ea_data_tmp.Write(), dofs, dofs, ne);
-   auto AT = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
-   MFEM_FORALL(e, ne,
+   if (add)
   {
-      for (int i = 0; i < dofs; i++)
+      Vector ea_data_tmp(ea_data.Size());
+      bfi->AssembleEA(fes, ea_data_tmp, false);
+      const int ne = fes.GetNE();
+      if (ne == 0) { return; }
+      const int dofs = fes.GetFE(0)->GetDof();
+      auto A = Reshape(ea_data_tmp.Read(), dofs, dofs, ne);
+      auto AT = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
+      MFEM_FORALL(e, ne,
      {
-         for (int j = 0; j < dofs; j++)
+         for (int i = 0; i < dofs; i++)
         {
-            const double a = A(i, j, e);
-            AT(j, i, e) += a;
+            for (int j = 0; j < dofs; j++)
+            {
+               const double a = A(i, j, e);
+               AT(j, i, e) += a;
+            }
         }
-      }
-   });
+      });
+   }
+   else
+   {
+      bfi->AssembleEA(fes, ea_data, false);
+      const int ne = fes.GetNE();
+      if (ne == 0) { return; }
+      const int dofs = fes.GetFE(0)->GetDof();
+      auto A = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
+      MFEM_FORALL(e, ne,
+      {
+         for (int i = 0; i < dofs; i++)
+         {
+            for (int j = i+1; j < dofs; j++)
+            {
+               const double aij = A(i, j, e);
+               const double aji = A(j, i, e);
+               A(j, i, e) = aij;
+               A(i, j, e) = aji;
+            }
+         }
+      });
+   }
 }

 void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
                                                  Vector &ea_data_int,
-                                                  Vector &ea_data_ext)
+                                                  Vector &ea_data_ext,
+                                                  const bool add)
 {
   const int nf = fes.GetNFbyType(FaceType::Interior);
   if (nf == 0) { return; }
-   Vector ea_data_int_tmp(ea_data_int.Size());
-   Vector ea_data_ext_tmp(ea_data_ext.Size());
-   ea_data_int_tmp = 0.0;
-   ea_data_ext_tmp = 0.0;
-   bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp);
-   const int faceDofs = fes.GetTraceElement(0,
-                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
-   auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
-   auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
-   auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
-   auto AT_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
-   MFEM_FORALL(f, nf,
+   if (add)
   {
-      for (int i = 0; i < faceDofs; i++)
+      Vector ea_data_int_tmp(ea_data_int.Size());
+      Vector ea_data_ext_tmp(ea_data_ext.Size());
+      bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
+      auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
+      auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      auto AT_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      MFEM_FORALL(f, nf,
      {
-         for (int j = 0; j < faceDofs; j++)
+         for (int i = 0; i < faceDofs; i++)
         {
-            const double a_int0 = A_int(i, j, 0, f);
-            const double a_int1 = A_int(i, j, 1, f);
-            const double a_ext0 = A_ext(i, j, 0, f);
-            const double a_ext1 = A_ext(i, j, 1, f);
-            AT_int(j, i, 0, f) += a_int0;
-            AT_int(j, i, 1, f) += a_int1;
-            AT_ext(j, i, 0, f) += a_ext1;
-            AT_ext(j, i, 1, f) += a_ext0;
+            for (int j = 0; j < faceDofs; j++)
+            {
+               const double a_int0 = A_int(i, j, 0, f);
+               const double a_int1 = A_int(i, j, 1, f);
+               const double a_ext0 = A_ext(i, j, 0, f);
+               const double a_ext1 = A_ext(i, j, 1, f);
+               AT_int(j, i, 0, f) += a_int0;
+               AT_int(j, i, 1, f) += a_int1;
+               AT_ext(j, i, 0, f) += a_ext1;
+               AT_ext(j, i, 1, f) += a_ext0;
+            }
         }
-      }
-   });
+      });
+   }
+   else
+   {
+      bfi->AssembleEAInteriorFaces(fes, ea_data_int, ea_data_ext, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      auto A_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      MFEM_FORALL(f, nf,
+      {
+         for (int i = 0; i < faceDofs; i++)
+         {
+            for (int j = i+1; j < faceDofs; j++)
+            {
+               const double aij_int0 = A_int(i, j, 0, f);
+               const double aij_int1 = A_int(i, j, 1, f);
+               const double aji_int0 = A_int(j, i, 0, f);
+               const double aji_int1 = A_int(j, i, 1, f);
+               A_int(j, i, 0, f) = aij_int0;
+               A_int(j, i, 1, f) = aij_int1;
+               A_int(i, j, 0, f) = aji_int0;
+               A_int(i, j, 1, f) = aji_int1;
+            }
+         }
+         for (int i = 0; i < faceDofs; i++)
+         {
+            for (int j = 0; j < faceDofs; j++)
+            {
+               const double aij_ext0 = A_ext(i, j, 0, f);
+               const double aji_ext1 = A_ext(j, i, 1, f);
+               A_ext(j, i, 1, f) = aij_ext0;
+               A_ext(i, j, 0, f) = aji_ext1;
+            }
+         }
+      });
+   }
 }

 void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                                  Vector &ea_data_bdr)
+                                                  Vector &ea_data_bdr,
+                                                  const bool add)
 {
   const int nf = fes.GetNFbyType(FaceType::Boundary);
   if (nf == 0) { return; }
-   Vector ea_data_bdr_tmp(ea_data_bdr.Size());
-   ea_data_bdr_tmp = 0.0;
-   bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp);
-   const int faceDofs = fes.GetTraceElement(0,
-                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
-   auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
-   auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
-   MFEM_FORALL(f, nf,
+   if (add)
   {
-      for (int i = 0; i < faceDofs; i++)
+      Vector ea_data_bdr_tmp(ea_data_bdr.Size());
+      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
+      auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
+      MFEM_FORALL(f, nf,
      {
-         for (int j = 0; j < faceDofs; j++)
+         for (int i = 0; i < faceDofs; i++)
         {
-            const double a_bdr = A_bdr(i, j, f);
-            AT_bdr(j, i, f) += a_bdr;
+            for (int j = 0; j < faceDofs; j++)
+            {
+               const double a_bdr = A_bdr(i, j, f);
+               AT_bdr(j, i, f) += a_bdr;
+            }
         }
-      }
-   });
+      });
+   }
+   else
+   {
+      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
+      MFEM_FORALL(f, nf,
+      {
+         for (int i = 0; i < faceDofs; i++)
+         {
+            for (int j = i+1; j < faceDofs; j++)
+            {
+               const double aij_bdr = A_bdr(i, j, f);
+               const double aji_bdr = A_bdr(j, i, f);
+               A_bdr(j, i, f) = aij_bdr;
+               A_bdr(i, j, f) = aji_bdr;
+            }
+         }
+      });
+   }
 }

 }
@@ -20,7 +20,7 @@ void PAHcurlSetup2D(const int Q1D,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
-                    Vector &_coeff,
+                    Vector &coeff,
                    Vector &op);

 void PAHcurlSetup3D(const int Q1D,
@@ -28,50 +28,73 @@ void PAHcurlSetup3D(const int Q1D,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
-                    Vector &_coeff,
+                    Vector &coeff,
                    Vector &op);

 void PAHcurlMassAssembleDiagonal2D(const int D1D,
                                   const int Q1D,
                                   const int NE,
                                   const bool symmetric,
-                                   const Array<double> &_Bo,
-                                   const Array<double> &_Bc,
-                                   const Vector &_op,
-                                   Vector &_diag);
+                                   const Array<double> &bo,
+                                   const Array<double> &bc,
+                                   const Vector &pa_data,
+                                   Vector &diag);

 void PAHcurlMassAssembleDiagonal3D(const int D1D,
                                   const int Q1D,
                                   const int NE,
                                   const bool symmetric,
-                                   const Array<double> &_Bo,
-                                   const Array<double> &_Bc,
-                                   const Vector &_op,
-                                   Vector &_diag);
+                                   const Array<double> &bo,
+                                   const Array<double> &bc,
+                                   const Vector &pa_data,
+                                   Vector &diag);
+
+template<int T_D1D = 0, int T_Q1D = 0>
+void SmemPAHcurlMassAssembleDiagonal3D(const int D1D,
+                                       const int Q1D,
+                                       const int NE,
+                                       const bool symmetric,
+                                       const Array<double> &bo,
+                                       const Array<double> &bc,
+                                       const Vector &pa_data,
+                                       Vector &diag);

 void PAHcurlMassApply2D(const int D1D,
                        const int Q1D,
                        const int NE,
                        const bool symmetric,
-                        const Array<double> &_Bo,
-                        const Array<double> &_Bc,
-                        const Array<double> &_Bot,
-                        const Array<double> &_Bct,
-                        const Vector &_op,
-                        const Vector &_x,
-                        Vector &_y);
+                        const Array<double> &bo,
+                        const Array<double> &bc,
+                        const Array<double> &bot,
+                        const Array<double> &bct,
+                        const Vector &pa_data,
+                        const Vector &x,
+                        Vector &y);

 void PAHcurlMassApply3D(const int D1D,
                        const int Q1D,
                        const int NE,
                        const bool symmetric,
-                        const Array<double> &_Bo,
-                        const Array<double> &_Bc,
-                        const Array<double> &_Bot,
-                        const Array<double> &_Bct,
-                        const Vector &_op,
-                        const Vector &_x,
-                        Vector &_y);
+                        const Array<double> &bo,
+                        const Array<double> &bc,
+                        const Array<double> &bot,
+                        const Array<double> &bct,
+                        const Vector &pa_data,
+                        const Vector &x,
+                        Vector &y);
+
+template<int T_D1D = 0, int T_Q1D = 0>
+void SmemPAHcurlMassApply3D(const int D1D,
+                            const int Q1D,
+                            const int NE,
+                            const bool symmetric,
+                            const Array<double> &bo,
+                            const Array<double> &bc,
+                            const Array<double> &bot,
+                            const Array<double> &bct,
+                            const Vector &pa_data,
+                            const Vector &x,
+                            Vector &y);

 void PAHdivSetup2D(const int Q1D,
                   const int NE,
@@ -90,24 +113,24 @@ void PAHdivSetup3D(const int Q1D,
 void PAHcurlH1Apply2D(const int D1D,
                      const int Q1D,
                      const int NE,
-                      const Array<double> &_Bc,
-                      const Array<double> &_Gc,
-                      const Array<double> &_Bot,
-                      const Array<double> &_Bct,
-                      const Vector &_op,
-                      const Vector &_x,
-                      Vector &_y);
+                      const Array<double> &bc,
+                      const Array<double> &gc,
+                      const Array<double> &bot,
+                      const Array<double> &bct,
+                      const Vector &pa_data,
+                      const Vector &x,
+                      Vector &y);

 void PAHcurlH1Apply3D(const int D1D,
                      const int Q1D,
                      const int NE,
-                      const Array<double> &_Bc,
-                      const Array<double> &_Gc,
-                      const Array<double> &_Bot,
-                      const Array<double> &_Bct,
-                      const Vector &_op,
-                      const Vector &_x,
-                      Vector &_y);
+                      const Array<double> &bc,
+                      const Array<double> &gc,
+                      const Array<double> &bot,
+                      const Array<double> &bct,
+                      const Vector &pa_data,
+                      const Vector &x,
+                      Vector &y);

 void PAHdivMassAssembleDiagonal2D(const int D1D,
                                  const int Q1D,
@@ -746,10 +769,12 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,

   symmetric = MQ ? MQ->IsSymmetric() : true;

-   if ((trial_fetype == mfem::FiniteElement::CURL &&
-        test_fetype == mfem::FiniteElement::DIV) ||
-       (trial_fetype == mfem::FiniteElement::DIV &&
-        test_fetype == mfem::FiniteElement::CURL))
+   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
+   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
+   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
+   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);
+
+   if ((trial_curl && test_div) || (trial_div && test_curl))
      pa_data.SetSize((coeffDim == 1 ? 1 : dim*dim) * nq * ne,
                      Device::GetMemoryType());
   else
@@ -829,34 +854,27 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
      }
   }

-   if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype
-       && dim == 3)
+   if (trial_curl && test_curl && dim == 3)
   {
      PAHcurlSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
   }
-   else if (trial_fetype == mfem::FiniteElement::CURL
-            && test_fetype == trial_fetype && dim == 2)
+   else if (trial_curl && test_curl && dim == 2)
   {
      PAHcurlSetup2D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
   }
-   else if (trial_fetype == mfem::FiniteElement::DIV
-            && test_fetype == trial_fetype && dim == 3)
+   else if (trial_div && test_div && dim == 3)
   {
      PAHdivSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
                    coeff, pa_data);
   }
-   else if (trial_fetype == mfem::FiniteElement::DIV
-            && test_fetype == trial_fetype && dim == 2)
+   else if (trial_div && test_div && dim == 2)
   {
      PAHdivSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
                    coeff, pa_data);
   }
-   else if (((trial_fetype == mfem::FiniteElement::CURL &&
-              test_fetype == mfem::FiniteElement::DIV) ||
-             (trial_fetype == mfem::FiniteElement::DIV &&
-              test_fetype == mfem::FiniteElement::CURL)) &&
+   else if (((trial_curl && test_div) || (trial_div && test_curl)) &&
            test_fel->GetOrder() == trial_fel->GetOrder())
   {
      if (coeffDim == 1)
@@ -865,8 +883,7 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
      }
      else
      {
-         const bool tr = (trial_fetype == mfem::FiniteElement::DIV &&
-                          test_fetype == mfem::FiniteElement::CURL);
+         const bool tr = (trial_div && test_curl);
         if (dim == 3)
            PAHcurlHdivSetup3D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
                               geom->J, coeff, pa_data);
@@ -887,8 +904,30 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
   {
      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
      {
-         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne, symmetric,
-                                       mapsO->B, mapsC->B, pa_data, diag);
+         if (Device::Allows(Backend::DEVICE_MASK))
+         {
+            const int ID = (dofs1D << 4) | quad1D;
+            switch (ID)
+            {
+               case 0x23: return SmemPAHcurlMassAssembleDiagonal3D<2,3>(dofs1D, quad1D, ne,
+                                                                           symmetric,
+                                                                           mapsO->B, mapsC->B, pa_data, diag);
+               case 0x34: return SmemPAHcurlMassAssembleDiagonal3D<3,4>(dofs1D, quad1D, ne,
+                                                                           symmetric,
+                                                                           mapsO->B, mapsC->B, pa_data, diag);
+               case 0x45: return SmemPAHcurlMassAssembleDiagonal3D<4,5>(dofs1D, quad1D, ne,
+                                                                           symmetric,
+                                                                           mapsO->B, mapsC->B, pa_data, diag);
+               case 0x56: return SmemPAHcurlMassAssembleDiagonal3D<5,6>(dofs1D, quad1D, ne,
+                                                                           symmetric,
+                                                                           mapsO->B, mapsC->B, pa_data, diag);
+               default: return SmemPAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne, symmetric,
+                                                                    mapsO->B, mapsC->B, pa_data, diag);
+            }
+         }
+         else
+            PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne, symmetric,
+                                          mapsO->B, mapsC->B, pa_data, diag);
      }
      else if (trial_fetype == mfem::FiniteElement::DIV &&
               test_fetype == trial_fetype)
@@ -923,29 +962,58 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)

 void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 {
+   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
+   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
+   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
+   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);
+
   if (dim == 3)
   {
-      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
+      if (trial_curl && test_curl)
      {
-         PAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
-                            mapsO->Bt, mapsC->Bt, pa_data, x, y);
+         if (Device::Allows(Backend::DEVICE_MASK))
+         {
+            const int ID = (dofs1D << 4) | quad1D;
+            switch (ID)
+            {
+               case 0x23: return SmemPAHcurlMassApply3D<2,3>(dofs1D, quad1D, ne, symmetric,
+                                                                mapsO->B,
+                                                                mapsC->B, mapsO->Bt,
+                                                                mapsC->Bt, pa_data, x, y);
+               case 0x34: return SmemPAHcurlMassApply3D<3,4>(dofs1D, quad1D, ne, symmetric,
+                                                                mapsO->B,
+                                                                mapsC->B, mapsO->Bt,
+                                                                mapsC->Bt, pa_data, x, y);
+               case 0x45: return SmemPAHcurlMassApply3D<4,5>(dofs1D, quad1D, ne, symmetric,
+                                                                mapsO->B,
+                                                                mapsC->B, mapsO->Bt,
+                                                                mapsC->Bt, pa_data, x, y);
+               case 0x56: return SmemPAHcurlMassApply3D<5,6>(dofs1D, quad1D, ne, symmetric,
+                                                                mapsO->B,
+                                                                mapsC->B, mapsO->Bt,
+                                                                mapsC->Bt, pa_data, x, y);
+               default: return SmemPAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric, mapsO->B,
+                                                         mapsC->B,
+                                                         mapsO->Bt, mapsC->Bt, pa_data, x, y);
+            }
+         }
+         else
+            PAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B, mapsO->Bt,
+                               mapsC->Bt, pa_data, x, y);
      }
-      else if (trial_fetype == mfem::FiniteElement::DIV &&
-               test_fetype == trial_fetype)
+      else if (trial_div && test_div)
      {
         PAHdivMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
                           mapsC->Bt, pa_data, x, y);
      }
-      else if (trial_fetype == mfem::FiniteElement::CURL &&
-               test_fetype == mfem::FiniteElement::DIV)
+      else if (trial_curl && test_div)
      {
         const bool scalarCoeff = !(VQ || MQ);
         PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
                                true, mapsO->B, mapsC->B, mapsOtest->Bt,
                                mapsCtest->Bt, pa_data, x, y);
      }
-      else if (trial_fetype == mfem::FiniteElement::DIV &&
-               test_fetype == mfem::FiniteElement::CURL)
+      else if (trial_div && test_curl)
      {
         const bool scalarCoeff = !(VQ || MQ);
         PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
@@ -959,26 +1027,21 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
   }
   else
   {
-      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
+      if (trial_curl && test_curl)
      {
         PAHcurlMassApply2D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
                            mapsO->Bt, mapsC->Bt, pa_data, x, y);
      }
-      else if (trial_fetype == mfem::FiniteElement::DIV &&
-               test_fetype == trial_fetype)
+      else if (trial_div && test_div)
      {
         PAHdivMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
                           mapsC->Bt, pa_data, x, y);
      }
-      else if ((trial_fetype == mfem::FiniteElement::CURL &&
-                test_fetype == mfem::FiniteElement::DIV) ||
-               (trial_fetype == mfem::FiniteElement::DIV &&
-                test_fetype == mfem::FiniteElement::CURL))
+      else if ((trial_curl && test_div) || (trial_div && test_curl))
      {
         const bool scalarCoeff = !(VQ || MQ);
-         const bool trialHcurl = (trial_fetype == mfem::FiniteElement::CURL);
         PAHcurlHdivMassApply2D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
-                                trialHcurl, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                trial_curl, mapsO->B, mapsC->B, mapsOtest->Bt,
                                mapsCtest->Bt, pa_data, x, y);
      }
      else
@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.

 #include "complex_fem.hpp"
+#include "../general/forall.hpp"

 using namespace std;

@@ -19,16 +20,21 @@ namespace mfem
 ComplexGridFunction::ComplexGridFunction(FiniteElementSpace *fes)
   : Vector(2*(fes->GetVSize()))
 {
-   gfr = new GridFunction(fes, data);
-   gfi = new GridFunction(fes, &data[fes->GetVSize()]);
+   UseDevice(true);
+   this->Vector::operator=(0.0);
+
+   gfr = new GridFunction();
+   gfr->MakeRef(fes, *this, 0);
+
+   gfi = new GridFunction();
+   gfi->MakeRef(fes, *this, fes->GetVSize());
 }

 void
 ComplexGridFunction::Update()
 {
-   FiniteElementSpace * fes = gfr->FESpace();
-
-   int vsize = fes->GetVSize();
+   FiniteElementSpace *fes = gfr->FESpace();
+   const int vsize = fes->GetVSize();

   const Operator *T = fes->GetUpdateOperator();
   if (T)
@@ -40,30 +46,36 @@ ComplexGridFunction::Update()

      // Our data array now contains old data as well as being the wrong size so
      // reallocate it.
+      UseDevice(true);
      this->SetSize(2 * vsize);
+      this->Vector::operator=(0.0);

      // Create temporary vectors which point to the new data array
-      Vector gf_r(data, vsize);
-      Vector gf_i((data) ? &data[vsize] : data, vsize);
+      Vector gf_r; gf_r.MakeRef(*this, 0, vsize);
+      Vector gf_i; gf_i.MakeRef(*this, vsize, vsize);

      // Copy the updated GridFunctions into the new data array
      gf_r = *gfr;
      gf_i = *gfi;
+      gf_r.SyncAliasMemory(*this);
+      gf_i.SyncAliasMemory(*this);

      // Replace the individual data arrays with pointers into the new data
      // array
-      gfr->NewDataAndSize(data, vsize);
-      gfi->NewDataAndSize((data) ? &data[vsize] : data, vsize);
+      gfr->MakeRef(*this, 0, vsize);
+      gfi->MakeRef(*this, vsize, vsize);
   }
   else
   {
      // The existing data will not be transferred to the new GridFunctions so
-      // delete it a allocate a new array
+      // delete it and allocate a new array
+      UseDevice(true);
      this->SetSize(2 * vsize);
+      this->Vector::operator=(0.0);

      // Point the individual GridFunctions to the new data array
-      gfr->NewDataAndSize(data, vsize);
-      gfi->NewDataAndSize((data) ? &data[vsize] : data, vsize);
+      gfr->MakeRef(*this, 0, vsize);
+      gfi->MakeRef(*this, vsize, vsize);

      // These updates will only set the proper 'sequence' value within the
      // individual GridFunction objects because their sizes are already correct
@@ -76,16 +88,24 @@ void
 ComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff,
                                        Coefficient &imag_coeff)
 {
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
   gfr->ProjectCoefficient(real_coeff);
   gfi->ProjectCoefficient(imag_coeff);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
 }

 void
 ComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
                                        VectorCoefficient &imag_vcoeff)
 {
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
   gfr->ProjectCoefficient(real_vcoeff);
   gfi->ProjectCoefficient(imag_vcoeff);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
 }

 void
@@ -93,8 +113,12 @@ ComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
                                           Coefficient &imag_coeff,
                                           Array<int> &attr)
 {
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
   gfr->ProjectBdrCoefficient(real_coeff, attr);
   gfi->ProjectBdrCoefficient(imag_coeff, attr);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
 }

 void
@@ -102,8 +126,12 @@ ComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient &real_vcoeff,
                                                 VectorCoefficient &imag_vcoeff,
                                                 Array<int> &attr)
 {
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
   gfr->ProjectBdrCoefficientNormal(real_vcoeff, attr);
   gfi->ProjectBdrCoefficientNormal(imag_vcoeff, attr);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
 }

 void
@@ -113,18 +141,28 @@ ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
                                                  &imag_vcoeff,
                                                  Array<int> &attr)
 {
+   gfr->SyncMemory(*this);
+   gfi->SyncMemory(*this);
   gfr->ProjectBdrCoefficientTangent(real_vcoeff, attr);
   gfi->ProjectBdrCoefficientTangent(imag_vcoeff, attr);
+   gfr->SyncAliasMemory(*this);
+   gfi->SyncAliasMemory(*this);
 }


-ComplexLinearForm::ComplexLinearForm(FiniteElementSpace *f,
+ComplexLinearForm::ComplexLinearForm(FiniteElementSpace *fes,
                                     ComplexOperator::Convention convention)
-   : Vector(2*(f->GetVSize())),
+   : Vector(2*(fes->GetVSize())),
     conv(convention)
 {
-   lfr = new LinearForm(f, data);
-   lfi = new LinearForm(f, &data[f->GetVSize()]);
+   UseDevice(true);
+   this->Vector::operator=(0.0);
+
+   lfr = new LinearForm();
+   lfr->MakeRef(fes, *this, 0);
+
+   lfi = new LinearForm();
+   lfi->MakeRef(fes, *this, fes->GetVSize());
 }

 ComplexLinearForm::ComplexLinearForm(FiniteElementSpace *fes,
@@ -133,8 +171,14 @@ ComplexLinearForm::ComplexLinearForm(FiniteElementSpace *fes,
   : Vector(2*(fes->GetVSize())),
     conv(convention)
 {
-   lfr = new LinearForm(fes, lf_r);  lfr->SetData(data);
-   lfi = new LinearForm(fes, lf_i);  lfi->SetData(&data[fes->GetVSize()]);
+   UseDevice(true);
+   this->Vector::operator=(0.0);
+
+   lfr = new LinearForm(fes, lf_r);
+   lfi = new LinearForm(fes, lf_i);
+
+   lfr->MakeRef(fes, *this, 0);
+   lfi->MakeRef(fes, *this, fes->GetVSize());
 }

 ComplexLinearForm::~ComplexLinearForm()
@@ -189,42 +233,43 @@ void
 ComplexLinearForm::Update()
 {
   FiniteElementSpace *fes = lfr->FESpace();
-
   this->Update(fes);
 }

 void
 ComplexLinearForm::Update(FiniteElementSpace *fes)
 {
-   int vsize = fes->GetVSize();
-   SetSize(2 * vsize);
+   UseDevice(true);
+   SetSize(2 * fes->GetVSize());
+   this->Vector::operator=(0.0);

-   Vector vlfr(data, vsize);
-   Vector vlfi((data) ? &data[vsize] : data, vsize);
-
-   lfr->Update(fes, vlfr, 0);
-   lfi->Update(fes, vlfi, 0);
+   lfr->MakeRef(fes, *this, 0);
+   lfi->MakeRef(fes, *this, fes->GetVSize());
 }

 void
 ComplexLinearForm::Assemble()
 {
+   lfr->SyncMemory(*this);
+   lfi->SyncMemory(*this);
   lfr->Assemble();
   lfi->Assemble();
-   if (conv == ComplexOperator::BLOCK_SYMMETRIC)
-   {
-      *lfi *= -1.0;
-   }
+   if (conv == ComplexOperator::BLOCK_SYMMETRIC) { *lfi *= -1.0; }
+   lfr->SyncAliasMemory(*this);
+   lfi->SyncAliasMemory(*this);
 }

 complex<double>
 ComplexLinearForm::operator()(const ComplexGridFunction &gf) const
 {
-   double s = (conv == ComplexOperator::HERMITIAN)?1.0:-1.0;
+   double s = (conv == ComplexOperator::HERMITIAN) ? 1.0 : -1.0;
+   lfr->SyncMemory(*this);
+   lfi->SyncMemory(*this);
   return complex<double>((*lfr)(gf.real()) - s * (*lfi)(gf.imag()),
                          (*lfr)(gf.imag()) + s * (*lfi)(gf.real()));
 }

+
 bool SesquilinearForm::RealInteg()
 {
   int nint = blfr->GetFBFI()->Size() + blfr->GetDBFI()->Size() +
@@ -341,34 +386,45 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
                                   Vector &X, Vector &B,
                                   int ci)
 {
-   FiniteElementSpace * fes = blfr->FESpace();
-   int vsize  = fes->GetVSize();
+   FiniteElementSpace *fes = blfr->FESpace();
+   const int vsize = fes->GetVSize();

-   // Allocate temporary vectors
-   Vector b_0(vsize); b_0 = 0.0;
+   // Allocate temporary vector
+   Vector b_0;
+   b_0.UseDevice(true);
+   b_0.SetSize(vsize);
+   b_0 = 0.0;

   // Extract the real and imaginary parts of the input vectors
   MFEM_ASSERT(x.Size() == 2 * vsize, "Input GridFunction of incorrect size!");
-   Vector x_r(x.GetData(), vsize);
-   Vector x_i(&(x.GetData())[vsize], vsize);
+   x.Read();
+   Vector x_r; x_r.MakeRef(x, 0, vsize);
+   Vector x_i; x_i.MakeRef(x, vsize, vsize);

   MFEM_ASSERT(b.Size() == 2 * vsize, "Input LinearForm of incorrect size!");
-   Vector b_r(b.GetData(), vsize);
-   Vector b_i(&(b.GetData())[vsize], vsize);
+   b.Read();
+   Vector b_r; b_r.MakeRef(b, 0, vsize);
+   Vector b_i; b_i.MakeRef(b, vsize, vsize);

   if (conv == ComplexOperator::BLOCK_SYMMETRIC) { b_i *= -1.0; }

-   int tvsize = fes->GetTrueVSize();
+   const int tvsize = fes->GetTrueVSize();
   OperatorHandle A_r, A_i;

+   X.UseDevice(true);
   X.SetSize(2 * tvsize);
-   B.SetSize(2 * tvsize);
+   X = 0.0;

-   Vector X_0(tvsize), B_0(tvsize);
-   Vector X_r(X.GetData(),tvsize);
-   Vector X_i(&(X.GetData())[tvsize], tvsize);
-   Vector B_r(B.GetData(), tvsize);
-   Vector B_i(&(B.GetData())[tvsize], tvsize);
+   B.UseDevice(true);
+   B.SetSize(2 * tvsize);
+   B = 0.0;
+
+   Vector X_r; X_r.MakeRef(X, 0, tvsize);
+   Vector X_i; X_i.MakeRef(X, tvsize, tvsize);
+   Vector B_r; B_r.MakeRef(B, 0, tvsize);
+   Vector B_i; B_i.MakeRef(B, tvsize, tvsize);
+
+   Vector X_0, B_0;

   if (RealInteg())
   {
@@ -418,13 +474,18 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
      // conform with standard essential BC treatment
      if (A_i.Is<ConstrainedOperator>())
      {
-         int n = ess_tdof_list.Size();
-         for (int k = 0; k < n; k++)
+         const int n = ess_tdof_list.Size();
+         auto d_B_r = B_r.Write();
+         auto d_B_i = B_i.Write();
+         auto d_X_r = X_r.Read();
+         auto d_X_i = X_i.Read();
+         auto d_idx = ess_tdof_list.Read();
+         MFEM_FORALL(i, n,
         {
-            int j = ess_tdof_list[k];
-            B_r(j) = X_r(j);
-            B_i(j) = X_i(j);
-         }
+            const int j = d_idx[i];
+            d_B_r[j] = d_X_r[j];
+            d_B_i[j] = d_X_i[j];
+         });
         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
      }
@@ -436,6 +497,16 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
      b_i *= -1.0;
   }

+   x_r.SyncAliasMemory(x);
+   x_i.SyncAliasMemory(x);
+   b_r.SyncAliasMemory(b);
+   b_i.SyncAliasMemory(b);
+
+   X_r.SyncAliasMemory(X);
+   X_i.SyncAliasMemory(X);
+   B_r.SyncAliasMemory(B);
+   B_i.SyncAliasMemory(B);
+
   // A = A_r + i A_i
   A.Clear();
   if ( A_r.Type() == Operator::MFEM_SPARSEMAT ||
@@ -528,29 +599,32 @@ void
 SesquilinearForm::RecoverFEMSolution(const Vector &X, const Vector &b,
                                     Vector &x)
 {
-   FiniteElementSpace * fes = blfr->FESpace();
+   FiniteElementSpace *fes = blfr->FESpace();

   const SparseMatrix *P = fes->GetConformingProlongation();
-
-   int vsize  = fes->GetVSize();
-   int tvsize = X.Size() / 2;
-
-   Vector X_r(X.GetData(), tvsize);
-   Vector X_i(&(X.GetData())[tvsize], tvsize);
-
-   Vector x_r(x.GetData(), vsize);
-   Vector x_i(&(x.GetData())[vsize], vsize);
-
   if (!P)
   {
      x = X;
+      return;
   }
-   else
-   {
-      // Apply conforming prolongation
-      P->Mult(X_r, x_r);
-      P->Mult(X_i, x_i);
-   }
+
+   const int vsize  = fes->GetVSize();
+   const int tvsize = X.Size() / 2;
+
+   X.Read();
+   Vector X_r; X_r.MakeRef(const_cast<Vector&>(X), 0, tvsize);
+   Vector X_i; X_i.MakeRef(const_cast<Vector&>(X), tvsize, tvsize);
+
+   x.Write();
+   Vector x_r; x_r.MakeRef(x, 0, vsize);
+   Vector x_i; x_i.MakeRef(x, vsize, vsize);
+
+   // Apply conforming prolongation
+   P->Mult(X_r, x_r);
+   P->Mult(X_i, x_i);
+
+   x_r.SyncAliasMemory(x);
+   x_i.SyncAliasMemory(x);
 }

 void
@@ -566,16 +640,21 @@ SesquilinearForm::Update(FiniteElementSpace *nfes)
 ParComplexGridFunction::ParComplexGridFunction(ParFiniteElementSpace *pfes)
   : Vector(2*(pfes->GetVSize()))
 {
-   pgfr = new ParGridFunction(pfes, data);
-   pgfi = new ParGridFunction(pfes, (data) ? &data[pfes->GetVSize()]:data);
+   UseDevice(true);
+   this->Vector::operator=(0.0);
+
+   pgfr = new ParGridFunction();
+   pgfr->MakeRef(pfes, *this, 0);
+
+   pgfi = new ParGridFunction();
+   pgfi->MakeRef(pfes, *this, pfes->GetVSize());
 }

 void
 ParComplexGridFunction::Update()
 {
-   ParFiniteElementSpace * pfes = pgfr->ParFESpace();
-
-   int vsize = pfes->GetVSize();
+   ParFiniteElementSpace *pfes = pgfr->ParFESpace();
+   const int vsize = pfes->GetVSize();

   const Operator *T = pfes->GetUpdateOperator();
   if (T)
@@ -587,30 +666,34 @@ ParComplexGridFunction::Update()

      // Our data array now contains old data as well as being the wrong size so
      // reallocate it.
+      UseDevice(true);
      this->SetSize(2 * vsize);
+      this->Vector::operator=(0.0);

      // Create temporary vectors which point to the new data array
-      Vector gf_r(data, vsize);
-      Vector gf_i((data) ? &data[vsize] : data, vsize);
+      Vector gf_r; gf_r.MakeRef(*this, 0, vsize);
+      Vector gf_i; gf_i.MakeRef(*this, vsize, vsize);

      // Copy the updated GridFunctions into the new data array
-      gf_r = *pgfr;
-      gf_i = *pgfi;
+      gf_r = *pgfr; gf_r.SyncAliasMemory(*this);
+      gf_i = *pgfi; gf_i.SyncAliasMemory(*this);

      // Replace the individual data arrays with pointers into the new data
      // array
-      pgfr->NewDataAndSize(data, vsize);
-      pgfi->NewDataAndSize((data) ? &data[vsize] : data, vsize);
+      pgfr->MakeRef(*this, 0, vsize);
+      pgfi->MakeRef(*this, vsize, vsize);
   }
   else
   {
      // The existing data will not be transferred to the new GridFunctions so
-      // delete it a allocate a new array
+      // delete it and allocate a new array
+      UseDevice(true);
      this->SetSize(2 * vsize);
+      this->Vector::operator=(0.0);

      // Point the individual GridFunctions to the new data array
-      pgfr->NewDataAndSize(data, vsize);
-      pgfi->NewDataAndSize((data) ? &data[vsize] : data, vsize);
+      pgfr->MakeRef(*this, 0, vsize);
+      pgfi->MakeRef(*this, vsize, vsize);

      // These updates will only set the proper 'sequence' value within the
      // individual GridFunction objects because their sizes are already correct
@@ -623,16 +706,24 @@ void
 ParComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff,
                                           Coefficient &imag_coeff)
 {
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->ProjectCoefficient(real_coeff);
   pgfi->ProjectCoefficient(imag_coeff);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
 }

 void
 ParComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
                                           VectorCoefficient &imag_vcoeff)
 {
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->ProjectCoefficient(real_vcoeff);
   pgfi->ProjectCoefficient(imag_vcoeff);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
 }

 void
@@ -640,8 +731,12 @@ ParComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
                                              Coefficient &imag_coeff,
                                              Array<int> &attr)
 {
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->ProjectBdrCoefficient(real_coeff, attr);
   pgfi->ProjectBdrCoefficient(imag_coeff, attr);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
 }

 void
@@ -651,8 +746,12 @@ ParComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient
                                                    &imag_vcoeff,
                                                    Array<int> &attr)
 {
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->ProjectBdrCoefficientNormal(real_vcoeff, attr);
   pgfi->ProjectBdrCoefficientNormal(imag_vcoeff, attr);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
 }

 void
@@ -662,36 +761,51 @@ ParComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
                                                     &imag_vcoeff,
                                                     Array<int> &attr)
 {
+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->ProjectBdrCoefficientTangent(real_vcoeff, attr);
   pgfi->ProjectBdrCoefficientTangent(imag_vcoeff, attr);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
 }

 void
 ParComplexGridFunction::Distribute(const Vector *tv)
 {
-   ParFiniteElementSpace * pfes = pgfr->ParFESpace();
-   HYPRE_Int size = pfes->GetTrueVSize();
+   ParFiniteElementSpace *pfes = pgfr->ParFESpace();
+   const int tvsize = pfes->GetTrueVSize();

-   double * tvd = tv->GetData();
-   Vector tvr(tvd, size);
-   Vector tvi((tvd) ? &tvd[size] : tvd, size);
+   tv->Read();
+   Vector tvr; tvr.MakeRef(const_cast<Vector&>(*tv), 0, tvsize);
+   Vector tvi; tvi.MakeRef(const_cast<Vector&>(*tv), tvsize, tvsize);

+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->Distribute(tvr);
   pgfi->Distribute(tvi);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
 }

 void
 ParComplexGridFunction::ParallelProject(Vector &tv) const
 {
-   ParFiniteElementSpace * pfes = pgfr->ParFESpace();
-   HYPRE_Int size = pfes->GetTrueVSize();
+   ParFiniteElementSpace *pfes = pgfr->ParFESpace();
+   const int tvsize = pfes->GetTrueVSize();

-   double * tvd = tv.GetData();
-   Vector tvr(tvd, size);
-   Vector tvi((tvd) ? &tvd[size] : tvd, size);
+   tv.Write();
+   Vector tvr; tvr.MakeRef(tv, 0, tvsize);
+   Vector tvi; tvi.MakeRef(tv, tvsize, tvsize);

+   pgfr->SyncMemory(*this);
+   pgfi->SyncMemory(*this);
   pgfr->ParallelProject(tvr);
   pgfi->ParallelProject(tvi);
+   pgfr->SyncAliasMemory(*this);
+   pgfi->SyncAliasMemory(*this);
+
+   tvr.SyncAliasMemory(tv);
+   tvi.SyncAliasMemory(tv);
 }


@@ -701,10 +815,16 @@ ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
   : Vector(2*(pfes->GetVSize())),
     conv(convention)
 {
-   plfr = new ParLinearForm(pfes, data);
-   plfi = new ParLinearForm(pfes, (data) ? &data[pfes->GetVSize()]:data);
+   UseDevice(true);
+   this->Vector::operator=(0.0);

-   HYPRE_Int * tdof_offsets_fes = pfes->GetTrueDofOffsets();
+   plfr = new ParLinearForm();
+   plfr->MakeRef(pfes, *this, 0);
+
+   plfi = new ParLinearForm();
+   plfi->MakeRef(pfes, *this, pfes->GetVSize());
+
+   HYPRE_Int *tdof_offsets_fes = pfes->GetTrueDofOffsets();

   int n = (HYPRE_AssumedPartitionCheck()) ? 2 : pfes->GetNRanks();
   tdof_offsets = new HYPRE_Int[n+1];
@@ -724,12 +844,16 @@ ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
   : Vector(2*(pfes->GetVSize())),
     conv(convention)
 {
-   plfr = new ParLinearForm(pfes, plf_r);
-   plfr->SetData(data);
-   plfi = new ParLinearForm(pfes, plf_i);
-   plfi->SetData((data) ? &data[pfes->GetVSize()]:data);
+   UseDevice(true);
+   this->Vector::operator=(0.0);

-   HYPRE_Int * tdof_offsets_fes = pfes->GetTrueDofOffsets();
+   plfr = new ParLinearForm(pfes, plf_r);
+   plfi = new ParLinearForm(pfes, plf_i);
+
+   plfr->MakeRef(pfes, *this, 0);
+   plfi->MakeRef(pfes, *this, pfes->GetVSize());
+
+   HYPRE_Int *tdof_offsets_fes = pfes->GetTrueDofOffsets();

   int n = (HYPRE_AssumedPartitionCheck()) ? 2 : pfes->GetNRanks();
   tdof_offsets = new HYPRE_Int[n+1];
@@ -792,58 +916,71 @@ ParComplexLinearForm::AddBdrFaceIntegrator(LinearFormIntegrator *lfi_real,
 void
 ParComplexLinearForm::Update(ParFiniteElementSpace *pf)
 {
-   ParFiniteElementSpace *pfes = (pf!=NULL)?pf:plfr->ParFESpace();
-   int vsize = pfes->GetVSize();
-   SetSize(2 * vsize);
+   ParFiniteElementSpace *pfes = (pf != NULL) ? pf : plfr->ParFESpace();

-   Vector vplfr(data, vsize);
-   Vector vplfi((data) ? &data[vsize] : data, vsize);
+   UseDevice(true);
+   SetSize(2 * pfes->GetVSize());
+   this->Vector::operator=(0.0);

-   plfr->Update(pfes, vplfr, 0);
-   plfi->Update(pfes, vplfi, 0);
+   plfr->MakeRef(pfes, *this, 0);
+   plfi->MakeRef(pfes, *this, pfes->GetVSize());
 }

 void
 ParComplexLinearForm::Assemble()
 {
+   plfr->SyncMemory(*this);
+   plfi->SyncMemory(*this);
   plfr->Assemble();
   plfi->Assemble();
-   if (conv == ComplexOperator::BLOCK_SYMMETRIC)
-   {
-      *plfi *= -1.0;
-   }
+   if (conv == ComplexOperator::BLOCK_SYMMETRIC) { *plfi *= -1.0; }
+   plfr->SyncAliasMemory(*this);
+   plfi->SyncAliasMemory(*this);
 }

 void
 ParComplexLinearForm::ParallelAssemble(Vector &tv)
 {
-   HYPRE_Int size = plfr->ParFESpace()->GetTrueVSize();
+   const int tvsize = plfr->ParFESpace()->GetTrueVSize();

-   double * tvd = tv.GetData();
-   Vector tvr(tvd, size);
-   Vector tvi((tvd) ? &tvd[size] : tvd, size);
+   tv.Write();
+   Vector tvr; tvr.MakeRef(tv, 0, tvsize);
+   Vector tvi; tvi.MakeRef(tv, tvsize, tvsize);

+   plfr->SyncMemory(*this);
+   plfi->SyncMemory(*this);
   plfr->ParallelAssemble(tvr);
   plfi->ParallelAssemble(tvi);
+   plfr->SyncAliasMemory(*this);
+   plfi->SyncAliasMemory(*this);
+
+   tvr.SyncAliasMemory(tv);
+   tvi.SyncAliasMemory(tv);
 }

 HypreParVector *
 ParComplexLinearForm::ParallelAssemble()
 {
-   const ParFiniteElementSpace * pfes = plfr->ParFESpace();
+   const ParFiniteElementSpace *pfes = plfr->ParFESpace();
+   const int tvsize = pfes->GetTrueVSize();

-   HypreParVector * tv = new HypreParVector(pfes->GetComm(),
-                                            2*(pfes->GlobalTrueVSize()),
-                                            tdof_offsets);
+   HypreParVector *tv = new HypreParVector(pfes->GetComm(),
+                                           2*(pfes->GlobalTrueVSize()),
+                                           tdof_offsets);

-   HYPRE_Int size = pfes->GetTrueVSize();
-
-   double * tvd = tv->GetData();
-   Vector tvr(tvd, size);
-   Vector tvi((tvd) ? &tvd[size] : tvd, size);
+   tv->Write();
+   Vector tvr; tvr.MakeRef(*tv, 0, tvsize);
+   Vector tvi; tvi.MakeRef(*tv, tvsize, tvsize);

+   plfr->SyncMemory(*this);
+   plfi->SyncMemory(*this);
   plfr->ParallelAssemble(tvr);
   plfi->ParallelAssemble(tvi);
+   plfr->SyncAliasMemory(*this);
+   plfi->SyncAliasMemory(*this);
+
+   tvr.SyncAliasMemory(*tv);
+   tvi.SyncAliasMemory(*tv);

   return tv;
 }
@@ -851,13 +988,14 @@ ParComplexLinearForm::ParallelAssemble()
 complex<double>
 ParComplexLinearForm::operator()(const ParComplexGridFunction &gf) const
 {
-   double s = (conv == ComplexOperator::HERMITIAN)?1.0:-1.0;
+   plfr->SyncMemory(*this);
+   plfi->SyncMemory(*this);
+   double s = (conv == ComplexOperator::HERMITIAN) ? 1.0 : -1.0;
   return complex<double>((*plfr)(gf.real()) - s * (*plfi)(gf.imag()),
                          (*plfr)(gf.imag()) + s * (*plfi)(gf.real()));
 }


-
 bool ParSesquilinearForm::RealInteg()
 {
   int nint = pblfr->GetFBFI()->Size() + pblfr->GetDBFI()->Size() +
@@ -964,7 +1102,6 @@ ParSesquilinearForm::ParallelAssemble()
   return new ComplexHypreParMatrix(pblfr->ParallelAssemble(),
                                    pblfi->ParallelAssemble(),
                                    true, true, conv);
-
 }

 void
@@ -974,35 +1111,45 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
                                      Vector &X, Vector &B,
                                      int ci)
 {
-   ParFiniteElementSpace * pfes = pblfr->ParFESpace();
-   int vsize = pfes->GetVSize();
+   ParFiniteElementSpace *pfes = pblfr->ParFESpace();
+   const int vsize = pfes->GetVSize();

-   // Allocate temporary vectors
-   Vector b_0(vsize); b_0 = 0.0;
+   // Allocate temporary vector
+   Vector b_0;
+   b_0.UseDevice(true);
+   b_0.SetSize(vsize);
+   b_0 = 0.0;

   // Extract the real and imaginary parts of the input vectors
   MFEM_ASSERT(x.Size() == 2 * vsize, "Input GridFunction of incorrect size!");
-   Vector x_r(x.GetData(), vsize);
-   Vector x_i(&(x.GetData())[vsize], vsize);
+   x.Read();
+   Vector x_r; x_r.MakeRef(x, 0, vsize);
+   Vector x_i; x_i.MakeRef(x, vsize, vsize);

   MFEM_ASSERT(b.Size() == 2 * vsize, "Input LinearForm of incorrect size!");
-   Vector b_r(b.GetData(), vsize);
-   Vector b_i(&(b.GetData())[vsize], vsize);
+   b.Read();
+   Vector b_r; b_r.MakeRef(b, 0, vsize);
+   Vector b_i; b_i.MakeRef(b, vsize, vsize);

   if (conv == ComplexOperator::BLOCK_SYMMETRIC) { b_i *= -1.0; }

-   int tvsize = pfes->GetTrueVSize();
-
+   const int tvsize = pfes->GetTrueVSize();
   OperatorHandle A_r, A_i;

+   X.UseDevice(true);
   X.SetSize(2 * tvsize);
-   B.SetSize(2 * tvsize);
+   X = 0.0;

-   Vector X_0(tvsize), B_0(tvsize);
-   Vector X_r(X.GetData(),tvsize);
-   Vector X_i(&(X.GetData())[tvsize], tvsize);
-   Vector B_r(B.GetData(), tvsize);
-   Vector B_i(&(B.GetData())[tvsize], tvsize);
+   B.UseDevice(true);
+   B.SetSize(2 * tvsize);
+   B = 0.0;
+
+   Vector X_r; X_r.MakeRef(X, 0, tvsize);
+   Vector X_i; X_i.MakeRef(X, tvsize, tvsize);
+   Vector B_r; B_r.MakeRef(B, 0, tvsize);
+   Vector B_i; B_i.MakeRef(B, tvsize, tvsize);
+
+   Vector X_0, B_0;

   if (RealInteg())
   {
@@ -1042,24 +1189,29 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,

   if (RealInteg() && ImagInteg())
   {
-      int n = ess_tdof_list.Size();
      // Modify RHS to conform with standard essential BC treatment
-      for (int k = 0; k < n; k++)
+      const int n = ess_tdof_list.Size();
+      auto d_B_r = B_r.Write();
+      auto d_B_i = B_i.Write();
+      auto d_X_r = X_r.Read();
+      auto d_X_i = X_i.Read();
+      auto d_idx = ess_tdof_list.Read();
+      MFEM_FORALL(i, n,
      {
-         int j=ess_tdof_list[k];
-         B_r(j) = X_r(j);
-         B_i(j) = X_i(j);
-      }
+         const int j = d_idx[i];
+         d_B_r[j] = d_X_r[j];
+         d_B_i[j] = d_X_i[j];
+      });
      // Modify offdiagonal blocks (imaginary parts of the matrix) to conform
      // with standard essential BC treatment
-      if ( A_i.Type() == Operator::Hypre_ParCSR )
+      if (A_i.Type() == Operator::Hypre_ParCSR)
      {
         HypreParMatrix * Ah;
         A_i.Get(Ah);
         hypre_ParCSRMatrix *Aih = *Ah;
         for (int k = 0; k < n; k++)
         {
-            int j = ess_tdof_list[k];
+            const int j = ess_tdof_list[k];
            Aih->diag->data[Aih->diag->i[j]] = 0.0;
         }
      }
@@ -1076,6 +1228,16 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
      b_i *= -1.0;
   }

+   x_r.SyncAliasMemory(x);
+   x_i.SyncAliasMemory(x);
+   b_r.SyncAliasMemory(b);
+   b_i.SyncAliasMemory(b);
+
+   X_r.SyncAliasMemory(X);
+   X_i.SyncAliasMemory(X);
+   B_r.SyncAliasMemory(B);
+   B_i.SyncAliasMemory(B);
+
   // A = A_r + i A_i
   A.Clear();
   if ( A_r.Type() == Operator::Hypre_ParCSR ||
@@ -1175,22 +1337,27 @@ void
 ParSesquilinearForm::RecoverFEMSolution(const Vector &X, const Vector &b,
                                        Vector &x)
 {
-   ParFiniteElementSpace * pfes = pblfr->ParFESpace();
+   ParFiniteElementSpace *pfes = pblfr->ParFESpace();

   const Operator &P = *pfes->GetProlongationMatrix();

-   int vsize  = pfes->GetVSize();
-   int tvsize = X.Size() / 2;
+   const int vsize  = pfes->GetVSize();
+   const int tvsize = X.Size() / 2;

-   Vector X_r(X.GetData(), tvsize);
-   Vector X_i(&(X.GetData())[tvsize], tvsize);
+   X.Read();
+   Vector X_r; X_r.MakeRef(const_cast<Vector&>(X), 0, tvsize);
+   Vector X_i; X_i.MakeRef(const_cast<Vector&>(X), tvsize, tvsize);

-   Vector x_r(x.GetData(), vsize);
-   Vector x_i(&(x.GetData())[vsize], vsize);
+   x.Write();
+   Vector x_r; x_r.MakeRef(x, 0, vsize);
+   Vector x_i; x_i.MakeRef(x, vsize, vsize);

   // Apply conforming prolongation
   P.Mult(X_r, x_r);
   P.Mult(X_i, x_i);
+
+   x_r.SyncAliasMemory(x);
+   x_i.SyncAliasMemory(x);
 }

 void
@@ -38,8 +38,8 @@ protected:
   void Destroy() { delete gfr; delete gfi; }

 public:
-   /* @brief Construct a ComplexGridFunction associated with the
-      FiniteElementSpace @a *f. */
+   /** @brief Construct a ComplexGridFunction associated with the
+       FiniteElementSpace @a *f. */
   ComplexGridFunction(FiniteElementSpace *f);

   void Update();
@@ -71,6 +71,14 @@ public:
   const GridFunction & real() const { return *gfr; }
   const GridFunction & imag() const { return *gfi; }

+   /// Update the memory location of the real and imaginary GridFunction @a gfr
+   /// and @a gfi to match the ComplexGridFunction.
+   void Sync() { gfr->SyncMemory(*this); gfi->SyncMemory(*this); }
+
+   /// Update the alias memory location of the real and imaginary GridFunction
+   /// @a gfr and @a gfi to match the ComplexGridFunction.
+   void SyncAlias() { gfr->SyncAliasMemory(*this); gfi->SyncAliasMemory(*this); }
+
   /// Destroys the grid function.
   virtual ~ComplexGridFunction() { Destroy(); }

@@ -99,8 +107,8 @@ public:
                     ComplexOperator::Convention
                     convention = ComplexOperator::HERMITIAN);

-   /** @brief Create a ComplexLinearForm on the FiniteElementSpace @a f, using
-       the same integrators as the LinearForms @a lfr (real) and @a lfi (imag) .
+   /** @brief Create a ComplexLinearForm on the FiniteElementSpace @a fes, using
+       the same integrators as the LinearForms @a lf_r (real) and @a lf_i (imag).

       The pointer @a fes is not owned by the newly constructed object.

@@ -157,6 +165,14 @@ public:
   const LinearForm & real() const { return *lfr; }
   const LinearForm & imag() const { return *lfi; }

+   /// Update the memory location of the real and imaginary LinearForm @a lfr
+   /// and @a lfi to match the ComplexLinearForm.
+   void Sync() { lfr->SyncMemory(*this); lfi->SyncMemory(*this); }
+
+   /// Update the alias memory location of the real and imaginary LinearForm @a
+   /// lfr and @a lfi to match the ComplexLinearForm.
+   void SyncAlias() { lfr->SyncAliasMemory(*this); lfi->SyncAliasMemory(*this); }
+
   void Update();
   void Update(FiniteElementSpace *f);

@@ -195,8 +211,8 @@ private:
   BilinearForm *blfr;
   BilinearForm *blfi;

-   /* These methods check if the real/imag parts of the sesqulinear form are not
-      empty */
+   /* These methods check if the real/imag parts of the sesquilinear form are
+      not empty */
   bool RealInteg();
   bool ImagInteg();

@@ -204,7 +220,7 @@ public:
   SesquilinearForm(FiniteElementSpace *fes,
                    ComplexOperator::Convention
                    convention = ComplexOperator::HERMITIAN);
-   /** @brief Create a SesquilinearForm on the FiniteElementSpace @a f, using
+   /** @brief Create a SesquilinearForm on the FiniteElementSpace @a fes, using
       the same integrators as the BilinearForms @a bfr and @a bfi .

       The pointer @a fes is not owned by the newly constructed object.
@@ -323,8 +339,8 @@ protected:

 public:

-   /* @brief Construct a ParComplexGridFunction associated with the
-      ParFiniteElementSpace @a *f. */
+   /** @brief Construct a ParComplexGridFunction associated with the
+       ParFiniteElementSpace @a *pf. */
   ParComplexGridFunction(ParFiniteElementSpace *pf);

   void Update();
@@ -365,6 +381,15 @@ public:
   const ParGridFunction & real() const { return *pgfr; }
   const ParGridFunction & imag() const { return *pgfi; }

+   /// Update the memory location of the real and imaginary ParGridFunction @a
+   /// pgfr and @a pgfi to match the ParComplexGridFunction.
+   void Sync() { pgfr->SyncMemory(*this); pgfi->SyncMemory(*this); }
+
+   /// Update the alias memory location of the real and imaginary
+   /// ParGridFunction @a pgfr and @a pgfi to match the ParComplexGridFunction.
+   void SyncAlias() { pgfr->SyncAliasMemory(*this); pgfi->SyncAliasMemory(*this); }
+
+
   virtual double ComputeL2Error(Coefficient &exsolr, Coefficient &exsoli,
                                 const IntegrationRule *irs[] = NULL) const
   {
@@ -416,8 +441,8 @@ public:
                        convention = ComplexOperator::HERMITIAN);

   /** @brief Create a ParComplexLinearForm on the ParFiniteElementSpace @a pf,
-       using the same integrators as the LinearForms @a plfr (real) and @a plfi
-       (imag) .
+       using the same integrators as the LinearForms @a plf_r (real) and
+       @a plf_i (imag).

      The pointer @a fes is not owned by the newly constructed object.

@@ -475,6 +500,14 @@ public:
   const ParLinearForm & real() const { return *plfr; }
   const ParLinearForm & imag() const { return *plfi; }

+   /// Update the memory location of the real and imaginary ParLinearForm @a lfr
+   /// and @a lfi to match the ParComplexLinearForm.
+   void Sync() { plfr->SyncMemory(*this); plfi->SyncMemory(*this); }
+
+   /// Update the alias memory location of the real and imaginary ParLinearForm
+   /// @a plfr and @a plfi to match the ParComplexLinearForm.
+   void SyncAlias() { plfr->SyncAliasMemory(*this); plfi->SyncAliasMemory(*this); }
+
   void Update(ParFiniteElementSpace *pf = NULL);

   /// Assembles the linear form i.e. sums over all domain/bdr integrators.
@@ -0,0 +1,297 @@
+#include "convergence.hpp"
+
+using namespace std;
+
+
+namespace mfem
+{
+
+void ConvergenceStudy::Reset()
+{
+   counter=0;
+   dcounter=0;
+   fcounter=0;
+   cont_type=-1;
+   print_flag=1;
+   L2Errors.SetSize(0);
+   L2Rates.SetSize(0);
+   DErrors.SetSize(0);
+   DRates.SetSize(0);
+   EnErrors.SetSize(0);
+   EnRates.SetSize(0);
+   DGFaceErrors.SetSize(0);
+   DGFaceRates.SetSize(0);
+   ndofs.SetSize(0);
+}
+
+double ConvergenceStudy::GetNorm(GridFunction *gf, Coefficient *scalar_u,
+                                 VectorCoefficient *vector_u)
+{
+   bool norm_set = false;
+   double norm=0.0;
+   int order = gf->FESpace()->GetOrder(0);
+   int order_quad = std::max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+#ifdef MFEM_USE_MPI
+   ParGridFunction *pgf = dynamic_cast<ParGridFunction *>(gf);
+   if (pgf)
+   {
+      ParMesh *pmesh = pgf->ParFESpace()->GetParMesh();
+      if (scalar_u)
+      {
+         norm = ComputeGlobalLpNorm(2.0,*scalar_u,*pmesh,irs);
+      }
+      else if (vector_u)
+      {
+         norm = ComputeGlobalLpNorm(2.0,*vector_u,*pmesh,irs);
+      }
+      norm_set = true;
+   }
+#endif
+   if (!norm_set)
+   {
+      Mesh *mesh = gf->FESpace()->GetMesh();
+      if (scalar_u)
+      {
+         norm = ComputeLpNorm(2.0,*scalar_u,*mesh,irs);
+      }
+      else if (vector_u)
+      {
+         norm = ComputeLpNorm(2.0,*vector_u,*mesh,irs);
+      }
+   }
+   return norm;
+}
+
+void ConvergenceStudy::AddL2Error(GridFunction *gf,
+                                  Coefficient *scalar_u, VectorCoefficient *vector_u)
+{
+   int tdofs=0;
+#ifdef MFEM_USE_MPI
+   ParGridFunction *pgf = dynamic_cast<ParGridFunction *>(gf);
+   if (pgf)
+   {
+      MPI_Comm comm = pgf->ParFESpace()->GetComm();
+      int rank;
+      MPI_Comm_rank(comm, &rank);
+      print_flag = 0;
+      if (rank==0) { print_flag = 1; }
+      tdofs = pgf->ParFESpace()->GlobalTrueVSize();
+   }
+#endif
+   if (!tdofs) { tdofs = gf->FESpace()->GetTrueVSize(); }
+   ndofs.Append(tdofs);
+   double L2Err;
+   if (scalar_u)
+   {
+      L2Err = gf->ComputeL2Error(*scalar_u);
+      CoeffNorm = GetNorm(gf,scalar_u,nullptr);
+   }
+   else if (vector_u)
+   {
+      L2Err = gf->ComputeL2Error(*vector_u);
+      CoeffNorm = GetNorm(gf,nullptr,vector_u);
+   }
+   else
+   {
+      MFEM_ABORT("Exact Solution Coefficient pointer is NULL");
+   }
+   L2Errors.Append(L2Err);
+   // Compute the rate of convergence by:
+   // rate = log (||u - u_h|| / ||u - u_{h/2}||)/log(2)
+   double val = (counter) ? log(L2Errors[counter-1]/L2Err)/log(2.0) : 0.0;
+   L2Rates.Append(val);
+   counter++;
+}
+
+void ConvergenceStudy::AddGf(GridFunction *gf, Coefficient *scalar_u,
+                             VectorCoefficient *grad,
+                             Coefficient *ell_coeff, double Nu)
+{
+   cont_type = gf->FESpace()->FEColl()->GetContType();
+
+   MFEM_VERIFY((cont_type == mfem::FiniteElementCollection::CONTINUOUS) ||
+               (cont_type == mfem::FiniteElementCollection::DISCONTINUOUS),
+               "This constructor is intended for H1 or L2 Elements")
+
+   AddL2Error(gf,scalar_u, nullptr);
+
+   if (grad)
+   {
+      double GradErr = gf->ComputeGradError(grad);
+      DErrors.Append(GradErr);
+      double err = sqrt(L2Errors[counter-1]*L2Errors[counter-1]+GradErr*GradErr);
+      EnErrors.Append(err);
+      // Compute the rate of convergence by:
+      // rate = log (||u - u_h|| / ||u - u_{h/2}||)/log(2)
+      double val = (dcounter) ? log(DErrors[dcounter-1]/GradErr)/log(2.0) : 0.0;
+      double eval = (dcounter) ? log(EnErrors[dcounter-1]/err)/log(2.0) : 0.0;
+      DRates.Append(val);
+      EnRates.Append(eval);
+      CoeffDNorm = GetNorm(gf,nullptr,grad);
+      dcounter++;
+      MFEM_VERIFY(counter == dcounter,
+                  "Number of added solutions and derivatives do not match")
+   }
+
+   if (cont_type == mfem::FiniteElementCollection::DISCONTINUOUS && ell_coeff)
+   {
+      double DGErr = gf->ComputeDGFaceJumpError(scalar_u,ell_coeff,Nu);
+      DGFaceErrors.Append(DGErr);
+      // Compute the rate of convergence by:
+      // rate = log (||u - u_h|| / ||u - u_{h/2}||)/log(2)
+      double val=(fcounter) ? log(DGFaceErrors[fcounter-1]/DGErr)/log(2.0):0.;
+      DGFaceRates.Append(val);
+      fcounter++;
+      MFEM_VERIFY(fcounter == counter, "Number of added solutions mismatch");
+   }
+}
+
+void ConvergenceStudy::AddGf(GridFunction *gf, VectorCoefficient *vector_u,
+                             VectorCoefficient *curl, Coefficient *div)
+{
+   cont_type = gf->FESpace()->FEColl()->GetContType();
+
+   AddL2Error(gf,nullptr,vector_u);
+   double DErr = 0.0;
+   bool derivative = false;
+   if (curl)
+   {
+      DErr = gf->ComputeCurlError(curl);
+      CoeffDNorm = GetNorm(gf,nullptr,curl);
+      derivative = true;
+   }
+   else if (div)
+   {
+      DErr = gf->ComputeDivError(div);
+      // update coefficient norm
+      CoeffDNorm = GetNorm(gf,div,nullptr);
+      derivative = true;
+   }
+   if (derivative)
+   {
+      double err = sqrt(L2Errors[counter-1]*L2Errors[counter-1] + DErr*DErr);
+      DErrors.Append(DErr);
+      EnErrors.Append(err);
+      // Compute the rate of convergence by:
+      // rate = log (||u - u_h|| / ||u - u_{h/2}||)/log(2)
+      double val = (dcounter) ? log(DErrors[dcounter-1]/DErr)/log(2.0) : 0.0;
+      double eval = (dcounter) ? log(EnErrors[dcounter-1]/err)/log(2.0) : 0.0;
+      DRates.Append(val);
+      EnRates.Append(eval);
+      dcounter++;
+      MFEM_VERIFY(counter == dcounter,
+                  "Number of added solutions and derivatives do not match")
+   }
+}
+
+void ConvergenceStudy::Print(bool relative, std::ostream &out)
+{
+   if (print_flag)
+   {
+      std::string title = (relative) ? "Relative " : "Absolute ";
+      out << "\n";
+      out << " -------------------------------------------" << "\n";
+      out <<  std::setw(21) << title << "L2 Error " << "\n";
+      out << " -------------------------------------------"
+          << "\n";
+      out << std::right<< std::setw(11)<< "DOFs "<< std::setw(13) << "Error ";
+      out <<  std::setw(15) << "Rate " << "\n";
+      out << " -------------------------------------------"
+          << "\n";
+      out << std::setprecision(4);
+      double d = (relative) ? CoeffNorm : 1.0;
+      for (int i =0; i<counter; i++)
+      {
+         out << std::right << std::setw(10)<< ndofs[i] << std::setw(16)
+             << std::scientific << L2Errors[i]/d << std::setw(13)
+             << std::fixed << L2Rates[i] << "\n";
+      }
+      out << "\n";
+      if (dcounter == counter)
+      {
+         std::string dname;
+         switch (cont_type)
+         {
+            case 0: dname = "Grad"; break;
+            case 1: dname = "Curl"; break;
+            case 2: dname = "Div";  break;
+            case 3: dname = "DG Grad";  break;
+            default: break;
+         }
+         out << " -------------------------------------------" << "\n";
+         out <<  std::setw(21) << title << dname << " Error  " << "\n";
+         out << " -------------------------------------------" << "\n";
+         out << std::right<<std::setw(11)<< "DOFs "<< std::setw(13) << "Error";
+         out << std::setw(15) << "Rate " << "\n";
+         out << " -------------------------------------------"
+             << "\n";
+         out << std::setprecision(4);
+         d = (relative) ? CoeffDNorm : 1.0;
+         for (int i =0; i<dcounter; i++)
+         {
+            out << std::right << std::setw(10)<< ndofs[i] << std::setw(16)
+                << std::scientific << DErrors[i]/d << std::setw(13)
+                << std::fixed << DRates[i] << "\n";
+         }
+         out << "\n";
+         switch (cont_type)
+         {
+            case 0: dname = "H1"; break;
+            case 1: dname = "H(Curl)"; break;
+            case 2: dname = "H(Div)";  break;
+            case 3: dname = "DG H1";  break;
+            default: break;
+         }
+
+         if (dcounter)
+         {
+            d = (relative) ?
+                sqrt(CoeffNorm*CoeffNorm + CoeffDNorm*CoeffDNorm):1.0;
+
+            out << " -------------------------------------------" << "\n";
+            out << std::setw(21) << title << dname << " Error   " << "\n";
+            out << " -------------------------------------------" << "\n";
+            out << std::right<< std::setw(11)<< "DOFs "<< std::setw(13);
+            out << "Error ";
+            out << std::setw(15) << "Rate " << "\n";
+            out << " -------------------------------------------"
+                << "\n";
+            out << std::setprecision(4);
+            for (int i =0; i<dcounter; i++)
+            {
+               out << std::right << std::setw(10)<< ndofs[i] << std::setw(16)
+                   << std::scientific << EnErrors[i]/d << std::setw(13)
+                   << std::fixed << EnRates[i] << "\n";
+            }
+            out << "\n";
+         }
+         if (cont_type == 3 && fcounter)
+         {
+            out << " -------------------------------------------" << "\n";
+            out << "            DG Face Jump Error          " << "\n";
+            out << " -------------------------------------------"
+                << "\n";
+            out << std::right<< std::setw(11)<< "DOFs "<< std::setw(13);
+            out << "Error ";
+            out << std::setw(15) << "Rate " << "\n";
+            out << " -------------------------------------------"
+                << "\n";
+            out << std::setprecision(4);
+            for (int i =0; i<fcounter; i++)
+            {
+               out << std::right << std::setw(10)<< ndofs[i] << std::setw(16)
+                   << std::scientific << DGFaceErrors[i] << std::setw(13)
+                   << std::fixed << DGFaceRates[i] << "\n";
+            }
+            out << "\n";
+         }
+      }
+   }
+}
+
+} // namespace mfem
@@ -0,0 +1,149 @@
+// Copyright (c) 2010-2020, 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_CONVERGENCE
+#define MFEM_CONVERGENCE
+
+#include "../linalg/linalg.hpp"
+#include "gridfunc.hpp"
+#ifdef MFEM_USE_MPI
+#include "pgridfunc.hpp"
+#endif
+
+namespace mfem
+{
+
+/** @brief Class to compute error and convergence rates.
+    It supports H1, H(curl) (ND elements), H(div) (RT elements) and L2 (DG).
+
+    For "smooth enough" solutions the Galerkin error measured in the appropriate
+    norm satisfies || u - u_h || ~ h^k
+
+    Here, k is called the asymptotic rate of convergence
+
+    For successive uniform h-refinements the rate can be estimated by
+    k = log(||u - u_h|| / ||u - u_{h/2}||)/log(2)
+*/
+class ConvergenceStudy
+{
+private:
+   // counters for solutions/derivatives
+   int counter=0;
+   int dcounter=0;
+   int fcounter=0;
+
+   // space continuity type
+   int cont_type=-1;
+
+   // printing flag for helpful for MPI calls
+   int print_flag=1;
+
+   // exact solution and derivatives
+   double CoeffNorm;
+   double CoeffDNorm;
+
+   // Arrays to store error/rates
+   Array<double> L2Errors, DGFaceErrors, DErrors, EnErrors;
+   Array<double> L2Rates, DGFaceRates, DRates, EnRates;
+   Array<int> ndofs;
+
+   void AddL2Error(GridFunction *gf, Coefficient *scalar_u,
+                   VectorCoefficient *vector_u);
+   void AddGf(GridFunction *gf, Coefficient *scalar_u,
+              VectorCoefficient *grad=nullptr,
+              Coefficient *ell_coeff=nullptr, double Nu=1.0);
+   void AddGf(GridFunction *gf, VectorCoefficient *vector_u,
+              VectorCoefficient *curl, Coefficient *div);
+   // returns the L2-norm of scalar_u or vector_u
+   double GetNorm(GridFunction *gf, Coefficient *scalar_u,
+                  VectorCoefficient *vector_u);
+
+public:
+
+   /// Clear any internal data
+   void Reset();
+
+   /// Add L2 GridFunction, the exact solution and possibly its gradient and/or
+   /// DG face jumps parameters
+   void AddL2GridFunction(GridFunction *gf, Coefficient *scalar_u,
+                          VectorCoefficient *grad=nullptr,
+                          Coefficient *ell_coeff=nullptr, double Nu=1.0)
+   {
+      AddGf(gf, scalar_u, grad, ell_coeff, Nu);
+   }
+
+   /// Add H1 GridFunction, the exact solution and possibly its gradient
+   void AddH1GridFunction(GridFunction *gf, Coefficient *scalar_u,
+                          VectorCoefficient *grad=nullptr)
+   {
+      AddGf(gf, scalar_u, grad);
+   }
+
+   /// Add H(curl) GridFunction, the exact solution and possibly its curl
+   void AddHcurlGridFunction(GridFunction *gf, VectorCoefficient *vector_u,
+                             VectorCoefficient *curl=nullptr)
+   {
+      AddGf(gf, vector_u, curl, nullptr);
+   }
+
+   /// Add H(div) GridFunction, the exact solution and possibly its div
+   void AddHdivGridFunction(GridFunction *gf, VectorCoefficient *vector_u,
+                            Coefficient *div=nullptr)
+   {
+      AddGf(gf,vector_u, nullptr, div);
+   }
+
+   /// Get the L2 error at step n
+   double GetL2Error(int n)
+   {
+      MFEM_VERIFY( n <= counter,"Step out of bounds")
+      return L2Errors[n];
+   }
+
+   /// Get all L2 errors
+   void GetL2Errors(Array<double> & L2Errors_)
+   {
+      L2Errors_ = L2Errors;
+   }
+
+   /// Get the Grad/Curl/Div error at step n
+   double GetDError(int n)
+   {
+      MFEM_VERIFY(n <= dcounter,"Step out of bounds")
+      return DErrors[n];
+   }
+
+   /// Get all Grad/Curl/Div errors
+   void GetDErrors(Array<double> & DErrors_)
+   {
+      DErrors_ = DErrors;
+   }
+
+   /// Get the DGFaceJumps error at step n
+   double GetDGFaceJumpsError(int n)
+   {
+      MFEM_VERIFY(n<= fcounter,"Step out of bounds")
+      return DGFaceErrors[n];
+   }
+
+   /// Get all DGFaceJumps errors
+   void GetDGFaceJumpsErrors(Array<double> & DGFaceErrors_)
+   {
+      DGFaceErrors_ = DGFaceErrors;
+   }
+
+   /// Print rates and errors
+   void Print(bool relative = false, std::ostream &out = mfem::out);
+};
+
+} // namespace mfem
+
+#endif // MFEM_CONVERGENCE
@@ -563,6 +563,8 @@ void VisItDataCollection::LoadVisItRootFile(const std::string& root_name)

 void VisItDataCollection::LoadMesh()
 {
+   // GetMeshFileName() uses 'serial', so we need to set it in advance.
+   serial = (format == SERIAL_FORMAT);
   std::string mesh_fname = GetMeshFileName();
   named_ifgzstream file(mesh_fname);
   // TODO: in parallel, check for errors on all processors
@@ -77,6 +77,9 @@ public:

   ElementTransformation();

+   /** @brief Force the reevaluation of the Jacobian in the next call. */
+   void Reset() { EvalState = 0; }
+
   /** @brief Set the integration point @a ip that weights and Jacobians will
       be evaluated at. */
   void SetIntPoint(const IntegrationPoint *ip)
@@ -357,9 +360,17 @@ private:
   // Evaluate the Hessian of the transformation at the IntPoint and store it
   // in d2Fdx2.
   virtual const DenseMatrix &EvalHessian();
+
 public:
+   IsoparametricTransformation() : FElem(NULL) {}
+
   /// Set the element that will be used to compute the transformations
-   void SetFE(const FiniteElement *FE) { FElem = FE; geom = FE->GetGeomType(); }
+   void SetFE(const FiniteElement *FE)
+   {
+      MFEM_ASSERT(FE != NULL, "Must provide a valid FiniteElement object!");
+      EvalState = (FE != FElem) ? 0 : EvalState;
+      FElem = FE; geom = FE->GetGeomType();
+   }

   /// Get the current element used to compute the transformations
   const FiniteElement* GetFE() const { return FElem; }
@@ -374,12 +385,15 @@ public:
       the column-vector of all basis functions evaluated at \f$ \hat x \f$ .
       The columns of @a P represent the control points in physical space
       defining the transformation. */
-   void SetPointMat(const DenseMatrix &pm) { PointMat = pm; }
+   void SetPointMat(const DenseMatrix &pm) { PointMat = pm; EvalState = 0; }

   /// Return the stored point matrix.
   const DenseMatrix &GetPointMat() const { return PointMat; }

-   /// Write access to the stored point matrix. Use with caution.
+   /// @brief Write access to the stored point matrix. Use with caution.
+   /** If the point matrix is altered using this member function the Reset
+       function should also be called to force the reevaluation of the
+       Jacobian, etc.. */
   DenseMatrix &GetPointMat() { return PointMat; }

   /// Set the FiniteElement Geometry for the reference elements being used.
@@ -139,6 +139,12 @@ void FiniteElement::Project (
   mfem_error ("FiniteElement::Project (...) (vector) is not overloaded !");
 }

+void FiniteElement::ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                     Vector &dofs) const
+{
+   mfem_error ("FiniteElement::ProjectFromNodes() (vector) is not overloaded!");
+}
+
 void FiniteElement::ProjectMatrixCoefficient(
   MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
 {
@@ -925,6 +931,23 @@ void VectorFiniteElement::Project_RT(
   }
 }

+void VectorFiniteElement::Project_RT(
+   const double *nk, const Array<int> &d2n,
+   Vector &vc, ElementTransformation &Trans, Vector &dofs) const
+{
+   const int sdim = Trans.GetSpaceDim();
+   const bool square_J = (dim == sdim);
+
+   for (int k = 0; k < dof; k++)
+   {
+      Trans.SetIntPoint(&Nodes.IntPoint(k));
+      // dof_k = nk^t adj(J) xk
+      Vector vk(vc.GetData()+k*sdim, sdim);
+      dofs(k) = Trans.AdjugateJacobian().InnerProduct(vk, nk + d2n[k]*dim);
+      if (!square_J) { dofs(k) /= Trans.Weight(); }
+   }
+}
+
 void VectorFiniteElement::ProjectMatrixCoefficient_RT(
   const double *nk, const Array<int> &d2n,
   MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
@@ -1101,6 +1124,19 @@ void VectorFiniteElement::Project_ND(
   }
 }

+void VectorFiniteElement::Project_ND(
+   const double *tk, const Array<int> &d2t,
+   Vector &vc, ElementTransformation &Trans, Vector &dofs) const
+{
+   for (int k = 0; k < dof; k++)
+   {
+      Trans.SetIntPoint(&Nodes.IntPoint(k));
+      Vector vk(vc.GetData()+k*dim, dim);
+      // dof_k = xk^t J tk
+      dofs(k) = Trans.Jacobian().InnerProduct(tk + d2t[k]*dim, vk);
+   }
+}
+
 void VectorFiniteElement::ProjectMatrixCoefficient_ND(
   const double *tk, const Array<int> &d2t,
   MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
@@ -7034,6 +7070,95 @@ void Poly_1D::Basis::Eval(const double y, Vector &u, Vector &d) const
   }
 }

+void Poly_1D::Basis::Eval(const double y, Vector &u, Vector &d,
+                          Vector &d2) const
+{
+   MFEM_VERIFY(etype == Barycentric,
+               "Basis::Eval with second order derivatives not implemented for"
+               " etype = " << etype);
+   switch (etype)
+   {
+      case ChangeOfBasis:
+      {
+         CalcBasis(Ai.Width() - 1, y, x, w);
+         Ai.Mult(x, u);
+         Ai.Mult(w, d);
+         // set d2 (not implemented yet)
+         break;
+      }
+      case Barycentric:
+      {
+         int i, k, p = x.Size() - 1;
+         double l, lp, lp2, lk, sk, si, sk2;
+
+         if (p == 0)
+         {
+            u(0) = 1.0;
+            d(0) = 0.0;
+            d2(0) = 0.0;
+            return;
+         }
+
+         lk = 1.0;
+         for (k = 0; k < p; k++)
+         {
+            if (y >= (x(k) + x(k+1))/2)
+            {
+               lk *= y - x(k);
+            }
+            else
+            {
+               for (i = k+1; i <= p; i++)
+               {
+                  lk *= y - x(i);
+               }
+               break;
+            }
+         }
+         l = lk * (y - x(k));
+
+         sk = 0.0;
+         sk2 = 0.0;
+         for (i = 0; i < k; i++)
+         {
+            si = 1.0/(y - x(i));
+            sk += si;
+            sk2 -= si * si;
+            u(i) = l * si * w(i);
+         }
+         u(k) = lk * w(k);
+         for (i++; i <= p; i++)
+         {
+            si = 1.0/(y - x(i));
+            sk += si;
+            sk2 -= si * si;
+            u(i) = l * si * w(i);
+         }
+         lp = l * sk + lk;
+         lp2 = lp * sk + l * sk2 + sk * lk;
+
+         for (i = 0; i < k; i++)
+         {
+            d(i) = (lp * w(i) - u(i))/(y - x(i));
+            d2(i) = (lp2 * w(i) - 2 * d(i))/(y - x(i));
+         }
+         d(k) = sk * u(k);
+         d2(k) = sk2 * u(k) + sk * d(k);
+         for (i++; i <= p; i++)
+         {
+            d(i) = (lp * w(i) - u(i))/(y - x(i));
+            d2(i) = (lp2 * w(i) - 2 * d(i))/(y - x(i));
+         }
+         break;
+      }
+      case Positive:
+         CalcBernstein(x.Size() - 1, y, u, d);
+         break;
+
+      default: break;
+   }
+}
+
 const int *Poly_1D::Binom(const int p)
 {
   if (binom.NumCols() <= p)
@@ -7589,6 +7714,7 @@ H1_SegmentElement::H1_SegmentElement(const int p, const int btype)
 #ifndef MFEM_THREAD_SAFE
   shape_x.SetSize(p+1);
   dshape_x.SetSize(p+1);
+   d2shape_x.SetSize(p+1);
 #endif

   Nodes.IntPoint(0).x = cp[0];
@@ -7637,6 +7763,25 @@ void H1_SegmentElement::CalcDShape(const IntegrationPoint &ip,
   }
 }

+void H1_SegmentElement::CalcHessian(const IntegrationPoint &ip,
+                                    DenseMatrix &Hessian) const
+{
+   const int p = order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+1), dshape_x(p+1), d2shape_x(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+
+   Hessian(0,0) = d2shape_x(0);
+   Hessian(1,0) = d2shape_x(p);
+   for (int i = 1; i < p; i++)
+   {
+      Hessian(i+1,0) = d2shape_x(i);
+   }
+}
+
 void H1_SegmentElement::ProjectDelta(int vertex, Vector &dofs) const
 {
   const int p = order;
@@ -7677,6 +7822,8 @@ H1_QuadrilateralElement::H1_QuadrilateralElement(const int p, const int btype)
   shape_y.SetSize(p1);
   dshape_x.SetSize(p1);
   dshape_y.SetSize(p1);
+   d2shape_x.SetSize(p1);
+   d2shape_y.SetSize(p1);
 #endif

   int o = 0;
@@ -7730,6 +7877,30 @@ void H1_QuadrilateralElement::CalcDShape(const IntegrationPoint &ip,
   }
 }

+void H1_QuadrilateralElement::CalcHessian(const IntegrationPoint &ip,
+                                          DenseMatrix &Hessian) const
+{
+   const int p = order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+1), shape_y(p+1), dshape_x(p+1), dshape_y(p+1),
+          d2shape_x(p+1), d2shape_y(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+   basis1d.Eval(ip.y, shape_y, dshape_y, d2shape_y);
+
+   for (int o = 0, j = 0; j <= p; j++)
+   {
+      for (int i = 0; i <= p; i++)
+      {
+         Hessian(dof_map[o],0) = d2shape_x(i)*  shape_y(j);
+         Hessian(dof_map[o],1) =  dshape_x(i)* dshape_y(j);
+         Hessian(dof_map[o],2) =   shape_x(i)*d2shape_y(j);  o++;
+      }
+   }
+}
+
 void H1_QuadrilateralElement::ProjectDelta(int vertex, Vector &dofs) const
 {
   const int p = order;
@@ -7793,6 +7964,9 @@ H1_HexahedronElement::H1_HexahedronElement(const int p, const int btype)
   dshape_x.SetSize(p1);
   dshape_y.SetSize(p1);
   dshape_z.SetSize(p1);
+   d2shape_x.SetSize(p1);
+   d2shape_y.SetSize(p1);
+   d2shape_z.SetSize(p1);
 #endif

   int o = 0;
@@ -7849,6 +8023,35 @@ void H1_HexahedronElement::CalcDShape(const IntegrationPoint &ip,
         }
 }

+void H1_HexahedronElement::CalcHessian(const IntegrationPoint &ip,
+                                       DenseMatrix &Hessian) const
+{
+   const int p = order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+1),  shape_y(p+1),  shape_z(p+1);
+   Vector dshape_x(p+1), dshape_y(p+1), dshape_z(p+1);
+   Vector d2shape_x(p+1), d2shape_y(p+1), d2shape_z(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+   basis1d.Eval(ip.y, shape_y, dshape_y, d2shape_y);
+   basis1d.Eval(ip.z, shape_z, dshape_z, d2shape_z);
+
+   for (int o = 0, k = 0; k <= p; k++)
+      for (int j = 0; j <= p; j++)
+         for (int i = 0; i <= p; i++)
+         {
+            Hessian(dof_map[o],0) = d2shape_x(i)*  shape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],1) =  dshape_x(i)* dshape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],2) =  dshape_x(i)*  shape_y(j)* dshape_z(k);
+            Hessian(dof_map[o],3) =   shape_x(i)*d2shape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],4) =   shape_x(i)* dshape_y(j)* dshape_z(k);
+            Hessian(dof_map[o],5) =   shape_x(i)*  shape_y(j)*d2shape_z(k);
+            o++;
+         }
+}
+
 void H1_HexahedronElement::ProjectDelta(int vertex, Vector &dofs) const
 {
   const int p = order;
@@ -446,7 +446,7 @@ public:
   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
       part of the Hessian of one shape function.
       The order in 2D is {u_xx, u_xy, u_yy}.
-       The size (#dof x (#dim (#dim-1)/2) of @a Hessian must be set in advance.*/
+       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
   virtual void CalcHessian (const IntegrationPoint &ip,
                             DenseMatrix &Hessian) const;

@@ -504,14 +504,21 @@ public:
   /** @brief Given a coefficient and a transformation, compute its projection
       (approximation) in the local finite dimensional space in terms
       of the degrees of freedom. */
-   virtual void Project (Coefficient &coeff,
-                         ElementTransformation &Trans, Vector &dofs) const;
+   virtual void Project(Coefficient &coeff,
+                        ElementTransformation &Trans, Vector &dofs) const;

   /** @brief Given a vector coefficient and a transformation, compute its
       projection (approximation) in the local finite dimensional space
       in terms of the degrees of freedom. (VectorFiniteElements) */
-   virtual void Project (VectorCoefficient &vc,
-                         ElementTransformation &Trans, Vector &dofs) const;
+   virtual void Project(VectorCoefficient &vc,
+                        ElementTransformation &Trans, Vector &dofs) const;
+
+   /** @brief Given a vector of values at the finite element nodes and a
+       transformation, compute its projection (approximation) in the local
+       finite dimensional space in terms of the degrees of freedom. Valid for
+       VectorFiniteElements. */
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const;

   /** @brief Given a matrix coefficient and a transformation, compute an
       approximation ("projection") in the local finite dimensional space in
@@ -797,7 +804,12 @@ protected:
                   VectorCoefficient &vc, ElementTransformation &Trans,
                   Vector &dofs) const;

-   // project the rows of the matrix coefficient in an RT space
+   /// Projects the vector of values given at FE nodes to RT space
+   void Project_RT(const double *nk, const Array<int> &d2n,
+                   Vector &vc, ElementTransformation &Trans,
+                   Vector &dofs) const;
+
+   /// Project the rows of the matrix coefficient in an RT space
   void ProjectMatrixCoefficient_RT(
      const double *nk, const Array<int> &d2n,
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
@@ -825,7 +837,12 @@ protected:
                   VectorCoefficient &vc, ElementTransformation &Trans,
                   Vector &dofs) const;

-   /// project the rows of the matrix coefficient in an ND space
+   /// Projects the vector of values given at FE nodes to ND space
+   void Project_ND(const double *tk, const Array<int> &d2t,
+                   Vector &vc, ElementTransformation &Trans,
+                   Vector &dofs) const;
+
+   /// Project the rows of the matrix coefficient in an ND space
   void ProjectMatrixCoefficient_ND(
      const double *tk, const Array<int> &d2t,
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const;
@@ -1850,6 +1867,7 @@ public:
      Basis(const int p, const double *nodes, EvalType etype = Barycentric);
      void Eval(const double x, Vector &u) const;
      void Eval(const double x, Vector &u, Vector &d) const;
+      void Eval(const double x, Vector &u, Vector &d, Vector &d2) const;
   };

 private:
@@ -2100,7 +2118,7 @@ class H1_SegmentElement : public NodalTensorFiniteElement
 {
 private:
 #ifndef MFEM_THREAD_SAFE
-   mutable Vector shape_x, dshape_x;
+   mutable Vector shape_x, dshape_x, d2shape_x;
 #endif

 public:
@@ -2109,6 +2127,8 @@ public:
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
 };

@@ -2118,7 +2138,7 @@ class H1_QuadrilateralElement : public NodalTensorFiniteElement
 {
 private:
 #ifndef MFEM_THREAD_SAFE
-   mutable Vector shape_x, shape_y, dshape_x, dshape_y;
+   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
 #endif

 public:
@@ -2128,6 +2148,8 @@ public:
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
 };

@@ -2137,7 +2159,8 @@ class H1_HexahedronElement : public NodalTensorFiniteElement
 {
 private:
 #ifndef MFEM_THREAD_SAFE
-   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
+   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z,
+           d2shape_x, d2shape_y, d2shape_z;
 #endif

 public:
@@ -2146,6 +2169,8 @@ public:
   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
   virtual void CalcDShape(const IntegrationPoint &ip,
                           DenseMatrix &dshape) const;
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
   virtual void ProjectDelta(int vertex, Vector &dofs) const;
 };

@@ -2681,6 +2706,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
@@ -2739,6 +2767,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
@@ -2790,6 +2821,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
@@ -2847,6 +2881,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
@@ -2906,6 +2943,10 @@ public:
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }

+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
+
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
@@ -2965,6 +3006,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
@@ -3016,6 +3060,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
@@ -3072,6 +3119,9 @@ public:
   virtual void Project(VectorCoefficient &vc,
                        ElementTransformation &Trans, Vector &dofs) const
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
+   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                                 Vector &dofs) const
+   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
   virtual void ProjectMatrixCoefficient(
      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
@@ -19,6 +19,7 @@
 #include "eltrans.hpp"
 #include "coefficient.hpp"
 #include "complex_fem.hpp"
+#include "convergence.hpp"
 #include "lininteg.hpp"
 #include "nonlininteg.hpp"
 #include "bilininteg.hpp"
@@ -440,6 +440,7 @@ void FiniteElementSpace::MarkerToList(const Array<int> &marker,
      if (marker[i]) { num_marked++; }
   }
   list.SetSize(0);
+   list.HostWrite();
   list.Reserve(num_marked);
   for (int i = 0; i < marker.Size(); i++)
   {
@@ -451,7 +452,9 @@ void FiniteElementSpace::MarkerToList(const Array<int> &marker,
 void FiniteElementSpace::ListToMarker(const Array<int> &list, int marker_size,
                                      Array<int> &marker, int mark_val)
 {
+   list.HostRead(); // make sure we can read the array on host
   marker.SetSize(marker_size);
+   marker.HostWrite();
   marker = 0;
   for (int i = 0; i < list.Size(); i++)
   {
@@ -199,8 +199,7 @@ void GridFunction::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
   if (f != fes) { Destroy(); }
   fes = f;
   v.UseDevice(true);
-   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, fes->GetVSize()),
-                    fes->GetVSize(), true);
+   this->Vector::MakeRef(v, v_offset, fes->GetVSize());
   sequence = fes->GetSequence();
 }

@@ -1834,6 +1833,19 @@ void GridFunction::ImposeBounds(int i, const Vector &weights,
   ImposeBounds(i, weights, minv, maxv);
 }

+void GridFunction::RestrictConforming()
+{
+   const SparseMatrix *R = fes->GetRestrictionMatrix();
+   const Operator *P = fes->GetProlongationMatrix();
+
+   if (P && R)
+   {
+      Vector tmp(R->Height());
+      R->Mult(*this, tmp);
+      P->Mult(tmp, *this);
+   }
+}
+
 void GridFunction::GetNodalValues(Vector &nval, int vdim) const
 {
   int i, j;
@@ -2602,11 +2614,7 @@ double GridFunction::ComputeL2Error(
      }
   }

-   if (error < 0.0)
-   {
-      return -sqrt(-error);
-   }
-   return sqrt(error);
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
 }

 double GridFunction::ComputeL2Error(
@@ -2647,94 +2655,199 @@ double GridFunction::ComputeL2Error(
      }
   }

-   if (error < 0.0)
-   {
-      return -sqrt(-error);
-   }
-   return sqrt(error);
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
 }

-double GridFunction::ComputeH1Error(
-   Coefficient *exsol, VectorCoefficient *exgrad,
-   Coefficient *ell_coeff, double Nu, int norm_type) const
+double GridFunction::ComputeGradError(VectorCoefficient *exgrad,
+                                      const IntegrationRule *irs[]) const
 {
-   // assuming vdim is 1
-   int i, fdof, dim, intorder, j, k;
+   double error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *Tr;
+   Array<int> dofs;
+   Vector grad;
+   int intorder;
+   int dim = fes->GetMesh()->SpaceDimension();
+   Vector vec(dim);
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      Tr = fes->GetElementTransformation(i);
+      intorder = 2*fe->GetOrder() + 3; // <--------
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      fes->GetElementDofs(i, dofs);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         Tr->SetIntPoint(&ip);
+         GetGradient(*Tr,grad);
+         exgrad->Eval(vec,*Tr,ip);
+         vec-=grad;
+         error += ip.weight * Tr->Weight() * (vec * vec);
+      }
+   }
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeCurlError(VectorCoefficient *excurl,
+                                      const IntegrationRule *irs[]) const
+{
+   double error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *Tr;
+   Array<int> dofs;
+   Vector curl;
+   int intorder;
+   int dim = fes->GetMesh()->SpaceDimension();
+   int n = (dim == 3) ? dim : 1;
+   Vector vec(n);
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      Tr = fes->GetElementTransformation(i);
+      intorder = 2*fe->GetOrder() + 3;
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      fes->GetElementDofs(i, dofs);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         Tr->SetIntPoint(&ip);
+         GetCurl(*Tr,curl);
+         excurl->Eval(vec,*Tr,ip);
+         vec-=curl;
+         error += ip.weight * Tr->Weight() * ( vec * vec );
+      }
+   }
+
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeDivError(
+   Coefficient *exdiv, const IntegrationRule *irs[]) const
+{
+   double error = 0.0, a;
+   const FiniteElement *fe;
+   ElementTransformation *Tr;
+   Array<int> dofs;
+   int intorder;
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      Tr = fes->GetElementTransformation(i);
+      intorder = 2*fe->GetOrder() + 3;
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      fes->GetElementDofs(i, dofs);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         Tr->SetIntPoint (&ip);
+         a = GetDivergence(*Tr) - exdiv->Eval(*Tr, ip);
+         error += ip.weight * Tr->Weight() * a * a;
+      }
+   }
+
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeDGFaceJumpError(Coefficient *exsol,
+                                            Coefficient *ell_coeff, double Nu,
+                                            const IntegrationRule *irs[])  const
+{
+   int fdof, dim, intorder, k;
   Mesh *mesh;
   const FiniteElement *fe;
   ElementTransformation *transf;
   FaceElementTransformations *face_elem_transf;
-   Vector e_grad, a_grad, shape, el_dofs, err_val, ell_coeff_val;
-   DenseMatrix dshape, dshapet, Jinv;
+   Vector shape, el_dofs, err_val, ell_coeff_val;
   Array<int> vdofs;
   IntegrationPoint eip;
   double error = 0.0;

   mesh = fes->GetMesh();
   dim = mesh->Dimension();
-   e_grad.SetSize(dim);
-   a_grad.SetSize(dim);
-   Jinv.SetSize(dim);

-   if (norm_type & 1)
-      for (i = 0; i < mesh->GetNE(); i++)
-      {
-         fe = fes->GetFE(i);
-         fdof = fe->GetDof();
-         transf = mesh->GetElementTransformation(i);
-         el_dofs.SetSize(fdof);
-         dshape.SetSize(fdof, dim);
-         dshapet.SetSize(fdof, dim);
-         intorder = 2 * fe->GetOrder(); // <----------
-         const IntegrationRule &ir = IntRules.Get(fe->GetGeomType(), intorder);
-         fes->GetElementVDofs(i, vdofs);
-         for (k = 0; k < fdof; k++)
-            if (vdofs[k] >= 0)
-            {
-               el_dofs(k) =   (*this)(vdofs[k]);
-            }
-            else
-            {
-               el_dofs(k) = - (*this)(-1-vdofs[k]);
-            }
-         for (j = 0; j < ir.GetNPoints(); j++)
+   for (int i = 0; i < mesh->GetNumFaces(); i++)
+   {
+      face_elem_transf = mesh->GetFaceElementTransformations(i, 5);
+      int i1 = face_elem_transf->Elem1No;
+      int i2 = face_elem_transf->Elem2No;
+      intorder = fes->GetFE(i1)->GetOrder();
+      if (i2 >= 0)
+         if ( (k = fes->GetFE(i2)->GetOrder()) > intorder )
         {
-            const IntegrationPoint &ip = ir.IntPoint(j);
-            fe->CalcDShape(ip, dshape);
-            transf->SetIntPoint(&ip);
-            exgrad->Eval(e_grad, *transf, ip);
-            CalcInverse(transf->Jacobian(), Jinv);
-            Mult(dshape, Jinv, dshapet);
-            dshapet.MultTranspose(el_dofs, a_grad);
-            e_grad -= a_grad;
-            error += (ip.weight * transf->Weight() *
-                      ell_coeff->Eval(*transf, ip) *
-                      (e_grad * e_grad));
+            intorder = k;
         }
-      }
-
-   if (norm_type & 2)
-      for (i = 0; i < mesh->GetNFaces(); i++)
+      intorder = 2 * intorder;  // <-------------
+      const IntegrationRule *ir;
+      if (irs)
      {
-         face_elem_transf = mesh->GetFaceElementTransformations(i, 5);
-         int i1 = face_elem_transf->Elem1No;
-         int i2 = face_elem_transf->Elem2No;
-         intorder = fes->GetFE(i1)->GetOrder();
-         if (i2 >= 0)
-            if ( (k = fes->GetFE(i2)->GetOrder()) > intorder )
-            {
-               intorder = k;
-            }
-         intorder = 2 * intorder;  // <-------------
-         const IntegrationRule &ir =
-            IntRules.Get(face_elem_transf->GetGeometryType(), intorder);
-         err_val.SetSize(ir.GetNPoints());
-         ell_coeff_val.SetSize(ir.GetNPoints());
-         // side 1
-         transf = face_elem_transf->Elem1;
-         fe = fes->GetFE(i1);
+         ir = irs[face_elem_transf->GetGeometryType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(face_elem_transf->GetGeometryType(), intorder));
+      }
+      err_val.SetSize(ir->GetNPoints());
+      ell_coeff_val.SetSize(ir->GetNPoints());
+      // side 1
+      transf = face_elem_transf->Elem1;
+      fe = fes->GetFE(i1);
+      fdof = fe->GetDof();
+      fes->GetElementVDofs(i1, vdofs);
+      shape.SetSize(fdof);
+      el_dofs.SetSize(fdof);
+      for (k = 0; k < fdof; k++)
+         if (vdofs[k] >= 0)
+         {
+            el_dofs(k) =   (*this)(vdofs[k]);
+         }
+         else
+         {
+            el_dofs(k) = - (*this)(-1-vdofs[k]);
+         }
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         face_elem_transf->Loc1.Transform(ir->IntPoint(j), eip);
+         fe->CalcShape(eip, shape);
+         transf->SetIntPoint(&eip);
+         ell_coeff_val(j) = ell_coeff->Eval(*transf, eip);
+         err_val(j) = exsol->Eval(*transf, eip) - (shape * el_dofs);
+      }
+      if (i2 >= 0)
+      {
+         // side 2
+         face_elem_transf = mesh->GetFaceElementTransformations(i, 10);
+         transf = face_elem_transf->Elem2;
+         fe = fes->GetFE(i2);
         fdof = fe->GetDof();
-         fes->GetElementVDofs(i1, vdofs);
+         fes->GetElementVDofs(i2, vdofs);
         shape.SetSize(fdof);
         el_dofs.SetSize(fdof);
         for (k = 0; k < fdof; k++)
@@ -2746,60 +2859,69 @@ double GridFunction::ComputeH1Error(
            {
               el_dofs(k) = - (*this)(-1-vdofs[k]);
            }
-         for (j = 0; j < ir.GetNPoints(); j++)
+         for (int j = 0; j < ir->GetNPoints(); j++)
         {
-            face_elem_transf->Loc1.Transform(ir.IntPoint(j), eip);
+            face_elem_transf->Loc2.Transform(ir->IntPoint(j), eip);
            fe->CalcShape(eip, shape);
            transf->SetIntPoint(&eip);
-            ell_coeff_val(j) = ell_coeff->Eval(*transf, eip);
-            err_val(j) = exsol->Eval(*transf, eip) - (shape * el_dofs);
-         }
-         if (i2 >= 0)
-         {
-            // side 2
-            face_elem_transf = mesh->GetFaceElementTransformations(i, 10);
-            transf = face_elem_transf->Elem2;
-            fe = fes->GetFE(i2);
-            fdof = fe->GetDof();
-            fes->GetElementVDofs(i2, vdofs);
-            shape.SetSize(fdof);
-            el_dofs.SetSize(fdof);
-            for (k = 0; k < fdof; k++)
-               if (vdofs[k] >= 0)
-               {
-                  el_dofs(k) =   (*this)(vdofs[k]);
-               }
-               else
-               {
-                  el_dofs(k) = - (*this)(-1-vdofs[k]);
-               }
-            for (j = 0; j < ir.GetNPoints(); j++)
-            {
-               face_elem_transf->Loc2.Transform(ir.IntPoint(j), eip);
-               fe->CalcShape(eip, shape);
-               transf->SetIntPoint(&eip);
-               ell_coeff_val(j) += ell_coeff->Eval(*transf, eip);
-               ell_coeff_val(j) *= 0.5;
-               err_val(j) -= (exsol->Eval(*transf, eip) - (shape * el_dofs));
-            }
-         }
-         face_elem_transf = mesh->GetFaceElementTransformations(i, 16);
-         transf = face_elem_transf;
-         for (j = 0; j < ir.GetNPoints(); j++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(j);
-            transf->SetIntPoint(&ip);
-            error += (ip.weight * Nu * ell_coeff_val(j) *
-                      pow(transf->Weight(), 1.0-1.0/(dim-1)) *
-                      err_val(j) * err_val(j));
+            ell_coeff_val(j) += ell_coeff->Eval(*transf, eip);
+            ell_coeff_val(j) *= 0.5;
+            err_val(j) -= (exsol->Eval(*transf, eip) - (shape * el_dofs));
         }
      }
-
-   if (error < 0.0)
-   {
-      return -sqrt(-error);
+      face_elem_transf = mesh->GetFaceElementTransformations(i, 16);
+      transf = face_elem_transf;
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         transf->SetIntPoint(&ip);
+         error += (ip.weight * Nu * ell_coeff_val(j) *
+                   pow(transf->Weight(), 1.0-1.0/(dim-1)) *
+                   err_val(j) * err_val(j));
+      }
   }
-   return sqrt(error);
+
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeH1Error(Coefficient *exsol,
+                                    VectorCoefficient *exgrad,
+                                    Coefficient *ell_coef, double Nu,
+                                    int norm_type) const
+{
+   double error1 = 0.0;
+   double error2 = 0.0;
+   if (norm_type & 1) { error1 = GridFunction::ComputeGradError(exgrad); }
+   if (norm_type & 2) { error2 = GridFunction::ComputeDGFaceJumpError(exsol,ell_coef,Nu); }
+
+   return sqrt(error1 * error1 + error2 * error2);
+}
+
+double GridFunction::ComputeH1Error(Coefficient *exsol,
+                                    VectorCoefficient *exgrad,
+                                    const IntegrationRule *irs[]) const
+{
+   double L2error = GridFunction::ComputeLpError(2.0,*exsol,NULL,irs);
+   double GradError = ComputeGradError(exgrad,irs);
+   return sqrt(L2error*L2error + GradError*GradError);
+}
+
+double GridFunction::ComputeHDivError(VectorCoefficient *exsol,
+                                      Coefficient *exdiv,
+                                      const IntegrationRule *irs[]) const
+{
+   double L2error = GridFunction::ComputeLpError(2.0,*exsol,NULL,NULL,irs);
+   double DivError = ComputeDivError(exdiv,irs);
+   return sqrt(L2error*L2error + DivError*DivError);
+}
+
+double GridFunction::ComputeHCurlError(VectorCoefficient *exsol,
+                                       VectorCoefficient *excurl,
+                                       const IntegrationRule *irs[]) const
+{
+   double L2error = GridFunction::ComputeLpError(2.0,*exsol,NULL,NULL,irs);
+   double CurlError = ComputeCurlError(excurl,irs);
+   return sqrt(L2error*L2error + CurlError*CurlError);
 }

 double GridFunction::ComputeMaxError(
@@ -2855,7 +2977,6 @@ double GridFunction::ComputeMaxError(
         }
      }
   }
-
   return error;
 }

@@ -334,6 +334,11 @@ public:
   void ImposeBounds(int i, const Vector &weights,
                     double _min = 0.0, double _max = infinity());

+   /** On a non-conforming mesh, make sure the function lies in the conforming
+       space by multiplying with R and then with P, the conforming restriction
+       and prolongation matrices of the space, respectively. */
+   void RestrictConforming();
+
   /** @brief Project the @a src GridFunction to @a this GridFunction, both of
       which must be on the same mesh. */
   /** The current implementation assumes that all elements use the same
@@ -422,6 +427,7 @@ public:
   virtual void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                             Array<int> &bdr_attr);

+
   virtual double ComputeL2Error(Coefficient &exsol,
                                 const IntegrationRule *irs[] = NULL) const
   { return ComputeLpError(2.0, exsol, NULL, irs); }
@@ -433,10 +439,50 @@ public:
                                 const IntegrationRule *irs[] = NULL,
                                 Array<int> *elems = NULL) const;

+   /// Returns ||grad u_ex - grad u_h||_L2 for H1 or L2 elements
+   virtual double ComputeGradError(VectorCoefficient *exgrad,
+                                   const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns ||curl u_ex - curl u_h||_L2 for ND elements
+   virtual double ComputeCurlError(VectorCoefficient *excurl,
+                                   const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns ||div u_ex - div u_h||_L2 for RT elements
+   virtual double ComputeDivError(Coefficient *exdiv,
+                                  const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns the Face Jumps error for L2 elements
+   virtual double ComputeDGFaceJumpError(Coefficient *exsol,
+                                         Coefficient *ell_coeff,
+                                         double Nu,
+                                         const IntegrationRule *irs[] = NULL)
+   const;
+
+   /** This method is kept for backward compatibility.
+
+       Returns either the H1-seminorm, or the DG face jumps error, or both
+       depending on norm_type = 1, 2, 3. Additional arguments for the DG face
+       jumps norm: ell_coeff: mesh-depended coefficient (weight) Nu: scalar
+       constant weight */
   virtual double ComputeH1Error(Coefficient *exsol, VectorCoefficient *exgrad,
                                 Coefficient *ell_coef, double Nu,
                                 int norm_type) const;

+   /// Returns the error measured in H1-norm for H1 elements or in "broken"
+   /// H1-norm for L2 elements
+   virtual double ComputeH1Error(Coefficient *exsol, VectorCoefficient *exgrad,
+                                 const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns the error measured in H(div)-norm for RT elements
+   virtual double ComputeHDivError(VectorCoefficient *exsol,
+                                   Coefficient *exdiv,
+                                   const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns the error measured in H(curl)-norm for ND elements
+   virtual double ComputeHCurlError(VectorCoefficient *exsol,
+                                    VectorCoefficient *excurl,
+                                    const IntegrationRule *irs[] = NULL) const;
+
   virtual double ComputeMaxError(Coefficient &exsol,
                                  const IntegrationRule *irs[] = NULL) const
   {
@@ -29,10 +29,13 @@ namespace mfem
 {

 FindPointsGSLIB::FindPointsGSLIB()
-   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
-     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
+   : mesh(NULL), meshsplit(NULL), ir_simplex(NULL),
+     fdata2D(NULL), fdata3D(NULL), cr(NULL), gsl_comm(NULL),
+     dim(-1), points_cnt(0), setupflag(false), default_interp_value(0),
+     avgtype(AvgType::ARITHMETIC)
 {
   gsl_comm = new comm;
+   cr       = new crystal;
 #ifdef MFEM_USE_MPI
   int initialized;
   MPI_Initialized(&initialized);
@@ -47,15 +50,20 @@ FindPointsGSLIB::FindPointsGSLIB()
 FindPointsGSLIB::~FindPointsGSLIB()
 {
   delete gsl_comm;
+   delete cr;
   delete ir_simplex;
+   delete meshsplit;
 }

 #ifdef MFEM_USE_MPI
 FindPointsGSLIB::FindPointsGSLIB(MPI_Comm _comm)
-   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
-     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
+   : mesh(NULL), meshsplit(NULL), ir_simplex(NULL),
+     fdata2D(NULL), fdata3D(NULL), cr(NULL), gsl_comm(NULL),
+     dim(-1), points_cnt(0), setupflag(false), default_interp_value(0),
+     avgtype(AvgType::ARITHMETIC)
 {
   gsl_comm = new comm;
+   cr      = new crystal;
   comm_init(gsl_comm, _comm);
 }
 #endif
@@ -70,6 +78,7 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
   // call FreeData if FindPointsGSLIB::Setup has been called already
   if (setupflag) { FreeData(); }

+   crystal_init(cr, gsl_comm);
   mesh = &m;
   dim  = mesh->Dimension();
   const FiniteElement *fe = mesh->GetNodalFESpace()->GetFE(0);
@@ -113,14 +122,16 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
   setupflag = true;
 }

-void FindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                 Array<unsigned int> &codes,
-                                 Array<unsigned int> &proc_ids,
-                                 Array<unsigned int> &elem_ids,
-                                 Vector &ref_pos, Vector &dist)
+void FindPointsGSLIB::FindPoints(const Vector &point_pos)
 {
   MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
-   const int points_cnt = point_pos.Size() / dim;
+   points_cnt = point_pos.Size() / dim;
+   gsl_code.SetSize(points_cnt);
+   gsl_proc.SetSize(points_cnt);
+   gsl_elem.SetSize(points_cnt);
+   gsl_ref.SetSize(points_cnt * dim);
+   gsl_dist.SetSize(points_cnt);
+
   if (dim == 2)
   {
      const double *xv_base[2];
@@ -129,11 +140,11 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
      unsigned xv_stride[2];
      xv_stride[0] = sizeof(double);
      xv_stride[1] = sizeof(double);
-      findpts_2(codes.GetData(), sizeof(unsigned int),
-                proc_ids.GetData(), sizeof(unsigned int),
-                elem_ids.GetData(), sizeof(unsigned int),
-                ref_pos.GetData(), sizeof(double) * dim,
-                dist.GetData(), sizeof(double),
+      findpts_2(gsl_code.GetData(), sizeof(unsigned int),
+                gsl_proc.GetData(), sizeof(unsigned int),
+                gsl_elem.GetData(), sizeof(unsigned int),
+                gsl_ref.GetData(),  sizeof(double) * dim,
+                gsl_dist.GetData(), sizeof(double),
                xv_base, xv_stride, points_cnt, fdata2D);
   }
   else
@@ -146,25 +157,27 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
      xv_stride[0] = sizeof(double);
      xv_stride[1] = sizeof(double);
      xv_stride[2] = sizeof(double);
-      findpts_3(codes.GetData(), sizeof(unsigned int),
-                proc_ids.GetData(), sizeof(unsigned int),
-                elem_ids.GetData(), sizeof(unsigned int),
-                ref_pos.GetData(), sizeof(double) * dim,
-                dist.GetData(), sizeof(double),
+      findpts_3(gsl_code.GetData(), sizeof(unsigned int),
+                gsl_proc.GetData(), sizeof(unsigned int),
+                gsl_elem.GetData(), sizeof(unsigned int),
+                gsl_ref.GetData(),  sizeof(double) * dim,
+                gsl_dist.GetData(), sizeof(double),
                xv_base, xv_stride, points_cnt, fdata3D);
   }
-}

-void FindPointsGSLIB::FindPoints(const Vector &point_pos)
-{
-   const int points_cnt = point_pos.Size() / dim;
-   gsl_code.SetSize(points_cnt);
-   gsl_proc.SetSize(points_cnt);
-   gsl_elem.SetSize(points_cnt);
-   gsl_ref.SetSize(points_cnt * dim);
-   gsl_dist.SetSize(points_cnt);
+   // Set the element number and reference position to 0 for points not found
+   for (int i = 0; i < points_cnt; i++)
+   {
+      if (gsl_code[i] == 2)
+      {
+         gsl_elem[i] = 0;
+         for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
+      }
+   }

-   FindPoints(point_pos, gsl_code, gsl_proc, gsl_elem, gsl_ref, gsl_dist);
+   // Map element number for simplices, and ref_pos from [-1,1] to [0,1] for
+   // both simplices and quads.
+   MapRefPosAndElemIndices();
 }

 void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
@@ -178,72 +191,24 @@ void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
   FindPoints(point_pos);
 }

-void FindPointsGSLIB::Interpolate(Array<unsigned int> &codes,
-                                  Array<unsigned int> &proc_ids,
-                                  Array<unsigned int> &elem_ids,
-                                  Vector &ref_pos, const GridFunction &field_in,
-                                  Vector &field_out)
-{
-
-   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
-   GridFunction field_in_scalar(&ind_fes);
-   Vector node_vals;
-
-   const int ncomp      = field_in.FESpace()->GetVDim(),
-             points_fld = field_in.Size() / ncomp,
-             points_cnt = codes.Size();
-   field_out.SetSize(points_cnt*ncomp);
-
-   for (int i = 0; i < ncomp; i++)
-   {
-      const int dataptrin  = i*points_fld,
-                dataptrout = i*points_cnt;
-      field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
-      GetNodeValues(field_in_scalar, node_vals);
-
-      if (dim==2)
-      {
-         findpts_eval_2(field_out.GetData()+dataptrout, sizeof(double),
-                        codes.GetData(),       sizeof(unsigned int),
-                        proc_ids.GetData(),    sizeof(unsigned int),
-                        elem_ids.GetData(),    sizeof(unsigned int),
-                        ref_pos.GetData(),     sizeof(double) * dim,
-                        points_cnt, node_vals.GetData(), fdata2D);
-      }
-      else
-      {
-         findpts_eval_3(field_out.GetData()+dataptrout, sizeof(double),
-                        codes.GetData(),       sizeof(unsigned int),
-                        proc_ids.GetData(),    sizeof(unsigned int),
-                        elem_ids.GetData(),    sizeof(unsigned int),
-                        ref_pos.GetData(),     sizeof(double) * dim,
-                        points_cnt, node_vals.GetData(), fdata3D);
-      }
-   }
-}
-
-void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
-                                  Vector &field_out)
-{
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
-}
-
 void FindPointsGSLIB::Interpolate(const Vector &point_pos,
                                  const GridFunction &field_in, Vector &field_out)
 {
   FindPoints(point_pos);
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+   Interpolate(field_in, field_out);
 }

 void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
                                  const GridFunction &field_in, Vector &field_out)
 {
   FindPoints(m, point_pos);
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+   Interpolate(field_in, field_out);
 }

 void FindPointsGSLIB::FreeData()
 {
+   if (!setupflag) { return; }
+   crystal_free(cr);
   if (dim == 2)
   {
      findpts_free_2(fdata2D);
@@ -252,13 +217,13 @@ void FindPointsGSLIB::FreeData()
   {
      findpts_free_3(fdata3D);
   }
-   setupflag = false;
   gsl_code.DeleteAll();
   gsl_proc.DeleteAll();
   gsl_elem.DeleteAll();
   gsl_mesh.Destroy();
   gsl_ref.Destroy();
   gsl_dist.Destroy();
+   setupflag = false;
 }

 void FindPointsGSLIB::GetNodeValues(const GridFunction &gf_in,
@@ -358,9 +323,8 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
   const FiniteElement *fe   = mesh->GetNodalFESpace()->GetFE(0);
   const Geometry::Type gt   = fe->GetGeomType();
   const GridFunction *nodes = mesh->GetNodes();
-   Mesh *meshsplit           = NULL;
   const int NE              = mesh->GetNE();
-   int NEsplit = -1;
+   int NEsplit = 0;

   // Split the reference element into a reference submesh of quads or hexes.
   if (gt == Geometry::TRIANGLE)
@@ -516,8 +480,361 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
         pt_id++;
      }
   }
+}

-   delete meshsplit;
+void FindPointsGSLIB::MapRefPosAndElemIndices()
+{
+   gsl_mfem_ref = gsl_ref;
+   gsl_mfem_elem = gsl_elem;
+   const FiniteElement *fe = mesh->GetNodalFESpace()->GetFE(0);
+   const Geometry::Type gt = fe->GetGeomType();
+   int NEsplit = 0;
+
+   gsl_mfem_ref -= -1.;  // map  [-1, 1] to
+   gsl_mfem_ref *= 0.5;  //      [0,  1]
+   if (gt == Geometry::SQUARE || gt == Geometry::CUBE) { return; }
+
+   H1_FECollection feclin(1, dim);
+   FiniteElementSpace nodal_fes_lin(meshsplit, &feclin, dim);
+   GridFunction gf_lin(&nodal_fes_lin);
+
+   if (gt == Geometry::TRIANGLE)
+   {
+      const double quad_v[7][2] =
+      {
+         {0, 0}, {0.5, 0}, {1, 0}, {0, 0.5},
+         {1./3., 1./3.}, {0.5, 0.5}, {0, 1}
+      };
+      for (int k = 0; k < dim; k++)
+      {
+         for (int j = 0; j < gf_lin.Size()/dim; j++)
+         {
+            gf_lin(j+k*gf_lin.Size()/dim) = quad_v[j][k];
+         }
+      }
+      NEsplit = 3;
+   }
+   else if (gt == Geometry::TETRAHEDRON)
+   {
+      const double hex_v[15][3] =
+      {
+         {0, 0, 0.}, {1, 0., 0.}, {0., 1., 0.}, {0, 0., 1.},
+         {0.5, 0., 0.}, {0.5, 0.5, 0.}, {0., 0.5, 0.},
+         {0., 0., 0.5}, {0.5, 0., 0.5}, {0., 0.5, 0.5},
+         {1./3., 0., 1./3.}, {1./3., 1./3., 1./3.}, {0, 1./3., 1./3.},
+         {1./3., 1./3., 0}, {0.25, 0.25, 0.25}
+      };
+      for (int k = 0; k < dim; k++)
+      {
+         for (int j = 0; j < gf_lin.Size()/dim; j++)
+         {
+            gf_lin(j+k*gf_lin.Size()/dim) = hex_v[j][k];
+         }
+      }
+      NEsplit = 4;
+   }
+   else if (gt == Geometry::PRISM)
+   {
+      const double hex_v[14][3] =
+      {
+         {0, 0, 0}, {0.5, 0, 0}, {1, 0, 0}, {0, 0.5, 0},
+         {1./3., 1./3., 0}, {0.5, 0.5, 0}, {0, 1, 0},
+         {0, 0, 1}, {0.5, 0, 1}, {1, 0, 1}, {0, 0.5, 1},
+         {1./3., 1./3., 1}, {0.5, 0.5, 1}, {0, 1, 1}
+      };
+      for (int k = 0; k < dim; k++)
+      {
+         for (int j = 0; j < gf_lin.Size()/dim; j++)
+         {
+            gf_lin(j+k*gf_lin.Size()/dim) = hex_v[j][k];
+         }
+      }
+      NEsplit = 3;
+   }
+   else
+   {
+      MFEM_ABORT("Element type not currently supported.");
+   }
+
+   // Simplices are split into quads/hexes for GSLIB. For MFEM, we need to find
+   // the original element number and map the rst from micro to macro element.
+   for (int i = 0; i < points_cnt; i++)
+   {
+      if (gsl_code[i] == 2) { continue; }
+      int local_elem   = gsl_elem[i]%NEsplit;
+      gsl_mfem_elem[i] = (gsl_elem[i] - local_elem)/NEsplit; // macro element number
+
+      IntegrationPoint ip;
+      Vector mfem_ref(gsl_mfem_ref.GetData()+i*dim, dim);
+      ip.Set2(mfem_ref.GetData());
+      if (dim == 3) { ip.z = mfem_ref(2); }
+      gf_lin.GetVectorValue(local_elem, ip, mfem_ref); // map to rst of macro element
+   }
+}
+
+void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
+                                  Vector &field_out)
+{
+   const int  gf_order   = field_in.FESpace()->GetFE(0)->GetOrder(),
+              mesh_order = mesh->GetNodalFESpace()->GetFE(0)->GetOrder();
+
+   const FiniteElementCollection *fec_in =  field_in.FESpace()->FEColl();
+   const H1_FECollection *fec_h1 = dynamic_cast<const H1_FECollection *>(fec_in);
+   const L2_FECollection *fec_l2 = dynamic_cast<const L2_FECollection *>(fec_in);
+
+   if (fec_h1 && gf_order == mesh_order &&
+       fec_h1->GetBasisType() == BasisType::GaussLobatto)
+   {
+      InterpolateH1(field_in, field_out);
+      return;
+   }
+   else
+   {
+      InterpolateGeneral(field_in, field_out);
+      if (!fec_l2 || avgtype == AvgType::NONE) { return; }
+   }
+
+   // For points on element borders, project the L2 GridFunction to H1 and
+   // re-interpolate.
+   if (fec_l2)
+   {
+      Array<int> indl2;
+      for (int i = 0; i < points_cnt; i++)
+      {
+         if (gsl_code[i] == 1) { indl2.Append(i); }
+      }
+      if (indl2.Size() == 0) { return; } // no points on element borders
+
+      Vector field_out_l2(field_out.Size());
+      VectorGridFunctionCoefficient field_in_dg(&field_in);
+      int gf_order_h1 = std::max(gf_order, 1); // H1 should be at least order 1
+      H1_FECollection fec(gf_order_h1, dim);
+      const int ncomp = field_in.FESpace()->GetVDim();
+      FiniteElementSpace fes(mesh, &fec, ncomp);
+      GridFunction field_in_h1(&fes);
+
+      if (avgtype == AvgType::ARITHMETIC)
+      {
+         field_in_h1.ProjectDiscCoefficient(field_in_dg, GridFunction::ARITHMETIC);
+      }
+      else if (avgtype == AvgType::HARMONIC)
+      {
+         field_in_h1.ProjectDiscCoefficient(field_in_dg, GridFunction::HARMONIC);
+      }
+      else
+      {
+         MFEM_ABORT("Invalid averaging type.");
+      }
+
+      if (gf_order_h1 == mesh_order) // basis is GaussLobatto by default
+      {
+         InterpolateH1(field_in_h1, field_out_l2);
+      }
+      else
+      {
+         InterpolateGeneral(field_in_h1, field_out_l2);
+      }
+
+      // Copy interpolated values for the points on element border
+      for (int j = 0; j < ncomp; j++)
+      {
+         for (int i = 0; i < indl2.Size(); i++)
+         {
+            int idx = indl2[i] + j*points_cnt;
+            field_out(idx) = field_out_l2(idx);
+         }
+      }
+   }
+}
+
+void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
+                                    Vector &field_out)
+{
+   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
+   GridFunction field_in_scalar(&ind_fes);
+   Vector node_vals;
+
+   const int ncomp      = field_in.FESpace()->GetVDim(),
+             points_fld = field_in.Size() / ncomp,
+             points_cnt = gsl_code.Size();
+
+   field_out.SetSize(points_cnt*ncomp);
+   field_out = default_interp_value;
+
+   for (int i = 0; i < ncomp; i++)
+   {
+      const int dataptrin  = i*points_fld,
+                dataptrout = i*points_cnt;
+      field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
+      GetNodeValues(field_in_scalar, node_vals);
+
+      if (dim==2)
+      {
+         findpts_eval_2(field_out.GetData()+dataptrout, sizeof(double),
+                        gsl_code.GetData(),       sizeof(unsigned int),
+                        gsl_proc.GetData(),    sizeof(unsigned int),
+                        gsl_elem.GetData(),    sizeof(unsigned int),
+                        gsl_ref.GetData(),     sizeof(double) * dim,
+                        points_cnt, node_vals.GetData(), fdata2D);
+      }
+      else
+      {
+         findpts_eval_3(field_out.GetData()+dataptrout, sizeof(double),
+                        gsl_code.GetData(),       sizeof(unsigned int),
+                        gsl_proc.GetData(),    sizeof(unsigned int),
+                        gsl_elem.GetData(),    sizeof(unsigned int),
+                        gsl_ref.GetData(),     sizeof(double) * dim,
+                        points_cnt, node_vals.GetData(), fdata3D);
+      }
+   }
+}
+
+void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
+                                         Vector &field_out)
+{
+   int ncomp   = field_in.VectorDim(),
+       nptorig = points_cnt,
+       npt     = points_cnt;
+
+   field_out.SetSize(points_cnt*ncomp);
+   field_out = default_interp_value;
+
+   if (gsl_comm->np == 1) // serial
+   {
+      for (int index = 0; index < npt; index++)
+      {
+         if (gsl_code[index] == 2) { continue; }
+         IntegrationPoint ip;
+         ip.Set2(gsl_mfem_ref.GetData()+index*dim);
+         if (dim == 3) { ip.z = gsl_mfem_ref(index*dim + 2); }
+         Vector localval(ncomp);
+         field_in.GetVectorValue(gsl_mfem_elem[index], ip, localval);
+         for (int i = 0; i < ncomp; i++)
+         {
+            field_out(index + i*npt) = localval(i);
+         }
+      }
+   }
+   else // parallel
+   {
+      // Determine number of points to be sent
+      int nptsend = 0;
+      for (int index = 0; index < npt; index++)
+      {
+         if (gsl_code[index] != 2) { nptsend +=1; }
+      }
+
+      // Pack data to send via crystal router
+      struct array *outpt = new array;
+      struct out_pt { double r[3], ival; uint index, el, proc; };
+      struct out_pt *pt;
+      array_init(struct out_pt, outpt, nptsend);
+      outpt->n=nptsend;
+      pt = (struct out_pt *)outpt->ptr;
+      for (int index = 0; index < npt; index++)
+      {
+         if (gsl_code[index] == 2) { continue; }
+         for (int d = 0; d < dim; ++d) { pt->r[d]= gsl_mfem_ref(index*dim + d); }
+         pt->index = index;
+         pt->proc  = gsl_proc[index];
+         pt->el    = gsl_mfem_elem[index];
+         ++pt;
+      }
+
+      // Transfer data to target MPI ranks
+      sarray_transfer(struct out_pt, outpt, proc, 1, cr);
+
+      if (ncomp == 1)
+      {
+         // Interpolate the grid function
+         npt = outpt->n;
+         pt = (struct out_pt *)outpt->ptr;
+         for (int index = 0; index < npt; index++)
+         {
+            IntegrationPoint ip;
+            ip.Set3(&pt->r[0]);
+            pt->ival = field_in.GetValue(pt->el, ip, 1);
+            ++pt;
+         }
+
+         // Transfer data back to source MPI rank
+         sarray_transfer(struct out_pt, outpt, proc, 1, cr);
+         npt = outpt->n;
+         pt = (struct out_pt *)outpt->ptr;
+         for (int index = 0; index < npt; index++)
+         {
+            field_out(pt->index) = pt->ival;
+            ++pt;
+         }
+         array_free(outpt);
+         delete outpt;
+      }
+      else // ncomp > 1
+      {
+         // Interpolate data and store in a Vector
+         npt = outpt->n;
+         pt = (struct out_pt *)outpt->ptr;
+         Vector vec_int_vals(npt*ncomp);
+         for (int index = 0; index < npt; index++)
+         {
+            IntegrationPoint ip;
+            ip.Set3(&pt->r[0]);
+            Vector localval(vec_int_vals.GetData()+index*ncomp, ncomp);
+            field_in.GetVectorValue(pt->el, ip, localval);
+            ++pt;
+         }
+
+         // Save index and proc data in a struct
+         struct array *savpt = new array;
+         struct sav_pt { uint index, proc; };
+         struct sav_pt *spt;
+         array_init(struct sav_pt, savpt, npt);
+         savpt->n=npt;
+         spt = (struct sav_pt *)savpt->ptr;
+         pt  = (struct out_pt *)outpt->ptr;
+         for (int index = 0; index < npt; index++)
+         {
+            spt->index = pt->index;
+            spt->proc  = pt->proc;
+            ++pt; ++spt;
+         }
+
+         array_free(outpt);
+         delete outpt;
+
+         // Copy data from save struct to send struct and send component wise
+         struct array *sendpt = new array;
+         struct send_pt { double ival; uint index, proc; };
+         struct send_pt *sdpt;
+         for (int j = 0; j < ncomp; j++)
+         {
+            array_init(struct send_pt, sendpt, npt);
+            sendpt->n=npt;
+            spt  = (struct sav_pt *)savpt->ptr;
+            sdpt = (struct send_pt *)sendpt->ptr;
+            for (int index = 0; index < npt; index++)
+            {
+               sdpt->index = spt->index;
+               sdpt->proc  = spt->proc;
+               sdpt->ival  = vec_int_vals(j + index*ncomp);
+               ++sdpt; ++spt;
+            }
+
+            sarray_transfer(struct send_pt, sendpt, proc, 1, cr);
+            sdpt = (struct send_pt *)sendpt->ptr;
+            for (int index = 0; index < nptorig; index++)
+            {
+               int idx = sdpt->index + j*nptorig;
+               field_out(idx) = sdpt->ival;
+               ++sdpt;
+            }
+            array_free(sendpt);
+         }
+         array_free(savpt);
+         delete sendpt;
+         delete savpt;
+      } // ncomp > 1
+   } // parallel
 }

 } // namespace mfem
@@ -20,28 +20,66 @@
 struct comm;
 struct findpts_data_2;
 struct findpts_data_3;
+struct array;
+struct crystal;

 namespace mfem
 {

+/** \brief FindPointsGSLIB can robustly evaluate a GridFunction on an arbitrary
+ *  collection of points. There are three key functions in FindPointsGSLIB:
+ *
+ *  1. Setup - constructs the internal data structures of gslib.
+ *
+ *  2. FindPoints - for any given arbitrary set of points in physical space,
+ *     gslib finds the element number, MPI rank, and the reference space
+ *     coordinates inside the element that each point is located in. gslib also
+ *     returns a code that indicates whether the point was found inside an
+ *     element, on element border, or not found in the domain.
+ *
+ *  3. Interpolate - Interpolates any grid function at the points found using 2.
+ *
+ *  FindPointsGSLIB provides interface to use these functions individually or
+ *  using a single call.
+ */
 class FindPointsGSLIB
 {
+public:
+   enum AvgType {NONE, ARITHMETIC, HARMONIC}; // Average type for L2 functions
+
 protected:
-   Mesh *mesh;
-   IntegrationRule *ir_simplex;
-   struct findpts_data_2 *fdata2D;
-   struct findpts_data_3 *fdata3D;
-   int dim;
-   Array<unsigned int> gsl_code, gsl_proc, gsl_elem;
-   Vector gsl_mesh, gsl_ref, gsl_dist;
-   bool setupflag;
-
-   struct comm *gsl_comm;
+   Mesh *mesh, *meshsplit;
+   IntegrationRule *ir_simplex;    // IntegrationRule to split quads/hex -> simplex
+   struct findpts_data_2 *fdata2D; // gslib's internal data
+   struct findpts_data_3 *fdata3D; // gslib's internal data
+   struct crystal *cr;             // gslib's internal data
+   struct comm *gsl_comm;          // gslib's internal data
+   int dim, points_cnt;
+   Array<unsigned int> gsl_code, gsl_proc, gsl_elem, gsl_mfem_elem;
+   Vector gsl_mesh, gsl_ref, gsl_dist, gsl_mfem_ref;
+   bool setupflag;              // flag to indicate whether gslib data has been setup
+   double default_interp_value; // used for points that are not found in the mesh
+   AvgType avgtype;             // average type used for L2 functions

+   /// Get GridFunction from MFEM format to GSLIB format
   void GetNodeValues(const GridFunction &gf_in, Vector &node_vals);
+   /// Get nodal coordinates from mesh to the format expected by GSLIB for quads
+   /// and hexes
   void GetQuadHexNodalCoordinates();
+   /// Convert simplices to quad/hexes and then get nodal coordinates for each
+   /// split element into format expected by GSLIB
   void GetSimplexNodalCoordinates();

+   /// Use GSLIB for communication and interpolation
+   void InterpolateH1(const GridFunction &field_in, Vector &field_out);
+   /// Uses GSLIB Crystal Router for communication followed by MFEM's
+   /// interpolation functions
+   void InterpolateGeneral(const GridFunction &field_in, Vector &field_out);
+   /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices mesh
+   /// find the original element number (that was split into micro quads/hexes
+   /// by GetSimplexNodalCoordinates())
+   void MapRefPosAndElemIndices();
+
 public:
   FindPointsGSLIB();

@@ -64,45 +102,37 @@ public:
   void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
              const int npt_max = 256);

-   /** Searches positions given in physical space by @a point_pos. All output
-       Arrays and Vectors are expected to have the correct size.
-
-       @param[in]  point_pos  Positions to be found. Must by ordered by nodes
-                              (XXX...,YYY...,ZZZ).
-       @param[out] codes      Return codes for each point: inside element (0),
-                              element boundary (1), not found (2).
-       @param[out] proc_ids   MPI proc ids where the points were found.
-       @param[out] elem_ids   Element ids where the points were found.
-       @param[out] ref_pos    Reference coordinates of the found point. Ordered
-                              by vdim (XYZ,XYZ,XYZ...).
-                              Note: the gslib reference frame is [-1,1].
-       @param[out] dist       Distance between the sought and the found point
-                              in physical space. */
-   void FindPoints(const Vector &point_pos, Array<unsigned int> &codes,
-                   Array<unsigned int> &proc_ids, Array<unsigned int> &elem_ids,
-                   Vector &ref_pos, Vector &dist);
+   /** Searches positions given in physical space by @a point_pos. These positions
+       must by ordered by nodes: (XXX...,YYY...,ZZZ).
+       This function populates the following member variables:
+       #gsl_code        Return codes for each point: inside element (0),
+                        element boundary (1), not found (2).
+       #gsl_proc        MPI proc ids where the points were found.
+       #gsl_elem        Element ids where the points were found.
+                        Defaults to 0 for points that were not found.
+       #gsl_mfem_elem   Element ids corresponding to MFEM-mesh where the points
+                        were found. #gsl_mfem_elem != #gsl_elem for simplices
+                        Defaults to 0 for points that were not found.
+       #gsl_ref         Reference coordinates of the found point.
+                        Ordered by vdim (XYZ,XYZ,XYZ...). Defaults to -1 for
+                        points that were not found. Note: the gslib reference
+                        frame is [-1,1].
+       #gsl_mfem_ref    Reference coordinates #gsl_ref mapped to [0,1].
+                        Defaults to 0 for points that were not found.
+       #gsl_dist        Distance between the sought and the found point
+                        in physical space. */
   void FindPoints(const Vector &point_pos);
   /// Setup FindPoints and search positions
   void FindPoints(Mesh &m, const Vector &point_pos, const double bb_t = 0.1,
                   const double newt_tol = 1.0e-12,  const int npt_max = 256);

   /** Interpolation of field values at prescribed reference space positions.
-
-       @param[in] codes       Return codes for each point: inside element (0),
-                              element boundary (1), not found (2).
-       @param[in] proc_ids    MPI proc ids where the points were found.
-       @param[in] elem_ids    Element ids where the points were found.
-       @param[in] ref_pos     Reference coordinates of the found point. Ordered
-                              by vdim (XYZ,XYZ,XYZ...).
-                              Note: the gslib reference frame is [-1,1].
       @param[in] field_in    Function values that will be interpolated on the
                              reference positions. Note: it is assumed that
                              @a field_in is in H1 and in the same space as the
                              mesh that was given to Setup().
-       @param[out] field_out  Interpolated values. */
-   void Interpolate(Array<unsigned int> &codes, Array<unsigned int> &proc_ids,
-                    Array<unsigned int> &elem_ids, Vector &ref_pos,
-                    const GridFunction &field_in, Vector &field_out);
+       @param[out] field_out  Interpolated values. For points that are not found
+                              the value is set to #default_interp_value. */
   void Interpolate(const GridFunction &field_in, Vector &field_out);
   /** Search positions and interpolate */
   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
@@ -111,27 +141,45 @@ public:
   void Interpolate(Mesh &m, const Vector &point_pos,
                    const GridFunction &field_in, Vector &field_out);

+   /// Average type to be used for L2 functions in-case a point is located at
+   /// an element boundary where the function might be multi-valued.
+   void SetL2AvgType(AvgType avgtype_) { avgtype = avgtype_; }
+
+   /// Set the default interpolation value for points that are not found in the
+   /// mesh.
+   void SetDefaultInterpolationValue(double interp_value_)
+   {
+      default_interp_value = interp_value_;
+   }
+
   /** Cleans up memory allocated internally by gslib.
-       Note that in parallel, this must be called before MPI_Finalize(), as
-       it calls MPI_Comm_free() for internal gslib communicators. */
+       Note that in parallel, this must be called before MPI_Finalize(), as it
+       calls MPI_Comm_free() for internal gslib communicators. */
   void FreeData();

   /// Return code for each point searched by FindPoints: inside element (0), on
   /// element boundary (1), or not found (2).
   const Array<unsigned int> &GetCode() const { return gsl_code; }
   /// Return element number for each point found by FindPoints.
-   const Array<unsigned int> &GetElem() const { return gsl_elem; }
+   const Array<unsigned int> &GetElem() const { return gsl_mfem_elem; }
   /// Return MPI rank on which each point was found by FindPoints.
   const Array<unsigned int> &GetProc() const { return gsl_proc; }
   /// Return reference coordinates for each point found by FindPoints.
-   const Vector &GetReferencePosition() const { return gsl_ref;  }
+   const Vector &GetReferencePosition() const { return gsl_mfem_ref;  }
   /// Return distance Distance between the sought and the found point
   /// in physical space, for each point found by FindPoints.
   const Vector &GetDist()              const { return gsl_dist; }
+
+   /// Return element number for each point found by FindPoints corresponding to
+   /// GSLIB mesh. gsl_mfem_elem != gsl_elem for mesh with simplices.
+   const Array<unsigned int> &GetGSLIBElem() const { return gsl_elem; }
+   /// Return reference coordinates in [-1,1] (internal range in GSLIB) for each
+   /// point found by FindPoints.
+   const Vector &GetGSLIBReferencePosition() const { return gsl_ref; }
 };

 } // namespace mfem

-#endif //MFEM_USE_GSLIB
+#endif // MFEM_USE_GSLIB

-#endif //MFEM_GSLIB guard
+#endif // MFEM_GSLIB
@@ -35,6 +35,9 @@ extern Ceed ceed;

 std::string ceed_path;

+extern CeedBasisMap ceed_basis_map;
+extern CeedRestrMap ceed_restr_map;
+
 }

 void InitCeedCoeff(Coefficient* Q, CeedData* ptr)
@@ -81,10 +84,9 @@ static CeedElemTopology GetCeedTopology(Geometry::Type geom)
   }
 }

-static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
-                                                 const IntegrationRule &ir,
-                                                 Ceed ceed, CeedBasis *basis,
-                                                 CeedElemRestriction *restr)
+static void InitCeedNonTensorBasis(const FiniteElementSpace &fes,
+                                   const IntegrationRule &ir,
+                                   Ceed ceed, CeedBasis *basis)
 {
   Mesh *mesh = fes.GetMesh();
   const FiniteElement *fe = fes.GetFE(0);
@@ -97,7 +99,73 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
   Vector qweight(Q);
   Vector shape_i(P);
   DenseMatrix grad_i(P, dim);
+   const Table &el_dof = fes.GetElementToDofTable();
+   Array<int> tp_el_dof(el_dof.Size_of_connections());
+   const TensorBasisElement * tfe =
+      dynamic_cast<const TensorBasisElement *>(fe);
+   if (tfe) // Lexicographic ordering using dof_map
+   {
+      const Array<int>& dof_map = tfe->GetDofMap();
+      for (int i = 0; i < Q; i++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(i);
+         qref(0,i) = ip.x;
+         if (dim>1) { qref(1,i) = ip.y; }
+         if (dim>2) { qref(2,i) = ip.z; }
+         qweight(i) = ip.weight;
+         fe->CalcShape(ip, shape_i);
+         fe->CalcDShape(ip, grad_i);
+         for (int j = 0; j < P; j++)
+         {
+            shape(j, i) = shape_i(dof_map[j]);
+            for (int d = 0; d < dim; ++d)
+            {
+               grad(j+i*P+d*Q*P) = grad_i(dof_map[j], d);
+            }
+         }
+      }
+   }
+   else  // Native ordering
+   {
+      for (int i = 0; i < Q; i++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(i);
+         qref(0,i) = ip.x;
+         if (dim>1) { qref(1,i) = ip.y; }
+         if (dim>2) { qref(2,i) = ip.z; }
+         qweight(i) = ip.weight;
+         fe->CalcShape(ip, shape_i);
+         fe->CalcDShape(ip, grad_i);
+         for (int j = 0; j < P; j++)
+         {
+            shape(j, i) = shape_i(j);
+            for (int d = 0; d < dim; ++d)
+            {
+               grad(j+i*P+d*Q*P) = grad_i(j, d);
+            }
+         }
+      }
+   }
+   CeedBasisCreateH1(ceed, GetCeedTopology(fe->GetGeomType()), fes.GetVDim(),
+                     fe->GetDof(), ir.GetNPoints(), shape.GetData(),
+                     grad.GetData(), qref.GetData(), qweight.GetData(), basis);
+}

+static void InitCeedNonTensorRestriction(const FiniteElementSpace &fes,
+                                         const IntegrationRule &ir,
+                                         Ceed ceed, CeedElemRestriction *restr)
+{
+   Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fe = fes.GetFE(0);
+   const int dim = mesh->Dimension();
+   const int P = fe->GetDof();
+   const int Q = ir.GetNPoints();
+   DenseMatrix shape(P, Q);
+   Vector grad(P*dim*Q);
+   DenseMatrix qref(dim, Q);
+   Vector qweight(Q);
+   Vector shape_i(P);
+   DenseMatrix grad_i(P, dim);
   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
   const Table &el_dof = fes.GetElementToDofTable();
   Array<int> tp_el_dof(el_dof.Size_of_connections());
@@ -124,7 +192,6 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
            }
         }
      }
-
      for (int i = 0; i < mesh->GetNE(); i++)
      {
         const int el_offset = fe->GetDof() * i;
@@ -162,7 +229,6 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
            }
         }
      }
-
      for (int e = 0; e < mesh->GetNE(); e++)
      {
         for (int i = 0; i < P; i++)
@@ -178,19 +244,15 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
         }
      }
   }
-   CeedBasisCreateH1(ceed, GetCeedTopology(fe->GetGeomType()), fes.GetVDim(),
-                     fe->GetDof(), ir.GetNPoints(), shape.GetData(),
-                     grad.GetData(), qref.GetData(), qweight.GetData(), basis);
   CeedElemRestrictionCreate(ceed, mesh->GetNE(), fe->GetDof(), fes.GetVDim(),
                             compstride, (fes.GetVDim())*(fes.GetNDofs()),
                             CEED_MEM_HOST, CEED_COPY_VALUES,
                             tp_el_dof.GetData(), restr);
 }

-static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
-                                              const IntegrationRule &ir,
-                                              Ceed ceed, CeedBasis *basis,
-                                              CeedElemRestriction *restr)
+static void InitCeedTensorBasis(const FiniteElementSpace &fes,
+                                const IntegrationRule &ir,
+                                Ceed ceed, CeedBasis *basis)
 {
   Mesh *mesh = fes.GetMesh();
   const FiniteElement *fe = fes.GetFE(0);
@@ -198,7 +260,6 @@ static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
   const TensorBasisElement * tfe =
      dynamic_cast<const TensorBasisElement *>(fe);
   MFEM_VERIFY(tfe, "invalid FE");
-   const Array<int>& dof_map = tfe->GetDofMap();
   const FiniteElement *fe1d =
      fes.FEColl()->FiniteElementForGeometry(Geometry::SEGMENT);
   DenseMatrix shape1d(fe1d->GetDof(), ir.GetNPoints());
@@ -227,6 +288,28 @@ static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
                           ir.GetNPoints(), shape1d.GetData(),
                           grad1d.GetData(), qref1d.GetData(),
                           qweight1d.GetData(), basis);
+}
+
+static void InitCeedTensorRestriction(const FiniteElementSpace &fes,
+                                      const IntegrationRule &ir,
+                                      Ceed ceed, CeedElemRestriction *restr)
+{
+   Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fe = fes.GetFE(0);
+   const TensorBasisElement * tfe =
+      dynamic_cast<const TensorBasisElement *>(fe);
+   MFEM_VERIFY(tfe, "invalid FE");
+   const Array<int>& dof_map = tfe->GetDofMap();
+   const FiniteElement *fe1d =
+      fes.FEColl()->FiniteElementForGeometry(Geometry::SEGMENT);
+   DenseMatrix shape1d(fe1d->GetDof(), ir.GetNPoints());
+   DenseMatrix grad1d(fe1d->GetDof(), ir.GetNPoints());
+   Vector qref1d(ir.GetNPoints()), qweight1d(ir.GetNPoints());
+   Vector shape_i(shape1d.Height());
+   DenseMatrix grad_i(grad1d.Height(), 1);
+   const H1_SegmentElement *h1_fe1d =
+      dynamic_cast<const H1_SegmentElement *>(fe1d);
+   MFEM_VERIFY(h1_fe1d, "invalid FE");

   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
   const Table &el_dof = fes.GetElementToDofTable();
@@ -258,14 +341,52 @@ void InitCeedBasisAndRestriction(const FiniteElementSpace &fes,
                                 Ceed ceed, CeedBasis *basis,
                                 CeedElemRestriction *restr)
 {
-   if (UsesTensorBasis(fes))
+   // Check for FES -> basis, restriction in hash tables
+   const Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fe = fes.GetFE(0);
+   const int P = fe->GetDof();
+   const int Q = irm.GetNPoints();
+   const int nelem = mesh->GetNE();
+   const int ncomp = fes.GetVDim();
+   CeedBasisKey basis_key(&fes, &irm, ncomp, P, Q);
+   auto basis_itr = internal::ceed_basis_map.find(basis_key);
+   CeedRestrKey restr_key(&fes, nelem, P, ncomp);
+   auto restr_itr = internal::ceed_restr_map.find(restr_key);
+
+   // Init or retreive key values
+   if (basis_itr == internal::ceed_basis_map.end())
   {
-      const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, irm.GetOrder());
-      InitCeedTensorBasisAndRestriction(fes, ir, ceed, basis, restr);
+      if (UsesTensorBasis(fes))
+      {
+         const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, irm.GetOrder());
+         InitCeedTensorBasis(fes, ir, ceed, basis);
+      }
+      else
+      {
+         InitCeedNonTensorBasis(fes, irm, ceed, basis);
+      }
+      internal::ceed_basis_map[basis_key] = *basis;
   }
   else
   {
-      InitCeedNonTensorBasisAndRestriction(fes, irm, ceed, basis, restr);
+      *basis = basis_itr->second;
+   }
+   if (restr_itr == internal::ceed_restr_map.end())
+   {
+      if (UsesTensorBasis(fes))
+      {
+         const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, irm.GetOrder());
+         InitCeedTensorRestriction(fes, ir, ceed, restr);
+      }
+      else
+      {
+         InitCeedNonTensorRestriction(fes, irm, ceed, restr);
+      }
+      internal::ceed_restr_map[restr_key] = *restr;
+   }
+   else
+   {
+      *restr = restr_itr->second;
   }
 }

@@ -327,8 +448,8 @@ void CeedPAAssemble(const CeedPAOperator& op,
   CeedVectorCreate(ceed, nelem * nqpts * qdatasize, &ceedData.rho);

   // Context data to be passed to the 'f_build_diff' Q-function.
-   ceedData.build_ctx.dim = mesh->Dimension();
-   ceedData.build_ctx.space_dim = mesh->SpaceDimension();
+   ceedData.build_ctx_data.dim = mesh->Dimension();
+   ceedData.build_ctx_data.space_dim = mesh->SpaceDimension();

   std::string qf_file = GetCeedPath() + op.header;
   std::string qf;
@@ -342,7 +463,7 @@ void CeedPAAssemble(const CeedPAOperator& op,
         CeedQFunctionCreateInterior(ceed, 1, op.const_qf,
                                     qf.c_str(),
                                     &ceedData.build_qfunc);
-         ceedData.build_ctx.coeff = ((CeedConstCoeff*)ceedData.coeff)->val;
+         ceedData.build_ctx_data.coeff = ((CeedConstCoeff*)ceedData.coeff)->val;
         break;
      case CeedCoeff::Grid:
         qf = qf_file + op.grid_func;
@@ -358,8 +479,12 @@ void CeedPAAssemble(const CeedPAOperator& op,
   CeedQFunctionAddInput(ceedData.build_qfunc, "weights", 1, CEED_EVAL_WEIGHT);
   CeedQFunctionAddOutput(ceedData.build_qfunc, "qdata", qdatasize,
                          CEED_EVAL_NONE);
-   CeedQFunctionSetContext(ceedData.build_qfunc, &ceedData.build_ctx,
-                           sizeof(ceedData.build_ctx));
+
+   CeedQFunctionContextCreate(ceed, &ceedData.build_ctx);
+   CeedQFunctionContextSetData(ceedData.build_ctx, CEED_MEM_HOST, CEED_USE_POINTER,
+                               sizeof(ceedData.build_ctx_data),
+                               &ceedData.build_ctx_data);
+   CeedQFunctionSetContext(ceedData.build_qfunc, ceedData.build_ctx);

   // Create the operator that builds the quadrature data for the operator.
   CeedOperatorCreate(ceed, ceedData.build_qfunc, NULL, NULL,
@@ -399,8 +524,7 @@ void CeedPAAssemble(const CeedPAOperator& op,
   CeedQFunctionAddInput(ceedData.apply_qfunc, "qdata", qdatasize,
                         CEED_EVAL_NONE);
   CeedQFunctionAddOutput(ceedData.apply_qfunc, "v", dimV, op.test_op);
-   CeedQFunctionSetContext(ceedData.apply_qfunc, &ceedData.build_ctx,
-                           sizeof(ceedData.build_ctx));
+   CeedQFunctionSetContext(ceedData.apply_qfunc, ceedData.build_ctx);

   // Create the diff operator.
   CeedOperatorCreate(ceed, ceedData.apply_qfunc, NULL, NULL, &ceedData.oper);
@@ -415,6 +539,59 @@ void CeedPAAssemble(const CeedPAOperator& op,
   CeedVectorCreate(ceed, fes.GetNDofs(), &ceedData.v);
 }

+void CeedAddMultPA(const CeedData *ceedDataPtr,
+                   const Vector &x,
+                   Vector &y)
+{
+   const CeedScalar *x_ptr;
+   CeedScalar *y_ptr;
+   CeedMemType mem;
+   CeedGetPreferredMemType(internal::ceed, &mem);
+   if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
+   {
+      x_ptr = x.Read();
+      y_ptr = y.ReadWrite();
+   }
+   else
+   {
+      x_ptr = x.HostRead();
+      y_ptr = y.HostReadWrite();
+      mem = CEED_MEM_HOST;
+   }
+   CeedVectorSetArray(ceedDataPtr->u, mem, CEED_USE_POINTER,
+                      const_cast<CeedScalar*>(x_ptr));
+   CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, y_ptr);
+
+   CeedOperatorApplyAdd(ceedDataPtr->oper, ceedDataPtr->u, ceedDataPtr->v,
+                        CEED_REQUEST_IMMEDIATE);
+
+   CeedVectorTakeArray(ceedDataPtr->u, mem, const_cast<CeedScalar**>(&x_ptr));
+   CeedVectorTakeArray(ceedDataPtr->v, mem, &y_ptr);
+}
+
+void CeedAssembleDiagonalPA(const CeedData *ceedDataPtr,
+                            Vector &diag)
+{
+   CeedScalar *d_ptr;
+   CeedMemType mem;
+   CeedGetPreferredMemType(internal::ceed, &mem);
+   if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
+   {
+      d_ptr = diag.ReadWrite();
+   }
+   else
+   {
+      d_ptr = diag.HostReadWrite();
+      mem = CEED_MEM_HOST;
+   }
+   CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, d_ptr);
+
+   CeedOperatorLinearAssembleAddDiagonal(ceedDataPtr->oper, ceedDataPtr->v,
+                                         CEED_REQUEST_IMMEDIATE);
+
+   CeedVectorTakeArray(ceedDataPtr->v, mem, &d_ptr);
+}
+
 } // namespace mfem

 #endif // MFEM_USE_CEED
@@ -16,7 +16,11 @@

 #ifdef MFEM_USE_CEED
 #include "../../general/device.hpp"
+#include "../../linalg/vector.hpp"
 #include <ceed.h>
+#include <ceed-hash.h>
+#include <tuple>
+#include <unordered_map>

 namespace mfem
 {
@@ -26,7 +30,47 @@ class GridFunction;
 class IntegrationRule;
 class Coefficient;

-namespace internal { extern Ceed ceed; } // defined in device.cpp
+// Hash table for CeedBasis
+using CeedBasisKey =
+   std::tuple<const FiniteElementSpace*, const IntegrationRule*, int, int, int>;
+struct CeedBasisHash
+{
+   std::size_t operator()(const CeedBasisKey& k) const
+   {
+      return CeedHashCombine(CeedHashCombine(CeedHashInt(
+                                                reinterpret_cast<CeedHash64_t>(std::get<0>(k))),
+                                             CeedHashInt(
+                                                reinterpret_cast<CeedHash64_t>(std::get<1>(k)))),
+                             CeedHashCombine(CeedHashCombine(CeedHashInt(std::get<2>(k)),
+                                                             CeedHashInt(std::get<3>(k))),
+                                             CeedHashInt(std::get<4>(k))));
+   }
+};
+using CeedBasisMap =
+   std::unordered_map<const CeedBasisKey, CeedBasis, CeedBasisHash>;
+
+// Hash table for CeedElemRestriction
+using CeedRestrKey = std::tuple<const FiniteElementSpace*, int, int, int>;
+struct CeedRestrHash
+{
+   std::size_t operator()(const CeedRestrKey& k) const
+   {
+      return CeedHashCombine(CeedHashCombine(CeedHashInt(
+                                                reinterpret_cast<CeedHash64_t>(std::get<0>(k))),
+                                             CeedHashInt(std::get<1>(k))),
+                             CeedHashCombine(CeedHashInt(std::get<2>(k)),
+                                             CeedHashInt(std::get<3>(k))));
+   }
+};
+using CeedRestrMap =
+   std::unordered_map<const CeedRestrKey, CeedElemRestriction, CeedRestrHash>;
+
+namespace internal
+{
+extern Ceed ceed; // defined in device.cpp
+extern CeedBasisMap basis_map;
+extern CeedRestrMap restr_map;
+}

 /// A structure used to pass additional data to f_build_diff and f_apply_diff
 struct BuildContext { CeedInt dim, space_dim; CeedScalar coeff; };
@@ -55,7 +99,8 @@ struct CeedData
   CeedVector node_coords, rho;
   CeedCoeff coeff_type;
   void* coeff;
-   BuildContext build_ctx;
+   CeedQFunctionContext build_ctx;
+   BuildContext build_ctx_data;

   CeedVector u, v;

@@ -63,10 +108,6 @@ struct CeedData
   {
      CeedOperatorDestroy(&build_oper);
      CeedOperatorDestroy(&oper);
-      CeedBasisDestroy(&basis);
-      CeedBasisDestroy(&mesh_basis);
-      CeedElemRestrictionDestroy(&restr);
-      CeedElemRestrictionDestroy(&mesh_restr);
      CeedElemRestrictionDestroy(&restr_i);
      CeedElemRestrictionDestroy(&mesh_restr_i);
      CeedQFunctionDestroy(&apply_qfunc);
@@ -76,8 +117,6 @@ struct CeedData
      if (coeff_type==CeedCoeff::Grid)
      {
         CeedGridCoeff* c = (CeedGridCoeff*)coeff;
-         CeedBasisDestroy(&c->basis);
-         CeedElemRestrictionDestroy(&c->restr);
         CeedVectorDestroy(&c->coeffVector);
         delete c;
      }
@@ -144,6 +183,15 @@ const std::string &GetCeedPath();
 void CeedPAAssemble(const CeedPAOperator& op,
                    CeedData& ceedData);

+/** @brief Function that applies a libCEED PA operator. */
+void CeedAddMultPA(const CeedData *ceedDataPtr,
+                   const Vector &x,
+                   Vector &y);
+
+/** @brief Function that assembles a libCEED PA operator diagonal. */
+void CeedAssembleDiagonalPA(const CeedData *ceedDataPtr,
+                            Vector &diag);
+
 /** @brief Function that determines if a CEED kernel should be used, based on
    the current mfem::Device configuration. */
 inline bool DeviceCanUseCeed()
@@ -204,6 +204,14 @@ void LinearForm::Update(FiniteElementSpace *f, Vector &v, int v_offset)
   ResetDeltaLocations();
 }

+void LinearForm::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
+{
+   MFEM_ASSERT(v.Size() >= v_offset + f->GetVSize(), "");
+   fes = f;
+   v.UseDevice(true);
+   this->Vector::MakeRef(v, v_offset, fes->GetVSize());
+}
+
 void LinearForm::AssembleDelta()
 {
   if (dlfi_delta.Size() == 0) { return; }
@@ -26,7 +26,7 @@ protected:
   /// FE space on which the LinearForm lives. Not owned.
   FiniteElementSpace *fes;

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

@@ -175,6 +175,16 @@ public:
       @note This method does not perform assembly. */
   void Update(FiniteElementSpace *f, Vector &v, int v_offset);

+   /** @brief Make the LinearForm reference external data on a new
+       FiniteElementSpace. */
+   /** This method changes the FiniteElementSpace associated with the LinearForm
+       @a *f and sets the data of the Vector @a v (plus the @a v_offset) as
+       external data in the LinearForm.
+
+       @note This version of the method will also perform bounds checks when the
+       build option MFEM_DEBUG is enabled. */
+   virtual void MakeRef(FiniteElementSpace *f, Vector &v, int v_offset);
+
   /// Return the action of the LinearForm as a linear mapping.
   /** Linear forms are linear functionals which map GridFunctions to
       the real numbers.  This method performs this mapping which in
@@ -457,20 +457,8 @@ void VectorFEDomainLFCurlIntegrator::AssembleRHSElementVect(

      Tr.SetIntPoint (&ip);
      el.CalcPhysCurlShape(Tr, curlshape);
+      QF->Eval(vec, Tr, ip);

-      switch (spaceDim)
-      {
-         case 3:
-            MFEM_VERIFY(QF, "VectorFunctionCoefficient not provided");
-            QF->Eval(vec, Tr, ip);
-            break;
-         case 2:
-            MFEM_VERIFY(Q, "FunctionCoefficient (Scalar) not provided");
-            vec[0] = Q->Eval(Tr, ip);
-            break;
-         default:
-            break; // This should be unreachable
-      }
      vec *= ip.weight * Tr.Weight();
      curlshape.AddMult (vec, elvect);
   }
@@ -480,38 +468,17 @@ void VectorFEDomainLFCurlIntegrator::AssembleDeltaElementVect(
   const FiniteElement &fe, ElementTransformation &Trans, Vector &elvect)
 {
   int spaceDim = Trans.GetSpaceDim();
-   switch (spaceDim)
-   {
-      case 3:
-         MFEM_ASSERT(vec_delta != NULL,
-                     "coefficient must be VectorDeltaCoefficient");
-         break;
-      case 2:
-         MFEM_ASSERT(delta != NULL,
-                     "coefficient must be DeltaCoefficient");
-         break;
-      default:
-         break; // This should be unreachable
-   }
+   MFEM_ASSERT(vec_delta != NULL,
+               "coefficient must be VectorDeltaCoefficient");
   int dof = fe.GetDof();
   int n=(spaceDim == 3)? spaceDim : 1;
+   vec.SetSize(n);
   curlshape.SetSize(dof, n);
   elvect.SetSize(dof);
   fe.CalcPhysCurlShape(Trans, curlshape);

-   switch (spaceDim)
-   {
-      case 3:
-         vec_delta->EvalDelta(vec, Trans, Trans.GetIntPoint());
-         curlshape.Mult(vec, elvect);
-         break;
-      case 2:
-         curlshape.GetColumn(0,elvect);
-         elvect *= delta->EvalDelta(Trans, Trans.GetIntPoint());
-         break;
-      default:
-         break; // This should be unreachable
-   }
+   vec_delta->EvalDelta(vec, Trans, Trans.GetIntPoint());
+   curlshape.Mult(vec, elvect);
 }

 void VectorFEDomainLFDivIntegrator::AssembleRHSElementVect(
@@ -284,7 +284,6 @@ class VectorFEDomainLFCurlIntegrator : public DeltaLFIntegrator
 {
 private:
   VectorCoefficient *QF=nullptr;
-   Coefficient *Q=nullptr;
   DenseMatrix curlshape;
   Vector vec;

@@ -292,8 +291,6 @@ public:
   /// Constructs the domain integrator (Q, curl v)
   VectorFEDomainLFCurlIntegrator(VectorCoefficient &F)
      : DeltaLFIntegrator(F), QF(&F) { }
-   VectorFEDomainLFCurlIntegrator(Coefficient &F)
-      : DeltaLFIntegrator(F), Q(&F) { }

   virtual void AssembleRHSElementVect(const FiniteElement &el,
                                       ElementTransformation &Tr,
@@ -581,6 +581,13 @@ double BlockNonlinearForm::GetEnergyBlocked(const BlockVector &bx) const
         }
      }

+   // free the allocated memory
+   for (int i = 0; i < fes.Size(); ++i)
+   {
+      delete el_x[i];
+      delete vdofs[i];
+   }
+
   if (fnfi.Size())
   {
      MFEM_ABORT("TODO: add energy contribution from interior face terms");
@@ -655,6 +655,167 @@ void ParGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
 #endif
 }

+double ParGridFunction::ComputeDGFaceJumpError(Coefficient *exsol,
+                                               Coefficient *ell_coeff,
+                                               double Nu,
+                                               const IntegrationRule *irs[]) const
+{
+   const_cast<ParGridFunction *>(this)->ExchangeFaceNbrData();
+
+   int fdof, dim, intorder, k;
+   ElementTransformation *transf;
+   Vector shape, el_dofs, err_val, ell_coeff_val;
+   Array<int> vdofs;
+   IntegrationPoint eip;
+   double error = 0.0;
+
+   ParMesh *mesh = pfes->GetParMesh();
+   dim = mesh->Dimension();
+
+   std::map<int,int> local_to_shared;
+   for (int i = 0; i < mesh->GetNSharedFaces(); ++i)
+   {
+      int i_local = mesh->GetSharedFace(i);
+      local_to_shared[i_local] = i;
+   }
+
+   for (int i = 0; i < mesh->GetNumFaces(); i++)
+   {
+      double shared_face_factor = 1.0;
+      bool shared_face = false;
+      int iel1, iel2, info1, info2;
+      mesh->GetFaceElements(i, &iel1, &iel2);
+      mesh->GetFaceInfos(i, &info1, &info2);
+
+      intorder = fes->GetFE(iel1)->GetOrder();
+
+      FaceElementTransformations *face_elem_transf;
+      const FiniteElement *fe1, *fe2;
+      if (info2 >= 0 && iel2 < 0)
+      {
+         int ishared = local_to_shared[i];
+         face_elem_transf = mesh->GetSharedFaceTransformations(ishared);
+         iel2 = face_elem_transf->Elem2No - mesh->GetNE();
+         fe2 = pfes->GetFaceNbrFE(iel2);
+         if ( (k = fe2->GetOrder()) > intorder )
+         {
+            intorder = k;
+         }
+         shared_face = true;
+         shared_face_factor = 0.5;
+      }
+      else
+      {
+         face_elem_transf = mesh->GetFaceElementTransformations(i);
+
+         if (iel2 >= 0)
+         {
+            fe2 = pfes->GetFE(iel2);
+            if ( (k = fe2->GetOrder()) > intorder )
+            {
+               intorder = k;
+            }
+         }
+         else
+         {
+            fe2 = NULL;
+         }
+      }
+
+      intorder = 2 * intorder;  // <-------------
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[face_elem_transf->GetGeometryType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(face_elem_transf->GetGeometryType(), intorder));
+      }
+      err_val.SetSize(ir->GetNPoints());
+      ell_coeff_val.SetSize(ir->GetNPoints());
+      // side 1
+      transf = face_elem_transf->Elem1;
+      fe1 = fes->GetFE(iel1);
+      fdof = fe1->GetDof();
+      fes->GetElementVDofs(iel1, vdofs);
+      shape.SetSize(fdof);
+      el_dofs.SetSize(fdof);
+      for (k = 0; k < fdof; k++)
+         if (vdofs[k] >= 0)
+         {
+            el_dofs(k) =   (*this)(vdofs[k]);
+         }
+         else
+         {
+            el_dofs(k) = - (*this)(-1-vdofs[k]);
+         }
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         face_elem_transf->Loc1.Transform(ir->IntPoint(j), eip);
+         fe1->CalcShape(eip, shape);
+         transf->SetIntPoint(&eip);
+         ell_coeff_val(j) = ell_coeff->Eval(*transf, eip);
+         err_val(j) = exsol->Eval(*transf, eip) - (shape * el_dofs);
+      }
+      if (fe2 != NULL)
+      {
+         // side 2
+         transf = face_elem_transf->Elem2;
+         fdof = fe2->GetDof();
+         shape.SetSize(fdof);
+         el_dofs.SetSize(fdof);
+         if (shared_face)
+         {
+            pfes->GetFaceNbrElementVDofs(iel2, vdofs);
+            for (k = 0; k < fdof; k++)
+               if (vdofs[k] >= 0)
+               {
+                  el_dofs(k) = face_nbr_data[vdofs[k]];
+               }
+               else
+               {
+                  el_dofs(k) = - face_nbr_data[-1-vdofs[k]];
+               }
+         }
+         else
+         {
+            pfes->GetElementVDofs(iel2, vdofs);
+            for (k = 0; k < fdof; k++)
+               if (vdofs[k] >= 0)
+               {
+                  el_dofs(k) = (*this)(vdofs[k]);
+               }
+               else
+               {
+                  el_dofs(k) = - (*this)(-1 - vdofs[k]);
+               }
+         }
+         for (int j = 0; j < ir->GetNPoints(); j++)
+         {
+            face_elem_transf->Loc2.Transform(ir->IntPoint(j), eip);
+            fe2->CalcShape(eip, shape);
+            transf->SetIntPoint(&eip);
+            ell_coeff_val(j) += ell_coeff->Eval(*transf, eip);
+            ell_coeff_val(j) *= 0.5;
+            err_val(j) -= (exsol->Eval(*transf, eip) - (shape * el_dofs));
+         }
+      }
+      transf = face_elem_transf;
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         transf->SetIntPoint(&ip);
+         error += shared_face_factor*(ip.weight * Nu * ell_coeff_val(j) *
+                                      pow(transf->Weight(), 1.0-1.0/(dim-1)) *
+                                      err_val(j) * err_val(j));
+      }
+   }
+
+   error = (error < 0.0) ? -sqrt(-error) : sqrt(error);
+   return GlobalLpNorm(2.0, error, pfes->GetComm());
+}
+
 void ParGridFunction::Save(std::ostream &out) const
 {
   double *data_  = const_cast<double*>(HostRead());
@@ -860,7 +1021,6 @@ double GlobalLpNorm(const double p, double loc_norm, MPI_Comm comm)
   return glob_norm;
 }

-
 void ParGridFunction::ComputeFlux(
   BilinearFormIntegrator &blfi,
   GridFunction &flux, bool wcoef, int subdomain)
@@ -1001,6 +1161,6 @@ double L2ZZErrorEstimator(BilinearFormIntegrator &flux_integrator,
   return pow(glob_error, 1.0/norm_p);
 }

-}
+} // namespace mfem

 #endif // MFEM_USE_MPI
@@ -283,6 +283,77 @@ public:
                          pfes->GetComm());
   }

+   /// Returns ||grad u_ex - grad u_h||_L2 for H1 or L2 elements
+   virtual double ComputeGradError(VectorCoefficient *exgrad,
+                                   const IntegrationRule *irs[] = NULL) const
+   {
+      return GlobalLpNorm(2.0, GridFunction::ComputeGradError(exgrad,irs),
+                          pfes->GetComm());
+   }
+
+   /// Returns ||curl u_ex - curl u_h||_L2 for ND elements
+   virtual double ComputeCurlError(VectorCoefficient *excurl,
+                                   const IntegrationRule *irs[] = NULL) const
+   {
+      return GlobalLpNorm(2.0, GridFunction::ComputeCurlError(excurl,irs),
+                          pfes->GetComm());
+   }
+
+   /// Returns ||div u_ex - div u_h||_L2 for RT elements
+   virtual double ComputeDivError(Coefficient *exdiv,
+                                  const IntegrationRule *irs[] = NULL) const
+   {
+      return GlobalLpNorm(2.0, GridFunction::ComputeDivError(exdiv,irs),
+                          pfes->GetComm());
+   }
+
+   /// Returns the Face Jumps error for L2 elements
+   virtual double ComputeDGFaceJumpError(Coefficient *exsol,
+                                         Coefficient *ell_coeff,
+                                         double Nu,
+                                         const IntegrationRule *irs[]=NULL)
+   const;
+
+   /// Returns either the H1-seminorm or the DG Face Jumps error or both
+   /// depending on norm_type = 1, 2, 3
+   virtual double ComputeH1Error(Coefficient *exsol, VectorCoefficient *exgrad,
+                                 Coefficient *ell_coef, double Nu,
+                                 int norm_type) const
+   {
+      return GlobalLpNorm(2.0,
+                          GridFunction::ComputeH1Error(exsol,exgrad,ell_coef,
+                                                       Nu, norm_type),
+                          pfes->GetComm());
+   }
+
+   /// Returns the error measured in H1-norm for H1 elements or in "broken"
+   /// H1-norm for L2 elements
+   virtual double ComputeH1Error(Coefficient *exsol, VectorCoefficient *exgrad,
+                                 const IntegrationRule *irs[] = NULL) const
+   {
+      return GlobalLpNorm(2.0, GridFunction::ComputeH1Error(exsol,exgrad,irs),
+                          pfes->GetComm());
+   }
+
+   /// Returns the error measured H(div)-norm for RT elements
+   virtual double ComputeHDivError(VectorCoefficient *exsol,
+                                   Coefficient *exdiv,
+                                   const IntegrationRule *irs[] = NULL) const
+   {
+      return GlobalLpNorm(2.0, GridFunction::ComputeHDivError(exsol,exdiv,irs),
+                          pfes->GetComm());
+   }
+
+   /// Returns the error measured H(curl)-norm for ND elements
+   virtual double ComputeHCurlError(VectorCoefficient *exsol,
+                                    VectorCoefficient *excurl,
+                                    const IntegrationRule *irs[] = NULL) const
+   {
+      return GlobalLpNorm(2.0,
+                          GridFunction::ComputeHCurlError(exsol,excurl,irs),
+                          pfes->GetComm());
+   }
+
   virtual double ComputeMaxError(Coefficient *exsol[],
                                  const IntegrationRule *irs[] = NULL) const
   {
@@ -21,7 +21,6 @@ namespace mfem
 void ParLinearForm::Update(ParFiniteElementSpace *pf)
 {
   if (pf) { pfes = pf; }
-
   LinearForm::Update(pfes);
 }

@@ -31,6 +30,19 @@ void ParLinearForm::Update(ParFiniteElementSpace *pf, Vector &v, int v_offset)
   LinearForm::Update(pf,v,v_offset);
 }

+void ParLinearForm::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
+{
+   LinearForm::MakeRef(f, v, v_offset);
+   pfes = dynamic_cast<ParFiniteElementSpace*>(f);
+   MFEM_ASSERT(pfes != NULL, "not a ParFiniteElementSpace");
+}
+
+void ParLinearForm::MakeRef(ParFiniteElementSpace *pf, Vector &v, int v_offset)
+{
+   LinearForm::MakeRef(pf, v, v_offset);
+   pfes = pf;
+}
+
 void ParLinearForm::ParallelAssemble(Vector &tv)
 {
   const Operator* prolong = pfes->GetProlongationMatrix();
@@ -92,6 +92,27 @@ public:
       @note This method does not perform assembly. */
   void Update(ParFiniteElementSpace *pf, Vector &v, int v_offset);

+
+   /** @brief Make the ParLinearForm reference external data on a new
+       FiniteElementSpace. */
+   /** This method changes the FiniteElementSpace associated with the
+       ParLinearForm to @a *f and sets the data of the Vector @a v (plus the @a
+       v_offset) as external data in the ParLinearForm.
+
+       @note This version of the method will also perform bounds checks when the
+       build option MFEM_DEBUG is enabled. */
+   virtual void MakeRef(FiniteElementSpace *f, Vector &v, int v_offset);
+
+   /** @brief Make the ParLinearForm reference external data on a new
+       ParFiniteElementSpace. */
+   /** This method changes the ParFiniteElementSpace associated with the
+       ParLinearForm to @a *pf and sets the data of the Vector @a v (plus the @a
+       v_offset) as external data in the ParLinearForm.
+
+       @note This version of the method will also perform bounds checks when the
+       build option MFEM_DEBUG is enabled. */
+   void MakeRef(ParFiniteElementSpace *pf, Vector &v, int v_offset);
+
   /// Assemble the vector on the true dofs, i.e. P^t v.
   void ParallelAssemble(Vector &tv);

@@ -99,10 +120,10 @@ public:
   HypreParVector *ParallelAssemble();

   /// Return the action of the ParLinearForm as a linear mapping.
-   /** Linear forms are linear functionals which map ParGridFunction%s to
-       the real numbers.  This method performs this mapping which in
-       this case is equivalent as an inner product of the ParLinearForm
-       and ParGridFunction. */
+   /** Linear forms are linear functionals which map ParGridFunction%s to the
+       real numbers. This method performs this mapping which in this case is
+       equivalent as an inner product of the ParLinearForm and
+       ParGridFunction. */
   double operator()(const ParGridFunction &gf) const
   {
      return InnerProduct(pfes->GetComm(), *this, gf);
@@ -62,6 +62,7 @@ void QuadratureInterpolator::Eval2D(
   const int nq = maps.nqpt;
   const int ND = T_ND ? T_ND : nd;
   const int NQ = T_NQ ? T_NQ : nq;
+   const int NMAX = NQ > ND ? NQ : ND;
   const int VDIM = T_VDIM ? T_VDIM : vdim;
   MFEM_VERIFY(ND <= MAX_ND2D, "");
   MFEM_VERIFY(NQ <= MAX_NQ2D, "");
@@ -72,22 +73,24 @@ void QuadratureInterpolator::Eval2D(
   auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
   auto der = Reshape(q_der.Write(), NQ, VDIM, 2, NE);
   auto det = Reshape(q_det.Write(), NQ, NE);
-   MFEM_FORALL(e, NE,
+   MFEM_FORALL_2D(e, NE, NMAX, 1, 1,
   {
      const int ND = T_ND ? T_ND : nd;
      const int NQ = T_NQ ? T_NQ : nq;
      const int VDIM = T_VDIM ? T_VDIM : vdim;
      constexpr int max_ND = T_ND ? T_ND : MAX_ND2D;
      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM2D;
-      double s_E[max_VDIM*max_ND];
-      for (int d = 0; d < ND; d++)
+      MFEM_SHARED double s_E[max_VDIM*max_ND];
+      MFEM_FOREACH_THREAD(d, x, ND)
      {
         for (int c = 0; c < VDIM; c++)
         {
            s_E[c+d*VDIM] = E(d,c,e);
         }
      }
-      for (int q = 0; q < NQ; ++q)
+      MFEM_SYNC_THREAD;
+
+      MFEM_FOREACH_THREAD(q, x, NQ)
      {
         if (eval_flags & VALUES)
         {
@@ -150,6 +153,7 @@ void QuadratureInterpolator::Eval3D(
   const int nq = maps.nqpt;
   const int ND = T_ND ? T_ND : nd;
   const int NQ = T_NQ ? T_NQ : nq;
+   const int NMAX = NQ > ND ? NQ : ND;
   const int VDIM = T_VDIM ? T_VDIM : vdim;
   MFEM_VERIFY(ND <= MAX_ND3D, "");
   MFEM_VERIFY(NQ <= MAX_NQ3D, "");
@@ -160,22 +164,24 @@ void QuadratureInterpolator::Eval3D(
   auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
   auto der = Reshape(q_der.Write(), NQ, VDIM, 3, NE);
   auto det = Reshape(q_det.Write(), NQ, NE);
-   MFEM_FORALL(e, NE,
+   MFEM_FORALL_2D(e, NE, NMAX, 1, 1,
   {
      const int ND = T_ND ? T_ND : nd;
      const int NQ = T_NQ ? T_NQ : nq;
      const int VDIM = T_VDIM ? T_VDIM : vdim;
      constexpr int max_ND = T_ND ? T_ND : MAX_ND3D;
      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM3D;
-      double s_E[max_VDIM*max_ND];
-      for (int d = 0; d < ND; d++)
+      MFEM_SHARED double s_E[max_VDIM*max_ND];
+      MFEM_FOREACH_THREAD(d, x, ND)
      {
         for (int c = 0; c < VDIM; c++)
         {
            s_E[c+d*VDIM] = E(d,c,e);
         }
      }
-      for (int q = 0; q < NQ; ++q)
+      MFEM_SYNC_THREAD;
+
+      MFEM_FOREACH_THREAD(q, x, NQ)
      {
         if (eval_flags & VALUES)
         {
@@ -1968,11 +1968,11 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
   Jpt.SetSize(dim);
   PMatI.UseExternalData(elfun.GetData(), dof, dim);

-   const IntegrationRule *ir = EnergyIntegrationRule(el);
+   const IntegrationRule &ir = EnergyIntegrationRule(el);

   energy = 0.0;
-   DenseTensor Jtr(dim, dim, ir->GetNPoints());
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+   DenseTensor Jtr(dim, dim, ir.GetNPoints());
+   targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);

   // Limited case.
   Vector shape, p, p0, d_vals;
@@ -1989,11 +1989,11 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
      nodes0->GetSubVector(pos_dofs, pos0V);
      if (lim_dist)
      {
-         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+         lim_dist->GetValues(T.ElementNo, ir, d_vals);
      }
      else
      {
-         d_vals.SetSize(ir->GetNPoints()); d_vals = 1.0;
+         d_vals.SetSize(ir.GetNPoints()); d_vals = 1.0;
      }
   }

@@ -2019,13 +2019,13 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
   Vector zeta_q, zeta0_q;
   if (adaptive_limiting)
   {
-      zeta->GetValues(T.ElementNo, *ir, zeta_q);
-      zeta_0->GetValues(T.ElementNo, *ir, zeta0_q);
+      zeta->GetValues(T.ElementNo, ir, zeta_q);
+      zeta_0->GetValues(T.ElementNo, ir, zeta0_q);
   }

-   for (int i = 0; i < ir->GetNPoints(); i++)
+   for (int i = 0; i < ir.GetNPoints(); i++)
   {
-      const IntegrationPoint &ip = ir->IntPoint(i);
+      const IntegrationPoint &ip = ir.IntPoint(i);
      const DenseMatrix &Jtr_i = Jtr(i);
      metric->SetTargetJacobian(Jtr_i);
      CalcInverse(Jtr_i, Jrt);
@@ -2105,14 +2105,14 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
   elvect.SetSize(dof*dim);
   PMatO.UseExternalData(elvect.GetData(), dof, dim);

-   const IntegrationRule *ir = ActionIntegrationRule(el);
-   const int nqp = ir->GetNPoints();
+   const IntegrationRule &ir = ActionIntegrationRule(el);
+   const int nqp = ir.GetNPoints();

   elvect = 0.0;
   Vector weights(nqp);
   DenseTensor Jtr(dim, dim, nqp);
   DenseTensor dJtr(dim, dim, dim*nqp);
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);

   // Limited case.
   DenseMatrix pos0;
@@ -2129,7 +2129,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
      nodes0->GetSubVector(pos_dofs, pos0V);
      if (lim_dist)
      {
-         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+         lim_dist->GetValues(T.ElementNo, ir, d_vals);
      }
      else
      {
@@ -2144,11 +2144,12 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
      Tpr = new IsoparametricTransformation;
      Tpr->SetFE(&el);
      Tpr->ElementNo = T.ElementNo;
+      Tpr->ElementType = ElementTransformation::ELEMENT;
      Tpr->Attribute = T.Attribute;
      Tpr->GetPointMat().Transpose(PMatI); // PointMat = PMatI^T
      if (exact_action)
      {
-         targetC->ComputeElementTargetsGradient(*ir, elfun, *Tpr, dJtr);
+         targetC->ComputeElementTargetsGradient(ir, elfun, *Tpr, dJtr);
      }
   }

@@ -2158,7 +2159,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,

   for (int q = 0; q < nqp; q++)
   {
-      const IntegrationPoint &ip = ir->IntPoint(q);
+      const IntegrationPoint &ip = ir.IntPoint(q);
      const DenseMatrix &Jtr_q = Jtr(q);
      metric->SetTargetJacobian(Jtr_q);
      CalcInverse(Jtr_q, Jrt);
@@ -2185,7 +2186,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
         DenseMatrix dwdx(dim);
         for (int d = 0; d < dim; d++)
         {
-            const DenseMatrix &dJtr_q = dJtr(q + d*ir->GetNPoints());
+            const DenseMatrix &dJtr_q = dJtr(q + d * nqp);
            Mult(Jrt, dJtr_q, dwdx );
            d_detW_dx(d) = dwdx.Trace();
         }
@@ -2220,7 +2221,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
      }
   }

-   if (zeta) { AssembleElemVecAdaptLim(el, weights, *Tpr, *ir, PMatO); }
+   if (zeta) { AssembleElemVecAdaptLim(el, weights, *Tpr, ir, PMatO); }

   delete Tpr;
 }
@@ -2239,13 +2240,13 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
   PMatI.UseExternalData(elfun.GetData(), dof, dim);
   elmat.SetSize(dof*dim);

-   const IntegrationRule *ir = GradientIntegrationRule(el);
-   const int nqp = ir->GetNPoints();
+   const IntegrationRule &ir = GradientIntegrationRule(el);
+   const int nqp = ir.GetNPoints();

   elmat = 0.0;
   Vector weights(nqp);
   DenseTensor Jtr(dim, dim, nqp);
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);

   // Limited case.
   DenseMatrix pos0, grad_grad;
@@ -2262,7 +2263,7 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
      nodes0->GetSubVector(pos_dofs, pos0V);
      if (lim_dist)
      {
-         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+         lim_dist->GetValues(T.ElementNo, ir, d_vals);
      }
      else
      {
@@ -2284,7 +2285,7 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,

   for (int q = 0; q < nqp; q++)
   {
-      const IntegrationPoint &ip = ir->IntPoint(q);
+      const IntegrationPoint &ip = ir.IntPoint(q);
      const DenseMatrix &Jtr_q = Jtr(q);
      metric->SetTargetJacobian(Jtr_q);
      CalcInverse(Jtr_q, Jrt);
@@ -2301,7 +2302,6 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,

      // TODO: derivatives of adaptivity-based targets.

-      // TODO optimize by symmetry.
      if (coeff0)
      {
         el.CalcShape(ip, shape);
@@ -2327,7 +2327,7 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
      }
   }

-   if (zeta) { AssembleElemGradAdaptLim(el, weights, *Tpr, *ir, elmat); }
+   if (zeta) { AssembleElemGradAdaptLim(el, weights, *Tpr, ir, elmat); }

   delete Tpr;
 }
@@ -2498,10 +2498,10 @@ void TMOP_Integrator::AssembleElementVectorFD(const FiniteElement &el,
   // Contributions from adaptive limiting (exact derivatives).
   if (zeta)
   {
-      const IntegrationRule *ir = ActionIntegrationRule(el);
-      const int nqp = ir->GetNPoints();
+      const IntegrationRule &ir = ActionIntegrationRule(el);
+      const int nqp = ir.GetNPoints();
      DenseTensor Jtr(dim, dim, nqp);
-      targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+      targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);

      IsoparametricTransformation Tpr;
      Tpr.SetFE(&el);
@@ -2513,11 +2513,11 @@ void TMOP_Integrator::AssembleElementVectorFD(const FiniteElement &el,
      Vector weights(nqp);
      for (int q = 0; q < nqp; q++)
      {
-         weights(q) = ir->IntPoint(q).weight * Jtr(q).Det();
+         weights(q) = ir.IntPoint(q).weight * Jtr(q).Det();
      }

      PMatO.UseExternalData(elvect.GetData(), dof, dim);
-      AssembleElemVecAdaptLim(el, weights, Tpr, *ir, PMatO);
+      AssembleElemVecAdaptLim(el, weights, Tpr, ir, PMatO);
   }
 }

@@ -2594,10 +2594,10 @@ void TMOP_Integrator::AssembleElementGradFD(const FiniteElement &el,
   // Contributions from adaptive limiting.
   if (zeta)
   {
-      const IntegrationRule *ir = GradientIntegrationRule(el);
-      const int nqp = ir->GetNPoints();
+      const IntegrationRule &ir = GradientIntegrationRule(el);
+      const int nqp = ir.GetNPoints();
      DenseTensor Jtr(dim, dim, nqp);
-      targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+      targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);

      IsoparametricTransformation Tpr;
      Tpr.SetFE(&el);
@@ -2609,10 +2609,10 @@ void TMOP_Integrator::AssembleElementGradFD(const FiniteElement &el,
      Vector weights(nqp);
      for (int q = 0; q < nqp; q++)
      {
-         weights(q) = ir->IntPoint(q).weight * Jtr(q).Det();
+         weights(q) = ir.IntPoint(q).weight * Jtr(q).Det();
      }

-      AssembleElemGradAdaptLim(el, weights, Tpr, *ir, elmat);
+      AssembleElemGradAdaptLim(el, weights, Tpr, ir, elmat);
   }
 }

@@ -2642,33 +2642,32 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
   Array<int> vdofs;
   Vector x_vals;
   const FiniteElementSpace* const fes = x.FESpace();
-   const FiniteElement *fe = fes->GetFE(0);

-   const int dof = fes->GetFE(0)->GetDof(), dim = fes->GetFE(0)->GetDim();
-
-   DSh.SetSize(dof, dim);
+   const int dim = fes->GetMesh()->Dimension();
   Jrt.SetSize(dim);
   Jpr.SetSize(dim);
   Jpt.SetSize(dim);

-   const IntegrationRule *ir = EnergyIntegrationRule(*fe);
-   const int nqp =  ir->GetNPoints();
-   DenseTensor Jtr(dim, dim, nqp);
-
   metric_energy = 0.0;
   lim_energy = 0.0;
   for (int i = 0; i < fes->GetNE(); i++)
   {
-      fe = fes->GetFE(i);
+      const FiniteElement *fe = fes->GetFE(i);
+      const IntegrationRule &ir = EnergyIntegrationRule(*fe);
+      const int nqp = ir.GetNPoints();
+      DenseTensor Jtr(dim, dim, nqp);
+      const int dof = fe->GetDof();
+      DSh.SetSize(dof, dim);
+
      fes->GetElementVDofs(i, vdofs);
      x.GetSubVector(vdofs, x_vals);
      PMatI.UseExternalData(x_vals.GetData(), dof, dim);

-      targetC->ComputeElementTargets(i, *fe, *ir, x_vals, Jtr);
+      targetC->ComputeElementTargets(i, *fe, ir, x_vals, Jtr);

      for (int q = 0; q < nqp; q++)
      {
-         const IntegrationPoint &ip = ir->IntPoint(q);
+         const IntegrationPoint &ip = ir.IntPoint(q);
         metric->SetTargetJacobian(Jtr(q));
         CalcInverse(Jtr(q), Jrt);
         const double weight = ip.weight * Jtr(q).Det();
@@ -2692,9 +2691,9 @@ void TMOP_Integrator::ComputeMinJac(const Vector &x,
                                    const FiniteElementSpace &fes)
 {
   const FiniteElement *fe = fes.GetFE(0);
-   const IntegrationRule *ir = EnergyIntegrationRule(*fe);
+   const IntegrationRule &ir = EnergyIntegrationRule(*fe);
   const int NE = fes.GetMesh()->GetNE(), dim = fe->GetDim(),
-             dof = fe->GetDof(), nsp = ir->GetNPoints();
+             dof = fe->GetDof(), nsp = ir.GetNPoints();

   Array<int> xdofs(dof * dim);
   DenseMatrix Jpr(dim), dshape(dof, dim), pos(dof, dim);
@@ -2711,7 +2710,7 @@ void TMOP_Integrator::ComputeMinJac(const Vector &x,
      detv_sum = 0.;
      for (int j = 0; j < nsp; j++)
      {
-         fes.GetFE(i)->CalcDShape(ir->IntPoint(j), dshape);
+         fes.GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
         MultAtB(pos, dshape, Jpr);
         detv_sum += std::fabs(Jpr.Det());
      }
@@ -890,6 +890,10 @@ protected:
   TMOP_QualityMetric *metric;        // not owned
   const TargetConstructor *targetC;  // not owned

+   // Custom integration rules.
+   IntegrationRules *IntegRules;
+   int integ_order;
+
   // Weight Coefficient multiplying the quality metric term.
   Coefficient *coeff1; // not owned, if NULL -> coeff1 is 1.
   // Normalization factor for the metric term.
@@ -988,17 +992,21 @@ protected:
      nodes0 = NULL; coeff0 = NULL; lim_dist = NULL; lim_func = NULL;
   }

-   const IntegrationRule *EnergyIntegrationRule(const FiniteElement &el) const
+   const IntegrationRule &EnergyIntegrationRule(const FiniteElement &el) const
   {
-      return (IntRule) ? IntRule
-             /*     */ : &(IntRules.Get(el.GetGeomType(), 2*el.GetOrder() + 3));
+      if (IntegRules)
+      {
+         return IntegRules->Get(el.GetGeomType(), integ_order);
+      }
+      return (IntRule) ? *IntRule
+             /*     */ : IntRules.Get(el.GetGeomType(), 2*el.GetOrder() + 3);
   }
-   const IntegrationRule *ActionIntegrationRule(const FiniteElement &el) const
+   const IntegrationRule &ActionIntegrationRule(const FiniteElement &el) const
   {
      // TODO the energy most likely needs less integration points.
      return EnergyIntegrationRule(el);
   }
-   const IntegrationRule *GradientIntegrationRule(const FiniteElement &el) const
+   const IntegrationRule &GradientIntegrationRule(const FiniteElement &el) const
   {
      // TODO the action and energy most likely need less integration points.
      return EnergyIntegrationRule(el);
@@ -1008,7 +1016,7 @@ public:
   /** @param[in] m  TMOP_QualityMetric that will be integrated (not owned).
       @param[in] tc Target-matrix construction algorithm to use (not owned). */
   TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc)
-      : metric(m), targetC(tc),
+      : metric(m), targetC(tc), IntegRules(NULL), integ_order(-1),
        coeff1(NULL), metric_normal(1.0),
        nodes0(NULL), coeff0(NULL),
        lim_dist(NULL), lim_func(NULL), lim_normal(1.0),
@@ -1019,6 +1027,14 @@ public:

   ~TMOP_Integrator();

+   /// Prescribe a set of integration rules; relevant for mixed meshes.
+   /** This function has priority over SetIntRule(), if both are called. */
+   void SetIntegrationRules(IntegrationRules &irules, int order)
+   {
+      IntegRules = &irules;
+      integ_order = order;
+   }
+
   /// Sets a scaling Coefficient for the quality metric term of the integrator.
   /** With this addition, the integrator becomes
          @f$ \int w1 W(Jpt) dx @f$.
@@ -176,8 +176,8 @@ SerialAdvectorCGOper::SerialAdvectorCGOper(const Vector &x_start,

   MassIntegrator *Minteg = new MassIntegrator;
   M.AddDomainIntegrator(Minteg);
-   M.Assemble();
-   M.Finalize();
+   M.Assemble(0);
+   M.Finalize(0);
 }

 void SerialAdvectorCGOper::Mult(const Vector &ind, Vector &di_dt) const
@@ -220,8 +220,8 @@ ParAdvectorCGOper::ParAdvectorCGOper(const Vector &x_start,

   MassIntegrator *Minteg = new MassIntegrator;
   M.AddDomainIntegrator(Minteg);
-   M.Assemble();
-   M.Finalize();
+   M.Assemble(0);
+   M.Finalize(0);
 }

 void ParAdvectorCGOper::Mult(const Vector &ind, Vector &di_dt) const
@@ -298,34 +298,12 @@ void InterpolatorFP::SetInitialField(const Vector &init_nodes,
   field0_gf = init_field;

   dim = f->GetFE(0)->GetDim();
-   const int pts_cnt = init_nodes.Size() / dim;
-   el_id_out.SetSize(pts_cnt);
-   code_out.SetSize(pts_cnt);
-   task_id_out.SetSize(pts_cnt);
-   pos_r_out.SetSize(pts_cnt*dim);
-   dist_p_out.SetSize(pts_cnt);
 }

 void InterpolatorFP::ComputeAtNewPosition(const Vector &new_nodes,
                                          Vector &new_field)
 {
-   const int pts_cnt = new_nodes.Size() / dim;
-
-   // The sizes may change between calls due to AMR.
-   if (el_id_out.Size() != pts_cnt)
-   {
-      el_id_out.SetSize(pts_cnt);
-      code_out.SetSize(pts_cnt);
-      task_id_out.SetSize(pts_cnt);
-      pos_r_out.SetSize(pts_cnt*dim);
-      dist_p_out(pts_cnt);
-   }
-
-   // Interpolate FE function values on the found points.
-   finder->FindPoints(new_nodes, code_out, task_id_out,
-                      el_id_out, pos_r_out, dist_p_out);
-   finder->Interpolate(code_out, task_id_out, el_id_out,
-                       pos_r_out, field0_gf, new_field);
+   finder->Interpolate(new_nodes, field0_gf, new_field);
 }

 #endif
@@ -353,13 +331,12 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
      energy_in = nlf->GetEnergy(x);
   }

-   const int NE = fes->GetMesh()->GetNE(), dim = fes->GetFE(0)->GetDim(),
-             dof = fes->GetFE(0)->GetDof(), nsp = ir.GetNPoints();
-   Array<int> xdofs(dof * dim);
-   DenseMatrix Jpr(dim), dshape(dof, dim), pos(dof, dim);
-   Vector posV(pos.Data(), dof * dim);
-   Vector x_out_loc(fes->GetVSize());
+   const int NE = fes->GetMesh()->GetNE(), dim = fes->GetMesh()->Dimension();
+   Array<int> xdofs;
+   DenseMatrix Jpr(dim);

+   // Get the local prolongation of the solution vector.
+   Vector x_out_loc(fes->GetVSize());
   if (serial)
   {
      const SparseMatrix *cP = fes->GetConformingProlongation();
@@ -373,15 +350,23 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
   }
 #endif

+   // Check if the starting mesh (given by x) is inverted.
+   // Note that x hasn't been modified by the Newton update yet.
   double min_detJ = infinity();
   for (int i = 0; i < NE; i++)
   {
+      const int dof = fes->GetFE(i)->GetDof();
+      DenseMatrix dshape(dof, dim), pos(dof, dim);
+      Vector posV(pos.Data(), dof * dim);
+
      fes->GetElementVDofs(i, xdofs);
      x_out_loc.GetSubVector(xdofs, posV);

+      const IntegrationRule &irule = GetIntegrationRule(*fes->GetFE(i));
+      const int nsp = irule.GetNPoints();
      for (int j = 0; j < nsp; j++)
      {
-         fes->GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
+         fes->GetFE(i)->CalcDShape(irule.IntPoint(j), dshape);
         MultAtB(pos, dshape, Jpr);
         min_detJ = std::min(min_detJ, Jpr.Det());
      }
@@ -394,18 +379,18 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
                    p_nlf->ParFESpace()->GetComm());
   }
 #endif
-   bool untangling = false;
-   if (min_detJ_all <= 0) { untangling = true; }
+   const bool untangling = (min_detJ_all <= 0) ? true : false;

   const bool have_b = (b.Size() == Height());

   Vector x_out(x.Size());
   bool x_out_ok = false;
   double scale = 1.0, energy_out = 0.0;
-   double norm0 = Norm(r);
+   const double norm0 = Norm(r);

   const double detJ_factor = (solver_type == 1) ? 0.25 : 0.5;

+   // Perform the line search.
   for (int i = 0; i < 12; i++)
   {
      add(x, -scale, c, x_out);
@@ -429,11 +414,18 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
         int jac_ok = 1;
         for (int i = 0; i < NE; i++)
         {
+            const int dof = fes->GetFE(i)->GetDof();
+            DenseMatrix dshape(dof, dim), pos(dof, dim);
+            Vector posV(pos.Data(), dof * dim);
+
            fes->GetElementVDofs(i, xdofs);
            x_out_loc.GetSubVector(xdofs, posV);
+
+            const IntegrationRule &irule = GetIntegrationRule(*fes->GetFE(i));
+            const int nsp = irule.GetNPoints();
            for (int j = 0; j < nsp; j++)
            {
-               fes->GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
+               fes->GetFE(i)->CalcDShape(irule.IntPoint(j), dshape);
               MultAtB(pos, dshape, Jpr);
               if (Jpr.Det() <= 0.0) { jac_ok = 0; goto break2; }
            }
@@ -49,8 +49,6 @@ private:
   Vector nodes0;
   GridFunction field0_gf;
   FindPointsGSLIB *finder;
-   Array<uint> el_id_out, code_out, task_id_out;
-   Vector pos_r_out, dist_p_out;
   int dim;
 public:
   InterpolatorFP() : finder(NULL) { }
@@ -118,16 +116,39 @@ protected:

   // Quadrature points that are checked for negative Jacobians etc.
   const IntegrationRule &ir;
+   // These fields are relevant for mixed meshes.
+   IntegrationRules *IntegRules;
+   int integ_order;
+
+   const IntegrationRule &GetIntegrationRule(const FiniteElement &el) const
+   {
+      if (IntegRules)
+      {
+         return IntegRules->Get(el.GetGeomType(), integ_order);
+      }
+      return ir;
+   }

   void UpdateDiscreteTC(const TMOP_Integrator &ti, const Vector &x_new) const;

 public:
 #ifdef MFEM_USE_MPI
   TMOPNewtonSolver(MPI_Comm comm, const IntegrationRule &irule, int type = 0)
-      : LBFGSSolver(comm), solver_type(type), parallel(true), ir(irule) { }
+      : LBFGSSolver(comm), solver_type(type), parallel(true),
+        ir(irule), IntegRules(NULL), integ_order(-1) { }
 #endif
   TMOPNewtonSolver(const IntegrationRule &irule, int type = 0)
-      : LBFGSSolver(), solver_type(type), parallel(false), ir(irule) { }
+      : LBFGSSolver(), solver_type(type), parallel(false),
+        ir(irule), IntegRules(NULL), integ_order(-1) { }
+
+   /// Prescribe a set of integration rules; relevant for mixed meshes.
+   /** If called, this function has priority over the IntegrationRule given to
+       the constructor of the class. */
+   void SetIntegrationRules(IntegrationRules &irules, int order)
+   {
+      IntegRules = &irules;
+      integ_order = order;
+   }

   virtual double ComputeScalingFactor(const Vector &x, const Vector &b) const;

@@ -235,8 +235,8 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
      }

      // format info
-      SafeDefineAttribute<std::string>(io, "format", "MFEM ADIOS2 BP v0.1" );
-      SafeDefineAttribute<std::string>(io, "format/version", "0.1" );
+      SafeDefineAttribute<std::string>(io, "format", "MFEM ADIOS2 BP v0.2" );
+      SafeDefineAttribute<std::string>(io, "format/version", "0.2" );
      std::string mesh_type = "Unknown";
      std::vector<std::string> viz_tools;
      viz_tools.reserve(2); //for now
@@ -298,6 +298,7 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
         element_nvertices = static_cast<size_t>(mesh.elements[0]->GetNVertices());
      }
      SafeDefineVariable<uint64_t>(io, "connectivity", {}, {}, {nelements, element_nvertices+1});
+      SafeDefineVariable<int32_t>(io, "material", {}, {}, {nelements});

      // vertices
      SafeDefineVariable<uint32_t>(io,"NumOfVertices", {adios2::LocalValueDim});
@@ -348,8 +349,15 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
         io.InquireVariable<uint64_t>("connectivity");
      adios2::Variable<uint64_t>::Span span_connectivity = engine.Put<uint64_t>
                                                           (var_connectivity);
+
+      adios2::Variable<int32_t> var_element_attribute =
+         io.InquireVariable<int32_t>("material");
+      adios2::Variable<int32_t>::Span span_element_attribute = engine.Put<int32_t>
+                                                               (var_element_attribute);
+
      size_t span_vertices_offset = 0;
      size_t span_connectivity_offset = 0;
+      size_t span_element_attribute_offset = 0;
      // use for setting absolute node id for each element
      size_t point_id = 0;
      DenseMatrix pmatrix;
@@ -370,6 +378,9 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
         }
         span_vertices_offset += static_cast<size_t>(pmatrix.Width()*pmatrix.Height());

+         // element attribute
+         const int element_attribute = mesh.GetAttribute(e);
+
         // connectivity
         const int nv = Geometries.GetVertices(type)->GetNPoints();
         const Array<int> &element_vertices = refined_geometry->RefGeoms;
@@ -379,6 +390,10 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
            span_connectivity[span_connectivity_offset] = static_cast<uint64_t>(nv);
            ++span_connectivity_offset;

+            span_element_attribute[span_element_attribute_offset] = static_cast<int32_t>
+                                                                    (element_attribute);
+            ++span_element_attribute_offset;
+
            for (int k =0; k < nv; k++, v++ )
            {
               span_connectivity[span_connectivity_offset] = static_cast<uint64_t>
@@ -419,9 +434,17 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
      adios2::Variable<uint64_t>::Span spanConnectivity =
         engine.Put<uint64_t>(varConnectivity);

+      adios2::Variable<int32_t> varElementAttribute =
+         io.InquireVariable<int32_t>("material");
+      // zero-copy access to adios2 buffer to put non-contiguous to contiguous memory
+      adios2::Variable<int32_t>::Span spanElementAttribute =
+         engine.Put<int32_t>(varElementAttribute);
+
      size_t elementPosition = 0;
      for (int e = 0; e < mesh.GetNE(); ++e)
      {
+         spanElementAttribute[e] = static_cast<int32_t>(mesh.GetAttribute(e));
+
         const int nVertices = mesh.elements[e]->GetNVertices();
         spanConnectivity[elementPosition] = nVertices;
         for (int v = 0; v < nVertices; ++v)
@@ -688,7 +711,7 @@ std::string adios2stream::VTKSchema() const noexcept
 {
   std::string vtkSchema = R"(
 <?xml version="1.0"?>
-<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+<VTKFile type="UnstructuredGrid" version="0.2" byte_order="LittleEndian">
  <UnstructuredGrid>
    <Piece NumberOfPoints="NumOfVertices" NumberOfCells="NumOfElements">
      <Points>
@@ -696,6 +719,9 @@ std::string adios2stream::VTKSchema() const noexcept

   vtkSchema += R"(
      </Points>
+	  <CellData>
+        <DataArray Name="material" />
+	  </CellData>
      <Cells>
        <DataArray Name="connectivity" />
        <DataArray Name="types" />
@@ -12,9 +12,10 @@
 #include "forall.hpp"
 #include "occa.hpp"
 #ifdef MFEM_USE_CEED
-#include <ceed.h>
+#include "../fem/libceed/ceed.hpp"
 #endif

+#include <unordered_map>
 #include <string>
 #include <map>

@@ -33,13 +34,16 @@ occa::device occaDevice;

 #ifdef MFEM_USE_CEED
 Ceed ceed = NULL;
+
+CeedBasisMap ceed_basis_map;
+CeedRestrMap ceed_restr_map;
 #endif

 // Backends listed by priority, high to low:
 static const Backend::Id backend_list[Backend::NUM_BACKENDS] =
 {
   Backend::CEED_CUDA, Backend::OCCA_CUDA, Backend::RAJA_CUDA, Backend::CUDA,
-   Backend::HIP, Backend::DEBUG,
+   Backend::HIP, Backend::DEBUG_DEVICE,
   Backend::OCCA_OMP, Backend::RAJA_OMP, Backend::OMP,
   Backend::CEED_CPU, Backend::OCCA_CPU, Backend::RAJA_CPU, Backend::CPU
 };
@@ -154,6 +158,16 @@ Device::~Device()
   {
      free(device_option);
 #ifdef MFEM_USE_CEED
+      // Destroy FES -> CeedBasis, CeedElemRestriction hash table contents
+      for (auto entry : internal::ceed_basis_map)
+      {
+         CeedBasisDestroy(&entry.second);
+      }
+      for (auto entry : internal::ceed_restr_map)
+      {
+         CeedElemRestrictionDestroy(&entry.second);
+      }
+      // Destroy Ceed context
      CeedDestroy(&internal::ceed);
 #endif
      mm.Destroy();
@@ -266,7 +280,7 @@ void Device::Print(std::ostream &out)

 void Device::UpdateMemoryTypeAndClass()
 {
-   const bool debug = Device::Allows(Backend::DEBUG);
+   const bool debug = Device::Allows(Backend::DEBUG_DEVICE);

   const bool device = Device::Allows(Backend::DEVICE_MASK);

@@ -504,7 +518,7 @@ void Device::Setup(const int device)
         CeedDeviceSetup(device_option);
      }
   }
-   if (Allows(Backend::DEBUG)) { ngpu = 1; }
+   if (Allows(Backend::DEBUG_DEVICE)) { ngpu = 1; }
 }

 } // mfem
@@ -64,8 +64,9 @@ struct Backend
      /** @brief [device] Debug backend: host memory is READ/WRITE protected
          while a device is in use. It allows to test the "device" code-path
          (using separate host/device memory pools and host <-> device
-          transfers) without any GPU hardware. */
-      DEBUG = 1 << 12
+          transfers) without any GPU hardware. As 'DEBUG' is sometimes used
+          as a macro, `_DEVICE` has been added to avoid conflicts. */
+      DEBUG_DEVICE = 1 << 12
   };

   /** @brief Additional useful constants. For example, the *_MASK constants can
@@ -86,7 +87,7 @@ struct Backend
      /// Bitwise-OR of all CEED backends
      CEED_MASK = CEED_CPU | CEED_CUDA,
      /// Biwise-OR of all device backends
-      DEVICE_MASK = CUDA_MASK | HIP_MASK | DEBUG,
+      DEVICE_MASK = CUDA_MASK | HIP_MASK | DEBUG_DEVICE,

      /// Biwise-OR of all RAJA backends
      RAJA_MASK = RAJA_CPU | RAJA_OMP | RAJA_CUDA,
@@ -193,7 +194,8 @@ public:
       * The available backends are described by the Backend class.
       * The string name of a backend is the lowercase version of the
         Backend::Id enumeration constant with '_' replaced by '-', e.g. the
-         string name of 'RAJA_CPU' is 'raja-cpu'.
+         string name of 'RAJA_CPU' is 'raja-cpu'. The string name of the debug
+         backend (Backend::Id 'DEBUG_DEVICE') is exceptionally set to 'debug'.
       * The 'cpu' backend is always enabled with lowest priority.
       * The current backend priority from highest to lowest is:
         'ceed-cuda', 'occa-cuda', 'raja-cuda', 'cuda', 'hip', 'debug',
@@ -343,7 +343,7 @@ inline void ForallWrap(const bool use_dev, const int N,
   { return HipWrap3D(N, d_body, X, Y, Z); }
 #endif

-   if (Device::Allows(Backend::DEBUG)) { goto backend_cpu; }
+   if (Device::Allows(Backend::DEBUG_DEVICE)) { goto backend_cpu; }

 #if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_OPENMP)
   // Handle all allowed OpenMP backends except Backend::OMP
@@ -136,8 +136,10 @@ struct Memory
   void *d_ptr;
   const size_t bytes;
   const MemoryType h_mt, d_mt;
+   mutable bool h_rw, d_rw;
   Memory(void *p, size_t b, MemoryType h, MemoryType d):
-      h_ptr(p), d_ptr(nullptr), bytes(b), h_mt(h), d_mt(d) { }
+      h_ptr(p), d_ptr(nullptr), bytes(b), h_mt(h), d_mt(d),
+      h_rw(true), d_rw(true) { }
 };

 /// Alias class that holds the base memory region and the offset
@@ -173,8 +175,8 @@ public:
   virtual ~HostMemorySpace() { }
   virtual void Alloc(void **ptr, size_t bytes) { *ptr = std::malloc(bytes); }
   virtual void Dealloc(void *ptr) { std::free(ptr); }
-   virtual void Protect(const void*, size_t) { }
-   virtual void Unprotect(const void*, size_t) { }
+   virtual void Protect(const Memory&, size_t) { }
+   virtual void Unprotect(const Memory&, size_t) { }
   virtual void AliasProtect(const void*, size_t) { }
   virtual void AliasUnprotect(const void*, size_t) { }
 };
@@ -352,8 +354,10 @@ public:
   MmuHostMemorySpace(): HostMemorySpace() { MmuInit(); }
   void Alloc(void **ptr, size_t bytes) { MmuAlloc(ptr, bytes); }
   void Dealloc(void *ptr) { MmuDealloc(ptr, maps->memories.at(ptr).bytes); }
-   void Protect(const void *ptr, size_t bytes) { MmuProtect(ptr, bytes); }
-   void Unprotect(const void *ptr, size_t bytes) { MmuAllow(ptr, bytes); }
+   void Protect(const Memory& mem, size_t bytes)
+   { if (mem.h_rw) { mem.h_rw = false; MmuProtect(mem.h_ptr, bytes); } }
+   void Unprotect(const Memory &mem, size_t bytes)
+   { if (!mem.h_rw) { mem.h_rw = true; MmuAllow(mem.h_ptr, bytes); } }
   /// Aliases need to be restricted during protection
   void AliasProtect(const void *ptr, size_t bytes)
   { MmuProtect(MmuAddrR(ptr), MmuLengthR(ptr, bytes)); }
@@ -442,8 +446,10 @@ public:
   MmuDeviceMemorySpace(): DeviceMemorySpace() { }
   void Alloc(Memory &m) { MmuAlloc(&m.d_ptr, m.bytes); }
   void Dealloc(Memory &m) { MmuDealloc(m.d_ptr, m.bytes); }
-   void Protect(const Memory &m) { MmuProtect(m.d_ptr, m.bytes); }
-   void Unprotect(const Memory &m) { MmuAllow(m.d_ptr, m.bytes); }
+   void Protect(const Memory &m)
+   { if (m.d_rw) { m.d_rw = false; MmuProtect(m.d_ptr, m.bytes); } }
+   void Unprotect(const Memory &m)
+   { if (!m.d_rw) { m.d_rw = true; MmuAllow(m.d_ptr, m.bytes); } }
   /// Aliases need to be restricted during protection
   void AliasProtect(const void *ptr, size_t bytes)
   { MmuProtect(MmuAddrR(ptr), MmuLengthR(ptr, bytes)); }
@@ -969,11 +975,8 @@ void MemoryManager::Copy_(void *dst_h_ptr, const void *src_h_ptr,
      {
         if (dst_h_ptr != src_d_ptr && bytes != 0)
         {
-            internal::Memory &dst_h_base = maps->memories.at(dst_h_ptr);
            internal::Memory &src_d_base = maps->memories.at(src_d_ptr);
-            MemoryType dst_h_mt = dst_h_base.h_mt;
            MemoryType src_d_mt = src_d_base.d_mt;
-            ctrl->Host(dst_h_mt)->Unprotect(dst_h_ptr, bytes);
            ctrl->Device(src_d_mt)->DtoH(dst_h_ptr, src_d_ptr, bytes);
         }
      }
@@ -1174,13 +1177,14 @@ void *MemoryManager::GetDevicePtr(const void *h_ptr, size_t bytes,
   const MemoryType &d_mt = mem.d_mt;
   MFEM_VERIFY_TYPES(h_mt, d_mt);
   if (!mem.d_ptr) { ctrl->Device(d_mt)->Alloc(mem); }
+   // Aliases might have done some protections
   ctrl->Device(d_mt)->Unprotect(mem);
   if (copy_data)
   {
      MFEM_ASSERT(bytes <= mem.bytes, "invalid copy size");
      ctrl->Device(d_mt)->HtoD(mem.d_ptr, h_ptr, bytes);
   }
-   ctrl->Host(h_mt)->Protect(h_ptr, bytes);
+   ctrl->Host(h_mt)->Protect(mem, bytes);
   return mem.d_ptr;
 }

@@ -1206,6 +1210,7 @@ void *MemoryManager::GetAliasDevicePtr(const void *alias_ptr, size_t bytes,
   void *alias_d_ptr = static_cast<char*>(mem.d_ptr) + offset;
   MFEM_ASSERT(alias_h_ptr == alias_ptr, "internal error");
   MFEM_ASSERT(bytes <= alias.bytes, "internal error");
+   mem.d_rw = false;
   ctrl->Device(d_mt)->AliasUnprotect(alias_d_ptr, bytes);
   ctrl->Host(h_mt)->AliasUnprotect(alias_ptr, bytes);
   if (copy) { ctrl->Device(d_mt)->HtoD(alias_d_ptr, alias_h_ptr, bytes); }
@@ -1221,8 +1226,8 @@ void *MemoryManager::GetHostPtr(const void *ptr, size_t bytes, bool copy)
   const MemoryType &h_mt = mem.h_mt;
   const MemoryType &d_mt = mem.d_mt;
   MFEM_VERIFY_TYPES(h_mt, d_mt);
-   ctrl->Host(h_mt)->Unprotect(mem.h_ptr, bytes);
   // Aliases might have done some protections
+   ctrl->Host(h_mt)->Unprotect(mem, bytes);
   if (mem.d_ptr) { ctrl->Device(d_mt)->Unprotect(mem); }
   if (copy && mem.d_ptr) { ctrl->Device(d_mt)->DtoH(mem.h_ptr, mem.d_ptr, bytes); }
   if (mem.d_ptr) { ctrl->Device(d_mt)->Protect(mem); }
@@ -1240,6 +1245,7 @@ void *MemoryManager::GetAliasHostPtr(const void *ptr, size_t bytes,
   void *alias_h_ptr = static_cast<char*>(mem->h_ptr) + alias.offset;
   void *alias_d_ptr = static_cast<char*>(mem->d_ptr) + alias.offset;
   MFEM_ASSERT(alias_h_ptr == ptr,  "internal error");
+   mem->h_rw = false;
   ctrl->Host(h_mt)->AliasUnprotect(alias_h_ptr, bytes);
   if (mem->d_ptr) { ctrl->Device(d_mt)->AliasUnprotect(alias_d_ptr, bytes); }
   if (copy_data && mem->d_ptr)
@@ -26,10 +26,10 @@ ComplexOperator::ComplexOperator(Operator * Op_Real, Operator * Op_Imag,
   , ownReal_(ownReal)
   , ownImag_(ownImag)
   , convention_(convention)
-   , x_r_(NULL, width / 2)
-   , x_i_(NULL, width / 2)
-   , y_r_(NULL, height / 2)
-   , y_i_(NULL, height / 2)
+   , x_r_()
+   , x_i_()
+   , y_r_()
+   , y_i_()
   , u_(NULL)
   , v_(NULL)
 {}
@@ -68,14 +68,26 @@ const Operator & ComplexOperator::imag() const

 void ComplexOperator::Mult(const Vector &x, Vector &y) const
 {
-   double * x_data = x.GetData();
-   x_r_.SetData(x_data);
-   x_i_.SetData(&x_data[width / 2]);
+   x.Read();
+   y.UseDevice(true); y = 0.0;

-   y_r_.SetData(&y[0]);
-   y_i_.SetData(&y[height / 2]);
+   x_r_.MakeRef(const_cast<Vector&>(x), 0, width/2);
+   x_i_.MakeRef(const_cast<Vector&>(x), width/2, width/2);
+
+   y_r_.MakeRef(y, 0, height/2);
+   y_i_.MakeRef(y, height/2, height/2);

   this->Mult(x_r_, x_i_, y_r_, y_i_);
+
+   y_r_.SyncAliasMemory(y);
+   y_i_.SyncAliasMemory(y);
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   x_r_.Destroy();
+   x_i_.Destroy();
+   y_r_.Destroy();
+   y_i_.Destroy();
 }

 void ComplexOperator::Mult(const Vector &x_r, const Vector &x_i,
@@ -91,31 +103,47 @@ void ComplexOperator::Mult(const Vector &x_r, const Vector &x_i,
      y_r = 0.0;
      y_i = 0.0;
   }
+
   if (Op_Imag_)
   {
-      if (!v_) { v_ = new Vector(Op_Imag_->Height()); }
+      if (!v_) { v_ = new Vector(); }
+      v_->UseDevice(true);
+      v_->SetSize(Op_Imag_->Height());
+
      Op_Imag_->Mult(x_i, *v_);
-      y_r_ -= *v_;
+      y_r.Add(-1.0, *v_);
      Op_Imag_->Mult(x_r, *v_);
-      y_i_ += *v_;
+      y_i.Add(1.0, *v_);
   }

   if (convention_ == BLOCK_SYMMETRIC)
   {
-      y_i_ *= -1.0;
+      y_i *= -1.0;
   }
 }

 void ComplexOperator::MultTranspose(const Vector &x, Vector &y) const
 {
-   double * x_data = x.GetData();
-   y_r_.SetData(x_data);
-   y_i_.SetData(&x_data[height / 2]);
+   x.Read();
+   y.UseDevice(true); y = 0.0;

-   x_r_.SetData(&y[0]);
-   x_i_.SetData(&y[width / 2]);
+   x_r_.MakeRef(const_cast<Vector&>(x), 0, height/2);
+   x_i_.MakeRef(const_cast<Vector&>(x), height/2, height/2);

-   this->MultTranspose(y_r_, y_i_, x_r_, x_i_);
+   y_r_.MakeRef(y, 0, width/2);
+   y_i_.MakeRef(y, width/2, width/2);
+
+   this->MultTranspose(x_r_, x_i_, y_r_, y_i_);
+
+   y_r_.SyncAliasMemory(y);
+   y_i_.SyncAliasMemory(y);
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   x_r_.Destroy();
+   x_i_.Destroy();
+   y_r_.Destroy();
+   y_i_.Destroy();
 }

 void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
@@ -136,13 +164,17 @@ void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
      y_r = 0.0;
      y_i = 0.0;
   }
+
   if (Op_Imag_)
   {
-      if (!u_) { u_ = new Vector(Op_Imag_->Width()); }
+      if (!u_) { u_ = new Vector(); }
+      u_->UseDevice(true);
+      u_->SetSize(Op_Imag_->Width());
+
      Op_Imag_->MultTranspose(x_i, *u_);
-      y_r_.Add(convention_ == BLOCK_SYMMETRIC ? -1.0 : 1.0, *u_);
+      y_r.Add(convention_ == BLOCK_SYMMETRIC ? -1.0 : 1.0, *u_);
      Op_Imag_->MultTranspose(x_r, *u_);
-      y_i_ -= *u_;
+      y_i.Add(-1.0, *u_);
   }
 }

@@ -100,7 +100,7 @@ public:
   /** @brief Real or imaginary part accessor methods

       The following accessor methods should only be called if the requested
-       part of the opertor is known to exist.  This can be checked with
+       part of the operator is known to exist. This can be checked with
       hasRealPart() or hasImagPart().
   */
   virtual Operator & real();
@@ -166,7 +166,7 @@ public:
   /** Combine the blocks making up this complex operator into a single
       SparseMatrix. The resulting matrix can be passed to solvers which require
       access to the matrix entries themselves, such as sparse direct solvers,
-       rather than simply the action of the opertor. Note that this combined
+       rather than simply the action of the operator. Note that this combined
       operator requires roughly twice the memory of the block structured
       operator. */
   SparseMatrix * GetSystemMatrix() const;
@@ -269,7 +269,7 @@ public:
       HypreParMatrix. The resulting matrix can be passed to solvers which
       require access to the matrix entries themselves, such as sparse direct
       solvers or Hypre preconditioners, rather than simply the action of the
-       opertor. Note that this combined operator requires roughly twice the
+       operator. Note that this combined operator requires roughly twice the
       memory of the block structured operator. */
   HypreParMatrix * GetSystemMatrix() const;

@@ -373,7 +373,7 @@ void DenseMatrix::SymmetricScaling(const Vector & s)
 {
   if (height != width || s.Size() != height)
   {
-      mfem_error("DenseMatrix::SymmetricScaling");
+      mfem_error("DenseMatrix::SymmetricScaling: dimension mismatch");
   }

   double * ss = new double[width];
@@ -401,7 +401,7 @@ void DenseMatrix::InvSymmetricScaling(const Vector & s)
 {
   if (height != width || s.Size() != width)
   {
-      mfem_error("DenseMatrix::SymmetricScaling");
+      mfem_error("DenseMatrix::InvSymmetricScaling: dimension mismatch");
   }

   double * ss = new double[width];
@@ -528,7 +528,7 @@ double DenseMatrix::Weight() const
      double F = d[0] * d[3] + d[1] * d[4] + d[2] * d[5];
      return sqrt(E * G - F * F);
   }
-   mfem_error("DenseMatrix::Weight()");
+   mfem_error("DenseMatrix::Weight(): mismatched or unsupported dimensions");
   return 0.0;
 }

@@ -639,7 +639,7 @@ void DenseMatrix::Invert()
 #ifdef MFEM_DEBUG
   if (Height() <= 0 || Height() != Width())
   {
-      mfem_error("DenseMatrix::Invert()");
+      mfem_error("DenseMatrix::Invert(): dimension mismatch");
   }
 #endif

@@ -1083,7 +1083,7 @@ void DenseMatrix::Eigensystem(Vector &ev, DenseMatrix *evect)

   MFEM_CONTRACT_VAR(ev);
   MFEM_CONTRACT_VAR(evect);
-   mfem_error("DenseMatrix::Eigensystem");
+   mfem_error("DenseMatrix::Eigensystem: Compiled without LAPACK");

 #endif
 }
@@ -1164,7 +1164,7 @@ void DenseMatrix::Eigensystem(DenseMatrix &b, Vector &ev,
   MFEM_CONTRACT_VAR(b);
   MFEM_CONTRACT_VAR(ev);
   MFEM_CONTRACT_VAR(evect);
-   mfem_error("DenseMatrix::Eigensystem for generalized eigenvalues");
+   mfem_error("DenseMatrix::Eigensystem(generalized): Compiled without LAPACK");
 #endif
 }

@@ -1204,7 +1204,7 @@ void DenseMatrix::SingularValues(Vector &sv) const
 #else
   MFEM_CONTRACT_VAR(sv);
   // compiling without lapack
-   mfem_error("DenseMatrix::SingularValues");
+   mfem_error("DenseMatrix::SingularValues: Compiled without LAPACK");
 #endif
 }

@@ -1441,7 +1441,7 @@ void DenseMatrix::GradToCurl(DenseMatrix &curl)
   if ((Width() != 2 || curl.Width() != 1 || 2*n != curl.Height()) &&
       (Width() != 3 || curl.Width() != 3 || 3*n != curl.Height()))
   {
-      mfem_error("DenseMatrix::GradToCurl(...)");
+      mfem_error("DenseMatrix::GradToCurl(...): dimension mismatch");
   }
 #endif

@@ -1676,7 +1676,7 @@ void DenseMatrix::AddMatrix(DenseMatrix &A, int ro, int co)
 #ifdef MFEM_DEBUG
   if (co+aw > Width() || ro+ah > h)
   {
-      mfem_error("DenseMatrix::AddMatrix(...) 1");
+      mfem_error("DenseMatrix::AddMatrix(...) 1 : dimension mismatch");
   }
 #endif

@@ -1706,7 +1706,7 @@ void DenseMatrix::AddMatrix(double a, const DenseMatrix &A, int ro, int co)
 #ifdef MFEM_DEBUG
   if (co+aw > Width() || ro+ah > h)
   {
-      mfem_error("DenseMatrix::AddMatrix(...) 2");
+      mfem_error("DenseMatrix::AddMatrix(...) 2 : dimension mismatch");
   }
 #endif

@@ -1753,7 +1753,7 @@ void DenseMatrix::AdjustDofDirection(Array<int> &dofs)
 #ifdef MFEM_DEBUG
   if (dofs.Size() != n || Width() != n)
   {
-      mfem_error("DenseMatrix::AdjustDofDirection(...)");
+      mfem_error("DenseMatrix::AdjustDofDirection(...): dimension mismatch");
   }
 #endif

@@ -2093,11 +2093,11 @@ void CalcAdjugate(const DenseMatrix &a, DenseMatrix &adja)
 #ifdef MFEM_DEBUG
   if (a.Width() > a.Height() || a.Width() < 1 || a.Height() > 3)
   {
-      mfem_error("CalcAdjugate(...)");
+      mfem_error("CalcAdjugate(...): unsupported dimensions");
   }
   if (a.Width() != adja.Height() || a.Height() != adja.Width())
   {
-      mfem_error("CalcAdjugate(...)");
+      mfem_error("CalcAdjugate(...): dimension mismatch");
   }
 #endif

@@ -2166,7 +2166,7 @@ void CalcAdjugateTranspose(const DenseMatrix &a, DenseMatrix &adjat)
   if (a.Height() != a.Width() || adjat.Height() != adjat.Width() ||
       a.Width() != adjat.Width() || a.Width() < 1 || a.Width() > 3)
   {
-      mfem_error("CalcAdjugateTranspose(...)");
+      mfem_error("CalcAdjugateTranspose(...): dimension mismatch");
   }
 #endif
   if (a.Width() == 1)
@@ -2269,7 +2269,7 @@ void CalcInverseTranspose(const DenseMatrix &a, DenseMatrix &inva)
   if ( (a.Width() != a.Height()) || ( (a.Height()!= 1) && (a.Height()!= 2)
                                       && (a.Height()!= 3) ) )
   {
-      mfem_error("CalcInverseTranspose(...)");
+      mfem_error("CalcInverseTranspose(...): dimension mismatch");
   }
 #endif

@@ -2396,7 +2396,7 @@ void MultABt(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
   if (A.Height() != ABt.Height() || B.Height() != ABt.Width() ||
       A.Width() != B.Width())
   {
-      mfem_error("MultABt(...)");
+      mfem_error("MultABt(...): dimension mismatch");
   }
 #endif

@@ -2462,7 +2462,7 @@ void MultADBt(const DenseMatrix &A, const Vector &D,
   if (A.Height() != ADBt.Height() || B.Height() != ADBt.Width() ||
       A.Width() != B.Width() || A.Width() != D.Size())
   {
-      mfem_error("MultADBt(...)");
+      mfem_error("MultADBt(...): dimension mismatch");
   }
 #endif

@@ -2501,7 +2501,7 @@ void AddMultABt(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
   if (A.Height() != ABt.Height() || B.Height() != ABt.Width() ||
       A.Width() != B.Width())
   {
-      mfem_error("AddMultABt(...)");
+      mfem_error("AddMultABt(...): dimension mismatch");
   }
 #endif

@@ -2559,7 +2559,7 @@ void AddMultADBt(const DenseMatrix &A, const Vector &D,
   if (A.Height() != ADBt.Height() || B.Height() != ADBt.Width() ||
       A.Width() != B.Width() || A.Width() != D.Size())
   {
-      mfem_error("AddMultADBt(...)");
+      mfem_error("AddMultADBt(...): dimension mismatch");
   }
 #endif

@@ -2595,7 +2595,7 @@ void AddMult_a_ABt(double a, const DenseMatrix &A, const DenseMatrix &B,
   if (A.Height() != ABt.Height() || B.Height() != ABt.Width() ||
       A.Width() != B.Width())
   {
-      mfem_error("AddMult_a_ABt(...)");
+      mfem_error("AddMult_a_ABt(...): dimension mismatch");
   }
 #endif

@@ -2653,7 +2653,7 @@ void MultAtB(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &AtB)
   if (A.Width() != AtB.Height() || B.Width() != AtB.Width() ||
       A.Height() != B.Height())
   {
-      mfem_error("MultAtB(...)");
+      mfem_error("MultAtB(...): dimension mismatch");
   }
 #endif

@@ -2761,7 +2761,7 @@ void MultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 #ifdef MFEM_DEBUG
   if (v.Size() != VWt.Height() || w.Size() != VWt.Width())
   {
-      mfem_error("MultVWt(...)");
+      mfem_error("MultVWt(...): dimension mismatch");
   }
 #endif

@@ -2782,7 +2782,7 @@ void AddMultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 #ifdef MFEM_DEBUG
   if (VWt.Height() != m || VWt.Width() != n)
   {
-      mfem_error("AddMultVWt(...)");
+      mfem_error("AddMultVWt(...): dimension mismatch");
   }
 #endif

@@ -2803,7 +2803,7 @@ void AddMultVVt(const Vector &v, DenseMatrix &VVt)
 #ifdef MFEM_DEBUG
   if (VVt.Height() != n || VVt.Width() != n)
   {
-      mfem_error("AddMultVVt(...)");
+      mfem_error("AddMultVVt(...): dimension mismatch");
   }
 #endif

@@ -2828,7 +2828,7 @@ void AddMult_a_VWt(const double a, const Vector &v, const Vector &w,
 #ifdef MFEM_DEBUG
   if (VWt.Height() != m || VWt.Width() != n)
   {
-      mfem_error("AddMult_a_VWt(...)");
+      mfem_error("AddMult_a_VWt(...): dimension mismatch");
   }
 #endif

@@ -3353,7 +3353,7 @@ void DenseMatrixEigensystem::Eval()
 #ifdef MFEM_DEBUG
   if (mat.Width() != n)
   {
-      mfem_error("DenseMatrixEigensystem::Eval()");
+      mfem_error("DenseMatrixEigensystem::Eval(): dimension mismatch");
   }
 #endif

@@ -1048,6 +1048,36 @@ HYPRE_Int HypreParMatrix::MultTranspose(HypreParVector & x, HypreParVector & y,
   return hypre_ParCSRMatrixMatvecT(a, A, x, b, y);
 }

+void HypreParMatrix::AbsMult(double a, const Vector &x,
+                             double b, Vector &y) const
+{
+   MFEM_ASSERT(x.Size() == Width(), "invalid x.Size() = " << x.Size()
+               << ", expected size = " << Width());
+   MFEM_ASSERT(y.Size() == Height(), "invalid y.Size() = " << y.Size()
+               << ", expected size = " << Height());
+
+   auto x_data = x.HostRead();
+   auto y_data = (b == 0.0) ? y.HostWrite() : y.HostReadWrite();
+
+   internal::hypre_ParCSRMatrixAbsMatvec(A, a, const_cast<double*>(x_data),
+                                         b, y_data);
+}
+
+void HypreParMatrix::AbsMultTranspose(double a, const Vector &x,
+                                      double b, Vector &y) const
+{
+   MFEM_ASSERT(x.Size() == Height(), "invalid x.Size() = " << x.Size()
+               << ", expected size = " << Height());
+   MFEM_ASSERT(y.Size() == Width(), "invalid y.Size() = " << y.Size()
+               << ", expected size = " << Width());
+
+   auto x_data = x.HostRead();
+   auto y_data = (b == 0.0) ? y.HostWrite() : y.HostReadWrite();
+
+   internal::hypre_ParCSRMatrixAbsMatvecT(A, a, const_cast<double*>(x_data),
+                                          b, y_data);
+}
+
 HypreParMatrix* HypreParMatrix::LeftDiagMult(const SparseMatrix &D,
                                             HYPRE_Int* row_starts) const
 {
@@ -3185,10 +3215,31 @@ void HypreBoomerAMG::SetOperator(const Operator &op)
   B = X = NULL;
 }

-void HypreBoomerAMG::SetSystemsOptions(int dim)
+void HypreBoomerAMG::SetSystemsOptions(int dim, bool order_bynodes)
 {
   HYPRE_BoomerAMGSetNumFunctions(amg_precond, dim);

+   // The default "system" ordering in hypre is Ordering::byVDIM. When we are
+   // using Ordering::byNODES, we have to specify the ordering explicitly with
+   // HYPRE_BoomerAMGSetDofFunc as in the following code.
+   if (order_bynodes)
+   {
+      // hypre actually deletes the following pointer in HYPRE_BoomerAMGDestroy,
+      // so we don't need to track it
+      HYPRE_Int *mapping = mfem_hypre_CTAlloc(HYPRE_Int, height);
+      int h_nnodes = height / dim; // nodes owned in linear algebra (not fem)
+      MFEM_VERIFY(height % dim == 0, "Ordering does not work as claimed!");
+      int k = 0;
+      for (int i = 0; i < dim; ++i)
+      {
+         for (int j = 0; j < h_nnodes; ++j)
+         {
+            mapping[k++] = i;
+         }
+      }
+      HYPRE_BoomerAMGSetDofFunc(amg_precond, mapping);
+   }
+
   // More robust options with respect to convergence
   HYPRE_BoomerAMGSetAggNumLevels(amg_precond, 0);
   HYPRE_BoomerAMGSetStrongThreshold(amg_precond, 0.5);
@@ -446,6 +446,12 @@ public:
   virtual void MultTranspose(const Vector &x, Vector &y) const
   { MultTranspose(1.0, x, 0.0, y); }

+   /// Computes y = a * |A| * x + b * y, using entry-wise absolute values of matrix A
+   void AbsMult(double a, const Vector &x, double b, Vector &y) const;
+
+   /// Computes y = a * |At| * x + b * y, using entry-wise absolute values of the transpose of matrix A
+   void AbsMultTranspose(double a, const Vector &x, double b, Vector &y) const;
+
   /** The "Boolean" analog of y = alpha * A * x + beta * y, where elements in
       the sparsity pattern of the matrix are treated as "true". */
   void BooleanMult(int alpha, const int *x, int beta, int *y)
@@ -986,16 +992,15 @@ public:

   virtual void SetOperator(const Operator &op);

-   /** More robust options for systems, such as elasticity. Note that BoomerAMG
-       assumes Ordering::byVDIM in the finite element space used to generate the
-       matrix A. */
-   void SetSystemsOptions(int dim);
+   /** More robust options for systems, such as elasticity. */
+   void SetSystemsOptions(int dim, bool order_bynodes=false);

   /** A special elasticity version of BoomerAMG that takes advantage of
       geometric rigid body modes and could perform better on some problems, see
       "Improving algebraic multigrid interpolation operators for linear
       elasticity problems", Baker, Kolev, Yang, NLAA 2009, DOI:10.1002/nla.688.
-       As with SetSystemsOptions(), this solver assumes Ordering::byVDIM. */
+       This solver assumes Ordering::byVDIM in the FiniteElementSpace used to
+       construct A. */
   void SetElasticityOptions(ParFiniteElementSpace *fespace);

   void SetPrintLevel(int print_level)
@@ -16,6 +16,7 @@

 #include "hypre_parcsr.hpp"
 #include <limits>
+#include <cmath>

 namespace mfem
 {
@@ -977,6 +978,196 @@ void hypre_ParCSRMatrixSplit(hypre_ParCSRMatrix *A,
   }
 }

+/* Based on hypre_CSRMatrixMatvec in hypre's csr_matvec.c */
+void hypre_CSRMatrixAbsMatvec(hypre_CSRMatrix *A,
+                              HYPRE_Real alpha,
+                              HYPRE_Real *x,
+                              HYPRE_Real beta,
+                              HYPRE_Real *y)
+{
+   HYPRE_Real       *A_data   = hypre_CSRMatrixData(A);
+   HYPRE_Int        *A_i      = hypre_CSRMatrixI(A);
+   HYPRE_Int        *A_j      = hypre_CSRMatrixJ(A);
+   HYPRE_Int         num_rows = hypre_CSRMatrixNumRows(A);
+
+   HYPRE_Int        *A_rownnz = hypre_CSRMatrixRownnz(A);
+   HYPRE_Int         num_rownnz = hypre_CSRMatrixNumRownnz(A);
+
+   HYPRE_Real       *x_data = x;
+   HYPRE_Real       *y_data = y;
+
+   HYPRE_Real        temp, tempx;
+
+   HYPRE_Int         i, jj;
+
+   HYPRE_Int         m;
+
+   HYPRE_Real        xpar=0.7;
+
+   /*-----------------------------------------------------------------------
+    * Do (alpha == 0.0) computation - RDF: USE MACHINE EPS
+    *-----------------------------------------------------------------------*/
+
+   if (alpha == 0.0)
+   {
+      for (i = 0; i < num_rows; i++)
+      {
+         y_data[i] *= beta;
+      }
+      return;
+   }
+
+   /*-----------------------------------------------------------------------
+    * y = (beta/alpha)*y
+    *-----------------------------------------------------------------------*/
+
+   temp = beta / alpha;
+
+   if (temp != 1.0)
+   {
+      if (temp == 0.0)
+      {
+         for (i = 0; i < num_rows; i++)
+         {
+            y_data[i] = 0.0;
+         }
+      }
+      else
+      {
+         for (i = 0; i < num_rows; i++)
+         {
+            y_data[i] *= temp;
+         }
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y += abs(A)*x
+    *-----------------------------------------------------------------*/
+
+   /* use rownnz pointer to do the abs(A)*x multiplication
+      when num_rownnz is smaller than num_rows */
+
+   if (num_rownnz < xpar*(num_rows))
+   {
+      for (i = 0; i < num_rownnz; i++)
+      {
+         m = A_rownnz[i];
+
+         tempx = 0;
+         for (jj = A_i[m]; jj < A_i[m+1]; jj++)
+         {
+            tempx += std::abs(A_data[jj])*x_data[A_j[jj]];
+         }
+         y_data[m] += tempx;
+      }
+   }
+   else
+   {
+      for (i = 0; i < num_rows; i++)
+      {
+         tempx = 0;
+         for (jj = A_i[i]; jj < A_i[i+1]; jj++)
+         {
+            tempx += std::abs(A_data[jj])*x_data[A_j[jj]];
+         }
+         y_data[i] += tempx;
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y = alpha*y
+    *-----------------------------------------------------------------*/
+
+   if (alpha != 1.0)
+   {
+      for (i = 0; i < num_rows; i++)
+      {
+         y_data[i] *= alpha;
+      }
+   }
+
+}
+
+/* Based on hypre_CSRMatrixMatvecT in hypre's csr_matvec.c */
+void hypre_CSRMatrixAbsMatvecT(hypre_CSRMatrix *A,
+                               HYPRE_Real alpha,
+                               HYPRE_Real *x,
+                               HYPRE_Real beta,
+                               HYPRE_Real *y)
+{
+   HYPRE_Real       *A_data   = hypre_CSRMatrixData(A);
+   HYPRE_Int        *A_i      = hypre_CSRMatrixI(A);
+   HYPRE_Int        *A_j      = hypre_CSRMatrixJ(A);
+   HYPRE_Int         num_rows = hypre_CSRMatrixNumRows(A);
+   HYPRE_Int         num_cols = hypre_CSRMatrixNumCols(A);
+
+   HYPRE_Real       *x_data = x;
+   HYPRE_Real       *y_data = y;
+
+   HYPRE_Int         i, j, jj;
+
+   HYPRE_Real        temp;
+
+   if (alpha == 0.0)
+   {
+      for (i = 0; i < num_cols; i++)
+      {
+         y_data[i] *= beta;
+      }
+      return;
+   }
+
+   /*-----------------------------------------------------------------------
+    * y = (beta/alpha)*y
+    *-----------------------------------------------------------------------*/
+
+   temp = beta / alpha;
+
+   if (temp != 1.0)
+   {
+      if (temp == 0.0)
+      {
+         for (i = 0; i < num_cols; i++)
+         {
+            y_data[i] = 0.0;
+         }
+      }
+      else
+      {
+         for (i = 0; i < num_cols; i++)
+         {
+            y_data[i] *= temp;
+         }
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y += abs(A)^T*x
+    *-----------------------------------------------------------------*/
+
+   for (i = 0; i < num_rows; i++)
+   {
+      for (jj = A_i[i]; jj < A_i[i+1]; jj++)
+      {
+         j = A_j[jj];
+         y_data[j] += std::abs(A_data[jj]) * x_data[i];
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y = alpha*y
+    *-----------------------------------------------------------------*/
+
+   if (alpha != 1.0)
+   {
+      for (i = 0; i < num_cols; i++)
+      {
+         y_data[i] *= alpha;
+      }
+   }
+}
+
 /* Based on hypre_CSRMatrixMatvec in hypre's csr_matvec.c */
 void hypre_CSRMatrixBooleanMatvec(hypre_CSRMatrix *A,
                                  HYPRE_Bool alpha,
@@ -1236,6 +1427,143 @@ hypre_ParCSRCommHandleCreate_bool(HYPRE_Int            job,
   return comm_handle;
 }

+/* Based on hypre_ParCSRMatrixMatvec in par_csr_matvec.c */
+void hypre_ParCSRMatrixAbsMatvec(hypre_ParCSRMatrix *A,
+                                 HYPRE_Real alpha,
+                                 HYPRE_Real *x,
+                                 HYPRE_Real beta,
+                                 HYPRE_Real *y)
+{
+   hypre_ParCSRCommHandle *comm_handle;
+   hypre_ParCSRCommPkg *comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   hypre_CSRMatrix   *diag   = hypre_ParCSRMatrixDiag(A);
+   hypre_CSRMatrix   *offd   = hypre_ParCSRMatrixOffd(A);
+
+   HYPRE_Int          num_cols_offd = hypre_CSRMatrixNumCols(offd);
+   HYPRE_Int          num_sends, i, j, index;
+
+   HYPRE_Real        *x_tmp, *x_buf;
+
+   x_tmp = mfem_hypre_CTAlloc(HYPRE_Real, num_cols_offd);
+
+   /*---------------------------------------------------------------------
+    * If there exists no CommPkg for A, a CommPkg is generated using
+    * equally load balanced partitionings
+    *--------------------------------------------------------------------*/
+   if (!comm_pkg)
+   {
+      hypre_MatvecCommPkgCreate(A);
+      comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   }
+
+   num_sends = hypre_ParCSRCommPkgNumSends(comm_pkg);
+   x_buf = mfem_hypre_CTAlloc(
+              HYPRE_Real, hypre_ParCSRCommPkgSendMapStart(comm_pkg, num_sends));
+
+   index = 0;
+   for (i = 0; i < num_sends; i++)
+   {
+      j = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i);
+      for ( ; j < hypre_ParCSRCommPkgSendMapStart(comm_pkg, i+1); j++)
+      {
+         x_buf[index++] = x[hypre_ParCSRCommPkgSendMapElmt(comm_pkg, j)];
+      }
+   }
+
+   comm_handle = hypre_ParCSRCommHandleCreate(1, comm_pkg, x_buf, x_tmp);
+
+   hypre_CSRMatrixAbsMatvec(diag, alpha, x, beta, y);
+
+   hypre_ParCSRCommHandleDestroy(comm_handle);
+
+   if (num_cols_offd)
+   {
+      hypre_CSRMatrixAbsMatvec(offd, alpha, x_tmp, 1.0, y);
+   }
+
+   mfem_hypre_TFree(x_buf);
+   mfem_hypre_TFree(x_tmp);
+}
+
+/* Based on hypre_ParCSRMatrixMatvecT in par_csr_matvec.c */
+void hypre_ParCSRMatrixAbsMatvecT(hypre_ParCSRMatrix *A,
+                                  HYPRE_Real alpha,
+                                  HYPRE_Real *x,
+                                  HYPRE_Real beta,
+                                  HYPRE_Real *y)
+{
+   hypre_ParCSRCommHandle *comm_handle;
+   hypre_ParCSRCommPkg    *comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   hypre_CSRMatrix        *diag = hypre_ParCSRMatrixDiag(A);
+   hypre_CSRMatrix        *offd = hypre_ParCSRMatrixOffd(A);
+   HYPRE_Real             *y_tmp;
+   HYPRE_Real             *y_buf;
+
+   HYPRE_Int               num_cols_offd = hypre_CSRMatrixNumCols(offd);
+
+   HYPRE_Int               i, j, jj, end, num_sends;
+
+   y_tmp = mfem_hypre_TAlloc(HYPRE_Real, num_cols_offd);
+
+   /*---------------------------------------------------------------------
+    * If there exists no CommPkg for A, a CommPkg is generated using
+    * equally load balanced partitionings
+    *--------------------------------------------------------------------*/
+   if (!comm_pkg)
+   {
+      hypre_MatvecCommPkgCreate(A);
+      comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   }
+
+   num_sends = hypre_ParCSRCommPkgNumSends(comm_pkg);
+   y_buf = mfem_hypre_CTAlloc(
+              HYPRE_Real, hypre_ParCSRCommPkgSendMapStart(comm_pkg, num_sends));
+
+   if (num_cols_offd)
+   {
+#if MFEM_HYPRE_VERSION >= 21100
+      if (A->offdT)
+      {
+         // offdT is optional. Used only if it's present.
+         hypre_CSRMatrixAbsMatvec(A->offdT, alpha, x, 0., y_tmp);
+      }
+      else
+#endif
+      {
+         hypre_CSRMatrixAbsMatvecT(offd, alpha, x, 0., y_tmp);
+      }
+   }
+
+   comm_handle = hypre_ParCSRCommHandleCreate(2, comm_pkg, y_tmp, y_buf);
+
+#if MFEM_HYPRE_VERSION >= 21100
+   if (A->diagT)
+   {
+      // diagT is optional. Used only if it's present.
+      hypre_CSRMatrixAbsMatvec(A->diagT, alpha, x, beta, y);
+   }
+   else
+#endif
+   {
+      hypre_CSRMatrixAbsMatvecT(diag, alpha, x, beta, y);
+   }
+
+   hypre_ParCSRCommHandleDestroy(comm_handle);
+
+   for (i = 0; i < num_sends; i++)
+   {
+      end = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i+1);
+      for (j = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i); j < end; j++)
+      {
+         jj = hypre_ParCSRCommPkgSendMapElmt(comm_pkg, j);
+         y[jj] += y_buf[j];
+      }
+   }
+
+   mfem_hypre_TFree(y_buf);
+   mfem_hypre_TFree(y_tmp);
+}
+
 /* Based on hypre_ParCSRMatrixMatvec in par_csr_matvec.c */
 void hypre_ParCSRMatrixBooleanMatvec(hypre_ParCSRMatrix *A,
                                     HYPRE_Bool alpha,
@@ -118,6 +118,34 @@ void hypre_ParCSRMatrixSplit(hypre_ParCSRMatrix *A,
 typedef int HYPRE_Bool;
 #define HYPRE_MPI_BOOL MPI_INT

+/// Computes y = alpha * |A| * x + beta * y, using entry-wise absolute values of matrix A
+void hypre_CSRMatrixAbsMatvec(hypre_CSRMatrix *A,
+                              HYPRE_Real alpha,
+                              HYPRE_Real *x,
+                              HYPRE_Real beta,
+                              HYPRE_Real *y);
+
+/// Computes y = alpha * |At| * x + beta * y, using entry-wise absolute values of the transpose of matrix A
+void hypre_CSRMatrixAbsMatvecT(hypre_CSRMatrix *A,
+                               HYPRE_Real alpha,
+                               HYPRE_Real *x,
+                               HYPRE_Real beta,
+                               HYPRE_Real *y);
+
+/// Computes y = alpha * |A| * x + beta * y, using entry-wise absolute values of matrix A
+void hypre_ParCSRMatrixAbsMatvec(hypre_ParCSRMatrix *A,
+                                 HYPRE_Real alpha,
+                                 HYPRE_Real *x,
+                                 HYPRE_Real beta,
+                                 HYPRE_Real *y);
+
+/// Computes y = alpha * |At| * x + beta * y, using entry-wise absolute values of the transpose of matrix A
+void hypre_ParCSRMatrixAbsMatvecT(hypre_ParCSRMatrix *A,
+                                  HYPRE_Real alpha,
+                                  HYPRE_Real *x,
+                                  HYPRE_Real beta,
+                                  HYPRE_Real *y);
+
 /** The "Boolean" analog of y = alpha * A * x + beta * y, where elements in the
    sparsity pattern of the CSR matrix A are treated as "true". */
 void hypre_CSRMatrixBooleanMatvec(hypre_CSRMatrix *A,
@@ -2284,7 +2284,7 @@ void MinimumDiscardedFillOrdering(SparseMatrix &C, Array<int> &p)
      {
         int i = J[ii];
         // Find value of (i,k)
-         double C_ik;
+         double C_ik = 0.0;
         for (int kk=I[i]; kk<I[i+1]; ++kk)
         {
            if (J[kk] == k)
@@ -2334,7 +2334,7 @@ void MinimumDiscardedFillOrdering(SparseMatrix &C, Array<int> &p)
            int i = J[ii2];
            if (w_heap.picked(i)) { continue; }
            // Find value of (i,k)
-            double C_ik;
+            double C_ik = 0.0;
            for (int kk2=I[i]; kk2<I[i+1]; ++kk2)
            {
               if (J[kk2] == k)
@@ -2665,6 +2665,42 @@ void BlockILU::Mult(const Vector &b, Vector &x) const
   }
 }

+
+void ResidualBCMonitor::MonitorResidual(
+   int it, double norm, const Vector &r, bool final)
+{
+   if (!ess_dofs_list) { return; }
+
+   double bc_norm_squared = 0.0;
+   r.HostRead();
+   ess_dofs_list->HostRead();
+   for (int i = 0; i < ess_dofs_list->Size(); i++)
+   {
+      const double r_entry = r((*ess_dofs_list)[i]);
+      bc_norm_squared += r_entry*r_entry;
+   }
+   bool print = true;
+#ifdef MFEM_USE_MPI
+   MPI_Comm comm = iter_solver->GetComm();
+   if (comm != MPI_COMM_NULL)
+   {
+      double glob_bc_norm_squared = 0.0;
+      MPI_Reduce(&bc_norm_squared, &glob_bc_norm_squared, 1, MPI_DOUBLE,
+                 MPI_SUM, 0, comm);
+      bc_norm_squared = glob_bc_norm_squared;
+      int rank;
+      MPI_Comm_rank(comm, &rank);
+      print = (rank == 0);
+   }
+#endif
+   if ((it == 0 || final || bc_norm_squared > 0.0) && print)
+   {
+      mfem::out << "      ResidualBCMonitor : b.c. residual norm = "
+                << sqrt(bc_norm_squared) << endl;
+   }
+}
+
+
 #ifdef MFEM_USE_SUITESPARSE

 void UMFPackSolver::Init()
@@ -33,8 +33,12 @@ class BilinearForm;
 /// Abstract base class for an iterative solver monitor
 class IterativeSolverMonitor
 {
+protected:
+   /// The last IterativeSolver to which this monitor was attached.
+   const class IterativeSolver *iter_solver;
+
 public:
-   IterativeSolverMonitor() {}
+   IterativeSolverMonitor() : iter_solver(nullptr) {}

   virtual ~IterativeSolverMonitor() {}

@@ -49,6 +53,11 @@ public:
                                bool final)
   {
   }
+
+   /** @brief This method is invoked by ItertiveSolver::SetMonitor, informing
+       the monitor which IterativeSolver is using it. */
+   void SetIterativeSolver(const IterativeSolver &solver)
+   { iter_solver = &solver; }
 };

 /// Abstract base class for iterative solver
@@ -100,7 +109,15 @@ public:
   virtual void SetOperator(const Operator &op);

   /// Set the iterative solver monitor
-   void SetMonitor(IterativeSolverMonitor &m) { monitor = &m; }
+   void SetMonitor(IterativeSolverMonitor &m)
+   { monitor = &m; m.SetIterativeSolver(*this); }
+
+#ifdef MFEM_USE_MPI
+   /** @brief Return the associated MPI communicator, or MPI_COMM_NULL if no
+       communicator is set. */
+   MPI_Comm GetComm() const
+   { return dot_prod_type == 0 ? MPI_COMM_NULL : comm; }
+#endif
 };


@@ -689,6 +706,25 @@ private:
   mutable Array<int> ipiv;
 };

+
+/// Monitor that checks whether the residual is zero at a given set of dofs.
+/** This monitor is useful for checking if the initial guess, rhs, operator, and
+    preconditioner are properly setup for solving in the subspace with imposed
+    essential boundary conditions. */
+class ResidualBCMonitor : public IterativeSolverMonitor
+{
+protected:
+   const Array<int> *ess_dofs_list; ///< Not owned
+
+public:
+   ResidualBCMonitor(const Array<int> &ess_dofs_list_)
+      : ess_dofs_list(&ess_dofs_list_) { }
+
+   void MonitorResidual(int it, double norm, const Vector &r,
+                        bool final) override;
+};
+
+
 #ifdef MFEM_USE_SUITESPARSE

 /// Direct sparse solver using UMFPACK
@@ -28,6 +28,25 @@ namespace mfem

 using namespace std;

+#ifdef MFEM_USE_CUDA
+int SparseMatrix::SparseMatrixCount = 0;
+cusparseHandle_t SparseMatrix::handle;
+size_t SparseMatrix::bufferSize = 0;
+void * SparseMatrix::dBuffer = nullptr;
+#endif
+
+void SparseMatrix::InitCuSparse()
+{
+   // Initialize cuSPARSE library
+#ifdef MFEM_USE_CUDA
+   SparseMatrixCount++;
+   if (SparseMatrixCount == 1 && Device::Allows(Backend::CUDA_MASK))
+   {
+      cusparseCreate(&handle);
+   }
+#endif
+}
+
 SparseMatrix::SparseMatrix(int nrows, int ncols)
   : AbstractSparseMatrix(nrows, (ncols >= 0) ? ncols : nrows),
     Rows(new RowNode *[nrows]),
@@ -50,6 +69,8 @@ SparseMatrix::SparseMatrix(int nrows, int ncols)
 #ifdef MFEM_USE_MEMALLOC
   NodesMem = new RowNodeAlloc;
 #endif
+
+   InitCuSparse();
 }

 SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n)
@@ -67,6 +88,8 @@ SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n)
 #ifdef MFEM_USE_MEMALLOC
   NodesMem = NULL;
 #endif
+
+   InitCuSparse();
 }

 SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n,
@@ -98,6 +121,8 @@ SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n,
         A[i] = 0.0;
      }
   }
+
+   InitCuSparse();
 }

 SparseMatrix::SparseMatrix(int nrows, int ncols, int rowsize)
@@ -119,6 +144,8 @@ SparseMatrix::SparseMatrix(int nrows, int ncols, int rowsize)
   {
      I[i] = i * rowsize;
   }
+
+   InitCuSparse();
 }

 SparseMatrix::SparseMatrix(const SparseMatrix &mat, bool copy_graph)
@@ -184,6 +211,8 @@ SparseMatrix::SparseMatrix(const SparseMatrix &mat, bool copy_graph)
   ColPtrNode = NULL;
   At = NULL;
   isSorted = mat.isSorted;
+
+   InitCuSparse();
 }

 SparseMatrix::SparseMatrix(const Vector &v)
@@ -211,6 +240,8 @@ SparseMatrix::SparseMatrix(const Vector &v)
      J[r] = r;
      A[r] = v[r];
   }
+
+   InitCuSparse();
 }

 SparseMatrix& SparseMatrix::operator=(const SparseMatrix &rhs)
@@ -250,6 +281,16 @@ void SparseMatrix::SetEmpty()
   NodesMem = NULL;
 #endif
   isSorted = false;
+
+#ifdef MFEM_USE_CUDA
+   if (initBuffers)
+   {
+      cusparseDestroySpMat(matA_descr);
+      cusparseDestroyDnVec(vecX_descr);
+      cusparseDestroyDnVec(vecY_descr);
+      initBuffers = false;
+   }
+#endif
 }

 int SparseMatrix::RowSize(const int i) const
@@ -569,7 +610,7 @@ void SparseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
      const double *xp = x.HostRead();
      double *yp = y.HostReadWrite();

-      //  The matrix is not finalized, but multiplication is still possible
+      // The matrix is not finalized, but multiplication is still possible
      for (int i = 0; i < height; i++)
      {
         RowNode *row = Rows[i];
@@ -592,16 +633,72 @@ void SparseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
   auto d_A = Read(A, nnz);
   auto d_x = x.Read();
   auto d_y = y.ReadWrite();
-   MFEM_FORALL(i, height,
+
+   // Skip if matrix has no non-zeros
+   if (nnz == 0) {return;}
+   if (Device::Allows(Backend::CUDA_MASK) && useCuSparse)
   {
-      double d = 0.0;
-      const int end = d_I[i+1];
-      for (int j = d_I[i]; j < end; j++)
+#ifdef MFEM_USE_CUDA
+      const double alpha = a;
+      const double beta  = 1.0;
+
+      // Setup descriptors
+      if (!initBuffers)
      {
-         d += d_A[j] * d_x[d_J[j]];
+         // Setup matrix descriptor
+         cusparseCreateCsr(&matA_descr,Height(), Width(), J.Capacity(),
+                           const_cast<int *>(d_I),
+                           const_cast<int *>(d_J), const_cast<double *>(d_A), CUSPARSE_INDEX_32I,
+                           CUSPARSE_INDEX_32I, CUSPARSE_INDEX_BASE_ZERO, CUDA_R_64F);
+
+         // Create handles for input/output vectors
+         cusparseCreateDnVec(&vecX_descr, x.Size(), const_cast<double *>(d_x),
+                             CUDA_R_64F);
+         cusparseCreateDnVec(&vecY_descr, y.Size(), d_y, CUDA_R_64F);
+
+         initBuffers = true;
      }
-      d_y[i] += a * d;
-   });
+
+      // Allocate kernel space. Buffer is shared between different sparsemats
+      size_t newBufferSize = 0;
+      cusparseSpMV_bufferSize(handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &alpha,
+                              matA_descr,
+                              vecX_descr, &beta, vecY_descr, CUDA_R_64F,
+                              CUSPARSE_CSRMV_ALG1, &newBufferSize);
+
+      // Check if we need to resize
+      if (newBufferSize > bufferSize)
+      {
+         bufferSize = newBufferSize;
+         if (dBuffer != NULL) { CuMemFree(dBuffer); }
+         CuMemAlloc(&dBuffer, bufferSize);
+      }
+
+      // Update input/output vectors
+      cusparseDnVecSetValues(vecX_descr, const_cast<double *>(d_x));
+      cusparseDnVecSetValues(vecY_descr, d_y);
+
+      // Y = alpha A * X + beta * Y
+      cusparseSpMV(handle, CUSPARSE_OPERATION_NON_TRANSPOSE, &alpha, matA_descr,
+                   vecX_descr, &beta, vecY_descr, CUDA_R_64F, CUSPARSE_CSRMV_ALG1, dBuffer);
+#endif
+   }
+   else
+   {
+      // Native version
+      MFEM_FORALL(i, height,
+      {
+         double d = 0.0;
+         const int end = d_I[i+1];
+         for (int j = d_I[i]; j < end; j++)
+         {
+            d += d_A[j] * d_x[d_J[j]];
+         }
+         d_y[i] += a * d;
+      });
+
+   }
+
 #else
   const double *Ap = A, *xp = x.GetData();
   double *yp = y.GetData();
@@ -784,6 +881,101 @@ void SparseMatrix::BooleanMultTranspose(const Array<int> &x,
   }
 }

+void SparseMatrix::AbsMult(const Vector &x, Vector &y) const
+{
+   MFEM_ASSERT(width == x.Size(), "Input vector size (" << x.Size()
+               << ") must match matrix width (" << width << ")");
+   MFEM_ASSERT(height == y.Size(), "Output vector size (" << y.Size()
+               << ") must match matrix height (" << height << ")");
+
+   if (Finalized()) { y.UseDevice(true); }
+   y = 0.0;
+
+   if (!Finalized())
+   {
+      const double *xp = x.HostRead();
+      double *yp = y.HostReadWrite();
+
+      //  The matrix is not finalized, but multiplication is still possible
+      for (int i = 0; i < height; i++)
+      {
+         RowNode *row = Rows[i];
+         double b = 0.0;
+         for ( ; row != NULL; row = row->Prev)
+         {
+            b += std::abs(row->Value) * xp[row->Column];
+         }
+         *yp += b;
+         yp++;
+      }
+      return;
+   }
+
+   const int height = this->height;
+   const int nnz = J.Capacity();
+   auto d_I = Read(I, height+1);
+   auto d_J = Read(J, nnz);
+   auto d_A = Read(A, nnz);
+   auto d_x = x.Read();
+   auto d_y = y.ReadWrite();
+   MFEM_FORALL(i, height,
+   {
+      double d = 0.0;
+      const int end = d_I[i+1];
+      for (int j = d_I[i]; j < end; j++)
+      {
+         d += std::abs(d_A[j]) * d_x[d_J[j]];
+      }
+      d_y[i] += d;
+   });
+}
+
+void SparseMatrix::AbsMultTranspose(const Vector &x, Vector &y) const
+{
+   MFEM_ASSERT(height == x.Size(), "Input vector size (" << x.Size()
+               << ") must match matrix height (" << height << ")");
+   MFEM_ASSERT(width == y.Size(), "Output vector size (" << y.Size()
+               << ") must match matrix width (" << width << ")");
+
+   y = 0.0;
+
+   if (!Finalized())
+   {
+      double *yp = y.GetData();
+      // The matrix is not finalized, but multiplication is still possible
+      for (int i = 0; i < height; i++)
+      {
+         RowNode *row = Rows[i];
+         double b = x(i);
+         for ( ; row != NULL; row = row->Prev)
+         {
+            yp[row->Column] += fabs(row->Value) * b;
+         }
+      }
+      return;
+   }
+
+   if (At)
+   {
+      At->AbsMult(x, y);
+   }
+   else
+   {
+      MFEM_VERIFY(Device::IsDisabled(), "transpose action on device is not "
+                  "enabled; see BuildTranspose() for details.");
+      for (int i = 0; i < height; i++)
+      {
+         const double xi = x[i];
+         const int end = I[i+1];
+         for (int j = I[i]; j < end; j++)
+         {
+            const int Jj = J[j];
+            y[Jj] += std::abs(A[j]) * xi;
+         }
+      }
+   }
+}
+
 double SparseMatrix::InnerProduct(const Vector &x, const Vector &y) const
 {
   MFEM_ASSERT(x.Size() == Width(), "x.Size() = " << x.Size()
@@ -2962,6 +3154,16 @@ void SparseMatrix::Destroy()
   delete NodesMem;
 #endif
   delete At;
+
+#ifdef MFEM_USE_CUDA
+   if (initBuffers)
+   {
+      cusparseDestroySpMat(matA_descr);
+      cusparseDestroyDnVec(vecX_descr);
+      cusparseDestroyDnVec(vecY_descr);
+      initBuffers = false;
+   }
+#endif
 }

 int SparseMatrix::ActualWidth() const
@@ -21,6 +21,12 @@
 #include "../general/globals.hpp"
 #include "densemat.hpp"

+#ifdef MFEM_USE_CUDA
+#include <cusparse.h>
+#include <library_types.h>
+#include "../general/cuda.hpp"
+#endif
+
 namespace mfem
 {

@@ -80,9 +86,33 @@ protected:
   void Destroy();   // Delete all owned data
   void SetEmpty();  // Init all entries with empty values

+   bool useCuSparse{true}; // Use cuSPARSE if available
+
+   // Initialize cuSPARSE
+   void InitCuSparse();
+
+#ifdef MFEM_USE_CUDA
+   cusparseStatus_t status;
+   static cusparseHandle_t handle;
+   cusparseMatDescr_t descr=0;
+   static size_t bufferSize;
+   static void *dBuffer;
+   mutable bool initBuffers{false};
+
+   static int SparseMatrixCount;
+   mutable cusparseSpMatDescr_t matA_descr;
+   mutable cusparseDnVecDescr_t vecX_descr;
+   mutable cusparseDnVecDescr_t vecY_descr;
+#endif
+
 public:
   /// Create an empty SparseMatrix.
-   SparseMatrix() { SetEmpty(); }
+   SparseMatrix()
+   {
+      SetEmpty();
+
+      InitCuSparse();
+   }

   /** @brief Create a sparse matrix with flexible sparsity structure using a
       row-wise linked list (LIL) format. */
@@ -118,6 +148,8 @@ public:
   /// Create a SparseMatrix with diagonal @a v, i.e. A = Diag(v)
   SparseMatrix(const Vector & v);

+   // Runtime option to use cuSPARSE. Only valid when using a CUDA backend.
+   void UseCuSparse(bool _useCuSparse = true) { useCuSparse = _useCuSparse;}

   /// Assignment operator: deep copy
   SparseMatrix& operator=(const SparseMatrix &rhs);
@@ -308,16 +340,22 @@ public:

   /// y = A * x, treating all entries as booleans (zero=false, nonzero=true).
   /** The actual values stored in the data array, #A, are not used - this means
-       and that all entries in the sparsity pattern are considered to be true by
+       that all entries in the sparsity pattern are considered to be true by
       this method. */
   void BooleanMult(const Array<int> &x, Array<int> &y) const;

   /// y = At * x, treating all entries as booleans (zero=false, nonzero=true).
   /** The actual values stored in the data array, #A, are not used - this means
-       and that all entries in the sparsity pattern are considered to be true by
+       that all entries in the sparsity pattern are considered to be true by
       this method. */
   void BooleanMultTranspose(const Array<int> &x, Array<int> &y) const;

+   /// y = |A| * x, using entry-wise absolute values of matrix A
+   void AbsMult(const Vector &x, Vector &y) const;
+
+   /// y = |At| * x, using entry-wise absolute values of the transpose of matrix A
+   void AbsMultTranspose(const Vector &x, Vector &y) const;
+
   /// Compute y^t A x
   double InnerProduct(const Vector &x, const Vector &y) const;

@@ -573,7 +611,18 @@ public:
   void Swap(SparseMatrix &other);

   /// Destroys sparse matrix.
-   virtual ~SparseMatrix() { Destroy(); }
+   virtual ~SparseMatrix()
+   {
+      Destroy();
+#ifdef MFEM_USE_CUDA
+      if (handle && SparseMatrixCount==1 && Device::Allows(Backend::CUDA_MASK))
+      {
+         cusparseDestroy(handle);
+         CuMemFree(dBuffer);
+      }
+      SparseMatrixCount--;
+#endif
+   }

   Type GetType() const { return MFEM_SPARSEMAT; }
 };
@@ -537,7 +537,29 @@ void SuperLUSolver::Mult( const Vector & x, Vector & y ) const

   if ( info != 0 )
   {
-      if ( info <= A->ncol )
+      if ( info < 0 )
+      {
+         switch (-info)
+         {
+            case 1:
+               MFEM_ABORT("SuperLU:  SuperLU options are invalid.");
+               break;
+            case 2:
+               MFEM_ABORT("SuperLU:  Matrix A (in Ax=b) is invalid.");
+               break;
+            case 5:
+               MFEM_ABORT("SuperLU:  Vector b dimension (in Ax=b) is invalid.");
+               break;
+            case 6:
+               MFEM_ABORT("SuperLU:  Number of right-hand sides is invalid.");
+               break;
+            default:
+               MFEM_ABORT("SuperLU:  Parameter with index "
+                          << -info << "invalid. (1-indexed)");
+               break;
+         }
+      }
+      else if ( info <= A->ncol )
      {
         MFEM_ABORT("SuperLU:  Found a singular matrix, U("
                    << info << "," << info << ") is exactly zero.");
@@ -1071,7 +1071,7 @@ double Vector::operator*(const Vector &v) const
      return prod;
   }
 #endif
-   if (Device::Allows(Backend::DEBUG))
+   if (Device::Allows(Backend::DEBUG_DEVICE))
   {
      const int N = size;
      auto v_data = v.Read();
@@ -1131,7 +1131,7 @@ double Vector::Min() const
   }
 #endif

-   if (Device::Allows(Backend::DEBUG))
+   if (Device::Allows(Backend::DEBUG_DEVICE))
   {
      const int N = size;
      auto m_data = Read();
@@ -11,6 +11,7 @@

 set(SRCS
  element.cpp
+  gmsh.cpp
  hexahedron.cpp
  mesh.cpp
  mesh_operators.cpp
@@ -29,6 +30,7 @@ set(SRCS

 set(HDRS
  element.hpp
+  gmsh.hpp
  hexahedron.hpp
  mesh.hpp
  mesh_headers.hpp
@@ -0,0 +1,487 @@
+// Copyright (c) 2010-2020, 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 "gmsh.hpp"
+#include "vtk.hpp"
+
+namespace mfem
+{
+
+int BarycentricToGmshTet(int *b, int ref)
+{
+   int i = b[0];
+   int j = b[1];
+   int k = b[2];
+   int l = b[3];
+   bool ibdr = (i == 0);
+   bool jbdr = (j == 0);
+   bool kbdr = (k == 0);
+   bool lbdr = (l == 0);
+   if (ibdr && jbdr && kbdr)
+   {
+      return 0;
+   }
+   else if (jbdr && kbdr && lbdr)
+   {
+      return 1;
+   }
+   else if (ibdr && kbdr && lbdr)
+   {
+      return 2;
+   }
+   else if (ibdr && jbdr && lbdr)
+   {
+      return 3;
+   }
+   int offset = 4;
+   if (jbdr && kbdr) // Edge DOF on j == 0 and k == 0
+   {
+      return offset + i - 1;
+   }
+   else if (kbdr && lbdr) // Edge DOF on k == 0 and l == 0
+   {
+      return offset + ref - 1 + j - 1;
+   }
+   else if (ibdr && kbdr) // Edge DOF on i == 0 and k == 0
+   {
+      return offset + 2 * (ref - 1) + ref - j - 1;
+   }
+   else if (ibdr && jbdr) // Edge DOF on i == 0 and j == 0
+   {
+      return offset + 3 * (ref - 1) + ref - k - 1;
+   }
+   else if (ibdr && lbdr) // Edge DOF on i == 0 and l == 0
+   {
+      return offset + 4 * (ref - 1) + ref - k - 1;
+   }
+   else if (jbdr && lbdr) // Edge DOF on j == 0 and l == 0
+   {
+      return offset + 5 * (ref - 1) + ref - k - 1;
+   }
+
+   // Recursive numbering for the faces
+   offset += 6 * (ref - 1);
+   if (kbdr)
+   {
+      int b_out[3];
+      b_out[0] = j-1;
+      b_out[1] = i-1;
+      b_out[2] = ref - i - j - 1;
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+   else if (jbdr)
+   {
+      int b_out[3];
+      b_out[0] = i-1;
+      b_out[1] = k-1;
+      b_out[2] = ref - i - k - 1;
+      offset += (ref - 1) * (ref - 2) / 2;
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+   else if (ibdr)
+   {
+      int b_out[3];
+      b_out[0] = k-1;
+      b_out[1] = j-1;
+      b_out[2] = ref - j - k - 1;
+      offset += (ref - 1) * (ref - 2);
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+   else if (lbdr)
+   {
+      int b_out[3];
+      b_out[0] = ref-j-k-1;
+      b_out[1] = j-1;
+      b_out[2] = k-1;
+      offset += 3 * (ref - 1) * (ref - 2) / 2;
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+
+   // Recursive numbering for interior
+   {
+      int b_out[4];
+      b_out[0] = i-1;
+      b_out[1] = j-1;
+      b_out[2] = k-1;
+      b_out[3] = ref - i - j - k - 1;
+      offset += 2 * (ref - 1) * (ref - 2);
+      return offset + BarycentricToGmshTet(b_out, ref-4);
+   }
+}
+
+int CartesianToGmshQuad(int idx_in[], int ref)
+{
+   int i = idx_in[0];
+   int j = idx_in[1];
+   // Do we lie on any of the edges
+   bool ibdr = (i == 0 || i == ref);
+   bool jbdr = (j == 0 || j == ref);
+   if (ibdr && jbdr) // Vertex DOF
+   {
+      return (i ? (j ? 2 : 1) : (j ? 3 : 0));
+   }
+   int offset = 4;
+   if (jbdr) // Edge DOF on j==0 or j==ref
+   {
+      return offset + (j ? 3*ref - 3 - i : i - 1);
+   }
+   else if (ibdr) // Edge DOF on i==0 or i==ref
+   {
+      return offset + (i ? ref - 1 + j - 1 : 4*ref - 4 - j);
+   }
+   else // Recursive numbering for interior
+   {
+      int idx_out[2];
+      idx_out[0] = i-1;
+      idx_out[1] = j-1;
+      offset += 4 * (ref - 1);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+}
+
+int CartesianToGmshHex(int idx_in[], int ref)
+{
+   int i = idx_in[0];
+   int j = idx_in[1];
+   int k = idx_in[2];
+   // Do we lie on any of the edges
+   bool ibdr = (i == 0 || i == ref);
+   bool jbdr = (j == 0 || j == ref);
+   bool kbdr = (k == 0 || k == ref);
+   if (ibdr && jbdr && kbdr) // Vertex DOF
+   {
+      return (i ? (j ? (k ? 6 : 2) : (k ? 5 : 1)) :
+              (j ? (k ? 7 : 3) : (k ? 4 : 0)));
+   }
+   int offset = 8;
+   if (jbdr && kbdr) // Edge DOF on x-directed edge
+   {
+      return offset + (j ? (k ? 12*ref-12-i: 6*ref-6-i) :
+                       (k ? 8*ref-9+i: i-1));
+   }
+   else if (ibdr && kbdr) // Edge DOF on y-directed edge
+   {
+      return offset + (k ? (i ? 10*ref-11+j: 9*ref-10+j) :
+                       (i ? 3*ref-4+j: ref-2+j));
+   }
+   else if (ibdr && jbdr) // Edge DOF on z-directed edge
+   {
+      return offset + (i ? (j ? 6*ref-7+k: 4*ref-5+k) :
+                       (j ? 7*ref-8+k: 2*ref-3+k));
+   }
+   else if (ibdr) // Face DOF on x-directed face
+   {
+      int idx_out[2];
+      idx_out[0] = i ? j-1 : k-1;
+      idx_out[1] = i ? k-1 : j-1;
+      offset += (12 + (i ? 3 : 2) * (ref - 1)) * (ref - 1);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   else if (jbdr) // Face DOF on y-directed face
+   {
+      int idx_out[2];
+      idx_out[0] = j ? ref-i-1 : i-1;
+      idx_out[1] = j ? k-1 : k-1;
+      offset += (12 + (j ? 4 : 1) * (ref - 1)) * (ref - 1);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   else if (kbdr) // Face DOF on z-directed face
+   {
+      int idx_out[2];
+      idx_out[0] = k ? i-1 : j-1;
+      idx_out[1] = k ? j-1 : i-1;
+      offset += (12 + (k ? 5 : 0) * (ref - 1)) * (ref - 1);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   else // Recursive numbering for interior
+   {
+      int idx_out[3];
+      idx_out[0] = i-1;
+      idx_out[1] = j-1;
+      idx_out[2] = k-1;
+
+      offset += (12 + 6 * (ref - 1)) * (ref - 1);
+      return offset + CartesianToGmshHex(idx_out, ref-2);
+   }
+}
+
+int WedgeToGmshPri(int idx_in[], int ref)
+{
+   int i = idx_in[0];
+   int j = idx_in[1];
+   int k = idx_in[2];
+   int l = ref - i -j;
+   bool ibdr = (i == 0);
+   bool jbdr = (j == 0);
+   bool kbdr = (k == 0 || k == ref);
+   bool lbdr = (l == 0);
+   if (ibdr && jbdr && kbdr)
+   {
+      return k ? 3 : 0;
+   }
+   else if (jbdr && lbdr && kbdr)
+   {
+      return k ? 4 : 1;
+   }
+   else if (ibdr && lbdr && kbdr)
+   {
+      return k ? 5 : 2;
+   }
+   int offset = 6;
+   if (jbdr && kbdr)
+   {
+      return offset + (k ? 6 * (ref - 1) + i - 1: i - 1);
+   }
+   else if (ibdr && kbdr)
+   {
+      return offset + (k ? 7 * (ref -1) + j-1 : ref - 1 + j - 1);
+   }
+   else if (ibdr && jbdr)
+   {
+      return offset + 2 * (ref - 1) + k - 1;
+   }
+   else if (lbdr && kbdr)
+   {
+      return offset + (k ? 8 * (ref -1) + j - 1 : 3 * (ref - 1) + j - 1);
+   }
+   else if (jbdr && lbdr)
+   {
+      return offset + 4 * (ref - 1) + k - 1;
+   }
+   else if (ibdr && lbdr)
+   {
+      return offset + 5 * (ref - 1) + k - 1;
+   }
+   offset += 9 * (ref-1);
+   if (kbdr) // Triangular faces at k=0 and k=ref
+   {
+      int b_out[3];
+      b_out[0] = k ? i-1 : j-1;
+      b_out[1] = k ? j-1 : i-1;
+      b_out[2] = ref - i - j - 1;
+      offset += k ? (ref-1)*(ref-2) / 2: 0;
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+   offset += (ref-1)*(ref-2);
+   if (jbdr) // Quadrilateral face at j=0
+   {
+      int idx_out[2];
+      idx_out[0] = i-1;
+      idx_out[1] = k-1;
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   else if (ibdr) // Quadrilateral face at i=0
+   {
+      int idx_out[2];
+      idx_out[0] = k-1;
+      idx_out[1] = j-1;
+      offset += (ref-1)*(ref-1);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   else if (lbdr) // Quadrilateral face at l=ref-i-j=0
+   {
+      int idx_out[2];
+      idx_out[0] = j-1;
+      idx_out[1] = k-1;
+      offset += 2*(ref-1)*(ref-1);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   offset += 3*(ref-1)*(ref-1);
+   // The Gmsh Prism interiors are a tensor product of segments of order ref-2
+   // and triangles of order ref-3
+   {
+      int b_out[3];
+      b_out[0] = i-1;
+      b_out[1] = j-1;
+      b_out[2] = ref - i - j - 1;
+      int ot = BarycentricToVTKTriangle(b_out, ref-3);
+      int os = (k==1) ? 0 : (k == ref-1 ? 1 : k);
+      return offset + (ref-1) * ot + os;
+   }
+}
+
+int CartesianToGmshPyramid(int idx_in[], int ref)
+{
+   int i = idx_in[0];
+   int j = idx_in[1];
+   int k = idx_in[2];
+   // Do we lie on any of the edges
+   bool ibdr = (i == 0 || i == ref-k);
+   bool jbdr = (j == 0 || j == ref-k);
+   bool kbdr = (k == 0);
+   if (ibdr && jbdr && kbdr)
+   {
+      return i ? (j ? 2 : 1): (j ? 3 : 0);
+   }
+   else if (k == ref)
+   {
+      return 4;
+   }
+   int offset = 5;
+   if (jbdr && kbdr)
+   {
+      return offset + (j ? (6 * ref - 6 - i) : (i - 1));
+   }
+   else if (ibdr && kbdr)
+   {
+      return offset + (i ? (3 * ref - 4 + j) : (ref - 2 + j));
+   }
+   else if (ibdr && jbdr)
+   {
+      return offset + (i ? (j ? 6 : 4) : (j ? 7 : 2 )) * (ref-1) + k - 1;
+   }
+   offset += 8*(ref-1);
+   if (jbdr)
+   {
+      int b_out[3];
+      b_out[0] = j ? ref - i - k - 1 : i - 1;
+      b_out[1] = k - 1;
+      b_out[2] = (j ? i - 1 : ref - i - k - 1);
+      offset += (j ? 3 : 0) * (ref - 1) * (ref - 2) / 2;
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+   else if (ibdr)
+   {
+      int b_out[3];
+      b_out[0] = i ? j - 1: ref - j - k - 1;
+      b_out[1] = k - 1;
+      b_out[2] = (i ? ref - j - k - 1: j - 1);
+      offset += (i ? 2 : 1) * (ref - 1) * (ref - 2) / 2;
+      return offset + BarycentricToVTKTriangle(b_out, ref-3);
+   }
+   else if (kbdr)
+   {
+      int idx_out[2];
+      idx_out[0] = k ? i-1 : j-1;
+      idx_out[1] = k ? j-1 : i-1;
+      offset += 2 * (ref - 1) * (ref - 2);
+      return offset + CartesianToGmshQuad(idx_out, ref-2);
+   }
+   offset += (2 * (ref - 2) + (ref - 1)) * (ref - 1) ;
+   {
+      int idx_out[3];
+      idx_out[0] = i-1;
+      idx_out[1] = j-1;
+      idx_out[2] = k-1;
+      return offset + CartesianToGmshPyramid(idx_out, ref-3);
+   }
+}
+
+void GmshHOSegmentMapping(int order, int *map)
+{
+   map[0] = 0;
+   map[order] = 1;
+   for (int i=1; i<order; i++)
+   {
+      map[i] = i + 1;
+   }
+}
+
+void GmshHOTriangleMapping(int order, int *map)
+{
+   int b[3];
+   int o = 0;
+   for (b[1]=0; b[1]<=order; ++b[1])
+   {
+      for (b[0]=0; b[0]<=order-b[1]; ++b[0])
+      {
+         b[2] = order - b[0] - b[1];
+         map[o] = BarycentricToVTKTriangle(b, order);
+         o++;
+      }
+   }
+}
+
+void GmshHOQuadrilateralMapping(int order, int *map)
+{
+   int b[2];
+   int o = 0;
+   for (b[1]=0; b[1]<=order; b[1]++)
+   {
+      for (b[0]=0; b[0]<=order; b[0]++)
+      {
+         map[o] = CartesianToGmshQuad(b, order);
+         o++;
+      }
+   }
+}
+
+void GmshHOTetrahedronMapping(int order, int *map)
+{
+   int b[4];
+   int o = 0;
+   for (b[2]=0; b[2]<=order; ++b[2])
+   {
+
+      for (b[1]=0; b[1]<=order-b[2]; ++b[1])
+      {
+         for (b[0]=0; b[0]<=order-b[1]-b[2]; ++b[0])
+         {
+            b[3] = order - b[0] - b[1] - b[2];
+            map[o] = BarycentricToGmshTet(b, order);
+            o++;
+         }
+      }
+   }
+}
+
+void GmshHOHexahedronMapping(int order, int *map)
+{
+   int b[3];
+   int o = 0;
+   for (b[2]=0; b[2]<=order; b[2]++)
+   {
+      for (b[1]=0; b[1]<=order; b[1]++)
+      {
+         for (b[0]=0; b[0]<=order; b[0]++)
+         {
+            map[o] = CartesianToGmshHex(b, order);
+            o++;
+         }
+      }
+   }
+}
+
+void GmshHOWedgeMapping(int order, int *map)
+{
+   int b[3];
+   int o = 0;
+   for (b[2]=0; b[2]<=order; b[2]++)
+   {
+      for (b[1]=0; b[1]<=order; b[1]++)
+      {
+         for (b[0]=0; b[0]<=order - b[1]; b[0]++)
+         {
+            map[o] = WedgeToGmshPri(b, order);
+            o++;
+         }
+      }
+   }
+}
+
+void GmshHOPyramidMapping(int order, int *map)
+{
+   int b[3];
+   int o = 0;
+   for (b[2]=0; b[2]<=order; b[2]++)
+   {
+      for (b[1]=0; b[1]<=order - b[2]; b[1]++)
+      {
+         for (b[0]=0; b[0]<=order - b[2]; b[0]++)
+         {
+            map[o] = CartesianToGmshPyramid(b, order);
+            o++;
+         }
+      }
+   }
+}
+
+} // namespace mfem
@@ -0,0 +1,55 @@
+// Copyright (c) 2010-2020, 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_GMSH
+#define MFEM_GMSH
+
+namespace mfem
+{
+
+// Helpers for reading high order elements in Gmsh format
+
+/** @name Gmsh High-Order Vertex Mappings
+
+    These functions generate the mappings needed to translate the order of
+    Gmsh's high-order vertices into MFEM's L2 degree of freedom ordering. The
+    mapping is defined so that MFEM_DoF[i] = Gmsh_Vert[map[i]]. The @a map
+    array must already be allocated with the proper number of entries for the
+    element type at the given element @a order.
+*/
+///@{
+
+/// @brief Generate Gmsh vertex mapping for a Segment
+void GmshHOSegmentMapping(int order, int *map);
+
+/// @brief Generate Gmsh vertex mapping for a Triangle
+void GmshHOTriangleMapping(int order, int *map);
+
+/// @brief Generate Gmsh vertex mapping for a Quadrilateral
+void GmshHOQuadrilateralMapping(int order, int *map);
+
+/// @brief Generate Gmsh vertex mapping for a Tetrahedron
+void GmshHOTetrahedronMapping(int order, int *map);
+
+/// @brief Generate Gmsh vertex mapping for a Hexahedron
+void GmshHOHexahedronMapping(int order, int *map);
+
+/// @brief Generate Gmsh vertex mapping for a Wedge
+void GmshHOWedgeMapping(int order, int *map);
+
+/// @brief Generate Gmsh vertex mapping for a Pyramid
+void GmshHOPyramidMapping(int order, int *map);
+
+///@}
+
+} // namespace mfem
+
+#endif
@@ -338,6 +338,7 @@ void Mesh::GetElementTransformation(int i, IsoparametricTransformation *ElTr)
   ElTr->Attribute = GetAttribute(i);
   ElTr->ElementNo = i;
   ElTr->ElementType = ElementTransformation::ELEMENT;
+   ElTr->Reset();
   if (Nodes == NULL)
   {
      GetPointMatrix(i, ElTr->GetPointMat());
@@ -370,6 +371,7 @@ void Mesh::GetElementTransformation(int i, const Vector &nodes,
   ElTr->ElementNo = i;
   ElTr->ElementType = ElementTransformation::ELEMENT;
   DenseMatrix &pm = ElTr->GetPointMat();
+   ElTr->Reset();
   nodes.HostRead();
   if (Nodes == NULL)
   {
@@ -424,6 +426,7 @@ void Mesh::GetBdrElementTransformation(int i, IsoparametricTransformation* ElTr)
   ElTr->ElementNo = i; // boundary element number
   ElTr->ElementType = ElementTransformation::BDR_ELEMENT;
   DenseMatrix &pm = ElTr->GetPointMat();
+   ElTr->Reset();
   if (Nodes == NULL)
   {
      GetBdrPointMatrix(i, pm);
@@ -480,6 +483,7 @@ void Mesh::GetFaceTransformation(int FaceNo, IsoparametricTransformation *FTr)
   FTr->ElementNo = FaceNo;
   FTr->ElementType = ElementTransformation::FACE;
   DenseMatrix &pm = FTr->GetPointMat();
+   FTr->Reset();
   if (Nodes == NULL)
   {
      const int *v = (Dim == 1) ? &FaceNo : faces[FaceNo]->GetVertices();
@@ -562,6 +566,7 @@ void Mesh::GetEdgeTransformation(int EdgeNo, IsoparametricTransformation *EdTr)
   EdTr->ElementNo = EdgeNo;
   EdTr->ElementType = ElementTransformation::EDGE;
   DenseMatrix &pm = EdTr->GetPointMat();
+   EdTr->Reset();
   if (Nodes == NULL)
   {
      Array<int> v;
@@ -614,6 +619,7 @@ void Mesh::GetLocalPtToSegTransformation(
 {
   const IntegrationRule *SegVert;
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&PointFE);
   SegVert = Geometries.GetVertices(Geometry::SEGMENT);
@@ -629,6 +635,7 @@ void Mesh::GetLocalSegToTriTransformation(
   const int *tv, *so;
   const IntegrationRule *TriVert;
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&SegmentFE);
   tv = tri_t::Edges[i/64];  //  (i/64) is the local face no. in the triangle
@@ -648,6 +655,7 @@ void Mesh::GetLocalSegToQuadTransformation(
   const int *qv, *so;
   const IntegrationRule *QuadVert;
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&SegmentFE);
   qv = quad_t::Edges[i/64]; //  (i/64) is the local face no. in the quad
@@ -665,6 +673,7 @@ void Mesh::GetLocalTriToTetTransformation(
   IsoparametricTransformation &Transf, int i)
 {
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&TriangleFE);
   //  (i/64) is the local face no. in the tet
@@ -688,6 +697,7 @@ void Mesh::GetLocalTriToWdgTransformation(
   IsoparametricTransformation &Transf, int i)
 {
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&TriangleFE);
   //  (i/64) is the local face no. in the pri
@@ -713,6 +723,7 @@ void Mesh::GetLocalQuadToHexTransformation(
   IsoparametricTransformation &Transf, int i)
 {
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&QuadrilateralFE);
   //  (i/64) is the local face no. in the hex
@@ -734,6 +745,7 @@ void Mesh::GetLocalQuadToWdgTransformation(
   IsoparametricTransformation &Transf, int i)
 {
   DenseMatrix &locpm = Transf.GetPointMat();
+   Transf.Reset();

   Transf.SetFE(&QuadrilateralFE);
   //  (i/64) is the local face no. in the pri
@@ -1211,58 +1223,136 @@ void Mesh::InitMesh(int _Dim, int _spaceDim, int NVert, int NElem, int NBdrElem)
   boundary.SetSize(NBdrElem);  // just allocate space for Element *
 }

-void Mesh::AddVertex(const double *x)
+template<typename T>
+static void CheckEnlarge(Array<T> &array, int size)
 {
-   double *y = vertices[NumOfVertices]();
+   if (size >= array.Size()) { array.SetSize(size + 1); }
+}

-   for (int i = 0; i < spaceDim; i++)
+int Mesh::AddVertex(double x, double y, double z)
+{
+   CheckEnlarge(vertices, NumOfVertices);
+   double *v = vertices[NumOfVertices]();
+   v[0] = x;
+   v[1] = y;
+   v[2] = z;
+   return NumOfVertices++;
+}
+
+int Mesh::AddVertex(const double *coords)
+{
+   CheckEnlarge(vertices, NumOfVertices);
+   vertices[NumOfVertices].SetCoords(spaceDim, coords);
+   return NumOfVertices++;
+}
+
+void Mesh::AddVertexParents(int i, int p1, int p2)
+{
+   tmp_vertex_parents.Append(Triple<int, int, int>(i, p1, p2));
+
+   // if vertex coordinates are defined, make sure the hanging vertex has the
+   // correct position
+   if (i < vertices.Size())
   {
-      y[i] = x[i];
+      double *vi = vertices[i](), *vp1 = vertices[p1](), *vp2 = vertices[p2]();
+      for (int j = 0; j < 3; j++)
+      {
+         vi[j] = (vp1[j] + vp2[j]) * 0.5;
+      }
   }
-   NumOfVertices++;
 }

-void Mesh::AddSegment(const int *vi, int attr)
+int Mesh::AddSegment(int v1, int v2, int attr)
 {
-   elements[NumOfElements++] = new Segment(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Segment(v1, v2, attr);
+   return NumOfElements++;
 }

-void Mesh::AddTri(const int *vi, int attr)
+int Mesh::AddSegment(const int *vi, int attr)
 {
-   elements[NumOfElements++] = new Triangle(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Segment(vi, attr);
+   return NumOfElements++;
 }

-void Mesh::AddTriangle(const int *vi, int attr)
+int Mesh::AddTriangle(int v1, int v2, int v3, int attr)
 {
-   elements[NumOfElements++] = new Triangle(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Triangle(v1, v2, v3, attr);
+   return NumOfElements++;
 }

-void Mesh::AddQuad(const int *vi, int attr)
+int Mesh::AddTriangle(const int *vi, int attr)
 {
-   elements[NumOfElements++] = new Quadrilateral(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Triangle(vi, attr);
+   return NumOfElements++;
 }

-void Mesh::AddTet(const int *vi, int attr)
+int Mesh::AddQuad(int v1, int v2, int v3, int v4, int attr)
 {
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Quadrilateral(v1, v2, v3, v4, attr);
+   return NumOfElements++;
+}
+
+int Mesh::AddQuad(const int *vi, int attr)
+{
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Quadrilateral(vi, attr);
+   return NumOfElements++;
+}
+
+int Mesh::AddTet(int v1, int v2, int v3, int v4, int attr)
+{
+   int vi[4] = {v1, v2, v3, v4};
+   return AddTet(vi, attr);
+}
+
+int Mesh::AddTet(const int *vi, int attr)
+{
+   CheckEnlarge(elements, NumOfElements);
 #ifdef MFEM_USE_MEMALLOC
   Tetrahedron *tet;
   tet = TetMemory.Alloc();
   tet->SetVertices(vi);
   tet->SetAttribute(attr);
-   elements[NumOfElements++] = tet;
+   elements[NumOfElements] = tet;
 #else
-   elements[NumOfElements++] = new Tetrahedron(vi, attr);
+   elements[NumOfElements] = new Tetrahedron(vi, attr);
 #endif
+   return NumOfElements++;
 }

-void Mesh::AddWedge(const int *vi, int attr)
+int Mesh::AddWedge(int v1, int v2, int v3, int v4, int v5, int v6, int attr)
 {
-   elements[NumOfElements++] = new Wedge(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Wedge(v1, v2, v3, v4, v5, v6, attr);
+   return NumOfElements++;
 }

-void Mesh::AddHex(const int *vi, int attr)
+int Mesh::AddWedge(const int *vi, int attr)
 {
-   elements[NumOfElements++] = new Hexahedron(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Wedge(vi, attr);
+   return NumOfElements++;
+}
+
+int Mesh::AddHex(int v1, int v2, int v3, int v4, int v5, int v6, int v7, int v8,
+                 int attr)
+{
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] =
+      new Hexahedron(v1, v2, v3, v4, v5, v6, v7, v8, attr);
+   return NumOfElements++;
+}
+
+int Mesh::AddHex(const int *vi, int attr)
+{
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = new Hexahedron(vi, attr);
+   return NumOfElements++;
 }

 void Mesh::AddHexAsTets(const int *vi, int attr)
@@ -1302,19 +1392,60 @@ void Mesh::AddHexAsWedges(const int *vi, int attr)
   }
 }

-void Mesh::AddBdrSegment(const int *vi, int attr)
+int Mesh::AddElement(Element *elem)
 {
-   boundary[NumOfBdrElements++] = new Segment(vi, attr);
+   CheckEnlarge(elements, NumOfElements);
+   elements[NumOfElements] = elem;
+   return NumOfElements++;
 }

-void Mesh::AddBdrTriangle(const int *vi, int attr)
+int Mesh::AddBdrElement(Element *elem)
 {
-   boundary[NumOfBdrElements++] = new Triangle(vi, attr);
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = elem;
+   return NumOfBdrElements++;
 }

-void Mesh::AddBdrQuad(const int *vi, int attr)
+int Mesh::AddBdrSegment(int v1, int v2, int attr)
 {
-   boundary[NumOfBdrElements++] = new Quadrilateral(vi, attr);
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = new Segment(v1, v2, attr);
+   return NumOfBdrElements++;
+}
+
+int Mesh::AddBdrSegment(const int *vi, int attr)
+{
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = new Segment(vi, attr);
+   return NumOfBdrElements++;
+}
+
+int Mesh::AddBdrTriangle(int v1, int v2, int v3, int attr)
+{
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = new Triangle(v1, v2, v3, attr);
+   return NumOfBdrElements++;
+}
+
+int Mesh::AddBdrTriangle(const int *vi, int attr)
+{
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = new Triangle(vi, attr);
+   return NumOfBdrElements++;
+}
+
+int Mesh::AddBdrQuad(int v1, int v2, int v3, int v4, int attr)
+{
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = new Quadrilateral(v1, v2, v3, v4, attr);
+   return NumOfBdrElements++;
+}
+
+int Mesh::AddBdrQuad(const int *vi, int attr)
+{
+   CheckEnlarge(boundary, NumOfBdrElements);
+   boundary[NumOfBdrElements] = new Quadrilateral(vi, attr);
+   return NumOfBdrElements++;
 }

 void Mesh::AddBdrQuadAsTriangles(const int *vi, int attr)
@@ -2407,6 +2538,15 @@ void Mesh::FinalizeTopology(bool generate_bdr)

   // generate the arrays 'attributes' and 'bdr_attributes'
   SetAttributes();
+
+   // if the user defined any hanging nodes (see AddVertexParent),
+   // initialize the NC mesh now
+   if (tmp_vertex_parents.Size())
+   {
+      MFEM_VERIFY(ncmesh == NULL, "");
+      EnsureNCMesh(true);
+      tmp_vertex_parents.DeleteAll();
+   }
 }

 void Mesh::Finalize(bool refine, bool fix_orientation)
@@ -206,6 +206,9 @@ public:
   Array<FaceGeometricFactors*>
   face_geom_factors; ///< Optional face geometric factors.

+   /// Used during initialization only.
+   Array<Triple<int, int, int> > tmp_vertex_parents;
+
   // Global parameter that can be used to control the removal of unused
   // vertices performed when reading a mesh in MFEM format. The default value
   // (true) is set in mesh_readers.cpp.
@@ -499,10 +502,7 @@ public:
       @brief _Init_ constructor: begin the construction of a Mesh object. */
   Mesh(int _Dim, int NVert, int NElem, int NBdrElem = 0, int _spaceDim = -1)
   {
-      if (_spaceDim == -1)
-      {
-         _spaceDim = _Dim;
-      }
+      if (_spaceDim == -1) { _spaceDim = _Dim; }
      InitMesh(_Dim, _spaceDim, NVert, NElem, NBdrElem);
   }

@@ -514,22 +514,45 @@ public:

   Element *NewElement(int geom);

-   void AddVertex(const double *);
-   void AddSegment(const int *vi, int attr = 1);
-   void AddTri(const int *vi, int attr = 1);
-   void AddTriangle(const int *vi, int attr = 1);
-   void AddQuad(const int *vi, int attr = 1);
-   void AddTet(const int *vi, int attr = 1);
-   void AddWedge(const int *vi, int attr = 1);
-   void AddHex(const int *vi, int attr = 1);
+   int AddVertex(double x, double y = 0.0, double z = 0.0);
+   int AddVertex(const double *coords);
+   /// Mark vertex @a i as non-conforming, with parent vertices @a p1 and @a p2.
+   void AddVertexParents(int i, int p1, int p2);
+
+   int AddSegment(int v1, int v2, int attr = 1);
+   int AddSegment(const int *vi, int attr = 1);
+
+   int AddTriangle(int v1, int v2, int v3, int attr = 1);
+   int AddTriangle(const int *vi, int attr = 1);
+   int AddTri(const int *vi, int attr = 1) { return AddTriangle(vi, attr); }
+
+   int AddQuad(int v1, int v2, int v3, int v4, int attr = 1);
+   int AddQuad(const int *vi, int attr = 1);
+
+   int AddTet(int v1, int v2, int v3, int v4, int attr = 1);
+   int AddTet(const int *vi, int attr = 1);
+
+   int AddWedge(int v1, int v2, int v3, int v4, int v5, int v6, int attr = 1);
+   int AddWedge(const int *vi, int attr = 1);
+
+   int AddHex(int v1, int v2, int v3, int v4, int v5, int v6, int v7, int v8,
+              int attr = 1);
+   int AddHex(const int *vi, int attr = 1);
   void AddHexAsTets(const int *vi, int attr = 1);
   void AddHexAsWedges(const int *vi, int attr = 1);
+
   /// The parameter @a elem should be allocated using the NewElement() method
-   void AddElement(Element *elem)     { elements[NumOfElements++] = elem; }
-   void AddBdrElement(Element *elem)  { boundary[NumOfBdrElements++] = elem; }
-   void AddBdrSegment(const int *vi, int attr = 1);
-   void AddBdrTriangle(const int *vi, int attr = 1);
-   void AddBdrQuad(const int *vi, int attr = 1);
+   int AddElement(Element *elem);
+   int AddBdrElement(Element *elem);
+
+   int AddBdrSegment(int v1, int v2, int attr = 1);
+   int AddBdrSegment(const int *vi, int attr = 1);
+
+   int AddBdrTriangle(int v1, int v2, int v3, int attr = 1);
+   int AddBdrTriangle(const int *vi, int attr = 1);
+
+   int AddBdrQuad(int v1, int v2, int v3, int v4, int attr = 1);
+   int AddBdrQuad(const int *vi, int attr = 1);
   void AddBdrQuadAsTriangles(const int *vi, int attr = 1);

   void GenerateBoundaryElements();
@@ -104,7 +104,16 @@ NCMesh::NCMesh(const Mesh *mesh, std::istream *vertex_parents)
   {
      LoadVertexParents(*vertex_parents);
   }
-   else
+   // alternatively, the user might have initialized hanging nodes with
+   // Mesh::AddVertexParents; copy the hierarchy now
+   else if (mesh->tmp_vertex_parents.Size())
+   {
+      for (const auto &triple : mesh->tmp_vertex_parents)
+      {
+         nodes.Reparent(triple.one, triple.two, triple.three);
+      }
+   }
+   else // otherwise we just assume a standard conforming coarse mesh
   {
      top_vertex_pos.SetSize(3*mesh->GetNV());
      for (int i = 0; i < mesh->GetNV(); i++)
@@ -1691,6 +1691,7 @@ void ParMesh::GetFaceNbrElementTransformation(
   ElTr->Attribute = elem->GetAttribute();
   ElTr->ElementNo = NumOfElements + i;
   ElTr->ElementType = ElementTransformation::ELEMENT;
+   ElTr->Reset();

   if (Nodes == NULL)
   {
@@ -2370,6 +2371,7 @@ void ParMesh::GetGhostFaceTransformation(
 {
   // calculate composition of FETr->Loc1 and FETr->Elem1
   DenseMatrix &face_pm = FETr->GetPointMat();
+   FETr->Reset();
   if (Nodes == NULL)
   {
      FETr->Elem1->Transform(FETr->Loc1.Transf.GetPointMat(), face_pm);
@@ -1066,9 +1066,9 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
      for (int j = mf.slaves_begin; j < mf.slaves_end; j++)
      {
         const Slave &sf = full_list.slaves[j];
-         if (sf.index < 0) { continue; }
+         if (sf.element < 0) { continue; }

-         MFEM_ASSERT(mf.element >= 0 && sf.element >= 0, "");
+         MFEM_ASSERT(mf.element >= 0, "");
         Element* e[2] = { &elements[mf.element], &elements[sf.element] };

         bool loc0 = (e[0]->rank == MyRank);
@@ -1224,9 +1224,9 @@ void ParNCMesh::GetFaceNeighbors(ParMesh &pmesh)
         for (int j = mf.slaves_begin; j < mf.slaves_end; j++)
         {
            const Slave &sf = full_list.slaves[j];
-            if (sf.index < 0) { continue; }
+            if (sf.element < 0) { continue; }

-            MFEM_ASSERT(sf.element >= 0 && mf.element >= 0, "");
+            MFEM_ASSERT(mf.element >= 0, "");
            Element &sfe = elements[sf.element];
            Element &mfe = elements[mf.element];

@@ -37,6 +37,8 @@ void CreateVTKElementConnectivity(Array<int> &con, Geometry::Type geom,
 void WriteVTKEncodedCompressed(std::ostream &out, const void *bytes,
                               uint32_t nbytes, int compression_level);

+int BarycentricToVTKTriangle(int *b, int ref);
+
 const char *VTKByteOrder();

 } // namespace mfem
--- a/Show More
+++ b/Show More