minor

Mesh bug fix and unit test

.gitignore

@@ -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
@@ -233,6 +235,7 @@ miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
 
 miniapps/gslib/field-diff
+miniapps/gslib/field-interp
 miniapps/gslib/findpts
 miniapps/gslib/pfindpts
 
@@ -253,20 +256,16 @@ tests/unit/unit_tests
 tests/unit/punit_tests
 tests/unit/sedov_tests_*
 tests/unit/psedov_tests_*
-tests/unit/tmop_tests_*
-tests/unit/ptmop_tests_*
-tests/unit/cube.mesh
-tests/unit/star.mesh
-tests/unit/blade.mesh
-tests/unit/square01.mesh
-tests/unit/toroid-hex.mesh
-tests/unit/beam-hex-nurbs.mesh
-tests/unit/square-disc-nurbs.mesh
 
 # Test script output
 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-*/*

.gitlab-ci.yml

@@ -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

.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

.gitlab/quartz.yml

@@ -22,10 +22,6 @@
     MAKE_PAR: 6
     BASELINE_PAR: 18
 
-# Setup
-setup_quartz:
-  extends: [.setup, .on_quartz]
-
 # Allocate
 allocate_quartz:
   variables:

CHANGELOG

@@ -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
@@ -50,11 +57,6 @@ Performance improvements
 Improved GPU capabilities
 -------------------------
 - Added support for Chebyshev accelerated polynomial smoother on GPU.
-- The TMOP mesh optimization algorithms were extended to GPU:
-   - QualityMetric #1, #2 and #7 are available in 2D, #302, #303 and #321 in 3D
-   - Both AnalyticAdaptTC and DiscreteAdaptTC TargetConstructor are available
-   - Kernels for normalization and limiting have been added
-   - The AdvectorCG now also support AssemblyLevel::PARTIAL
 
 - Optimized AMD/HIP kernel support.
 
@@ -63,8 +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
@@ -93,6 +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
@@ -118,6 +134,12 @@ 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.
+
+- Added an interface to the Intel MKL Parallel Direct Sparse Solver for
+  Clusters. An example usage of the interface is shown in Example 11p.
+
 New and updated examples and miniapps
 -------------------------------------
 - Added a new example, Example 25/25p, to demonstrate the use of a Perfectly
@@ -154,6 +176,9 @@ 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.
 
@@ -168,28 +193,47 @@ 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
 =======================================

CMakeLists.txt

@@ -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)
@@ -332,6 +346,12 @@ if (MFEM_USE_ADIOS2)
    find_package(ADIOS2 REQUIRED)
 endif()
 
+if (MFEM_USE_MKL_CPARDISO)
+  if (MFEM_USE_MPI)
+   find_package(MKL_CPARDISO REQUIRED MKL_SEQUENTIAL MKL_LP64 MKL_MPI_WRAPPER)
+  endif()
+endif()
+
 # MFEM_TIMER_TYPE
 if (NOT DEFINED MFEM_TIMER_TYPE)
   if (APPLE)
@@ -357,7 +377,8 @@ 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 MKL_CPARDISO)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")

INSTALL

@@ -486,6 +486,13 @@ MFEM_USE_CEED = YES/NO
    library for performant high-order operator evaluation developed by the Center
    for Efficient Exascale Discretizations in the Exascale Computing Project.
 
+MFEM_USE_MKL_CPARDISO = YES/NO
+   Enables the interface to the Intel MKL Parallel Direct Sparse Solver for
+   Clusters. Make sure to set the correct values for MKL_MPI_WRAPPER and
+   MKL_LIBRARY_SUBDIR as shown in defaults.mk. If you configure MFEM with
+   MFEM_USE_LAPACK=YES, verify that the MKL LAPACK libraries are used. The
+   OpenMP capabilities are disabled at link time.
+
 MFEM_BUILD_TAG = (any value)
    An optional tag to characterize the build. Exported to config/config.mk.
    Can be used to identify the MFEM build from other makefiles.
@@ -663,7 +670,7 @@ 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.

config/cmake/config.hpp.in

@@ -156,4 +156,7 @@
 // library.
 #cmakedefine MFEM_USE_SIMMETRIX
 
+// Enable interface to the MKL CPardiso library.
+#cmakedefine MFEM_USE_MKL_CPARDISO
+
 #endif // MFEM_CONFIG_HEADER

config/cmake/modules/FindADIOS2.cmake

@@ -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

config/cmake/modules/FindMKL_CPARDISO.cmake

@@ -0,0 +1,106 @@
+# 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.
+
+# Defines the following variables:
+#   - MKL_CPARDISO_FOUND
+#   - MKL_CPARDISO_LIBRARIES
+#   - MKL_CPARDISO_INCLUDE_DIRS
+
+if(NOT MKL_MPI_WRAPPER_LIB)
+  message(FATAL_ERROR "MKL CPardiso enabled but no MKL MPI Wrapper lib specified")
+endif()
+
+if(NOT MKL_LIBRARY_DIR)
+  message(WARNING "Using default MKL library path. Double check the variable MKL_LIBRARY_DIR")
+  set(MKL_LIBRARY_DIR "lib")
+endif()
+
+include(MfemCmakeUtilities)
+mfem_find_package(MKL_CPARDISO MKL_CPARDISO
+    MKL_CPARDISO_DIR "include" mkl_cluster_sparse_solver.h ${MKL_LIBRARY_DIR} mkl_core
+  "Paths to headers required by MKL CPardiso." "Libraries required by MKL CPARDISO."
+  ADD_COMPONENT MKL_LP64 "include" "" ${MKL_LIBRARY_DIR} mkl_intel_lp64
+  ADD_COMPONENT MKL_SEQUENTIAL "include" "" ${MKL_LIBRARY_DIR} mkl_sequential
+  ADD_COMPONENT MKL_MPI_WRAPPER "include" "" ${MKL_LIBRARY_DIR} ${MKL_MPI_WRAPPER_LIB}
+  CHECK_BUILD MKL_CPARDISO_VERSION_OK TRUE
+  "
+#include <mpi.h>
+#include <mkl.h>
+#include <mkl_cluster_sparse_solver.h>
+int main (void)
+{
+    MKL_INT n = 5;
+    MKL_INT ia[6]  = { 1, 4, 6, 9, 12, 14};
+    MKL_INT ja[13] = {  1, 2, 4,        /* index of non-zeros in 1 row*/
+                        1, 2,           /* index of non-zeros in 2 row*/
+                        3, 4, 5,        /* index of non-zeros in 3 row*/
+                        1, 3, 4,        /* index of non-zeros in 4 row*/
+                        2, 5            /* index of non-zeros in 5 row*/
+    };
+    double a[13] = {
+                         1.0, -1.0, /*0*/ -3.0, /*0*/
+                        -2.0,  5.0, /*0*/ /*0*/ /*0*/
+                        /*0*/  4.0,  6.0,  4.0, /*0*/
+                        -4.0, /*0*/  2.0,  7.0, /*0*/
+                        /*0*/  8.0, /*0*/ /*0*/ -5.0
+                    };
+
+    MKL_INT mtype = 11; /* set matrix type to \"real unsymmetric matrix\" */
+    MKL_INT nrhs  = 1;  /* Number of right hand sides. */
+    double b[5], x[5], bs[5], res, res0; /* RHS and solution vectors. */
+
+    /* Internal solver memory pointer pt
+     *       32-bit:      int pt[64] or void *pt[64];
+     *       64-bit: long int pt[64] or void *pt[64]; */
+    void *pt[64] = { 0 };
+
+    /* Cluster Sparse Solver control parameters. */
+    MKL_INT iparm[64] = { 0 };
+    MKL_INT maxfct, mnum, phase, msglvl, error;
+
+    /* Auxiliary variables. */
+    double  ddum; /* Double dummy   */
+    MKL_INT idum; /* Integer dummy. */
+    MKL_INT i, j;
+    int     mpi_stat = 0;
+    int     argc = 0;
+    int     comm, rank;
+    char*   uplo;
+    char**  argv;
+
+    mpi_stat = MPI_Init( &argc, &argv );
+    mpi_stat = MPI_Comm_rank( MPI_COMM_WORLD, &rank );
+    comm =  MPI_Comm_c2f( MPI_COMM_WORLD );
+
+    iparm[ 0] =  1; /* Solver default parameters overriden with provided by iparm */
+    iparm[ 1] =  2; /* Use METIS for fill-in reordering */
+    iparm[ 5] =  0; /* Write solution into x */
+    iparm[ 7] =  2; /* Max number of iterative refinement steps */
+    iparm[ 9] = 13; /* Perturb the pivot elements with 1E-13 */
+    iparm[10] =  1; /* Use nonsymmetric permutation and scaling MPS */
+    iparm[12] =  1; /* Switch on Maximum Weighted Matching algorithm (default for non-symmetric) */
+    iparm[17] = -1; /* Output: Number of nonzeros in the factor LU */
+    iparm[18] = -1; /* Output: Mflops for LU factorization */
+    iparm[26] =  1; /* Check input data for correctness */
+    iparm[39] =  0; /* Input: matrix/rhs/solution stored on master */
+    maxfct = 1; /* Maximum number of numerical factorizations. */
+    mnum   = 1; /* Which factorization to use. */
+    msglvl = 1; /* Print statistical information in file */
+    error  = 0; /* Initialize error flag */
+
+    phase = 11;
+    cluster_sparse_solver ( pt, &maxfct, &mnum, &mtype, &phase,
+                &n, a, ia, ja, &idum, &nrhs, iparm, &msglvl, &ddum, &ddum, &comm, &error );
+
+    mpi_stat = MPI_Finalize();
+    return error;
+}
+")

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -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

config/config.hpp

@@ -42,9 +42,15 @@
 #ifdef MFEM_USE_SUPERLU
 #error Building with SuperLU_DIST (MFEM_USE_SUPERLU=YES) requires MPI (MFEM_USE_MPI=YES)
 #endif
+#ifdef MFEM_USE_MUMPS
+#error Building with MUMPS (MFEM_USE_MUMPS=YES) requires MPI (MFEM_USE_MPI=YES)
+#endif
 #ifdef MFEM_USE_STRUMPACK
 #error Building with STRUMPACK (MFEM_USE_STRUMPACK=YES) requires MPI (MFEM_USE_MPI=YES)
 #endif
+#ifdef MFEM_USE_MKL_CPARDISO
+#error Building with MKL CPARDISO (MFEM_USE_MKL_CPARDISO=YES) requires MPI (MFEM_USE_MPI=YES)
+#endif
 #ifdef MFEM_USE_PETSC
 #error Building with PETSc (MFEM_USE_PETSC=YES) requires MPI (MFEM_USE_MPI=YES)
 #endif

config/config.hpp.in

@@ -94,6 +94,10 @@
 // Enable MFEM functionality based on the SuperLU library.
 // #define MFEM_USE_SUPERLU
 
+// Enable MFEM functionality based on the MUMPS library.
+// #define MFEM_USE_MUMPS
+// #define MFEM_MUMPS_VERSION @MFEM_MUMPS_VERSION@
+
 // Enable MFEM functionality based on the STRUMPACK library.
 // #define MFEM_USE_STRUMPACK
 
@@ -163,4 +167,7 @@
 // library.
 // #define MFEM_USE_SIMMETRIX
 
+// Enable interface to the MKL CPardiso library.
+// #define MFEM_USE_MKL_CPARDISO
+
 #endif // MFEM_CONFIG_HEADER

config/config.mk.in

@@ -32,6 +32,7 @@ MFEM_USE_SUNDIALS      = @MFEM_USE_SUNDIALS@
 MFEM_USE_MESQUITE      = @MFEM_USE_MESQUITE@
 MFEM_USE_SUITESPARSE   = @MFEM_USE_SUITESPARSE@
 MFEM_USE_SUPERLU       = @MFEM_USE_SUPERLU@
+MFEM_USE_MUMPS         = @MFEM_USE_MUMPS@
 MFEM_USE_STRUMPACK     = @MFEM_USE_STRUMPACK@
 MFEM_USE_GINKGO        = @MFEM_USE_GINKGO@
 MFEM_USE_GNUTLS        = @MFEM_USE_GNUTLS@
@@ -52,6 +53,7 @@ MFEM_USE_CEED          = @MFEM_USE_CEED@
 MFEM_USE_UMPIRE        = @MFEM_USE_UMPIRE@
 MFEM_USE_SIMD          = @MFEM_USE_SIMD@
 MFEM_USE_ADIOS2        = @MFEM_USE_ADIOS2@
+MFEM_USE_MKL_CPARDISO  = @MFEM_USE_MKL_CPARDISO@
 
 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@

config/defaults.cmake

@@ -52,6 +52,7 @@ option(MFEM_USE_CEED "Enable CEED" OFF)
 option(MFEM_USE_UMPIRE "Enable Umpire" OFF)
 option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" OFF)
 option(MFEM_USE_ADIOS2 "Enable ADIOS2" OFF)
+option(MFEM_USE_MKL_CPARDISO "Enable MKL CPardiso" OFF)
 
 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")
 
@@ -180,6 +181,10 @@ set(HIOP_DIR "${MFEM_DIR}/../hiop/install" CACHE STRING
 set(HIOP_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
     "Packages that HiOp depends on.")
 
+set(MKL_CPARDISO_DIR "" CACHE STRING "MKL installation path.")
+set(MKL_MPI_WRAPPER_LIB "mkl_blacs_mpich_lp64" CACHE STRING "MKL MPI wrapper library")
+set(MKL_LIBRARY_DIR "" CACHE STRING "Custom library subdirectory")
+
 set(OCCA_DIR "${MFEM_DIR}/../occa" CACHE PATH "Path to OCCA")
 set(RAJA_DIR "${MFEM_DIR}/../raja" CACHE PATH "Path to RAJA")
 set(CEED_DIR "${MFEM_DIR}/../libCEED" CACHE PATH "Path to libCEED")

config/defaults.mk

@@ -120,6 +120,7 @@ MFEM_USE_SUNDIALS      = NO
 MFEM_USE_MESQUITE      = NO
 MFEM_USE_SUITESPARSE   = NO
 MFEM_USE_SUPERLU       = NO
+MFEM_USE_MUMPS         = NO
 MFEM_USE_STRUMPACK     = NO
 MFEM_USE_GINKGO        = NO
 MFEM_USE_GNUTLS        = NO
@@ -138,9 +139,9 @@ MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
 MFEM_USE_CEED          = NO
 MFEM_USE_UMPIRE        = NO
-MFEM_USE_CAMP          = NO
 MFEM_USE_SIMD          = NO
 MFEM_USE_ADIOS2        = NO
+MFEM_USE_MKL_CPARDISO  = NO
 
 # Compile and link options for zlib.
 ZLIB_DIR =
@@ -157,7 +158,7 @@ HYPRE_OPT = -I$(HYPRE_DIR)/include
 HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
 
 # METIS library configuration
-ifeq ($(MFEM_USE_SUPERLU)$(MFEM_USE_STRUMPACK),NONO)
+ifeq ($(MFEM_USE_SUPERLU)$(MFEM_USE_STRUMPACK)$(MFEM_USE_MUMPS),NONONO)
    ifeq ($(MFEM_USE_METIS_5),NO)
      METIS_DIR = @MFEM_DIR@/../metis-4.0
      METIS_OPT =
@@ -233,7 +234,7 @@ SCALAPACK_DIR = @MFEM_DIR@/../scalapack-2.0.2
 SCALAPACK_OPT = -I$(SCALAPACK_DIR)/SRC
 SCALAPACK_LIB = -L$(SCALAPACK_DIR)/lib -lscalapack $(LAPACK_LIB)
 
-# MPI Fortran library, needed e.g. by STRUMPACK
+# MPI Fortran library, needed e.g. by STRUMPACK or MUMPS
 # MPICH:
 MPI_FORTRAN_LIB = -lmpifort
 # OpenMPI:
@@ -241,6 +242,11 @@ MPI_FORTRAN_LIB = -lmpifort
 # Additional Fortan library:
 # MPI_FORTRAN_LIB += -lgfortran
 
+# MUMPS library configuration
+MUMPS_DIR =
+MUMPS_OPT = -I$(MUMPS_DIR)/include
+MUMPS_LIB = -Wl,-rpath,$(MUMPS_DIR)/lib -L$(MUMPS_DIR)/lib -ldmumps -lmumps_common -lpord $(SCALAPACK_LIB) $(LAPACK_LIB) $(MPI_FORTRAN_LIB)
+
 # STRUMPACK library configuration
 STRUMPACK_DIR = @MFEM_DIR@/../STRUMPACK-build
 STRUMPACK_OPT = -I$(STRUMPACK_DIR)/include $(SCOTCH_OPT)
@@ -373,10 +379,14 @@ UMPIRE_DIR = @MFEM_DIR@/../umpire
 UMPIRE_OPT = -I$(UMPIRE_DIR)/include
 UMPIRE_LIB = -L$(UMPIRE_DIR)/lib -lumpire
 
-# CAMP library configuration
-CAMP_DIR = @MFEM_DIR@/../camp
-CAMP_OPT = -I$(CAMP_DIR)/include
-CAMP_LIB = -L$(CAMP_DIR)/lib
+# MKL CPardiso library configuration
+MKL_CPARDISO_DIR ?=
+MKL_MPI_WRAPPER ?= mkl_blacs_mpich_lp64
+MKL_LIBRARY_SUBDIR ?= lib
+MKL_CPARDISO_OPT = -I$(MKL_CPARDISO_DIR)/include
+MKL_CPARDISO_LIB = -Wl,-rpath,$(MKL_CPARDISO_DIR)/$(MKL_LIBRARY_SUBDIR)\
+                   -L$(MKL_CPARDISO_DIR)/$(MKL_LIBRARY_SUBDIR) -l$(MKL_MPI_WRAPPER)\
+                   -lmkl_intel_lp64 -lmkl_sequential -lmkl_core
 
 # If YES, enable some informational messages
 VERBOSE = NO

config/get_mumps_version.cpp

@@ -0,0 +1,33 @@
+// 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 "dmumps_c.h"
+#include <string>
+#include <iostream>
+#include <algorithm>
+
+// Macros to expand a macro as a string
+#define STR_EXPAND(s) #s
+#define STR(s) STR_EXPAND(s)
+
+int main()
+{
+#ifdef MUMPS_VERSION
+   const char *ptr = STR(MUMPS_VERSION);
+   std::string s(ptr);
+   s.erase(std::remove(s.begin(), s.end(), '"'), s.end());
+   s.erase(std::remove(s.begin(), s.end(), '.'), s.end());
+   std::cout << s << "\n";
+   return 0;
+#else
+   return -1;
+#endif
+}

config/makefile

@@ -42,6 +42,10 @@ GHV_FLAGS = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(HYPRE_OPT))
 SMX = $(if $(MFEM_USE_PUMI:NO=),MFEM_USE_SIMMETRIX)
 SMX_PATH = $(PUMI_DIR)/include/gmi_sim.h
 SMX_FILE = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(SMX_PATH))
+MUMPS = $(MFEM_USE_MUMPS:NO=)
+GMV_CXX ?= $(MFEM_CXX)
+GMV = get_mumps_version
+GMV_FLAGS = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(MUMPS_OPT))
 
 $(GHV): $(SRC)$(GHV).cpp
 	$(call mfem-info, Determining HYPRE version ...)
@@ -50,6 +54,13 @@ $(GHV).out: $(GHV)
 	./$(GHV) > $(GHV).out
 .INTERMEDIATE: $(GHV) $(GHV).out
 
+$(GMV): $(SRC)$(GMV).cpp
+	$(call mfem-info, Determining MUMPS version ...)
+	$(GMV_CXX) ${GMV_FLAGS} $(SRC)$(GMV).cpp -o $(GMV)
+$(GMV).out: $(GMV)
+	./$(GMV) > $(GMV).out
+.INTERMEDIATE: $(GMV) $(GMV).out
+
 get-hypre-version: $(GHV).out
 	$(eval MFEM_HYPRE_VERSION:=$(shell cat $(GHV).out))
 	$(if $(MFEM_HYPRE_VERSION),$(eval export MFEM_HYPRE_VERSION)\
@@ -62,10 +73,16 @@ check-smx:
 	$(call mfem-info, MFEM_USE_SIMMETRIX = $(MFEM_USE_SIMMETRIX))
 	$(eval export MFEM_USE_SIMMETRIX)
 
-header: $(if $(MPI),get-hypre-version,) $(if $(SMX),check-smx)
+get-mumps-version: $(GMV).out
+	$(eval MFEM_MUMPS_VERSION:=$(shell cat $(GMV).out))
+	$(if $(MFEM_MUMPS_VERSION),$(eval export MFEM_MUMPS_VERSION)\
+	$(info MUMPS version: $(MFEM_MUMPS_VERSION)),\
+	$(error Unable to determine MUMPS version))
+
+header: $(if $(MPI),get-hypre-version,) $(if $(SMX),check-smx,) $(if $(MUMPS),get-mumps-version,)
 	$(call mfem-info, Writing $(CONFIG_HPP) ...)
 	@set -- && \
-	for def in $${MFEM_DEFINES} $(if $(MPI),MFEM_HYPRE_VERSION) $(SMX); do \
+	for def in $${MFEM_DEFINES} $(if $(MPI),MFEM_HYPRE_VERSION) $(SMX) $(if $(MUMPS),MFEM_MUMPS_VERSION); do \
 	   eval var=\$$$$def && \
 	   if [ "NO" != "$${var}" ]; then \
 	      set -- "$$@" -e "s|// \(#define $${def} \)|\1|" && \

config/sample-runs.sh

@@ -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".

data/periodic-annulus-sector.geo

@@ -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

data/periodic-annulus-sector.msh

@@ -2,184 +2,191 @@ $MeshFormat
 2.2 0 8
 $EndMeshFormat
 $Nodes
-55
+136
 1 1 0 0
 2 2 0 0
 3 0.5000000000000001 0.8660254037844386 0
 4 1 1.732050807568877 0
-5 1.166666666666667 0 0
-6 1.333333333333333 0 0
-7 1.5 0 0
+5 1.5 0 0
+6 1.166666666666667 0 0
+7 1.333333333333333 0 0
 8 1.666666666666667 0 0
 9 1.833333333333333 0 0
-10 0.5833333333333335 1.010362971081845 0
-11 0.6666666666666667 1.154700538379251 0
-12 0.7500000000000002 1.299038105676658 0
+10 0.7500000000000002 1.299038105676658 0
+11 0.5833333333333335 1.010362971081845 0
+12 0.6666666666666667 1.154700538379251 0
 13 0.8333333333333335 1.443375672974064 0
 14 0.9166666666666669 1.587713240271471 0
 15 0.9396926207859085 0.3420201433256683 0
 16 0.7660444431189786 0.6427876096865386 0
-17 1.986476715483886 0.2321858282504602 0
-18 1.946089741159648 0.4612317414848793 0
-19 1.879385241571817 0.6840402866513365 0
-20 1.787265280646825 0.8975983604009234 0
-21 1.670975622825874 1.09901795614161 0
-22 1.532088886237958 1.285575219373077 0
-23 1.372483275737469 1.454747283146095 0
-24 1.194317183405575 1.604246385510085 0
-25 1.425989114816062 0.1915326920916892 0
-26 0.8788667344146573 1.13917645290495 0
-27 1.630372059110754 0.7154531062316609 0
-28 1.436395769298814 1.053728612482506 0
-29 1.081023776188756 0.6241293681829633 0
-30 1.168737372335971 1.428012728596308 0
-31 1.821063986059922 0.298149890497067 0
-32 1.234707097211386 0.3469796339295647 0
-33 1.377747393186519 0.6200150626754309 0
-34 1.457047681210906 0.3890895843559762 0
-35 0.917846726184522 0.8957978954532204 0
-36 1.218335619030348 0.9017812086952638 0
-37 1.066623110765233 1.061857005744772 0
-38 1.587029716281926 0.1355955181472859 0
-39 1.744445799211916 0.1441515753740107 0
-40 1.25 0.1443375672974065 0
-41 1.453660070628011 0.8435769396609902 0
-42 1.741367044061892 0.499612708014486 0
-43 1.30550638526547 1.257610469847477 0
-44 1.118213276932792 0.1666674689105279 0
-45 0.9109440214958271 1.306610291787315 0
-46 0.9970618258753989 1.438658589955562 0
-47 0.7499999999999998 1.010362971081845 0
-48 0.7034449005273667 0.8850673702175776 0
-49 1.605449512513618 0.9269067082200894 0
-50 1.561654019115059 0.5298592532912715 0
-51 1.229782222487711 1.096820457143683 0
-52 1.617066998712459 0.3090202662210922 0
-53 1.079645953234324 1.246963713711438 0
-54 1.877063966817811 0.1348974588243076 0
-55 1.055356609656722 1.558136350380461 0
+17 0.993238357741943 0.1160929141252301 0
+18 0.9730448705798238 0.2306158707424401 0
+19 0.8936326403234125 0.4487991802004617 0
+20 0.8354878114129367 0.5495089780708056 0
+21 0.6862416378687343 0.7273736415730481 0
+22 0.597158591702787 0.8021231927550432 0
+23 1.956295201467611 0.4158233816355181 0
+24 1.827090915285202 0.8134732861515996 0
+25 1.618033988749896 1.175570504584944 0
+26 1.338261212717719 1.486289650954786 0
+27 1.995128100519648 0.1395129474882505 0
+28 1.980536137483141 0.278346201920131 0
+29 1.922523391876638 0.551274711633998 0
+30 1.879385241571817 0.6840402866513373 0
+31 1.765895185717855 0.9389431255717802 0
+32 1.696096192312853 1.059838528466408 0
+33 1.532088886237958 1.285575219373077 0
+34 1.438679600677305 1.389316740917992 0
+35 1.231322950651319 1.576021507213442 0
+36 1.118385806941496 1.658075145110082 0
+37 1.162276263405681 0.6710405135499813 0
+38 1.248615852873337 1.079531485311822 0
+39 1.559209616901855 0.5415673055003691 0
+40 1.478306597054007 0.8535007117539289 0
+41 0.9210953433941653 0.9653302893212266 0
+42 1.296548225291847 0.3150268220262836 0
+43 1.055002035226811 1.358510675893086 0
+44 1.704005774249187 0.2344032256041583 0
+45 0.6403651144647218 0.8991270322967013 0
+46 0.7807302289294435 0.9322286608089638 0
+47 0.864063562262777 1.07656622810637 0
+48 0.8070317811313885 1.187802166891514 0
+49 0.7236984477980553 1.043464599594108 0
+50 1.432182741763949 0.1050089406754279 0
+51 1.364365483527898 0.2100178813508558 0
+52 1.197698816861231 0.2100178813508558 0
+53 1.098849408430616 0.1050089406754279 0
+54 1.265516075097282 0.1050089406754278 0
+55 0.8177280765440409 0.7503018362314346 0
+56 0.869411709969103 0.8578160627763305 0
+57 0.7348318576552288 0.8316090412164392 0
+58 1.177596357123201 0.3240245957927452 0
+59 1.058644488954555 0.3330223695592067 0
+60 1.087610484537871 0.2205785356313179 0
+61 1.267619707955123 0.7318605796179638 0
+62 1.372963152504565 0.7926806456859463 0
+63 1.40174301566045 0.9288443029398934 0
+64 1.325179434266893 1.004187894125858 0
+65 1.219835989717452 0.9433678280578752 0
+66 1.191056126561566 0.8072041708039283 0
+67 1.296399571111008 0.8680242368719107 0
+68 1.532241943619239 0.645545107584889 0
+69 1.505274270336623 0.7495229096694089 0
+70 1.294587381237739 0.6278827775334439 0
+71 1.426898499069797 0.5847250415169065 0
+72 1.399930825787181 0.6887028436014264 0
+73 1.139442349713613 1.041464419981624 0
+74 1.030268846553889 1.003397354651425 0
+75 1.001488983398004 0.8672336973974781 0
+76 1.081882623401843 0.7691371054737297 0
+77 1.110662486557728 0.9053007627276766 0
+78 1.207033584034403 0.5523692830420821 0
+79 1.251790904663125 0.4336980525341829 0
+80 1.384102022495183 0.3905403165176455 0
+81 1.471655819698519 0.4660538110090073 0
+82 1.339344701866461 0.5092115470255447 0
+83 1.73779714915742 0.7228379592678562 0
+84 1.648503383029637 0.6322026323841127 0
+85 1.691571478423774 0.4996526642120855 0
+86 1.823933339945692 0.4577380229238018 0
+87 1.787039416783436 0.5922941012619014 0
+88 1.308379426102925 1.350703595740465 0
+89 1.278497639488131 1.215117540526144 0
+90 1.371755231498856 1.111544491736196 0
+91 1.494894610124376 1.14355749816057 0
+92 1.4064614465962 1.25147448186763 0
+93 1.013887168325833 0.451693600067106 0
+94 1.088081715865757 0.5613670568085436 0
+95 1.03019898997678 0.6616228789288338 0
+96 0.8981217165478794 0.6522052443076862 0
+97 0.9637989050473432 0.5564495572737495 0
+98 1.432367408277627 0.2881522898855752 0
+99 1.568186591263407 0.2612777577448668 0
+100 1.655740388466743 0.3367912522362286 0
+101 1.607475002684299 0.4391792788682989 0
+102 1.519921205480963 0.3636657843769371 0
+103 1.184077913657828 1.17252454883891 0
+104 1.119539974442319 1.265517612365998 0
+105 1.010366471282595 1.2274505470358 0
+106 0.9657309073383804 1.096390418178513 0
+107 1.074904410498104 1.134457483508712 0
+108 1.901335258083062 0.07813440853471942 0
+109 1.802670516166124 0.1562688170694388 0
+110 1.636003849499458 0.156268817069439 0
+111 1.568001924749729 0.07813440853471942 0
+112 1.734668591416396 0.07813440853471944 0
+113 0.8516673450756037 1.318862295748801 0
+114 0.9533346901512071 1.338686485820944 0
+115 1.03666802348454 1.48302405311835 0
+116 1.01833401174227 1.607537430343614 0
+117 0.9350006784089369 1.463199863046207 0
+118 1.710829475874804 0.8268157613523761 0
+119 1.594568036464405 0.8401582365531526 0
+120 1.621535709747021 0.7361804344686326 0
+121 1.52488239428597 0.9608573093642675 0
+122 1.571458191517933 1.068213906974606 0
+123 1.448318812892413 1.036200900550232 0
+124 0.908699126206992 1.207626356963657 0
+125 1.500184666513678 0.1831433492101474 0
+126 1.646765991694905 0.9507607885973723 0
+127 0.9498053499729417 0.7597194708525821 0
+128 1.132839036494479 0.4426958263006443 0
+129 1.149421761057113 1.40110366758032 0
+130 1.243841486887416 1.443696659267553 0
+131 1.134903597606542 1.530869109405537 0
+132 1.872198725728137 0.3553499962917315 0
+133 1.788102249988661 0.2948766109479449 0
+134 1.893223337417325 0.2174207916708467 0
+135 1.213959700272622 1.308110604053232 0
+136 1.739836864206217 0.3972646375800152 0
 $EndNodes
 $Elements
-108
-1 1 2 3 1 1 5
-2 1 2 3 1 5 6
-3 1 2 3 1 6 7
-4 1 2 3 1 7 8
-5 1 2 3 1 8 9
-6 1 2 3 1 9 2
-7 1 2 4 2 3 10
-8 1 2 4 2 10 11
-9 1 2 4 2 11 12
-10 1 2 4 2 12 13
-11 1 2 4 2 13 14
-12 1 2 4 2 14 4
-13 1 2 1 3 1 15
-14 1 2 1 3 15 16
-15 1 2 1 3 16 3
-16 1 2 2 4 2 17
-17 1 2 2 4 17 18
-18 1 2 2 4 18 19
-19 1 2 2 4 19 20
-20 1 2 2 4 20 21
-21 1 2 2 4 21 22
-22 1 2 2 4 22 23
-23 1 2 2 4 23 24
-24 1 2 2 4 24 4
-25 2 2 1 1 32 40 25
-26 2 2 1 1 25 34 32
-27 2 2 1 1 33 41 36
-28 2 2 1 1 38 52 25
-29 2 2 1 1 33 36 29
-30 2 2 1 1 26 47 35
-31 2 2 1 1 35 37 26
-32 2 2 1 1 25 52 34
-33 2 2 1 1 32 44 40
-34 2 2 1 1 15 32 29
-35 2 2 1 1 15 29 16
-36 2 2 1 1 36 41 28
-37 2 2 1 1 32 33 29
-38 2 2 1 1 50 52 42
-39 2 2 1 1 32 34 33
-40 2 2 1 1 42 52 31
-41 2 2 1 1 43 53 51
-42 2 2 1 1 27 41 33
-43 2 2 1 1 26 53 45
-44 2 2 1 1 18 31 17
-45 2 2 1 1 29 35 16
-46 2 2 1 1 29 36 35
-47 2 2 1 1 24 30 23
-48 2 2 1 1 30 53 43
-49 2 2 1 1 17 54 2
-50 2 2 1 1 4 55 24
-51 2 2 1 1 28 51 36
-52 2 2 1 1 47 48 35
-53 2 2 1 1 36 37 35
-54 2 2 1 1 37 53 26
-55 2 2 1 1 22 28 21
-56 2 2 1 1 20 27 19
-57 2 2 1 1 33 50 27
-58 2 2 1 1 15 44 32
-59 2 2 1 1 18 42 31
-60 2 2 1 1 30 43 23
-61 2 2 1 1 35 48 16
-62 2 2 1 1 31 54 17
-63 2 2 1 1 9 39 8
-64 2 2 1 1 8 38 7
-65 2 2 1 1 7 25 6
-66 2 2 1 1 22 43 28
-67 2 2 1 1 23 43 22
-68 2 2 1 1 39 54 31
-69 2 2 1 1 19 42 18
-70 2 2 1 1 24 55 30
-71 2 2 1 1 27 42 19
-72 2 2 1 1 13 46 14
-73 2 2 1 1 51 53 37
-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

data/periodic-torus-sector.geo

@@ -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

data/square-mixed.mesh

@@ -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

doc/CodeDocumentation.dox

@@ -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
  *

doc/makefile

@@ -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
 

examples/ex11p.cpp

@@ -72,6 +72,7 @@ int main(int argc, char *argv[])
    int seed = 75;
    bool slu_solver  = false;
    bool sp_solver = false;
+   bool pardiso_solver = false;
    bool visualization = 1;
 
    OptionsParser args(argc, argv);
@@ -95,6 +96,14 @@ int main(int argc, char *argv[])
 #ifdef MFEM_USE_STRUMPACK
    args.AddOption(&sp_solver, "-sp", "--strumpack", "-no-sp",
                   "--no-strumpack", "Use the STRUMPACK Solver.");
+#endif
+#ifdef MFEM_USE_MKL_CPARDISO
+   args.AddOption(&pardiso_solver,
+                  "-pardiso",
+                  "--pardiso",
+                  "-no-pardiso",
+                  "--no-pardiso",
+                  "Use the MKL Cluster Pardiso Solver.");
 #endif
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
@@ -236,7 +245,7 @@ int main(int argc, char *argv[])
    //    preconditioner for A to be used within the solver. Set the matrices
    //    which define the generalized eigenproblem A x = lambda M x.
    Solver * precond = NULL;
-   if (!slu_solver && !sp_solver)
+   if (!slu_solver && !sp_solver && !pardiso_solver)
    {
       HypreBoomerAMG * amg = new HypreBoomerAMG(*A);
       amg->SetPrintLevel(0);
@@ -268,10 +277,19 @@ int main(int argc, char *argv[])
          strumpack->SetFromCommandLine();
          precond = strumpack;
       }
+#endif
+#ifdef MFEM_USE_MKL_CPARDISO
+      if (pardiso_solver)
+      {
+         auto pardiso = new CPardisoSolver(A->GetComm());
+         pardiso->SetMatrixType(CPardisoSolver::MatType::REAL_STRUCTURE_SYMMETRIC);
+         pardiso->SetPrintLevel(1);
+         pardiso->SetOperator(*A);
+         precond = pardiso;
+      }
 #endif
    }
 
-
    HypreLOBPCG * lobpcg = new HypreLOBPCG(MPI_COMM_WORLD);
    lobpcg->SetNumModes(nev);
    lobpcg->SetRandomSeed(seed);

examples/ex1p_mumps.cpp

@@ -0,0 +1,234 @@
+//                       MFEM Example 1 - Parallel Version
+//
+// Compile with: make ex1p
+//
+// Sample runs:  mpirun -np 4 ex1p -m ../data/square-disc.mesh
+//
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+int main(int argc, char *argv[])
+{
+   // 1. Initialize MPI.
+   int num_procs, myid;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+
+   // 2. Parse command-line options.
+   const char *mesh_file = "../data/inline-quad.mesh";
+   int order = 1;
+   bool static_cond = false;
+   bool visualization = true;
+   int sr = 1;
+   int pr = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree) or -1 for"
+                  " isoparametric space.");
+   args.AddOption(&sr, "-sr", "--serial_ref",
+                  "Number of serial refinements");        
+   args.AddOption(&pr, "-pr", "--parallel_ref",
+                  "Number of parallel refinements");                               
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 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(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
+   //    this example we do 'ref_levels' of uniform refinement. We choose
+   //    'ref_levels' to be the largest number that gives a final mesh with no
+   //    more than 10,000 elements.
+   {
+      for (int l = 0; l < sr; l++)
+      {
+         mesh.UniformRefinement();
+      }
+   }
+
+   // 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(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
+   {
+      for (int l = 0; l < pr; l++)
+      {
+         pmesh.UniformRefinement();
+      }
+   }
+
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
+   //    use continuous Lagrange finite elements of the specified order. If
+   //    order < 1, we instead use an isoparametric/isogeometric space.
+   FiniteElementCollection *fec = new H1_FECollection(order, dim);
+   ParFiniteElementSpace fespace(&pmesh, fec);
+   HYPRE_Int size = fespace.GlobalTrueVSize();
+   if (myid == 0)
+   {
+      cout << "Number of finite element unknowns: " << size << endl;
+   }
+
+   // 8. Determine the list of true (i.e. parallel conforming) essential
+   //    boundary dofs. In this example, the boundary conditions are defined
+   //    by marking all the boundary attributes from the mesh as essential
+   //    (Dirichlet) and converting them to a list of true dofs.
+   Array<int> ess_tdof_list;
+   if (pmesh.bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(pmesh.bdr_attributes.Max());
+      ess_bdr = 1;
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   // 9. Set up the parallel linear form b(.) which corresponds to the
+   //    right-hand side of the FEM linear system, which in this case is
+   //    (1,phi_i) where phi_i are the basis functions in fespace.
+   ParLinearForm b(&fespace);
+   ConstantCoefficient one(1.0);
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
+
+   // 10. Define the solution vector x as a parallel finite element grid function
+   //     corresponding to fespace. Initialize x with initial guess of zero,
+   //     which satisfies the boundary conditions.
+   ParGridFunction x(&fespace);
+   x = 0.0;
+
+   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
+   //     corresponding to the Laplacian operator -Delta, by adding the Diffusion
+   //     domain integrator.
+   ParBilinearForm a(&fespace);
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));
+
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();
+
+   HypreParMatrix A;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+   // // 13. Solve the linear system A X = B.
+   // //     * With full assembly, use the BoomerAMG preconditioner from hypre.
+   // //     * With partial assembly, use Jacobi smoothing, for now.
+   StopWatch chrono;
+   chrono.Clear();
+   chrono.Start();
+   HypreBoomerAMG *prec = new HypreBoomerAMG;
+   prec->SetPrintLevel(0);
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(1e-13);
+   cg.SetMaxIter(2000);
+   cg.SetPrintLevel(0);
+   if (prec) { cg.SetPreconditioner(*prec); }
+   cg.SetOperator(A);
+   cg.Mult(B, X);
+   delete prec;
+
+   if (myid == 0)
+   {
+      cout << "PCG-AMG time: " << chrono.RealTime() << endl;
+   }
+
+   chrono.Clear();
+   chrono.Start();
+   {
+      MUMPSSolver MA;
+      MA.SetMatrixSymType(0);
+      MA.SetOperator(A);
+      Vector Y(X.Size());
+      MA.Mult(B,Y);
+      Y-=X;
+      cout << "Mumps Diff norm = " << Y.Norml2() << endl;
+   }
+   if (myid == 0)
+   {
+      cout << "mumps time: " << chrono.RealTime() << endl;
+   }
+
+   chrono.Clear();
+   chrono.Start();
+
+   {
+      CPardisoSolver pardiso(A.GetComm());
+      // pardiso.SetMatrixType(CPardisoSolver::MatType::REAL_STRUCTURE_SYMMETRIC);
+      pardiso.SetMatrixType(CPardisoSolver::MatType::REAL_UNSYMMETRIC);
+      pardiso.SetPrintLevel(0);
+      pardiso.SetOperator(A);
+      Vector Y(X.Size());
+      pardiso.Mult(B, Y);
+      Y-=X;
+      cout << "Pardiso Diff norm = " << Y.Norml2() << endl;
+   }
+
+   if (myid == 0)
+   {
+      cout << "pardiso time: " << chrono.RealTime() << endl;
+   }
+
+   {
+      SuperLURowLocMatrix SA(A);
+      SuperLUSolver superlu(MPI_COMM_WORLD);
+      superlu.SetPrintStatistics(false);
+      superlu.SetSymmetricPattern(false);
+      superlu.SetColumnPermutation(superlu::PARMETIS);
+      superlu.SetOperator(SA);
+      Vector Y(X.Size());
+      superlu.Mult(B, Y);
+      Y-=X;
+      cout << "Superlu Diff norm = " << Y.Norml2() << endl;
+   }
+
+   if (myid == 0)
+   {
+      cout << "superlu time: " << chrono.RealTime() << endl;
+   }
+
+   a.RecoverFEMSolution(X, b, x);
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock << "parallel " << num_procs << " " << myid << "\n";
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << pmesh << x << flush;
+   }
+
+   // 17. Free the used memory.
+   delete fec;
+   MPI_Finalize();
+
+   return 0;
+}

examples/ex22.cpp

@@ -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;

examples/ex22p.cpp

@@ -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;

examples/ex24.cpp

@@ -70,7 +70,7 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
    args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
+                  "Choose between 0: grad, 1: curl, 2: div");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",

examples/ex24p.cpp

@@ -76,7 +76,7 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
    args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
+                  "Choose between 0: grad, 1: curl, 2: div");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",

examples/ex25.cpp

@@ -82,24 +82,24 @@ public:
 };
 
 // Class for returning the PML coefficients of the bilinear form
-class PMLMatrixCoefficient : public MatrixCoefficient
+class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
    CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , DenseMatrix &);
+   void (*Function)(const Vector &, CartesianPML * , Vector &);
 public:
-   PMLMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
-                                          DenseMatrix &),
-                        CartesianPML * pml_)
-      : MatrixCoefficient(dim), pml(pml_), Function(F)
+   PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
+                                              Vector &),
+                            CartesianPML * pml_)
+      : VectorCoefficient(dim), pml(pml_), Function(F)
    {}
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+   virtual void Eval(Vector &K, ElementTransformation &T,
                      const IntegrationPoint &ip)
    {
       double x[3];
       Vector transip(x, 3);
       T.Transform(ip, transip);
-      K.SetSize(height, width);
+      K.SetSize(vdim);
       (*Function)(transip, pml, K);
    }
 };
@@ -116,13 +116,13 @@ void source(const Vector &x, Vector & f);
 
 // Functions for computing the necessary coefficients after PML stretching.
 // J is the Jacobian matrix of the stretching function
-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector &D);
 
-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector &D);
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector &D);
 
 Array2D<double> comp_domain_bdr;
 Array2D<double> domain_bdr;
@@ -365,19 +365,19 @@ int main(int argc, char *argv[])
    a.AddDomainIntegrator(new VectorFEMassIntegrator(restr_omeg),NULL);
 
    int cdim = (dim == 2) ? 1 : dim;
-   PMLMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
-   PMLMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
-   ScalarMatrixProductCoefficient c1_Re(muinv,pml_c1_Re);
-   ScalarMatrixProductCoefficient c1_Im(muinv,pml_c1_Im);
-   MatrixRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
+   PMLDiagMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
+   ScalarVectorProductCoefficient c1_Re(muinv,pml_c1_Re);
+   ScalarVectorProductCoefficient c1_Im(muinv,pml_c1_Im);
+   VectorRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
+   VectorRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);
 
-   PMLMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
-   PMLMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
-   ScalarMatrixProductCoefficient c2_Re(omeg,pml_c2_Re);
-   ScalarMatrixProductCoefficient c2_Im(omeg,pml_c2_Im);
-   MatrixRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
+   PMLDiagMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
+   ScalarVectorProductCoefficient c2_Re(omeg,pml_c2_Re);
+   ScalarVectorProductCoefficient c2_Im(omeg,pml_c2_Im);
+   VectorRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
+   VectorRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);
 
    // Integrators inside the PML region
    a.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_Re),
@@ -419,13 +419,13 @@ int main(int argc, char *argv[])
       prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_muinv));
       prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_absomeg));
 
-      PMLMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
-      ScalarMatrixProductCoefficient c1_abs(muinv,pml_c1_abs);
-      MatrixRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
+      ScalarVectorProductCoefficient c1_abs(muinv,pml_c1_abs);
+      VectorRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);
 
-      PMLMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
-      ScalarMatrixProductCoefficient c2_abs(absomeg,pml_c2_abs);
-      MatrixRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
+      ScalarVectorProductCoefficient c2_abs(absomeg,pml_c2_abs);
+      VectorRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);
 
       prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_abs));
       prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_c2_abs));
@@ -763,7 +763,7 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
    }
 }
 
-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector &D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det(1.0, 0.0);
@@ -774,14 +774,13 @@ void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
       det *= dxs[i];
    }
 
-   M = 0.0;
    for (int i = 0; i < dim; ++i)
    {
-      M(i, i) = (det / pow(dxs[i], 2)).real();
+      D(i) = (det / pow(dxs[i], 2)).real();
    }
 }
 
-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector &D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -792,14 +791,13 @@ void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
       det *= dxs[i];
    }
 
-   M = 0.0;
    for (int i = 0; i < dim; ++i)
    {
-      M(i, i) = (det / pow(dxs[i], 2)).imag();
+      D(i) = (det / pow(dxs[i], 2)).imag();
    }
 }
 
-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector &D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -810,14 +808,13 @@ void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
       det *= dxs[i];
    }
 
-   M = 0.0;
    for (int i = 0; i < dim; ++i)
    {
-      M(i, i) = abs(det / pow(dxs[i], 2));
+      D(i) = abs(det / pow(dxs[i], 2));
    }
 }
 
-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector &D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det(1.0, 0.0);
@@ -831,19 +828,18 @@ void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
    // in the 2D case the coefficient is scalar 1/det(J)
    if (dim == 2)
    {
-      M = (1.0 / det).real();
+      D = (1.0 / det).real();
    }
    else
    {
-      M = 0.0;
       for (int i = 0; i < dim; ++i)
       {
-         M(i, i) = (pow(dxs[i], 2) / det).real();
+         D(i) = (pow(dxs[i], 2) / det).real();
       }
    }
 }
 
-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector &D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -856,19 +852,18 @@ void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
 
    if (dim == 2)
    {
-      M = (1.0 / det).imag();
+      D = (1.0 / det).imag();
    }
    else
    {
-      M = 0.0;
       for (int i = 0; i < dim; ++i)
       {
-         M(i, i) = (pow(dxs[i], 2) / det).imag();
+         D(i) = (pow(dxs[i], 2) / det).imag();
       }
    }
 }
 
-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector &D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -881,14 +876,13 @@ void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
 
    if (dim == 2)
    {
-      M = abs(1.0 / det);
+      D = abs(1.0 / det);
    }
    else
    {
-      M = 0.0;
       for (int i = 0; i < dim; ++i)
       {
-         M(i, i) = abs(pow(dxs[i], 2) / det);
+         D(i) = abs(pow(dxs[i], 2) / det);
       }
    }
 }

examples/ex25p.cpp

@@ -82,24 +82,24 @@ public:
 };
 
 // Class for returning the PML coefficients of the bilinear form
-class PMLMatrixCoefficient : public MatrixCoefficient
+class PMLDiagMatrixCoefficient : public VectorCoefficient
 {
 private:
    CartesianPML * pml = nullptr;
-   void (*Function)(const Vector &, CartesianPML * , DenseMatrix &);
+   void (*Function)(const Vector &, CartesianPML * , Vector &);
 public:
-   PMLMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
-                                          DenseMatrix &),
-                        CartesianPML * pml_)
-      : MatrixCoefficient(dim), pml(pml_), Function(F)
+   PMLDiagMatrixCoefficient(int dim, void(*F)(const Vector &, CartesianPML *,
+                                              Vector &),
+                            CartesianPML * pml_)
+      : VectorCoefficient(dim), pml(pml_), Function(F)
    {}
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
+   virtual void Eval(Vector &K, ElementTransformation &T,
                      const IntegrationPoint &ip)
    {
       double x[3];
       Vector transip(x, 3);
       T.Transform(ip, transip);
-      K.SetSize(height, width);
+      K.SetSize(vdim);
       (*Function)(transip, pml, K);
    }
 };
@@ -116,13 +116,13 @@ void source(const Vector &x, Vector & f);
 
 // Functions for computing the necessary coefficients after PML stretching.
 // J is the Jacobian matrix of the stretching function
-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector & D);
 
-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M);
-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M);
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector & D);
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector & D);
 
 Array2D<double> comp_domain_bdr;
 Array2D<double> domain_bdr;
@@ -393,19 +393,19 @@ int main(int argc, char *argv[])
    a.AddDomainIntegrator(new VectorFEMassIntegrator(restr_omeg),NULL);
 
    int cdim = (dim == 2) ? 1 : dim;
-   PMLMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
-   PMLMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
-   ScalarMatrixProductCoefficient c1_Re(muinv,pml_c1_Re);
-   ScalarMatrixProductCoefficient c1_Im(muinv,pml_c1_Im);
-   MatrixRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c1_Re(cdim,detJ_inv_JT_J_Re, pml);
+   PMLDiagMatrixCoefficient pml_c1_Im(cdim,detJ_inv_JT_J_Im, pml);
+   ScalarVectorProductCoefficient c1_Re(muinv,pml_c1_Re);
+   ScalarVectorProductCoefficient c1_Im(muinv,pml_c1_Im);
+   VectorRestrictedCoefficient restr_c1_Re(c1_Re,attrPML);
+   VectorRestrictedCoefficient restr_c1_Im(c1_Im,attrPML);
 
-   PMLMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
-   PMLMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
-   ScalarMatrixProductCoefficient c2_Re(omeg,pml_c2_Re);
-   ScalarMatrixProductCoefficient c2_Im(omeg,pml_c2_Im);
-   MatrixRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
-   MatrixRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);
+   PMLDiagMatrixCoefficient pml_c2_Re(dim, detJ_JT_J_inv_Re,pml);
+   PMLDiagMatrixCoefficient pml_c2_Im(dim, detJ_JT_J_inv_Im,pml);
+   ScalarVectorProductCoefficient c2_Re(omeg,pml_c2_Re);
+   ScalarVectorProductCoefficient c2_Im(omeg,pml_c2_Im);
+   VectorRestrictedCoefficient restr_c2_Re(c2_Re,attrPML);
+   VectorRestrictedCoefficient restr_c2_Im(c2_Im,attrPML);
 
    // Integrators inside the PML region
    a.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_Re),
@@ -453,13 +453,13 @@ int main(int argc, char *argv[])
       prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_muinv));
       prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_absomeg));
 
-      PMLMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
-      ScalarMatrixProductCoefficient c1_abs(muinv,pml_c1_abs);
-      MatrixRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c1_abs(cdim,detJ_inv_JT_J_abs, pml);
+      ScalarVectorProductCoefficient c1_abs(muinv,pml_c1_abs);
+      VectorRestrictedCoefficient restr_c1_abs(c1_abs,attrPML);
 
-      PMLMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
-      ScalarMatrixProductCoefficient c2_abs(absomeg,pml_c2_abs);
-      MatrixRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);
+      PMLDiagMatrixCoefficient pml_c2_abs(dim, detJ_JT_J_inv_abs,pml);
+      ScalarVectorProductCoefficient c2_abs(absomeg,pml_c2_abs);
+      VectorRestrictedCoefficient restr_c2_abs(c2_abs,attrPML);
 
       prec.AddDomainIntegrator(new CurlCurlIntegrator(restr_c1_abs));
       prec.AddDomainIntegrator(new VectorFEMassIntegrator(restr_c2_abs));
@@ -819,7 +819,7 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
    }
 }
 
-void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, Vector & D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det(1.0, 0.0);
@@ -830,14 +830,13 @@ void detJ_JT_J_inv_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
       det *= dxs[i];
    }
 
-   M = 0.0;
    for (int i = 0; i < dim; ++i)
    {
-      M(i, i) = (det / pow(dxs[i], 2)).real();
+      D(i) = (det / pow(dxs[i], 2)).real();
    }
 }
 
-void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, Vector & D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -848,14 +847,13 @@ void detJ_JT_J_inv_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
       det *= dxs[i];
    }
 
-   M = 0.0;
    for (int i = 0; i < dim; ++i)
    {
-      M(i, i) = (det / pow(dxs[i], 2)).imag();
+      D(i) = (det / pow(dxs[i], 2)).imag();
    }
 }
 
-void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, Vector & D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -866,14 +864,13 @@ void detJ_JT_J_inv_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
       det *= dxs[i];
    }
 
-   M = 0.0;
    for (int i = 0; i < dim; ++i)
    {
-      M(i, i) = abs(det / pow(dxs[i], 2));
+      D(i) = abs(det / pow(dxs[i], 2));
    }
 }
 
-void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, Vector & D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det(1.0, 0.0);
@@ -887,19 +884,18 @@ void detJ_inv_JT_J_Re(const Vector &x, CartesianPML * pml, DenseMatrix &M)
    // in the 2D case the coefficient is scalar 1/det(J)
    if (dim == 2)
    {
-      M = (1.0 / det).real();
+      D = (1.0 / det).real();
    }
    else
    {
-      M = 0.0;
       for (int i = 0; i < dim; ++i)
       {
-         M(i, i) = (pow(dxs[i], 2) / det).real();
+         D(i) = (pow(dxs[i], 2) / det).real();
       }
    }
 }
 
-void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, Vector & D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -912,19 +908,18 @@ void detJ_inv_JT_J_Im(const Vector &x, CartesianPML * pml, DenseMatrix &M)
 
    if (dim == 2)
    {
-      M = (1.0 / det).imag();
+      D = (1.0 / det).imag();
    }
    else
    {
-      M = 0.0;
       for (int i = 0; i < dim; ++i)
       {
-         M(i, i) = (pow(dxs[i], 2) / det).imag();
+         D(i) = (pow(dxs[i], 2) / det).imag();
       }
    }
 }
 
-void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
+void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, Vector & D)
 {
    vector<complex<double>> dxs(dim);
    complex<double> det = 1.0;
@@ -937,14 +932,13 @@ void detJ_inv_JT_J_abs(const Vector &x, CartesianPML * pml, DenseMatrix &M)
 
    if (dim == 2)
    {
-      M = abs(1.0 / det);
+      D = abs(1.0 / det);
    }
    else
    {
-      M = 0.0;
       for (int i = 0; i < dim; ++i)
       {
-         M(i, i) = abs(pow(dxs[i], 2) / det);
+         D(i) = abs(pow(dxs[i], 2) / det);
       }
    }
 }

examples/ex2p.cpp

@@ -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);

examples/ex6.cpp

@@ -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

examples/ex6p.cpp

@@ -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

examples/makefile

@@ -119,6 +119,11 @@ ex11p-test-superlu: ex11p
 	@$(call mfem-test,$<, $(RUN_MPI), SuperLU_DIST example,--superlu)
 test-par-YES: ex11p-test-superlu
 endif
+ifeq ($(MFEM_USE_MKL_CPARDISO),YES)
+ex11p-test-superlu: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), MKL_CPARDISO example,--pardiso)
+test-par-YES: ex11p-test-pardiso
+endif
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

fem/CMakeLists.txt

@@ -31,6 +31,7 @@ set(SRCS
   bilininteg_vecmass.cpp
   coefficient.cpp
   complex_fem.cpp
+  convergence.cpp
   datacollection.cpp
   eltrans.cpp
   estimators.cpp
@@ -50,43 +51,10 @@ set(SRCS
   fespacehierarchy.cpp
   nonlininteg_vectorconvection.cpp
   quadinterpolator.cpp
-  quadinterpolator_det.cpp
-  quadinterpolator_eval_by_nodes.cpp
-  quadinterpolator_eval_by_vdim.cpp
-  quadinterpolator_grad_by_nodes.cpp
-  quadinterpolator_grad_by_vdim.cpp
-  quadinterpolator_grad_phys_by_nodes.cpp
-  quadinterpolator_grad_phys_by_vdim.cpp
   quadinterpolator_face.cpp
   restriction.cpp
   staticcond.cpp
   tmop.cpp
-  tmop_pa.cpp
-  tmop_pa_h2d.cpp
-  tmop_pa_h2d_c0.cpp
-  tmop_pa_h2m.cpp
-  tmop_pa_h2m_c0.cpp
-  tmop_pa_h2s.cpp
-  tmop_pa_h2s_c0.cpp
-  tmop_pa_h3d.cpp
-  tmop_pa_h3d_c0.cpp
-  tmop_pa_h3m.cpp
-  tmop_pa_h3m_c0.cpp
-  tmop_pa_h3s.cpp
-  tmop_pa_h3s_c0.cpp
-  tmop_pa_jp2.cpp
-  tmop_pa_jp3.cpp
-  tmop_pa_jt2_tc.cpp
-  tmop_pa_jt3_datc.cpp
-  tmop_pa_jt3_tc.cpp
-  tmop_pa_p2.cpp
-  tmop_pa_p2_c0.cpp
-  tmop_pa_p3.cpp
-  tmop_pa_p3_c0.cpp
-  tmop_pa_w2.cpp
-  tmop_pa_w2_c0.cpp
-  tmop_pa_w3.cpp
-  tmop_pa_w3_c0.cpp
   tmop_tools.cpp
   gslib.cpp
   transfer.cpp
@@ -98,6 +66,7 @@ set(HDRS
   bilininteg.hpp
   coefficient.hpp
   complex_fem.hpp
+  convergence.hpp
   datacollection.hpp
   eltrans.hpp
   estimators.hpp
@@ -116,10 +85,7 @@ set(HDRS
   nonlinearform_ext.hpp
   nonlininteg.hpp
   quadinterpolator.hpp
-  quadinterpolator_eval.hpp
   quadinterpolator_face.hpp
-  quadinterpolator_grad.hpp
-  quadinterpolator_grad_phys.hpp
   restriction.hpp
   fespacehierarchy.hpp
   staticcond.hpp
@@ -132,7 +98,6 @@ set(HDRS
   tfespace.hpp
   tintrules.hpp
   tmop.hpp
-  tmop_pa.hpp
   tmop_tools.hpp
   gslib.hpp
   transfer.hpp

fem/bilinearform.cpp

@@ -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());

fem/bilinearform_ext.cpp

@@ -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)
@@ -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()

fem/bilininteg.cpp

@@ -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.");
@@ -1522,6 +1525,7 @@ void CurlCurlIntegrator::AssembleElementMatrix
    double w;
 
 #ifdef MFEM_THREAD_SAFE
+   Vector D;
    DenseMatrix curlshape(nd,dimc), curlshape_dFt(nd,dimc), M;
 #else
    curlshape.SetSize(nd,dimc);
@@ -1529,6 +1533,7 @@ void CurlCurlIntegrator::AssembleElementMatrix
 #endif
    elmat.SetSize(nd);
    if (MQ) { M.SetSize(dimc); }
+   if (DQ) { D.SetSize(dimc); }
 
    const IntegrationRule *ir = IntRule;
    if (ir == NULL)
@@ -1572,6 +1577,12 @@ void CurlCurlIntegrator::AssembleElementMatrix
          Mult(curlshape_dFt, M, curlshape);
          AddMultABt(curlshape, curlshape_dFt, elmat);
       }
+      else if (DQ)
+      {
+         DQ->Eval(D, Trans, ip);
+         D *= w;
+         AddMultADAt(curlshape_dFt, D, elmat);
+      }
       else if (Q)
       {
          w *= Q->Eval(Trans, ip);

fem/bilininteg.hpp

@@ -20,6 +20,13 @@
 namespace mfem
 {
 
+// Local maximum size of dofs and quads in 1D
+constexpr int HCURL_MAX_D1D = 5;
+constexpr int HCURL_MAX_Q1D = 6;
+
+constexpr int HDIV_MAX_D1D = 5;
+constexpr int HDIV_MAX_Q1D = 6;
+
 /// Abstract base class BilinearFormIntegrator
 class BilinearFormIntegrator : public NonlinearFormIntegrator
 {
@@ -79,9 +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,
@@ -89,10 +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,
@@ -255,14 +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; } }
 };
@@ -1945,7 +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);
 
@@ -2020,7 +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);
 
@@ -2076,7 +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;
 
@@ -2293,12 +2309,14 @@ class CurlCurlIntegrator: public BilinearFormIntegrator
 private:
    Vector vec, pointflux;
 #ifndef MFEM_THREAD_SAFE
+   Vector D;
    DenseMatrix curlshape, curlshape_dFt, M;
    DenseMatrix vshape, projcurl;
 #endif
 
 protected:
    Coefficient *Q;
+   VectorCoefficient *DQ;
    MatrixCoefficient *MQ;
 
    // PA extension
@@ -2307,12 +2325,17 @@ protected:
    const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
    const GeometricFactors *geom;   ///< Not owned
    int dim, ne, nq, dofs1D, quad1D;
+   bool symmetric = true; ///< False if using a nonsymmetric matrix coefficient
 
 public:
-   CurlCurlIntegrator() { Q = NULL; MQ = NULL; }
+   CurlCurlIntegrator() { Q = NULL; DQ = NULL; MQ = NULL; }
    /// Construct a bilinear form integrator for Nedelec elements
-   CurlCurlIntegrator(Coefficient &q) : Q(&q) { MQ = NULL; }
-   CurlCurlIntegrator(MatrixCoefficient &m) : MQ(&m) { Q = NULL; }
+   CurlCurlIntegrator(Coefficient &q, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), Q(&q) { DQ = NULL; MQ = NULL; }
+   CurlCurlIntegrator(VectorCoefficient &dq, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), DQ(&dq) { Q = NULL; MQ = NULL; }
+   CurlCurlIntegrator(MatrixCoefficient &mq, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), MQ(&mq) { Q = NULL; DQ = NULL; }
 
    /* Given a particular Finite Element, compute the
       element curl-curl matrix elmat */
@@ -2390,8 +2413,11 @@ protected:
    Vector pa_data;
    const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
    const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const DofToQuad *mapsOtest;     ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsCtest;     ///< Not owned. DOF-to-quad map, closed.
    const GeometricFactors *geom;   ///< Not owned
-   int dim, ne, nq, dofs1D, quad1D, fetype;
+   int dim, ne, nq, dofs1D, dofs1Dtest, quad1D, trial_fetype, test_fetype;
+   bool symmetric = true; ///< False if using a nonsymmetric matrix coefficient
 
 public:
    VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
@@ -2412,6 +2438,8 @@ public:
 
    using BilinearFormIntegrator::AssemblePA;
    virtual void AssemblePA(const FiniteElementSpace &fes);
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
    virtual void AddMultPA(const Vector &x, Vector &y) const;
    virtual void AssembleDiagonalPA(Vector& diag);
 };
@@ -2641,10 +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);

fem/bilininteg_convection_ea.cpp

@@ -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.");

fem/bilininteg_convection_pa.cpp

@@ -13,10 +13,6 @@
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
 
-#include "restriction.hpp"
-#include "tmop_pa.hpp"
-#include "../linalg/kernels.hpp"
-
 using namespace std;
 
 namespace mfem
@@ -72,53 +68,47 @@ static void PAConvectionSetup3D(const int Q1D,
                                 const double alpha,
                                 Vector &op)
 {
-   const auto W = Reshape(w.Read(), Q1D,Q1D,Q1D);
-   const auto J = Reshape(j.Read(), Q1D,Q1D,Q1D,3,3,NE);
+   const int NQ = Q1D*Q1D*Q1D;
+   auto W = w.Read();
+   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
    const bool const_v = vel.Size() == 3;
-   const auto V = const_v ?
-                  Reshape(vel.Read(), 3,1,1,1,1) :
-                  Reshape(vel.Read(), 3,Q1D,Q1D,Q1D,NE);
-   auto y = Reshape(op.Write(), Q1D,Q1D,Q1D,3,NE);
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
+   auto V =
+      const_v ? Reshape(vel.Read(), 3,1,1) : Reshape(vel.Read(), 3,NQ,NE);
+   auto y = Reshape(op.Write(), NQ, 3, NE);
+   MFEM_FORALL(e, NE,
    {
-      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      for (int q = 0; q < NQ; ++q)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qz,z,Q1D)
-            {
-               const double J11 = J(qx,qy,qz,0,0,e);
-               const double J12 = J(qx,qy,qz,0,1,e);
-               const double J13 = J(qx,qy,qz,0,2,e);
-               const double J21 = J(qx,qy,qz,1,0,e);
-               const double J22 = J(qx,qy,qz,1,1,e);
-               const double J23 = J(qx,qy,qz,1,2,e);
-               const double J31 = J(qx,qy,qz,2,0,e);
-               const double J32 = J(qx,qy,qz,2,1,e);
-               const double J33 = J(qx,qy,qz,2,2,e);
-               const double w = alpha * W(qx,qy,qz);
-               const double v0 = const_v ? V(0,0,0,0,0) : V(0,qx,qy,qz,e);
-               const double v1 = const_v ? V(1,0,0,0,0) : V(1,qx,qy,qz,e);
-               const double v2 = const_v ? V(2,0,0,0,0) : V(2,qx,qy,qz,e);
-               const double wx = w * v0;
-               const double wy = w * v1;
-               const double wz = w * v2;
-               // 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);
-               // q . J^{-1} = q . adj(J)
-               y(qx,qy,qz,0,e) = wx * A11 + wy * A12 + wz * A13;
-               y(qx,qy,qz,1,e) = wx * A21 + wy * A22 + wz * A23;
-               y(qx,qy,qz,2,e) = wx * A31 + wy * A32 + wz * A33;
-            }
-         }
+         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 w = alpha * W[q];
+         const double v0 = const_v ? V(0,0,0) : V(0,q,e);
+         const double v1 = const_v ? V(1,0,0) : V(1,q,e);
+         const double v2 = const_v ? V(2,0,0) : V(2,q,e);
+         const double wx = w * v0;
+         const double wy = w * v1;
+         const double wz = w * v2;
+         // 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);
+         // q . J^{-1} = q . adj(J)
+         y(q,0,e) =  wx * A11 + wy * A12 + wz * A13;
+         y(q,1,e) =  wx * A21 + wy * A22 + wz * A23;
+         y(q,2,e) =  wx * A31 + wy * A32 + wz * A33;
       }
    });
 }
@@ -194,8 +184,8 @@ void PAConvectionApply2D(const int ne,
             Gu[dy][qx] = 0.0;
             for (int dx = 0; dx < D1D; ++dx)
             {
-               const double bx = B(qx,dx);
-               const double gx = G(qx,dx);
+               const double bx  = B(qx,dx);
+               const double gx  = G(qx,dx);
                const double x = u[dy][dx];
                Bu[dy][qx] += bx * x;
                Gu[dy][qx] += gx * x;
@@ -212,8 +202,8 @@ void PAConvectionApply2D(const int ne,
             BGu[qy][qx] = 0.0;
             for (int dy = 0; dy < D1D; ++dy)
             {
-               const double bx = B(qy,dy);
-               const double gx = G(qy,dy);
+               const double bx  = B(qy,dy);
+               const double gx  = G(qy,dy);
                GBu[qy][qx] += gx * Bu[dy][qx];
                BGu[qy][qx] += bx * Gu[dy][qx];
             }
@@ -242,7 +232,7 @@ void PAConvectionApply2D(const int ne,
             BDGu[dy][qx] = 0.0;
             for (int qy = 0; qy < Q1D; ++qy)
             {
-               const double w = Bt(dy,qy);
+               const double w  = Bt(dy,qy);
                BDGu[dy][qx] += w * DGu[qy][qx];
             }
          }
@@ -254,7 +244,7 @@ void PAConvectionApply2D(const int ne,
             double BBDGu = 0.0;
             for (int qx = 0; qx < Q1D; ++qx)
             {
-               const double w = Bt(dx,qx);
+               const double w  = Bt(dx,qx);
                BBDGu += w * BDGu[dy][qx];
             }
             y(dx,dy,e) += BBDGu;
@@ -320,7 +310,7 @@ void SmemPAConvectionApply2D(const int ne,
             {
                const double bx = B(qx,dx);
                const double gx = G(qx,dx);
-               const double x = u[tidz][dy][dx];
+               const double x  = u[tidz][dy][dx];
                Bu[tidz][dy][qx] += bx * x;
                Gu[tidz][dy][qx] += gx * x;
             }
@@ -337,8 +327,8 @@ void SmemPAConvectionApply2D(const int ne,
             BGu[tidz][qy][qx] = 0.0;
             for (int dy = 0; dy < D1D; ++dy)
             {
-               const double bx = B(qy,dy);
-               const double gx = G(qy,dy);
+               const double bx  = B(qy,dy);
+               const double gx  = G(qy,dy);
                GBu[tidz][qy][qx] += gx * Bu[tidz][dy][qx];
                BGu[tidz][qy][qx] += bx * Gu[tidz][dy][qx];
             }
@@ -369,7 +359,7 @@ void SmemPAConvectionApply2D(const int ne,
             BDGu[tidz][dy][qx] = 0.0;
             for (int qy = 0; qy < Q1D; ++qy)
             {
-               const double w = Bt(dy,qy);
+               const double w  = Bt(dy,qy);
                BDGu[tidz][dy][qx] += w * DGu[tidz][qy][qx];
             }
          }
@@ -382,7 +372,7 @@ void SmemPAConvectionApply2D(const int ne,
             double BBDGu = 0.0;
             for (int qx = 0; qx < Q1D; ++qx)
             {
-               const double w = Bt(dx,qx);
+               const double w  = Bt(dx,qx);
                BBDGu += w * BDGu[tidz][dy][qx];
             }
             y(dx,dy,e) += BBDGu;
@@ -446,8 +436,8 @@ void PAConvectionApply3D(const int ne,
                Gu[dz][dy][qx] = 0.0;
                for (int dx = 0; dx < D1D; ++dx)
                {
-                  const double bx = B(qx,dx);
-                  const double gx = G(qx,dx);
+                  const double bx  = B(qx,dx);
+                  const double gx  = G(qx,dx);
                   const double x = u[dz][dy][dx];
                   Bu[dz][dy][qx] += bx * x;
                   Gu[dz][dy][qx] += gx * x;
@@ -469,8 +459,8 @@ void PAConvectionApply3D(const int ne,
                BGu[dz][qy][qx] = 0.0;
                for (int dy = 0; dy < D1D; ++dy)
                {
-                  const double bx = B(qy,dy);
-                  const double gx = G(qy,dy);
+                  const double bx  = B(qy,dy);
+                  const double gx  = G(qy,dy);
                   BBu[dz][qy][qx] += bx * Bu[dz][dy][qx];
                   GBu[dz][qy][qx] += gx * Bu[dz][dy][qx];
                   BGu[dz][qy][qx] += bx * Gu[dz][dy][qx];
@@ -492,8 +482,8 @@ void PAConvectionApply3D(const int ne,
                BBGu[qz][qy][qx] = 0.0;
                for (int dz = 0; dz < D1D; ++dz)
                {
-                  const double bx = B(qz,dz);
-                  const double gx = G(qz,dz);
+                  const double bx  = B(qz,dz);
+                  const double gx  = G(qz,dz);
                   GBBu[qz][qy][qx] += gx * BBu[dz][qy][qx];
                   BGBu[qz][qy][qx] += bx * GBu[dz][qy][qx];
                   BBGu[qz][qy][qx] += bx * BGu[dz][qy][qx];
@@ -531,7 +521,7 @@ void PAConvectionApply3D(const int ne,
                BDGu[dz][qy][qx] = 0.0;
                for (int qz = 0; qz < Q1D; ++qz)
                {
-                  const double w = Bt(dz,qz);
+                  const double w  = Bt(dz,qz);
                   BDGu[dz][qy][qx] += w * DGu[qz][qy][qx];
                }
             }
@@ -547,7 +537,7 @@ void PAConvectionApply3D(const int ne,
                BBDGu[dz][dy][qx] = 0.0;
                for (int qy = 0; qy < Q1D; ++qy)
                {
-                  const double w = Bt(dy,qy);
+                  const double w  = Bt(dy,qy);
                   BBDGu[dz][dy][qx] += w * BDGu[dz][qy][qx];
                }
             }
@@ -562,7 +552,7 @@ void PAConvectionApply3D(const int ne,
                double BBBDGu = 0.0;
                for (int qx = 0; qx < Q1D; ++qx)
                {
-                  const double w = Bt(dx,qx);
+                  const double w  = Bt(dx,qx);
                   BBBDGu += w * BBDGu[dz][dy][qx];
                }
                y(dx,dy,dz,e) += BBBDGu;
@@ -635,8 +625,8 @@ void SmemPAConvectionApply3D(const int ne,
                double Gu_ = 0.0;
                for (int dx = 0; dx < D1D; ++dx)
                {
-                  const double bx = B(qx,dx);
-                  const double gx = G(qx,dx);
+                  const double bx  = B(qx,dx);
+                  const double gx  = G(qx,dx);
                   const double x = u[dz][dy][dx];
                   Bu_ += bx * x;
                   Gu_ += gx * x;
@@ -661,8 +651,8 @@ void SmemPAConvectionApply3D(const int ne,
                double BGu_ = 0.0;
                for (int dy = 0; dy < D1D; ++dy)
                {
-                  const double bx = B(qy,dy);
-                  const double gx = G(qy,dy);
+                  const double bx  = B(qy,dy);
+                  const double gx  = G(qy,dy);
                   BBu_ += bx * Bu[dz][dy][qx];
                   GBu_ += gx * Bu[dz][dy][qx];
                   BGu_ += bx * Gu[dz][dy][qx];
@@ -688,8 +678,8 @@ void SmemPAConvectionApply3D(const int ne,
                double BBGu_ = 0.0;
                for (int dz = 0; dz < D1D; ++dz)
                {
-                  const double bx = B(qz,dz);
-                  const double gx = G(qz,dz);
+                  const double bx  = B(qz,dz);
+                  const double gx  = G(qz,dz);
                   GBBu_ += gx * BBu[dz][qy][qx];
                   BGBu_ += bx * GBu[dz][qy][qx];
                   BBGu_ += bx * BGu[dz][qy][qx];
@@ -731,7 +721,7 @@ void SmemPAConvectionApply3D(const int ne,
                double BDGu_ = 0.0;
                for (int qz = 0; qz < Q1D; ++qz)
                {
-                  const double w = Bt(dz,qz);
+                  const double w  = Bt(dz,qz);
                   BDGu_ += w * DGu[qz][qy][qx];
                }
                BDGu[dz][qy][qx] = BDGu_;
@@ -749,7 +739,7 @@ void SmemPAConvectionApply3D(const int ne,
                double BBDGu_ = 0.0;
                for (int qy = 0; qy < Q1D; ++qy)
                {
-                  const double w = Bt(dy,qy);
+                  const double w  = Bt(dy,qy);
                   BBDGu_ += w * BDGu[dz][qy][qx];
                }
                BBDGu[dz][dy][qx] = BBDGu_;
@@ -766,7 +756,7 @@ void SmemPAConvectionApply3D(const int ne,
                double BBBDGu = 0.0;
                for (int qx = 0; qx < Q1D; ++qx)
                {
-                  const double w = Bt(dx,qx);
+                  const double w  = Bt(dx,qx);
                   BBBDGu += w * BBDGu[dz][dy][qx];
                }
                y(dx,dy,dz,e) = BBBDGu;
@@ -776,117 +766,6 @@ void SmemPAConvectionApply3D(const int ne,
    });
 }
 
-template<int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0, int T_MAX = 0>
-static void QEvalVGF2D(const int NE,
-                       const double *b_,
-                       const double *x_,
-                       double *y_,
-                       const int vdim = 1,
-                       const int d1d = 0,
-                       const int q1d = 0)
-{
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-   const auto b = Reshape(b_, Q1D, D1D);
-   const auto X = Reshape(x_, D1D, D1D, VDIM, NE);
-   auto C = Reshape(y_, VDIM, Q1D, Q1D, NE);
-
-   MFEM_FORALL_2D(e, NE, Q1D, Q1D, 1,
-   {
-      constexpr int NBZ = 1;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MAX;
-      constexpr int MD1 = T_D1D ? T_D1D : T_MAX;
-
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-      MFEM_SHARED double B[MQ1*MD1];
-      mfem::kernels::LoadB<MD1,MQ1>(D1D,Q1D,b,B);
-
-      MFEM_SHARED double DD[NBZ][MD1*MD1];
-      MFEM_SHARED double DQ[NBZ][MD1*MQ1];
-      MFEM_SHARED double QQ[NBZ][MQ1*MQ1];
-
-      for (int c = 0; c < VDIM; c++)
-      {
-         mfem::kernels::LoadX<MD1,NBZ>(e,D1D,c,X,DD);
-         mfem::kernels::EvalX<MD1,MQ1,NBZ>(D1D,Q1D,B,DD,DQ);
-         mfem::kernels::EvalY<MD1,MQ1,NBZ>(D1D,Q1D,B,DQ,QQ);
-
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qy,y,Q1D)
-            {
-               double G;
-               mfem::kernels::PullEval<MQ1,NBZ>(qx,qy,QQ,G);
-               C(c,qx,qy,e) = G;
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
-}
-
-template<int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0, int T_MAX = 0>
-static void QEvalVGF3D(const int NE,
-                       const double *b_,
-                       const double *x_,
-                       double *y_,
-                       const int vdim = 1,
-                       const int d1d = 0,
-                       const int q1d = 0)
-{
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-   const auto b = Reshape(b_, Q1D, D1D);
-   const auto X = Reshape(x_, D1D, D1D, D1D, VDIM, NE);
-   auto C = Reshape(y_, VDIM, Q1D, Q1D, Q1D, NE);
-
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : T_MAX;
-      constexpr int MD1 = T_D1D ? T_D1D : T_MAX;
-
-      MFEM_SHARED double B[MQ1*MD1];
-      mfem::kernels::LoadB<MD1,MQ1>(D1D,Q1D,b,B);
-
-      MFEM_SHARED double DDD[MD1*MD1*MD1];
-      MFEM_SHARED double DDQ[MD1*MD1*MQ1];
-      MFEM_SHARED double DQQ[MD1*MQ1*MQ1];
-      MFEM_SHARED double QQQ[MQ1*MQ1*MQ1];
-
-      for (int c = 0; c < VDIM; c++)
-      {
-         mfem::kernels::LoadX<MD1>(e,D1D,c,X,DDD);
-         mfem::kernels::EvalX<MD1,MQ1>(D1D,Q1D,B,DDD,DDQ);
-         mfem::kernels::EvalY<MD1,MQ1>(D1D,Q1D,B,DDQ,DQQ);
-         mfem::kernels::EvalZ<MD1,MQ1>(D1D,Q1D,B,DQQ,QQQ);
-
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qy,y,Q1D)
-            {
-               MFEM_FOREACH_THREAD(qz,z,Q1D)
-               {
-                  double G;
-                  mfem::kernels::PullEval<MQ1>(qx,qy,qz,QQQ,G);
-                  C(c,qx,qy,qz,e) = G;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
-}
-
 void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
    // Assumes tensor-product elements
@@ -899,90 +778,16 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    const int nq = ir->GetNPoints();
    dim = mesh->Dimension();
    ne = fes.GetNE();
-   const DofToQuad::Mode mode = DofToQuad::TENSOR;
-#ifdef MFEM_USE_UMPIRE
-   const MemoryType temp_type = Device::GetDeviceMemoryType() == MemoryType::DEVICE_UMPIRE
-      ? MemoryType::DEVICE_UMPIRE_2 : Device::GetDeviceMemoryType();
-#else
-   const MemoryType temp_type = Device::GetDeviceMemoryType();
-#endif
-
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS, mode, temp_type);
-   maps = &el.GetDofToQuad(*ir, mode);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
-   pa_data.SetSize(symmDims * nq * ne, temp_type);
+   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
    Vector vel;
-   if (VectorConstantCoefficient *cQ =
-          dynamic_cast<VectorConstantCoefficient*>(Q))
+   if (VectorConstantCoefficient *cQ = dynamic_cast<VectorConstantCoefficient*>(Q))
    {
       vel = cQ->GetVec();
    }
-   else if (VectorGridFunctionCoefficient *vgfQ =
-               dynamic_cast<VectorGridFunctionCoefficient*>(Q))
-   {
-      Vector xe;
-      vel.SetSize(dim * nq * ne, temp_type);
-
-      const GridFunction *gf = vgfQ->GetGridFunction();
-      const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
-      const FiniteElementSpace &gf_fes = *gf->FESpace();
-
-      const int vdim = gf_fes.GetVDim();
-      const Operator *R = gf_fes.GetElementRestriction(ordering);
-      const FiniteElement &el_gf = *gf_fes.GetFE(0);
-      const DofToQuad *maps_gf = &el_gf.GetDofToQuad(*ir, mode);
-      const int D1D = maps_gf->ndof;
-      const int Q1D = maps_gf->nqpt;
-
-      MFEM_VERIFY(R,"");
-      MFEM_VERIFY(vdim == dim, "");
-      MFEM_VERIFY(dim==2 || dim==3,"");
-
-      xe.SetSize(R->Height(), Device::GetMemoryType());
-      xe.UseDevice(true);
-      R->Mult(*gf, xe);
-
-      const auto B = maps_gf->B.Read();
-      const auto x = xe.Read();
-      auto y = vel.Write();
-
-      const int id = (D1D << 4 ) | Q1D;
-      if (dim == 2)
-      {
-         switch (id)
-         {
-            case 0x22: QEvalVGF2D<2,2,2>(ne,B,x,y); break;
-            case 0x33: QEvalVGF2D<2,3,3>(ne,B,x,y); break;
-            case 0x34: QEvalVGF2D<2,3,4>(ne,B,x,y); break;
-            default:
-            {
-               constexpr int MAX_DQ = 8;
-               MFEM_VERIFY(D1D <= MAX_DQ, "");
-               MFEM_VERIFY(Q1D <= MAX_DQ, "");
-               QEvalVGF2D<0,0,0,MAX_DQ>(ne,B,x,y,vdim,D1D,Q1D);
-            }
-         }
-      }
-      if (dim == 3)
-      {
-         switch (id)
-         {
-            case 0x23: QEvalVGF3D<3,2,3>(ne,B,x,y); break;
-            case 0x34: QEvalVGF3D<3,3,4>(ne,B,x,y); break;
-            case 0x35: QEvalVGF3D<3,3,5>(ne,B,x,y); break;
-            case 0x46: QEvalVGF3D<3,4,6>(ne,B,x,y); break;
-            case 0x48: QEvalVGF3D<3,4,8>(ne,B,x,y); break;
-            default:
-            {
-               constexpr int MAX_DQ = 6;
-               MFEM_VERIFY(D1D <= MAX_DQ, "");
-               MFEM_VERIFY(Q1D <= MAX_DQ, "");
-               QEvalVGF3D<0,0,0,MAX_DQ>(ne,B,x,y,vdim,D1D,Q1D);
-            }
-         }
-      }
-   }
    else if (VectorQuadratureFunctionCoefficient* cQ =
                dynamic_cast<VectorQuadratureFunctionCoefficient*>(Q))
    {
@@ -1036,12 +841,9 @@ static void PAConvectionApply(const int dim,
       switch ((D1D << 4 ) | Q1D)
       {
          case 0x22: return SmemPAConvectionApply2D<2,2,8>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x33: return SmemPAConvectionApply2D<3,3,4>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x34: return SmemPAConvectionApply2D<3,4,4>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x44: return SmemPAConvectionApply2D<4,4,4>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x46: return SmemPAConvectionApply2D<4,6,4>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x33: return SmemPAConvectionApply2D<3,3,3>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x44: return SmemPAConvectionApply2D<4,4,2>(NE,B,G,Bt,Gt,op,x,y);
          case 0x55: return SmemPAConvectionApply2D<5,5,2>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x58: return SmemPAConvectionApply2D<5,8,2>(NE,B,G,Bt,Gt,op,x,y);
          case 0x66: return SmemPAConvectionApply2D<6,6,1>(NE,B,G,Bt,Gt,op,x,y);
          case 0x77: return SmemPAConvectionApply2D<7,7,1>(NE,B,G,Bt,Gt,op,x,y);
          case 0x88: return SmemPAConvectionApply2D<8,8,1>(NE,B,G,Bt,Gt,op,x,y);
@@ -1054,12 +856,8 @@ static void PAConvectionApply(const int dim,
       switch ((D1D << 4 ) | Q1D)
       {
          case 0x23: return SmemPAConvectionApply3D<2,3>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x24: return SmemPAConvectionApply3D<2,4>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x26: return SmemPAConvectionApply3D<2,6>(NE,B,G,Bt,Gt,op,x,y);
          case 0x34: return SmemPAConvectionApply3D<3,4>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x35: return SmemPAConvectionApply3D<3,5>(NE,B,G,Bt,Gt,op,x,y);
          case 0x45: return SmemPAConvectionApply3D<4,5>(NE,B,G,Bt,Gt,op,x,y);
-         case 0x48: return SmemPAConvectionApply3D<4,8>(NE,B,G,Bt,Gt,op,x,y);
          case 0x56: return SmemPAConvectionApply3D<5,6>(NE,B,G,Bt,Gt,op,x,y);
          case 0x67: return SmemPAConvectionApply3D<6,7>(NE,B,G,Bt,Gt,op,x,y);
          case 0x78: return SmemPAConvectionApply3D<7,8>(NE,B,G,Bt,Gt,op,x,y);

fem/bilininteg_dgtrace_ea.cpp

@@ -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.");

fem/bilininteg_diffusion_ea.cpp

@@ -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.");

fem/bilininteg_diffusion_pa.cpp

@@ -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
+         }
       }
    });
 }
@@ -282,10 +286,9 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes)
    const int nq = ir->GetNPoints();
    dim = mesh->Dimension();
    ne = fes.GetNE();
-   const DofToQuad::Mode mode = DofToQuad::TENSOR;
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS, mode);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
    const int sdim = mesh->SpaceDimension();
-   maps = &el.GetDofToQuad(*ir, mode);
+   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
    pa_data.SetSize(symmDims * nq * ne, Device::GetDeviceMemoryType());
@@ -740,7 +743,6 @@ static void PADiffusionAssembleDiagonal(const int dim,
          case 0x23: return SmemPADiffusionDiagonal3D<2,3>(NE,B,G,D,Y);
          case 0x34: return SmemPADiffusionDiagonal3D<3,4>(NE,B,G,D,Y);
          case 0x45: return SmemPADiffusionDiagonal3D<4,5>(NE,B,G,D,Y);
-         case 0x46: return SmemPADiffusionDiagonal3D<4,6>(NE,B,G,D,Y);
          case 0x56: return SmemPADiffusionDiagonal3D<5,6>(NE,B,G,D,Y);
          case 0x67: return SmemPADiffusionDiagonal3D<6,7>(NE,B,G,D,Y);
          case 0x78: return SmemPADiffusionDiagonal3D<7,8>(NE,B,G,D,Y);
@@ -1678,7 +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)
    {
@@ -1701,7 +1703,6 @@ static void PADiffusionApply(const int dim,
       switch (ID)
       {
          case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,D,X,Y);
-         case 0x24: return SmemPADiffusionApply3D<2,4>(NE,B,G,D,X,Y);
          case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,D,X,Y);
          case 0x45: return SmemPADiffusionApply3D<4,5>(NE,B,G,D,X,Y);
          case 0x46: return SmemPADiffusionApply3D<4,6>(NE,B,G,D,X,Y);

fem/bilininteg_hdiv.cpp

@@ -23,11 +23,6 @@ using namespace std;
 namespace mfem
 {
 
-// Local maximum size of dofs and quads in 1D
-constexpr int HDIV_MAX_D1D = 5;
-constexpr int HDIV_MAX_Q1D = 6;
-
-
 // PA H(div) Mass Assemble 2D kernel
 void PAHdivSetup2D(const int Q1D,
                    const int NE,

fem/bilininteg_mass_ea.cpp

@@ -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.");

fem/bilininteg_mass_pa.cpp

@@ -25,7 +25,6 @@ namespace mfem
 
 void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
 {
-
    // Assuming the same element type
    fespace = &fes;
    Mesh *mesh = fes.GetMesh();
@@ -46,38 +45,22 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
    dim = mesh->Dimension();
    ne = fes.GetMesh()->GetNE();
    nq = ir->GetNPoints();
-   const DofToQuad::Mode mode = DofToQuad::TENSOR;
-   const int flags = GeometricFactors::JACOBIANS |
-                     GeometricFactors::COORDINATES;
-#ifdef MFEM_USE_UMPIRE
-   const MemoryType temp_type = Device::GetDeviceMemoryType() == MemoryType::DEVICE_UMPIRE
-      ? MemoryType::DEVICE_UMPIRE_2 : Device::GetDeviceMemoryType();
-#else
-   const MemoryType temp_type = Device::GetDeviceMemoryType();
-#endif
-   geom = mesh->GetGeometricFactors(*ir, flags, mode, temp_type);
-   maps = &el.GetDofToQuad(*ir, mode);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
+                                    GeometricFactors::JACOBIANS);
+   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
    pa_data.SetSize(ne*nq, Device::GetDeviceMemoryType());
-   Vector *coeff{nullptr};
-   bool own_coeff{true};
+   Vector coeff;
    if (Q == nullptr)
    {
-      coeff = new Vector;
-      coeff->SetSize(1);
-      (*coeff)(0) = 1.0;
+      coeff.SetSize(1);
+      coeff(0) = 1.0;
    }
    else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
    {
-      coeff = new Vector;
-      coeff->SetSize(1);
-      (*coeff)(0) = cQ->constant;
-   }
-   else if (QuadratureCoefficient* cQ = dynamic_cast<QuadratureCoefficient*>(Q))
-   {
-      coeff = cQ->Data();
-      own_coeff = false;
+      coeff.SetSize(1);
+      coeff(0) = cQ->constant;
    }
    else if (QuadratureFunctionCoefficient* cQ =
                dynamic_cast<QuadratureFunctionCoefficient*>(Q))
@@ -90,13 +73,12 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
                   "IntegrationRule used within integrator and in"
                   " QuadratureFunction appear to be different");
       qFun.Read();
-      coeff->MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
    }
    else
    {
-      coeff = new Vector;
-      coeff->SetSize(nq * ne);
-      auto C = Reshape(coeff->HostWrite(), nq, ne);
+      coeff.SetSize(nq * ne);
+      auto C = Reshape(coeff.HostWrite(), nq, ne);
       for (int e = 0; e < ne; ++e)
       {
          ElementTransformation& T = *fes.GetElementTransformation(e);
@@ -110,24 +92,27 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
    if (dim==2)
    {
       const int NE = ne;
-      const int NQ = nq;
-      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 int Q1D = quad1D;
+      const bool const_c = coeff.Size() == 1;
+      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;
+            }
          }
       });
    }
@@ -135,13 +120,12 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
    {
       const int NE = ne;
       const int Q1D = quad1D;
-      const bool const_c = coeff->Size() == 1;
-      const auto W = Reshape(ir->GetWeights().Read(),Q1D,Q1D,Q1D);
+      const bool const_c = coeff.Size() == 1;
+      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);
+      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,
       {
          MFEM_FOREACH_THREAD(qx,x,Q1D)
@@ -151,26 +135,24 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
                MFEM_FOREACH_THREAD(qz,z,Q1D)
                {
                   const double J11 = J(qx,qy,qz,0,0,e);
-                  const double J12 = J(qx,qy,qz,0,1,e);
-                  const double J13 = J(qx,qy,qz,0,2,e);
                   const double J21 = J(qx,qy,qz,1,0,e);
-                  const double J22 = J(qx,qy,qz,1,1,e);
-                  const double J23 = J(qx,qy,qz,1,2,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;
+                  v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * detJ;
                }
             }
          }
       });
    }
-
-   if (own_coeff) { delete coeff; }
 }
 
 void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
@@ -472,12 +454,8 @@ static void PAMassAssembleDiagonal(const int dim, const int D1D,
       switch ((D1D << 4 ) | Q1D)
       {
          case 0x23: return SmemPAMassAssembleDiagonal3D<2,3>(NE,B,D,Y);
-         case 0x24: return SmemPAMassAssembleDiagonal3D<2,4>(NE,B,D,Y);
-         case 0x26: return SmemPAMassAssembleDiagonal3D<2,6>(NE,B,D,Y);
          case 0x34: return SmemPAMassAssembleDiagonal3D<3,4>(NE,B,D,Y);
-         case 0x35: return SmemPAMassAssembleDiagonal3D<3,5>(NE,B,D,Y);
          case 0x45: return SmemPAMassAssembleDiagonal3D<4,5>(NE,B,D,Y);
-         case 0x48: return SmemPAMassAssembleDiagonal3D<4,8>(NE,B,D,Y);
          case 0x56: return SmemPAMassAssembleDiagonal3D<5,6>(NE,B,D,Y);
          case 0x67: return SmemPAMassAssembleDiagonal3D<6,7>(NE,B,D,Y);
          case 0x78: return SmemPAMassAssembleDiagonal3D<7,8>(NE,B,D,Y);
@@ -1211,13 +1189,10 @@ static void PAMassApply(const int dim,
          case 0x24: return SmemPAMassApply2D<2,4,16>(NE,B,Bt,D,X,Y);
          case 0x33: return SmemPAMassApply2D<3,3,16>(NE,B,Bt,D,X,Y);
          case 0x34: return SmemPAMassApply2D<3,4,16>(NE,B,Bt,D,X,Y);
-         case 0x35: return SmemPAMassApply2D<3,5,16>(NE,B,Bt,D,X,Y);
          case 0x36: return SmemPAMassApply2D<3,6,16>(NE,B,Bt,D,X,Y);
          case 0x44: return SmemPAMassApply2D<4,4,8>(NE,B,Bt,D,X,Y);
-         case 0x46: return SmemPAMassApply2D<4,6,8>(NE,B,Bt,D,X,Y);
          case 0x48: return SmemPAMassApply2D<4,8,4>(NE,B,Bt,D,X,Y);
          case 0x55: return SmemPAMassApply2D<5,5,8>(NE,B,Bt,D,X,Y);
-         case 0x57: return SmemPAMassApply2D<5,7,8>(NE,B,Bt,D,X,Y);
          case 0x58: return SmemPAMassApply2D<5,8,2>(NE,B,Bt,D,X,Y);
          case 0x66: return SmemPAMassApply2D<6,6,4>(NE,B,Bt,D,X,Y);
          case 0x77: return SmemPAMassApply2D<7,7,4>(NE,B,Bt,D,X,Y);
@@ -1225,7 +1200,6 @@ static void PAMassApply(const int dim,
          case 0x99: return SmemPAMassApply2D<9,9,2>(NE,B,Bt,D,X,Y);
          default:   return PAMassApply2D(NE,B,Bt,D,X,Y,D1D,Q1D);
       }
-      mfem::out << "Unknown 2D kernel 0x" << std::hex << id << std::endl;
    }
    else if (dim == 3)
    {
@@ -1234,9 +1208,7 @@ static void PAMassApply(const int dim,
          case 0x23: return SmemPAMassApply3D<2,3>(NE,B,Bt,D,X,Y);
          case 0x24: return SmemPAMassApply3D<2,4>(NE,B,Bt,D,X,Y);
          case 0x34: return SmemPAMassApply3D<3,4>(NE,B,Bt,D,X,Y);
-         case 0x35: return SmemPAMassApply3D<3,5>(NE,B,Bt,D,X,Y);
          case 0x36: return SmemPAMassApply3D<3,6>(NE,B,Bt,D,X,Y);
-         case 0x37: return SmemPAMassApply3D<3,7>(NE,B,Bt,D,X,Y);
          case 0x45: return SmemPAMassApply3D<4,5>(NE,B,Bt,D,X,Y);
          case 0x46: return SmemPAMassApply3D<4,6>(NE,B,Bt,D,X,Y);
          case 0x48: return SmemPAMassApply3D<4,8>(NE,B,Bt,D,X,Y);
@@ -1248,8 +1220,8 @@ static void PAMassApply(const int dim,
          case 0x9A: return SmemPAMassApply3D<9,10>(NE,B,Bt,D,X,Y);
          default:   return PAMassApply3D(NE,B,Bt,D,X,Y,D1D,Q1D);
       }
-      mfem::out << "Unknown 3D kernel 0x" << std::hex << id << std::endl;
    }
+   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
    MFEM_ABORT("Unknown kernel.");
 }
 

fem/bilininteg_transpose_ea.cpp

@@ -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;
+            }
+         }
+      });
+   }
 }
 
 }

fem/coefficient.cpp

@@ -12,7 +12,6 @@
 // Implementation of Coefficient class
 
 #include "fem.hpp"
-#include "../linalg/dtensor.hpp"
 
 #include <cmath>
 #include <limits>
@@ -22,13 +21,6 @@ namespace mfem
 
 using namespace std;
 
-double QuadratureCoefficient::Eval(ElementTransformation & T,
-                                   const IntegrationPoint & ip)
-{
-   auto coeff = mfem::Reshape(qData->HostRead(), nip, NE);
-   return coeff(ip.index, T.ElementNo);
-}
-
 double PWConstCoefficient::Eval(ElementTransformation & T,
                                 const IntegrationPoint & ip)
 {
@@ -327,6 +319,31 @@ void MatrixFunctionCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
    }
 }
 
+void MatrixFunctionCoefficient::EvalSymmetric(Vector &K,
+                                              ElementTransformation &T,
+                                              const IntegrationPoint &ip)
+{
+   MFEM_VERIFY(symmetric && height == width && height < 4 && SymmFunction,
+               "MatrixFunctionCoefficient is not symmetric");
+
+   double x[3];
+   Vector transip(x, 3);
+
+   T.Transform(ip, transip);
+
+   K.SetSize((width * (width + 1)) / 2); // 1x1: 1, 2x2: 3, 3x3: 6
+
+   if (SymmFunction)
+   {
+      (*SymmFunction)(transip, K);
+   }
+
+   if (Q)
+   {
+      K *= Q->Eval(T, ip, GetTime());
+   }
+}
+
 MatrixArrayCoefficient::MatrixArrayCoefficient (int dim)
    : MatrixCoefficient (dim)
 {

fem/coefficient.hpp

@@ -87,33 +87,6 @@ public:
    { return (constant); }
 };
 
-
-/// class for quadrature coefficient
-class QuadratureCoefficient : public Coefficient
-{
-
-private:
-   const int nip;
-   const int NE;
-public:
-   Vector *qData{nullptr};
-
-   //Set external data
-   QuadratureCoefficient(Vector *Data, int in_nip, int in_NE)
-      : qData(Data), nip(in_nip), NE(in_NE)
-   { }
-
-   virtual double Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
-
-   Vector *Data()
-   {
-      return qData;
-   }
-
-};
-
-/// class for piecewise constant coefficient
 /** @brief A piecewise constant coefficient with the constants keyed
     off the element attribute numbers. */
 class PWConstCoefficient : public Coefficient
@@ -722,13 +695,16 @@ class MatrixCoefficient
 protected:
    int height, width;
    double time;
+   bool symmetric;
 
 public:
    /// Construct a dim x dim matrix coefficient.
-   explicit MatrixCoefficient(int dim) { height = width = dim; time = 0.; }
+   explicit MatrixCoefficient(int dim, bool symm=false)
+   { height = width = dim; time = 0.; symmetric = symm; }
 
    /// Construct a h x w matrix coefficient.
-   MatrixCoefficient(int h, int w) : height(h), width(w), time(0.) { }
+   MatrixCoefficient(int h, int w, bool symm=false) :
+      height(h), width(w), time(0.), symmetric(symm) { }
 
    /// Set the time for time dependent coefficients
    void SetTime(double t) { time = t; }
@@ -745,6 +721,9 @@ public:
    /// For backward compatibility get the width of the matrix.
    int GetVDim() const { return width; }
 
+   void SetSymmetric(bool s) { symmetric = s; }
+   bool IsSymmetric() const { return symmetric; }
+
    /** @brief Evaluate the matrix coefficient in the element described by @a T
        at the point @a ip, storing the result in @a K. */
    /** @note When this method is called, the caller must make sure that the
@@ -753,6 +732,15 @@ public:
    virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                      const IntegrationPoint &ip) = 0;
 
+   /** @brief Evaluate the upper triangular entries of the matrix coefficient
+       in the symmetric case, similarly to Eval. Matrix entry (i,j) is stored
+       in K[j - i + os_i] for 0 <= i <= j < width, os_0 = 0,
+       os_{i+1} = os_i + width - i. That is, K = {M(0,0), ..., M(0,w-1),
+       M(1,1), ..., M(1,w-1), ..., M(w-1,w-1) with w = width. */
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip)
+   { mfem_error("MatrixCoefficient::EvalSymmetric"); }
+
    virtual ~MatrixCoefficient() { }
 };
 
@@ -780,6 +768,7 @@ class MatrixFunctionCoefficient : public MatrixCoefficient
 {
 private:
    void (*Function)(const Vector &, DenseMatrix &);
+   void (*SymmFunction)(const Vector &, Vector &);
    void (*TDFunction)(const Vector &, double, DenseMatrix &);
    Coefficient *Q;
    DenseMatrix mat;
@@ -817,10 +806,26 @@ public:
       mat.SetSize(0);
    }
 
+   /// Construct a symmetric square matrix coefficient from a C-function
+   /// defining a vector function used by EvalSymmetric
+   MatrixFunctionCoefficient(int dim, void (*F)(const Vector &, Vector &),
+                             Coefficient *q = NULL)
+      : MatrixCoefficient(dim, true), Q(q)
+   {
+      SymmFunction = F;
+      Function = NULL;
+      TDFunction = NULL;
+      mat.SetSize(0);
+   }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                      const IntegrationPoint &ip);
 
+   /// Evaluate the symmetric matrix coefficient at @a ip.
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip);
+
    virtual ~MatrixFunctionCoefficient() { }
 };
 

fem/complex_fem.cpp

@@ -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

fem/complex_fem.hpp

@@ -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.

fem/convergence.cpp

@@ -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

fem/convergence.hpp

@@ -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

fem/datacollection.cpp

@@ -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

fem/eltrans.hpp

@@ -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.

fem/fe.cpp

@@ -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), ds2hape_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;

fem/fe.hpp

@@ -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); }

fem/fem.hpp

@@ -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"

fem/fespace.cpp

@@ -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++)
    {
@@ -944,7 +947,7 @@ const Operator *FiniteElementSpace::GetFaceRestriction(
 }
 
 const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
-   const IntegrationRule &ir, const DofToQuad::Mode mode) const
+   const IntegrationRule &ir) const
 {
    for (int i = 0; i < E2Q_array.Size(); i++)
    {
@@ -952,13 +955,13 @@ const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
       if (qi->IntRule == &ir) { return qi; }
    }
 
-   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, ir, mode);
+   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, ir);
    E2Q_array.Append(qi);
    return qi;
 }
 
 const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
-   const QuadratureSpace &qs, const DofToQuad::Mode mode) const
+   const QuadratureSpace &qs) const
 {
    for (int i = 0; i < E2Q_array.Size(); i++)
    {
@@ -966,7 +969,7 @@ const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
       if (qi->qspace == &qs) { return qi; }
    }
 
-   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, qs, mode);
+   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, qs);
    E2Q_array.Append(qi);
    return qi;
 }
@@ -983,8 +986,8 @@ const FaceQuadratureInterpolator
          if (qi->IntRule == &ir) { return qi; }
       }
 
-      FaceQuadratureInterpolator *qi =
-         new FaceQuadratureInterpolator(*this, ir, type);
+      FaceQuadratureInterpolator *qi = new FaceQuadratureInterpolator(*this, ir,
+                                                                      type);
       E2IFQ_array.Append(qi);
       return qi;
    }

fem/fespace.hpp

@@ -367,7 +367,7 @@ public:
        All elements will use the same IntegrationRule, @a ir as the target
        quadrature points. */
    const QuadratureInterpolator *GetQuadratureInterpolator(
-      const IntegrationRule &ir, const DofToQuad::Mode = DofToQuad::FULL) const;
+      const IntegrationRule &ir) const;
 
    /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
        quadrature point values and/or derivatives (Q-vectors). */
@@ -378,7 +378,7 @@ public:
        The target quadrature points in the elements are described by the given
        QuadratureSpace, @a qs. */
    const QuadratureInterpolator *GetQuadratureInterpolator(
-      const QuadratureSpace &qs, const DofToQuad::Mode = DofToQuad::FULL) const;
+      const QuadratureSpace &qs) const;
 
    /** @brief Return a FaceQuadratureInterpolator that interpolates E-vectors to
        quadrature point values and/or derivatives (Q-vectors). */

fem/gridfunc.cpp

@@ -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;
 }
 

fem/gridfunc.hpp

@@ -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
    {

fem/gslib.cpp

@@ -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

fem/gslib.hpp

@@ -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

fem/libceed/ceed.cpp

@@ -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);

fem/libceed/ceed.hpp

@@ -18,6 +18,9 @@
 #include "../../general/device.hpp"
 #include "../../linalg/vector.hpp"
 #include <ceed.h>
+#include <ceed-hash.h>
+#include <tuple>
+#include <unordered_map>
 
 namespace mfem
 {
@@ -27,7 +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; };
@@ -56,7 +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;
 
@@ -64,10 +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);
@@ -77,8 +117,6 @@ struct CeedData
       if (coeff_type==CeedCoeff::Grid)
       {
          CeedGridCoeff* c = (CeedGridCoeff*)coeff;
-         CeedBasisDestroy(&c->basis);
-         CeedElemRestrictionDestroy(&c->restr);
          CeedVectorDestroy(&c->coeffVector);
          delete c;
       }

fem/linearform.cpp

@@ -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; }

fem/linearform.hpp

@@ -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

fem/lininteg.cpp

@@ -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(

fem/lininteg.hpp

@@ -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,

fem/nonlinearform.cpp

@@ -10,7 +10,6 @@
 // CONTRIBUTING.md for details.
 
 #include "fem.hpp"
-#include "../general/forall.hpp"
 
 namespace mfem
 {
@@ -28,7 +27,7 @@ void NonlinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
          // This is the default behavior.
          break;
       case AssemblyLevel::PARTIAL:
-         ext = new PANonlinearForm(this);
+         ext = new PANonlinearFormExtension(this);
          break;
       default:
          mfem_error("Unknown assembly level for this form.");
@@ -81,13 +80,6 @@ void NonlinearForm::SetEssentialVDofs(const Array<int> &ess_vdofs_list)
 
 double NonlinearForm::GetGridFunctionEnergy(const Vector &x) const
 {
-   if (ext)
-   {
-      MFEM_VERIFY(!fnfi.Size(), "Interior faces terms not yet implemented!");
-      MFEM_VERIFY(!bfnfi.Size(), "Boundary face terms not yet implemented!");
-      return ext->GetGridFunctionEnergy(x);
-   }
-
    Array<int> vdofs;
    Vector el_x;
    const FiniteElement *fe;
@@ -146,14 +138,6 @@ void NonlinearForm::Mult(const Vector &x, Vector &y) const
    if (ext)
    {
       ext->Mult(px, py);
-      if (Serial())
-      {
-         if (cP) { cP->MultTranspose(py, y); }
-         const int N = ess_tdof_list.Size();
-         const auto tdof = ess_tdof_list.Read();
-         auto Y = y.ReadWrite();
-         MFEM_FORALL(i, N, Y[tdof[i]] = 0.0; );
-      }
       return;
    }
 
@@ -280,16 +264,7 @@ Operator &NonlinearForm::GetGradient(const Vector &x) const
 {
    if (ext)
    {
-      Operator &grad = ext->GetGradient(Prolongate(x));
-      hGrad.Reset(&grad, false);
-      if (Serial())
-      {
-         Operator *Gop;
-         if (cP) { hGrad.Reset(new RAPOperator(*cP, grad, *cP)); }
-         hGrad.Ptr()->Operator::FormSystemOperator(ess_tdof_list, Gop);
-         hGrad.Reset(Gop);
-      }
-      return *hGrad.Ptr();
+      MFEM_ABORT("Not yet implemented!");
    }
 
    const int skip_zeros = 0;
@@ -451,31 +426,7 @@ void NonlinearForm::Update()
 
 void NonlinearForm::Setup()
 {
-   if (ext) { return ext->Setup(); }
-}
-
-void NonlinearForm::AssembleGradientDiagonal(Vector &diag) const
-{
-   if (ext)
-   {
-      MFEM_ASSERT(diag.Size() == fes->GetTrueVSize(),
-                  "Vector for holding diagonal has wrong size!");
-      const Operator *P = fes->GetProlongationMatrix();
-      if (!IsIdentityProlongation(P))
-      {
-         Vector local_diag(P->Height());
-         ext->AssembleGradientDiagonal(local_diag);
-         P->MultTranspose(local_diag, diag);
-      }
-      else
-      {
-         ext->AssembleGradientDiagonal(diag);
-      }
-   }
-   else
-   {
-      MFEM_ABORT("Not implemented. Can be obtained through GetGradient().");
-   }
+   if (ext) { return ext->AssemblePA(); }
 }
 
 NonlinearForm::~NonlinearForm()

fem/nonlinearform.hpp

@@ -45,7 +45,6 @@ protected:
    Array<Array<int>*>              bfnfi_marker; // not owned
 
    mutable SparseMatrix *Grad, *cGrad; // owned
-   mutable OperatorHandle hGrad;
 
    /// A list of all essential true dofs
    Array<int> ess_tdof_list;
@@ -166,15 +165,6 @@ public:
    /// Setup the NonlinearForm
    virtual void Setup();
 
-   /** @brief Assemble the diagonal of the gradient into diag
-
-       For adaptively refined meshes, this returns P^T d_e, where d_e is the
-       locally assembled diagonal on each element and P^T is the transpose of
-       the conforming prolongation. In general this is not the correct diagonal
-       for an AMR mesh. */
-   void AssembleGradientDiagonal(Vector &diag) const;
-
-
    /// Get the finite element space prolongation matrix
    virtual const Operator *GetProlongation() const { return P; }
    /// Get the finite element space restriction matrix

fem/nonlinearform_ext.cpp

@@ -13,101 +13,62 @@
 // PABilinearFormExtension and MFBilinearFormExtension.
 
 #include "nonlinearform.hpp"
-#include "../general/forall.hpp"
 
 namespace mfem
 {
 
-NonlinearFormExtension::NonlinearFormExtension(const NonlinearForm *nlf)
-   : Operator(nlf->FESpace()->GetTrueVSize()), nlf(nlf) { }
-
-PANonlinearForm::PANonlinearForm(NonlinearForm *nlf):
-   NonlinearFormExtension(nlf),
-   x_grad(NULL),
-   fes(*nlf->FESpace()),
-   dnfi(*nlf->GetDNFI()),
-   R(fes.GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC))
+NonlinearFormExtension::NonlinearFormExtension(NonlinearForm *form)
+   : Operator(form->FESpace()->GetTrueVSize()), n(form)
 {
-   MFEM_VERIFY(R, "Not yet implemented!");
-   xe.SetSize(R->Height(), Device::GetMemoryType());
-   ye.SetSize(R->Height(), Device::GetMemoryType());
-   ye.UseDevice(true);
+   // empty
 }
 
-double PANonlinearForm::GetGridFunctionEnergy(const Vector &x) const
+PANonlinearFormExtension::PANonlinearFormExtension(NonlinearForm *form):
+   NonlinearFormExtension(form), fes(*form->FESpace())
 {
-   double energy = 0.0;
-
-   R->Mult(x, xe);
-   for (int i = 0; i < dnfi.Size(); i++)
+   const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
+   elem_restrict_lex = fes.GetElementRestriction(ordering);
+   if (elem_restrict_lex)
    {
-      energy += dnfi[i]->GetGridFunctionEnergyPA(xe);
+      localX.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+      localY.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+      localY.UseDevice(true); // ensure 'localY = 0.0' is done on device
    }
-   return energy;
 }
 
-void PANonlinearForm::Setup()
+void PANonlinearFormExtension::AssemblePA()
 {
-   for (int i = 0; i < dnfi.Size(); ++i) { dnfi[i]->AssemblePA(fes); }
-}
-
-void PANonlinearForm::Mult(const Vector &x, Vector &y) const
-{
-   ye = 0.0;
-   R->Mult(x, xe);
-   for (int i = 0; i < dnfi.Size(); ++i) { dnfi[i]->AddMultPA(xe, ye); }
-   R->MultTranspose(ye, y);
-}
-
-void PANonlinearForm::AssembleGradientDiagonal(Vector &diag) const
-{
-   MFEM_VERIFY(x_grad, "GetGradient() has not been called");
-   R->Mult(*x_grad, xe);
-
-   ye = 0.0;
-   for (int i = 0; i < dnfi.Size(); ++i)
+   Array<NonlinearFormIntegrator*> &integrators = *n->GetDNFI();
+   const int Ni = integrators.Size();
+   for (int i = 0; i < Ni; ++i)
    {
-      dnfi[i]->AssembleGradientDiagonalPA(xe, ye);
+      integrators[i]->AssemblePA(*n->FESpace());
    }
-   R->MultTranspose(ye, diag);
 }
 
-Operator &PANonlinearForm::GetGradient(const Vector &x) const
+void PANonlinearFormExtension::Mult(const Vector &x, Vector &y) const
 {
-   // Store the last x that was used to compute the gradient.
-   x_grad = &x;
-
-   Grad.Reset(new PANonlinearForm::Gradient(x, *this));
-   return *Grad.Ptr();
+   Array<NonlinearFormIntegrator*> &integrators = *n->GetDNFI();
+   const int iSz = integrators.Size();
+   if (elem_restrict_lex)
+   {
+      elem_restrict_lex->Mult(x, localX);
+      localY = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultPA(localX, localY);
+      }
+      elem_restrict_lex->MultTranspose(localY, y);
+   }
+   else
+   {
+      y.UseDevice(true); // typically this is a large vector, so store on device
+      y = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultPA(x, y);
+      }
+   }
 }
 
-PANonlinearForm::Gradient::Gradient(const Vector &x, const PANonlinearForm &e):
-   Operator(e.fes.GetVSize()), R(e.R), dnfi(e.dnfi)
-{
-   ge.UseDevice(true);
-   ge.SetSize(R->Height(), Device::GetMemoryType());
-   R->Mult(x, ge);
-
-   xe.UseDevice(true);
-   xe.SetSize(R->Height(), Device::GetMemoryType());
-
-   ye.UseDevice(true);
-   ye.SetSize(R->Height(), Device::GetMemoryType());
-
-   ze.UseDevice(true);
-   ze.SetSize(R->Height(), Device::GetMemoryType());
-
-   // Do we still need to do this?
-   for (int i = 0; i < dnfi.Size(); ++i) { dnfi[i]->AssemblePA(e.fes); }
 }
-
-void PANonlinearForm::Gradient::Mult(const Vector &x, Vector &y) const
-{
-   ze = x;
-   ye = 0.0;
-   R->Mult(ze, xe);
-   for (int i = 0; i < dnfi.Size(); ++i) { dnfi[i]->AddMultGradPA(ge, xe, ye); }
-   R->MultTranspose(ye, y);
-}
-
-} // namespace mfem

fem/nonlinearform_ext.hpp

@@ -17,60 +17,28 @@
 
 namespace mfem
 {
-
 class NonlinearForm;
-class NonlinearFormIntegrator;
 
-/** @brief Class extending the NonlinearForm class to support the different
-    AssemblyLevel%s. */
 class NonlinearFormExtension : public Operator
 {
 protected:
-   const NonlinearForm *nlf;
+   NonlinearForm *n; ///< Not owned
 public:
-   NonlinearFormExtension(const NonlinearForm*);
-   virtual void Setup() = 0;
-   virtual Operator &GetGradient(const Vector&) const = 0;
-   virtual double GetGridFunctionEnergy(const Vector &x) const = 0;
-   virtual void AssembleGradientDiagonal(Vector &diag) const
-   {
-      MFEM_ABORT("Not implemented for this assembly level!");
-   }
+   NonlinearFormExtension(NonlinearForm *form);
+   virtual void AssemblePA() = 0;
 };
 
-class PANonlinearForm;
-
-
 /// Data and methods for partially-assembled nonlinear forms
-class PANonlinearForm : public NonlinearFormExtension
+class PANonlinearFormExtension : public NonlinearFormExtension
 {
-private:
-   class Gradient : public Operator
-   {
-   protected:
-      const Operator *R;
-      mutable Vector ge, xe, ye, ze;
-      const Array<NonlinearFormIntegrator*> &dnfi;
-   public:
-      Gradient(const Vector &x, const PANonlinearForm &ext);
-      virtual void Mult(const Vector &x, Vector &y) const;
-   };
-
 protected:
-   mutable Vector xe, ye;
-   mutable const Vector *x_grad;
-   mutable OperatorHandle Grad;
-   const FiniteElementSpace &fes;
-   const Array<NonlinearFormIntegrator*> &dnfi;
-   const Operator *R;
-
+   const FiniteElementSpace &fes; // Not owned
+   mutable Vector localX, localY;
+   const Operator *elem_restrict_lex; // Not owned
 public:
-   PANonlinearForm(NonlinearForm *nlf);
-   void Setup();
+   PANonlinearFormExtension(NonlinearForm*);
+   void AssemblePA();
    void Mult(const Vector &x, Vector &y) const;
-   Operator &GetGradient(const Vector &x) const;
-   double GetGridFunctionEnergy(const Vector &x) const;
-   void AssembleGradientDiagonal(Vector &diag) const;
 };
 }
 #endif // NONLINEARFORM_EXT_HPP

fem/nonlininteg.cpp

@@ -15,13 +15,6 @@
 namespace mfem
 {
 
-double NonlinearFormIntegrator::GetGridFunctionEnergyPA(const Vector &x) const
-{
-   mfem_error ("NonlinearFormIntegrator::GetGridFunctionEnergyPA(...)\n"
-               "   is not implemented for this class.");
-   return 0.0;
-}
-
 void NonlinearFormIntegrator::AssemblePA(const FiniteElementSpace&)
 {
    mfem_error ("NonlinearFormIntegrator::AssemblePA(...)\n"
@@ -41,20 +34,6 @@ void NonlinearFormIntegrator::AddMultPA(const Vector &, Vector &) const
                "   is not implemented for this class.");
 }
 
-void NonlinearFormIntegrator::AddMultGradPA(const Vector&,
-                                            const Vector&, Vector&) const
-{
-   mfem_error ("NonlinearFormIntegrator::AddMultGradPA(...)\n"
-               "   is not implemented for this class.");
-}
-
-void NonlinearFormIntegrator::AssembleGradientDiagonalPA(const mfem::Vector &x,
-                                                         mfem::Vector &diag) const
-{
-   mfem_error ("NonlinearFormIntegrator::AssembleDiagonalPA(...)\n"
-               "   is not implemented for this class.");
-}
-
 void NonlinearFormIntegrator::AssembleElementVector(
    const FiniteElement &el, ElementTransformation &Tr,
    const Vector &elfun, Vector &elvect)

fem/nonlininteg.hpp

@@ -68,9 +68,6 @@ public:
                                    ElementTransformation &Tr,
                                    const Vector &elfun);
 
-   /// Compute the local energy with partial assembly.
-   virtual double GetGridFunctionEnergyPA(const Vector &x) const;
-
    /// Method defining partial assembly.
    /** The result of the partial assembly is stored internally so that it can be
        used later in the methods AddMultPA(). */
@@ -91,12 +88,6 @@ public:
        called. */
    virtual void AddMultPA(const Vector &x, Vector &y) const;
 
-   /// Method for partially assembled gradient action.
-   virtual void AddMultGradPA(const Vector &g,
-                              const Vector &x, Vector &y) const;
-
-   virtual void AssembleGradientDiagonalPA(const Vector &x, Vector &diag) const;
-
    virtual ~NonlinearFormIntegrator() { }
 };
 

fem/pfespace.cpp

@@ -3147,7 +3147,7 @@ static void SetSubVector(const int N,
                          const Array<int> &indices,
                          const Vector &in, Vector &out)
 {
-   auto y = out.ReadWrite();
+   auto y = out.Write();
    const auto x = in.Read();
    const auto I = indices.Read();
    MFEM_FORALL(i, N, y[I[i]] = x[i];);
@@ -3234,7 +3234,7 @@ static void AddSubVector(const int num_unique_dst_indices,
                          const Vector &src,
                          Vector &dst)
 {
-   auto y = dst.ReadWrite();
+   auto y = dst.Write();
    const auto x = src.Read();
    const auto DST_I = unique_dst_indices.Read();
    const auto SRC_O = unique_to_src_offsets.Read();

fem/pgridfunc.cpp

@@ -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());
@@ -711,9 +872,9 @@ void ParGridFunction::SaveAsOne(std::ostream &out)
    int *nfdofs = new int[NRanks];
    int *nrdofs = new int[NRanks];
 
-   HostReadWrite();
-   values[0] = data;
+   double * h_data = const_cast<double *>(this->HostRead());
 
+   values[0] = h_data;
    nv[0]     = pfes -> GetVSize();
    nvdofs[0] = pfes -> GetNVDofs();
    nedofs[0] = pfes -> GetNEDofs();
@@ -814,7 +975,7 @@ void ParGridFunction::SaveAsOne(std::ostream &out)
       MPI_Send(&nvdofs[0], 1, MPI_INT, 0, 456, MyComm);
       MPI_Send(&nedofs[0], 1, MPI_INT, 0, 457, MyComm);
       MPI_Send(&nfdofs[0], 1, MPI_INT, 0, 458, MyComm);
-      MPI_Send(data, nv[0], MPI_DOUBLE, 0, 460, MyComm);
+      MPI_Send(h_data, nv[0], MPI_DOUBLE, 0, 460, MyComm);
    }
 
    delete [] values;
@@ -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

fem/pgridfunc.hpp

@@ -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
    {

fem/plinearform.cpp

@@ -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();

fem/plinearform.hpp

@@ -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);

fem/pnonlinearform.cpp

@@ -14,7 +14,6 @@
 #ifdef MFEM_USE_MPI
 
 #include "fem.hpp"
-#include "../general/forall.hpp"
 
 namespace mfem
 {
@@ -50,7 +49,6 @@ void ParNonlinearForm::Mult(const Vector &x, Vector &y) const
 
    if (fnfi.Size())
    {
-      MFEM_VERIFY(!NonlinearForm::ext,"");
       // Terms over shared interior faces in parallel.
       ParFiniteElementSpace *pfes = ParFESpace();
       ParMesh *pmesh = pfes->GetParMesh();
@@ -88,16 +86,15 @@ void ParNonlinearForm::Mult(const Vector &x, Vector &y) const
 
    P->MultTranspose(aux2, y);
 
-   const int N = ess_tdof_list.Size();
-   const auto idx = ess_tdof_list.Read();
-   auto Y = y.ReadWrite();
-   MFEM_FORALL(i, N, Y[idx[i]] = 0.0; );
+   y.HostReadWrite();
+   for (int i = 0; i < ess_tdof_list.Size(); i++)
+   {
+      y(ess_tdof_list[i]) = 0.0;
+   }
 }
 
 const SparseMatrix &ParNonlinearForm::GetLocalGradient(const Vector &x) const
 {
-   if (NonlinearForm::ext) { MFEM_ABORT("Not yet implemented!"); }
-
    NonlinearForm::GetGradient(x); // (re)assemble Grad, no b.c.
 
    return *Grad;
@@ -107,20 +104,16 @@ Operator &ParNonlinearForm::GetGradient(const Vector &x) const
 {
    ParFiniteElementSpace *pfes = ParFESpace();
 
-   Operator &grad = NonlinearForm::GetGradient(x); // (re)assemble Grad, no b.c.
-
    pGrad.Clear();
 
+   NonlinearForm::GetGradient(x); // (re)assemble Grad, no b.c.
+
    OperatorHandle dA(pGrad.Type()), Ph(pGrad.Type());
 
    if (fnfi.Size() == 0)
    {
-      if (NonlinearForm::ext) { dA.Reset(&grad, false); }
-      else
-      {
-         dA.MakeSquareBlockDiag(pfes->GetComm(), pfes->GlobalVSize(),
-                                pfes->GetDofOffsets(), Grad);
-      }
+      dA.MakeSquareBlockDiag(pfes->GetComm(), pfes->GlobalVSize(),
+                             pfes->GetDofOffsets(), Grad);
    }
    else
    {

fem/quadinterpolator.hpp

@@ -41,11 +41,10 @@ protected:
    const FiniteElementSpace *fespace;  ///< Not owned
    const QuadratureSpace *qspace;      ///< Not owned
    const IntegrationRule *IntRule;     ///< Not owned
-
    mutable QVectorLayout q_layout;     ///< Output Q-vector layout
-   mutable bool use_tensor_products;   ///< Tensor product evaluation mmode
 
-public:
+   mutable bool use_tensor_products;
+
    static const int MAX_NQ2D = 100;
    static const int MAX_ND2D = 100;
    static const int MAX_VDIM2D = 3;
@@ -54,6 +53,7 @@ public:
    static const int MAX_ND3D = 1000;
    static const int MAX_VDIM3D = 3;
 
+public:
    enum EvalFlags
    {
       VALUES       = 1 << 0,  ///< Evaluate the values at quadrature points
@@ -61,28 +61,21 @@ public:
       /** @brief Assuming the derivative at quadrature points form a matrix,
           this flag can be used to compute and store their determinants. This
           flag can only be used in Mult(). */
-      DETERMINANTS = 1 << 2,
-      PHYSICAL_DERIVATIVES = 1 << 3 ///< Evaluate the physical derivatives
+      DETERMINANTS = 1 << 2
    };
 
    QuadratureInterpolator(const FiniteElementSpace &fes,
-                          const IntegrationRule &ir,
-                          const bool use_tensor_products = false);
+                          const IntegrationRule &ir);
 
    QuadratureInterpolator(const FiniteElementSpace &fes,
-                          const QuadratureSpace &qs,
-                          const bool use_tensor_products = false);
+                          const QuadratureSpace &qs);
 
    /** @brief Disable the use of tensor product evaluations, for tensor-product
        elements, e.g. quads and hexes. */
-   void DisableTensorProducts() const { use_tensor_products = false; }
-
-   /** @brief Enable the use of tensor product evaluations, for tensor-product
-       elements, e.g. quads and hexes. */
-   void EnableTensorProducts() const { use_tensor_products = true; }
-
-   /** @brief Query the current evaluation mode. */
-   bool UseTensorProducts() const { return use_tensor_products; }
+   /** Currently, tensor product evaluations are not implemented and this method
+       has no effect. */
+   void DisableTensorProducts(bool disable = true) const
+   { use_tensor_products = !disable; }
 
    /** @brief Query the current output Q-vector layout. The default value is
        QVectorLayout::byNODES. */
@@ -90,7 +83,8 @@ public:
 
    /** @brief Set the desired output Q-vector layout. The default value is
        QVectorLayout::byNODES. */
-   void SetOutputLayout(QVectorLayout layout) const { q_layout = layout; }
+   void SetOutputLayout(QVectorLayout out_layout) const
+   { q_layout = out_layout; }
 
    /// Interpolate the E-vector @a e_vec to quadrature points.
    /** The @a eval_flags are a bitwise mask of constants from the EvalFlags
@@ -105,36 +99,26 @@ public:
              Vector &q_val, Vector &q_der, Vector &q_det) const;
 
    /// Interpolate the values of the E-vector @a e_vec at quadrature points.
-   template <QVectorLayout>
-   void Values(const Vector &e_vec, Vector &q_val) const;
    void Values(const Vector &e_vec, Vector &q_val) const;
 
    /** @brief Interpolate the derivatives of the E-vector @a e_vec at quadrature
        points. */
-   template <QVectorLayout>
-   void Derivatives(const Vector &e_vec, Vector &q_der) const;
    void Derivatives(const Vector &e_vec, Vector &q_der) const;
 
    /** @brief Interpolate the derivatives in physical space of the E-vector
        @a e_vec at quadrature points. */
-   template <QVectorLayout>
    void PhysDerivatives(const Vector &e_vec, Vector &q_der) const;
-   void PhysDerivatives(const Vector &e_vec, Vector &q_der) const;
-
-   /// Compute the determinant of the E-vector @a e_vec at quadrature points.
-   void Determinants(const Vector &e_vec, Vector &q_det) const;
 
    /// Perform the transpose operation of Mult(). (TODO)
    void MultTranspose(unsigned eval_flags, const Vector &q_val,
                       const Vector &q_der, Vector &e_vec) const;
 
    // Compute kernels follow (cannot be private or protected with nvcc)
+
    /// Template compute kernel for 2D.
    template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
-   static void Mult2D(const int NE,
+   static void Eval2D(const int NE,
                       const int vdim,
-                      const QVectorLayout q_layout,
-                      const GeometricFactors *geom,
                       const DofToQuad &maps,
                       const Vector &e_vec,
                       Vector &q_val,
@@ -144,10 +128,8 @@ public:
 
    /// Template compute kernel for 3D.
    template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
-   static void Mult3D(const int NE,
+   static void Eval3D(const int NE,
                       const int vdim,
-                      const QVectorLayout q_layout,
-                      const GeometricFactors *geom,
                       const DofToQuad &maps,
                       const Vector &e_vec,
                       Vector &q_val,

fem/quadinterpolator_det.cpp

@@ -1,208 +0,0 @@
-// 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 "tmop_pa.hpp"
-#include "quadinterpolator.hpp"
-#include "../general/forall.hpp"
-#include "../linalg/dtensor.hpp"
-#include "../fem/kernels.hpp"
-#include "../linalg/kernels.hpp"
-
-using namespace mfem;
-
-namespace mfem
-{
-
-template<int T_D1D = 0, int T_Q1D = 0, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Det2D(const int NE,
-                  const double *b,
-                  const double *g,
-                  const double *x,
-                  double *y,
-                  const int vdim = 1,
-                  const int d1d = 0,
-                  const int q1d = 0)
-{
-   constexpr int DIM = 2;
-   constexpr int NBZ = 1;
-
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-
-   const auto B = Reshape(b, Q1D, D1D);
-   const auto G = Reshape(g, Q1D, D1D);
-   const auto X = Reshape(x,  D1D, D1D, DIM, NE);
-   auto Y = Reshape(y, Q1D, Q1D, NE);
-
-   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
-   {
-      constexpr int NBZ = 1;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-
-      MFEM_SHARED double BG[2][MQ1*MD1];
-      MFEM_SHARED double XY[2][NBZ][MD1*MD1];
-      MFEM_SHARED double DQ[4][NBZ][MD1*MQ1];
-      MFEM_SHARED double QQ[4][NBZ][MQ1*MQ1];
-
-      kernels::LoadX<MD1,NBZ>(e,D1D,X,XY);
-      kernels::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
-
-      kernels::GradX<MD1,MQ1,NBZ>(D1D,Q1D,BG,XY,DQ);
-      kernels::GradY<MD1,MQ1,NBZ>(D1D,Q1D,BG,DQ,QQ);
-
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            double J[4];
-            kernels::PullGrad<MQ1,NBZ>(qx,qy,QQ,J);
-            Y(qx,qy,e) = kernels::Det<2>(J);
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Det3D(const int NE,
-                  const double *b,
-                  const double *g,
-                  const double *x,
-                  double *y,
-                  const int vdim = 1,
-                  const int d1d = 0,
-                  const int q1d = 0)
-{
-   constexpr int DIM = 3;
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-
-   const auto B = Reshape(b, Q1D, D1D);
-   const auto G = Reshape(g, Q1D, D1D);
-   const auto X = Reshape(x, D1D, D1D, D1D, DIM, NE);
-   auto Y = Reshape(y, Q1D, Q1D, Q1D, NE);
-
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
-
-      MFEM_SHARED double BG[2][MQ1*MD1];
-      MFEM_SHARED double sm0[9][MDQ*MDQ*MDQ];
-      MFEM_SHARED double sm1[9][MDQ*MDQ*MDQ];
-
-      double (*DDD)[MD1*MD1*MD1] = (double (*)[MD1*MD1*MD1]) (sm0);
-      double (*DDQ)[MD1*MD1*MQ1] = (double (*)[MD1*MD1*MQ1]) (sm1);
-      double (*DQQ)[MD1*MQ1*MQ1] = (double (*)[MD1*MQ1*MQ1]) (sm0);
-      double (*QQQ)[MQ1*MQ1*MQ1] = (double (*)[MQ1*MQ1*MQ1]) (sm1);
-
-      kernels::LoadX<MD1>(e,D1D,X,DDD);
-      kernels::LoadBG<MD1,MQ1>(D1D,Q1D,B,G,BG);
-
-      kernels::GradX<MD1,MQ1>(D1D,Q1D,BG,DDD,DDQ);
-      kernels::GradY<MD1,MQ1>(D1D,Q1D,BG,DDQ,DQQ);
-      kernels::GradZ<MD1,MQ1>(D1D,Q1D,BG,DQQ,QQQ);
-
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double J[9];
-               kernels::PullGrad<MQ1>(qx,qy,qz, QQQ, J);
-               Y(qx,qy,qz,e) = kernels::Det<3>(J);
-            }
-         }
-      }
-   });
-}
-
-void QuadratureInterpolator::Determinants(const Vector &e_vec,
-                                          Vector &q_det) const
-{
-   if (use_tensor_products)
-   {
-      const int NE = fespace->GetNE();
-      if (NE == 0) { return; }
-      const int vdim = fespace->GetVDim();
-      const int dim = fespace->GetMesh()->Dimension();
-      const FiniteElement *fe = fespace->GetFE(0);
-      const IntegrationRule *ir =
-         IntRule ? IntRule : &qspace->GetElementIntRule(0);
-      const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::TENSOR);
-      const int D1D = maps.ndof;
-      const int Q1D = maps.nqpt;
-      const double *B = maps.B.Read();
-      const double *G = maps.G.Read();
-      const double *X = e_vec.Read();
-      double *Y = q_det.Write();
-
-      const int id = (dim<<12) | (vdim<<8) | (D1D<<4) | Q1D;
-
-      switch (id)
-      {
-         case 0x2222: return Det2D<2,2>(NE,B,G,X,Y);
-         case 0x2223: return Det2D<2,3>(NE,B,G,X,Y);
-         case 0x2224: return Det2D<2,4>(NE,B,G,X,Y);
-         case 0x2226: return Det2D<2,6>(NE,B,G,X,Y);
-         case 0x2234: return Det2D<3,4>(NE,B,G,X,Y);
-         case 0x2236: return Det2D<3,6>(NE,B,G,X,Y);
-         case 0x2244: return Det2D<4,4>(NE,B,G,X,Y);
-         case 0x2246: return Det2D<4,6>(NE,B,G,X,Y);
-         case 0x2256: return Det2D<5,6>(NE,B,G,X,Y);
-
-         case 0x3324: return Det3D<2,4>(NE,B,G,X,Y);
-         case 0x3333: return Det3D<3,3>(NE,B,G,X,Y);
-         case 0x3335: return Det3D<3,5>(NE,B,G,X,Y);
-         case 0x3336: return Det3D<3,6>(NE,B,G,X,Y);
-         //case 0x3348: return Det3D<4,8>(NE,B,G,X,Y);
-
-         default:
-         {
-            if (dim == 2)
-            {
-               constexpr int MD1 = 8;
-               constexpr int MQ1 = 8;
-               MFEM_VERIFY(D1D <= MD1, "Orders higher than " << MD1-1
-                           << " are not supported!");
-               MFEM_VERIFY(Q1D <= MQ1, "Quadrature rules with more than "
-                           << MQ1 << " 1D points are not supported!");
-               return Det2D<0,0,MD1,MQ1>(NE,B,G,X,Y,vdim,D1D,Q1D);
-            }
-            if (dim == 3)
-            {
-               constexpr int MD1 = 6;
-               constexpr int MQ1 = 6;
-               MFEM_VERIFY(D1D <= MD1, "Orders higher than " << MD1-1
-                           << " are not supported!");
-               MFEM_VERIFY(Q1D <= MQ1, "Quadrature rules with more than "
-                           << MQ1 << " 1D points are not supported!");
-               return Det3D<0,0,MD1,MQ1>(NE,B,G,X,Y,vdim,D1D,Q1D);
-            }
-         }
-
-      }
-      MFEM_ABORT("Kernel " << std::hex << id << std::dec << " not supported yet");
-   }
-   else
-   {
-      Vector empty;
-      Mult(e_vec, DETERMINANTS, empty, empty, q_det);
-   }
-}
-
-} // namespace mfem

fem/quadinterpolator_eval.hpp

@@ -1,233 +0,0 @@
-// 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 "quadinterpolator.hpp"
-#include "../general/forall.hpp"
-#include "../linalg/dtensor.hpp"
-#include "../linalg/kernels.hpp"
-
-namespace mfem
-{
-
-template<QVectorLayout Q_LAYOUT,
-         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
-         int T_NBZ = 1, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Eval2D(const int NE,
-                   const double *b_,
-                   const double *x_,
-                   double *y_,
-                   const int vdim = 0,
-                   const int d1d = 0,
-                   const int q1d = 0)
-{
-   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
-
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-   const auto b = Reshape(b_, Q1D, D1D);
-   const auto x = Reshape(x_, D1D, D1D, VDIM, NE);
-   auto y = Q_LAYOUT == QVectorLayout:: byNODES ?
-            Reshape(y_, Q1D, Q1D, VDIM, NE):
-            Reshape(y_, VDIM, Q1D, Q1D, NE);
-
-   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
-      const int tidz = MFEM_THREAD_ID(z);
-
-      MFEM_SHARED double s_B[MQ1*MD1];
-      DeviceTensor<2,double> B(s_B, Q1D, D1D);
-
-      MFEM_SHARED double s_DD[NBZ][MD1*MD1];
-      DeviceTensor<2,double> DD((double*)(s_DD+tidz), MD1, MD1);
-
-      MFEM_SHARED double s_DQ[NBZ][MD1*MQ1];
-      DeviceTensor<2,double> DQ((double*)(s_DQ+tidz), MD1, MQ1);
-
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B(q,d) = b(q,d);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-
-      for (int c = 0; c < VDIM; c++)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            MFEM_FOREACH_THREAD(dy,y,D1D)
-            {
-               DD(dx,dy) = x(dx,dy,c,e);
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  u += B(qx,dx) *  DD(dx,dy);
-               }
-               DQ(dy,qx) = u;
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               for (int dy = 0; dy < D1D; ++dy)
-               {
-                  u += DQ(dy,qx) * B(qy,dy);
-               }
-               if (Q_LAYOUT == QVectorLayout::byVDIM) { y(c,qx,qy,e) = u; }
-               if (Q_LAYOUT == QVectorLayout::byNODES) { y(qx,qy,c,e) = u; }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
-}
-
-template<QVectorLayout Q_LAYOUT,
-         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
-         int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Eval3D(const int NE,
-                   const double *b_,
-                   const double *x_,
-                   double *y_,
-                   const int vdim = 0,
-                   const int d1d = 0,
-                   const int q1d = 0)
-{
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-   const auto b = Reshape(b_, Q1D, D1D);
-   const auto x = Reshape(x_, D1D, D1D, D1D, VDIM, NE);
-   auto y = Q_LAYOUT == QVectorLayout:: byNODES ?
-            Reshape(y_, Q1D, Q1D, Q1D, VDIM, NE):
-            Reshape(y_, VDIM, Q1D, Q1D, Q1D, NE);
-
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
-      const int tidz = MFEM_THREAD_ID(z);
-
-      MFEM_SHARED double s_B[MQ1*MD1];
-      DeviceTensor<2,double> B(s_B, Q1D, D1D);
-
-      MFEM_SHARED double sm0[MDQ*MDQ*MDQ];
-      MFEM_SHARED double sm1[MDQ*MDQ*MDQ];
-      DeviceTensor<3,double> DDD(sm0, MD1, MD1, MD1);
-      DeviceTensor<3,double> DDQ(sm1, MD1, MD1, MQ1);
-      DeviceTensor<3,double> DQQ(sm0, MD1, MQ1, MQ1);
-
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B(q,d) = b(q,d);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-
-      for (int c = 0; c < VDIM; c++)
-      {
-         MFEM_FOREACH_THREAD(dz,z,D1D)
-         {
-            MFEM_FOREACH_THREAD(dy,y,D1D)
-            {
-               MFEM_FOREACH_THREAD(dx,x,D1D)
-               {
-                  DDD(dx,dy,dz) = x(dx,dy,dz,c,e);
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dz,z,D1D)
-         {
-            MFEM_FOREACH_THREAD(dy,y,D1D)
-            {
-               MFEM_FOREACH_THREAD(qx,x,Q1D)
-               {
-                  double u = 0.0;
-                  for (int dx = 0; dx < D1D; ++dx)
-                  {
-                     u += B(qx,dx) * DDD(dx,dy,dz);
-                  }
-                  DDQ(dz,dy,qx) = u;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dz,z,D1D)
-         {
-            MFEM_FOREACH_THREAD(qy,y,Q1D)
-            {
-               MFEM_FOREACH_THREAD(qx,x,Q1D)
-               {
-                  double u = 0.0;
-                  for (int dy = 0; dy < D1D; ++dy)
-                  {
-                     u += DDQ(dz,dy,qx) * B(qy,dy);
-                  }
-                  DQQ(dz,qy,qx) = u;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(qz,z,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qy,y,Q1D)
-            {
-               MFEM_FOREACH_THREAD(qx,x,Q1D)
-               {
-                  double u = 0.0;
-                  for (int dz = 0; dz < D1D; ++dz)
-                  {
-                     u +=  DQQ(dz,qy,qx) * B(qz,dz);
-                  }
-                  if (Q_LAYOUT == QVectorLayout::byVDIM) { y(c,qx,qy,qz,e) = u; }
-                  if (Q_LAYOUT == QVectorLayout::byNODES) { y(qx,qy,qz,c,e) = u; }
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
-}
-
-} // namespace mfem

fem/quadinterpolator_eval_by_nodes.cpp

@@ -1,110 +0,0 @@
-// 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 "quadinterpolator.hpp"
-#include "quadinterpolator_eval.hpp"
-#include "../general/forall.hpp"
-#include "../linalg/dtensor.hpp"
-#include "../linalg/kernels.hpp"
-
-namespace mfem
-{
-
-template<>
-void QuadratureInterpolator::Values<QVectorLayout::byNODES>(
-   const Vector &e_vec, Vector &q_val) const
-{
-   const int NE = fespace->GetNE();
-   if (NE == 0) { return; }
-   const int vdim = fespace->GetVDim();
-   const int dim = fespace->GetMesh()->Dimension();
-   const FiniteElement *fe = fespace->GetFE(0);
-   const IntegrationRule *ir =
-      IntRule ? IntRule : &qspace->GetElementIntRule(0);
-   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const double *B = maps.B.Read();
-   const double *X = e_vec.Read();
-   double *Y = q_val.Write();
-
-   constexpr QVectorLayout L = QVectorLayout::byNODES;
-
-   const int id = (dim<<12) | (vdim<<8) | (D1D<<4) | Q1D;
-
-   switch (id)
-   {
-      case 0x2133: return Eval2D<L,1,3,3>(NE,B,X,Y);
-      case 0x2124: return Eval2D<L,1,2,4>(NE,B,X,Y);
-      case 0x2132: return Eval2D<L,1,3,2>(NE,B,X,Y);
-      case 0x2134: return Eval2D<L,1,3,4>(NE,B,X,Y);
-      case 0x2143: return Eval2D<L,1,4,3>(NE,B,X,Y);
-      case 0x2144: return Eval2D<L,1,4,4>(NE,B,X,Y);
-
-      case 0x2222: return Eval2D<L,2,2,2>(NE,B,X,Y);
-      case 0x2223: return Eval2D<L,2,2,3>(NE,B,X,Y);
-      case 0x2224: return Eval2D<L,2,2,4>(NE,B,X,Y);
-      case 0x2225: return Eval2D<L,2,2,5>(NE,B,X,Y);
-      case 0x2226: return Eval2D<L,2,2,6>(NE,B,X,Y);
-      case 0x2233: return Eval2D<L,2,3,3>(NE,B,X,Y);
-      case 0x2234: return Eval2D<L,2,3,4>(NE,B,X,Y);
-      case 0x2236: return Eval2D<L,2,3,6>(NE,B,X,Y);
-      case 0x2243: return Eval2D<L,2,4,3>(NE,B,X,Y);
-      case 0x2244: return Eval2D<L,2,4,4>(NE,B,X,Y);
-      case 0x2245: return Eval2D<L,2,4,5>(NE,B,X,Y);
-      case 0x2246: return Eval2D<L,2,4,6>(NE,B,X,Y);
-      case 0x2247: return Eval2D<L,2,4,7>(NE,B,X,Y);
-      case 0x2256: return Eval2D<L,2,5,6>(NE,B,X,Y);
-
-      case 0x3124: return Eval3D<L,1,2,4>(NE,B,X,Y);
-      case 0x3133: return Eval3D<L,1,3,3>(NE,B,X,Y);
-      case 0x3134: return Eval3D<L,1,3,4>(NE,B,X,Y);
-      case 0x3136: return Eval3D<L,1,3,6>(NE,B,X,Y);
-      case 0x3143: return Eval3D<L,1,4,3>(NE,B,X,Y);
-      case 0x3144: return Eval3D<L,1,4,4>(NE,B,X,Y);
-      case 0x3148: return Eval3D<L,1,4,8>(NE,B,X,Y);
-
-      case 0x3222: return Eval3D<L,2,2,2>(NE,B,X,Y);
-      case 0x3223: return Eval3D<L,2,2,3>(NE,B,X,Y);
-      case 0x3234: return Eval3D<L,2,3,4>(NE,B,X,Y);
-
-      case 0x3323: return Eval3D<L,3,2,3>(NE,B,X,Y);
-      case 0x3324: return Eval3D<L,3,2,4>(NE,B,X,Y);
-      case 0x3325: return Eval3D<L,3,2,5>(NE,B,X,Y);
-      case 0x3326: return Eval3D<L,3,2,6>(NE,B,X,Y);
-      case 0x3333: return Eval3D<L,3,3,3>(NE,B,X,Y);
-      case 0x3334: return Eval3D<L,3,3,4>(NE,B,X,Y);
-      case 0x3335: return Eval3D<L,3,3,5>(NE,B,X,Y);
-      case 0x3336: return Eval3D<L,3,3,6>(NE,B,X,Y);
-      case 0x3343: return Eval3D<L,3,4,3>(NE,B,X,Y);
-      case 0x3344: return Eval3D<L,3,4,4>(NE,B,X,Y);
-      case 0x3346: return Eval3D<L,3,4,6>(NE,B,X,Y);
-      case 0x3347: return Eval3D<L,3,4,7>(NE,B,X,Y);
-      case 0x3348: return Eval3D<L,3,4,8>(NE,B,X,Y);
-
-      default:
-      {
-         constexpr int MD1 = 8;
-         constexpr int MQ1 = 8;
-         MFEM_VERIFY(D1D <= MD1, "Orders higher than " << MD1-1
-                     << " are not supported!");
-         MFEM_VERIFY(Q1D <= MQ1, "Quadrature rules with more than "
-                     << MQ1 << " 1D points are not supported!");
-         if (dim == 2) { Eval2D<L,0,0,0,0,MD1,MQ1>(NE,B,X,Y,vdim,D1D,Q1D); }
-         if (dim == 3) { Eval3D<L,0,0,0,MD1,MQ1>(NE,B,X,Y,vdim,D1D,Q1D); }
-         return;
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
-}
-
-} // namespace mfem

fem/quadinterpolator_eval_by_vdim.cpp

@@ -1,79 +0,0 @@
-// 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 "quadinterpolator.hpp"
-#include "quadinterpolator_eval.hpp"
-#include "../general/forall.hpp"
-#include "../linalg/dtensor.hpp"
-#include "../linalg/kernels.hpp"
-
-namespace mfem
-{
-
-template<>
-void QuadratureInterpolator::Values<QVectorLayout::byVDIM>(
-   const Vector &e_vec, Vector &q_val) const
-{
-   const int NE = fespace->GetNE();
-   if (NE == 0) { return; }
-   const int vdim = fespace->GetVDim();
-   const int dim = fespace->GetMesh()->Dimension();
-   const FiniteElement *fe = fespace->GetFE(0);
-   const IntegrationRule *ir =
-      IntRule ? IntRule : &qspace->GetElementIntRule(0);
-   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const double *B = maps.B.Read();
-   const double *X = e_vec.Read();
-   double *Y = q_val.Write();
-
-   constexpr QVectorLayout L = QVectorLayout::byVDIM;
-
-   const int id = (dim<<12) | (vdim<<8) | (D1D<<4) | Q1D;
-
-   switch (id)
-   {
-      case 0x2124: return Eval2D<L,1,2,4,8>(NE,B,X,Y);
-      case 0x2136: return Eval2D<L,1,3,6,4>(NE,B,X,Y);
-      case 0x2148: return Eval2D<L,1,4,8,2>(NE,B,X,Y);
-
-      case 0x2224: return Eval2D<L,2,2,4,8>(NE,B,X,Y);
-      case 0x2234: return Eval2D<L,2,3,4,8>(NE,B,X,Y);
-      case 0x2236: return Eval2D<L,2,3,6,4>(NE,B,X,Y);
-      case 0x2248: return Eval2D<L,2,4,8,2>(NE,B,X,Y);
-
-      case 0x3124: return Eval3D<L,1,2,4>(NE,B,X,Y);
-      case 0x3136: return Eval3D<L,1,3,6>(NE,B,X,Y);
-      case 0x3148: return Eval3D<L,1,4,8>(NE,B,X,Y);
-
-      case 0x3324: return Eval3D<L,3,2,4>(NE,B,X,Y);
-      case 0x3336: return Eval3D<L,3,3,6>(NE,B,X,Y);
-      case 0x3348: return Eval3D<L,3,4,8>(NE,B,X,Y);
-
-      default:
-      {
-         constexpr int MD1 = 8;
-         constexpr int MQ1 = 8;
-         MFEM_VERIFY(D1D <= MD1, "Orders higher than " << MD1-1
-                     << " are not supported!");
-         MFEM_VERIFY(Q1D <= MQ1, "Quadrature rules with more than "
-                     << MQ1 << " 1D points are not supported!");
-         if (dim == 2) { Eval2D<L,0,0,0,0,MD1,MQ1>(NE,B,X,Y,vdim,D1D,Q1D); }
-         if (dim == 3) { Eval3D<L,0,0,0,MD1,MQ1>(NE,B,X,Y,vdim,D1D,Q1D); }
-         return;
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
-}
-
-} // namespace mfem

fem/quadinterpolator_face.cpp

@@ -495,9 +495,8 @@ void FaceQuadratureInterpolator::Mult(
    }
 }
 
-
-void FaceQuadratureInterpolator::Values(const Vector &e_vec,
-                                        Vector &q_val) const
+void FaceQuadratureInterpolator::Values(
+   const Vector &e_vec, Vector &q_val) const
 {
    Vector q_der, q_det, q_nor;
    Mult(e_vec, VALUES, q_val, q_der, q_det, q_nor);

fem/quadinterpolator_grad.hpp

@@ -1,282 +0,0 @@
-// 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 "quadinterpolator.hpp"
-#include "../general/forall.hpp"
-#include "../linalg/dtensor.hpp"
-#include "../linalg/kernels.hpp"
-
-namespace mfem
-{
-
-template<QVectorLayout Q_LAYOUT,
-         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
-         int T_NBZ = 1, int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Grad2D(const int NE,
-                   const double *b_,
-                   const double *g_,
-                   const double *x_,
-                   double *y_,
-                   const int vdim = 0,
-                   const int d1d = 0,
-                   const int q1d = 0)
-{
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-   const auto b = Reshape(b_, Q1D, D1D);
-   const auto g = Reshape(g_, Q1D, D1D);
-   const auto x = Reshape(x_, D1D, D1D, VDIM, NE);
-   auto y = Q_LAYOUT ==QVectorLayout:: byNODES ?
-            Reshape(y_, Q1D, Q1D, VDIM, 2, NE):
-            Reshape(y_, VDIM, 2, Q1D, Q1D, NE);
-
-   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
-      const int tidz = MFEM_THREAD_ID(z);
-      MFEM_SHARED double s_B[MQ1*MD1];
-      MFEM_SHARED double s_G[MQ1*MD1];
-      DeviceTensor<2,double> B(s_B, Q1D, D1D);
-      DeviceTensor<2,double> G(s_G, Q1D, D1D);
-
-      MFEM_SHARED double s_X[NBZ][MD1*MD1];
-      DeviceTensor<2,double> X((double*)(s_X+tidz), MD1, MD1);
-
-      MFEM_SHARED double s_DQ[2][NBZ][MD1*MQ1];
-      DeviceTensor<2,double> DQ0((double*)(s_DQ[0]+tidz), MD1, MQ1);
-      DeviceTensor<2,double> DQ1((double*)(s_DQ[1]+tidz), MD1, MQ1);
-
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B(q,d) = b(q,d);
-               G(q,d) = g(q,d);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-
-      for (int c = 0; c < VDIM; ++c)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            MFEM_FOREACH_THREAD(dy,y,D1D)
-            {
-               X(dx,dy) = x(dx,dy,c,e);
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  const double input = X(dx,dy);
-                  u += input * B(qx,dx);
-                  v += input * G(qx,dx);
-               }
-               DQ0(dy,qx) = u;
-               DQ1(dy,qx) = v;
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               for (int dy = 0; dy < D1D; ++dy)
-               {
-                  u += DQ1(dy,qx) * B(qy,dy);
-                  v += DQ0(dy,qx) * G(qy,dy);
-               }
-               if (Q_LAYOUT == QVectorLayout::byNODES)
-               {
-                  y(qx,qy,c,0,e) = u;
-                  y(qx,qy,c,1,e) = v;
-               }
-               if (Q_LAYOUT == QVectorLayout::byVDIM)
-               {
-                  y(c,0,qx,qy,e) = u;
-                  y(c,1,qx,qy,e) = v;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
-}
-
-template<QVectorLayout Q_LAYOUT,
-         int T_VDIM = 0, int T_D1D = 0, int T_Q1D = 0,
-         int MAX_D1D = 0, int MAX_Q1D = 0>
-static void Grad3D(const int NE,
-                   const double *b_,
-                   const double *g_,
-                   const double *x_,
-                   double *y_,
-                   const int vdim = 0,
-                   const int d1d = 0,
-                   const int q1d = 0)
-{
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
-
-   const auto b = Reshape(b_, Q1D, D1D);
-   const auto g = Reshape(g_, Q1D, D1D);
-   const auto x = Reshape(x_, D1D, D1D, D1D, VDIM, NE);
-   auto y = Q_LAYOUT ==QVectorLayout:: byNODES ?
-            Reshape(y_, Q1D, Q1D, Q1D, VDIM, 3, NE):
-            Reshape(y_, VDIM, 3, Q1D, Q1D, Q1D, NE);
-
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-
-      const int tidz = MFEM_THREAD_ID(z);
-      MFEM_SHARED double s_B[MQ1*MD1];
-      MFEM_SHARED double s_G[MQ1*MD1];
-      DeviceTensor<2,double> B(s_B, Q1D, D1D);
-      DeviceTensor<2,double> G(s_G, Q1D, D1D);
-
-      MFEM_SHARED double sm0[3][MQ1*MQ1*MQ1];
-      MFEM_SHARED double sm1[3][MQ1*MQ1*MQ1];
-      DeviceTensor<3,double> X((double*)(sm0+2), MD1, MD1, MD1);
-      DeviceTensor<3,double> DDQ0((double*)(sm0+0), MD1, MD1, MQ1);
-      DeviceTensor<3,double> DDQ1((double*)(sm0+1), MD1, MD1, MQ1);
-      DeviceTensor<3,double> DQQ0((double*)(sm1+0), MD1, MQ1, MQ1);
-      DeviceTensor<3,double> DQQ1((double*)(sm1+1), MD1, MQ1, MQ1);
-      DeviceTensor<3,double> DQQ2((double*)(sm1+2), MD1, MQ1, MQ1);
-
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B(q,d) = b(q,d);
-               G(q,d) = g(q,d);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-
-      for (int c = 0; c < VDIM; ++c)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            MFEM_FOREACH_THREAD(dy,y,D1D)
-            {
-               MFEM_FOREACH_THREAD(dz,z,D1D)
-               {
-                  X(dx,dy,dz) = x(dx,dy,dz,c,e);
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dz,z,D1D)
-         {
-            MFEM_FOREACH_THREAD(dy,y,D1D)
-            {
-               MFEM_FOREACH_THREAD(qx,x,Q1D)
-               {
-                  double u = 0.0;
-                  double v = 0.0;
-                  for (int dx = 0; dx < D1D; ++dx)
-                  {
-                     const double input = X(dx,dy,dz);
-                     u += input * B(qx,dx);
-                     v += input * G(qx,dx);
-                  }
-                  DDQ0(dz,dy,qx) = u;
-                  DDQ1(dz,dy,qx) = v;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(dz,z,D1D)
-         {
-            MFEM_FOREACH_THREAD(qy,y,Q1D)
-            {
-               MFEM_FOREACH_THREAD(qx,x,Q1D)
-               {
-                  double u = 0.0;
-                  double v = 0.0;
-                  double w = 0.0;
-                  for (int dy = 0; dy < D1D; ++dy)
-                  {
-                     u += DDQ1(dz,dy,qx) * B(qy,dy);
-                     v += DDQ0(dz,dy,qx) * G(qy,dy);
-                     w += DDQ0(dz,dy,qx) * B(qy,dy);
-                  }
-                  DQQ0(dz,qy,qx) = u;
-                  DQQ1(dz,qy,qx) = v;
-                  DQQ2(dz,qy,qx) = w;
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-         MFEM_FOREACH_THREAD(qz,z,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qy,y,Q1D)
-            {
-               MFEM_FOREACH_THREAD(qx,x,Q1D)
-               {
-                  double u = 0.0;
-                  double v = 0.0;
-                  double w = 0.0;
-                  for (int dz = 0; dz < D1D; ++dz)
-                  {
-                     u += DQQ0(dz,qy,qx) * B(qz,dz);
-                     v += DQQ1(dz,qy,qx) * B(qz,dz);
-                     w += DQQ2(dz,qy,qx) * G(qz,dz);
-                  }
-                  if (Q_LAYOUT == QVectorLayout::byNODES)
-                  {
-                     y(qx,qy,qz,c,0,e) = u;
-                     y(qx,qy,qz,c,1,e) = v;
-                     y(qx,qy,qz,c,2,e) = w;
-                  }
-                  if (Q_LAYOUT == QVectorLayout::byVDIM)
-                  {
-                     y(c,0,qx,qy,qz,e) = u;
-                     y(c,1,qx,qy,qz,e) = v;
-                     y(c,2,qx,qy,qz,e) = w;
-                  }
-               }
-            }
-         }
-         MFEM_SYNC_THREAD;
-      }
-   });
-}
-
-} // namespace mfem

fem/quadinterpolator_grad_by_nodes.cpp

@@ -1,109 +0,0 @@
-// 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 "quadinterpolator.hpp"
-#include "quadinterpolator_grad.hpp"
-
-namespace mfem
-{
-
-template<>
-void QuadratureInterpolator::Derivatives<QVectorLayout::byNODES>(
-   const Vector &e_vec, Vector &q_der) const
-{
-   const int NE = fespace->GetNE();
-   if (NE == 0) { return; }
-
-   const int vdim = fespace->GetVDim();
-   const int dim = fespace->GetMesh()->Dimension();
-   const FiniteElement *fe = fespace->GetFE(0);
-   const IntegrationRule *ir =
-      IntRule ? IntRule : &qspace->GetElementIntRule(0);
-   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const double *B = maps.B.Read();
-   const double *G = maps.G.Read();
-   const double *X = e_vec.Read();
-   double *Y = q_der.Write();
-
-   constexpr QVectorLayout L = QVectorLayout::byNODES;
-
-   const int id = (dim<<12) | (vdim<<8) | (D1D<<4) | Q1D;
-
-   switch (id)
-   {
-      case 0x2133: return Grad2D<L,1,3,3,16>(NE,B,G,X,Y);
-      case 0x2134: return Grad2D<L,1,3,4,16>(NE,B,G,X,Y);
-      case 0x2143: return Grad2D<L,1,4,3,16>(NE,B,G,X,Y);
-      case 0x2144: return Grad2D<L,1,4,4,16>(NE,B,G,X,Y);
-
-      case 0x2222: return Grad2D<L,2,2,2,16>(NE,B,G,X,Y);
-      case 0x2223: return Grad2D<L,2,2,3,8>(NE,B,G,X,Y);
-      case 0x2224: return Grad2D<L,2,2,4,4>(NE,B,G,X,Y);
-      case 0x2225: return Grad2D<L,2,2,5,4>(NE,B,G,X,Y);
-      case 0x2226: return Grad2D<L,2,2,6,2>(NE,B,G,X,Y);
-
-      case 0x2233: return Grad2D<L,2,3,3,2>(NE,B,G,X,Y);
-      case 0x2234: return Grad2D<L,2,3,4,4>(NE,B,G,X,Y);
-      case 0x2243: return Grad2D<L,2,4,3,4>(NE,B,G,X,Y);
-      case 0x2236: return Grad2D<L,2,3,6,2>(NE,B,G,X,Y);
-
-      case 0x2244: return Grad2D<L,2,4,4,2>(NE,B,G,X,Y);
-      case 0x2245: return Grad2D<L,2,4,5,2>(NE,B,G,X,Y);
-      case 0x2246: return Grad2D<L,2,4,6,2>(NE,B,G,X,Y);
-      case 0x2247: return Grad2D<L,2,4,7,2>(NE,B,G,X,Y);
-
-      case 0x2256: return Grad2D<L,2,5,6,2>(NE,B,G,X,Y);
-
-      case 0x3124: return Grad3D<L,1,2,4>(NE,B,G,X,Y);
-      case 0x3133: return Grad3D<L,1,3,3>(NE,B,G,X,Y);
-      case 0x3134: return Grad3D<L,1,3,4>(NE,B,G,X,Y);
-      case 0x3136: return Grad3D<L,1,3,6>(NE,B,G,X,Y);
-      case 0x3144: return Grad3D<L,1,4,4>(NE,B,G,X,Y);
-      case 0x3148: return Grad3D<L,1,4,8>(NE,B,G,X,Y);
-
-      case 0x3323: return Grad3D<L,3,2,3>(NE,B,G,X,Y);
-      case 0x3324: return Grad3D<L,3,2,4>(NE,B,G,X,Y);
-      case 0x3325: return Grad3D<L,3,2,5>(NE,B,G,X,Y);
-      case 0x3326: return Grad3D<L,3,2,6>(NE,B,G,X,Y);
-
-      case 0x3333: return Grad3D<L,3,3,3>(NE,B,G,X,Y);
-      case 0x3334: return Grad3D<L,3,3,4>(NE,B,G,X,Y);
-      case 0x3335: return Grad3D<L,3,3,5>(NE,B,G,X,Y);
-      case 0x3336: return Grad3D<L,3,3,6>(NE,B,G,X,Y);
-      case 0x3344: return Grad3D<L,3,4,4>(NE,B,G,X,Y);
-      case 0x3346: return Grad3D<L,3,4,6>(NE,B,G,X,Y);
-      case 0x3347: return Grad3D<L,3,4,7>(NE,B,G,X,Y);
-      case 0x3348: return Grad3D<L,3,4,8>(NE,B,G,X,Y);
-      default:
-      {
-         constexpr int MD1 = 8;
-         constexpr int MQ1 = 8;
-         MFEM_VERIFY(D1D <= MD1, "Orders higher than " << MD1-1
-                     << " are not supported!");
-         MFEM_VERIFY(Q1D <= MQ1, "Quadrature rules with more than "
-                     << MQ1 << " 1D points are not supported!");
-         if (dim == 2)
-         {
-            return Grad2D<L,0,0,0,0,MD1,MQ1>(NE,B,G,X,Y,vdim,D1D,Q1D);
-         }
-         if (dim == 3)
-         {
-            return Grad3D<L,0,0,0,MD1,MQ1>(NE,B,G,X,Y,vdim,D1D,Q1D);
-         }
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
-}
-
-} // namespace mfem

fem/quadinterpolator_grad_by_vdim.cpp

@@ -1,76 +0,0 @@
-// 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 "quadinterpolator.hpp"
-#include "quadinterpolator_grad.hpp"
-
-namespace mfem
-{
-
-template<>
-void QuadratureInterpolator::Derivatives<QVectorLayout::byVDIM>(
-   const Vector &e_vec, Vector &q_der) const
-{
-   const int NE = fespace->GetNE();
-   if (NE == 0) { return; }
-
-   const int vdim = fespace->GetVDim();
-   const int dim = fespace->GetMesh()->Dimension();
-   const FiniteElement *fe = fespace->GetFE(0);
-   const IntegrationRule *ir =
-      IntRule ? IntRule : &qspace->GetElementIntRule(0);
-   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   const int D1D = maps.ndof;
-   const int Q1D = maps.nqpt;
-   const double *B = maps.B.Read();
-   const double *G = maps.G.Read();
-   const double *X = e_vec.Read();
-   double *Y = q_der.Write();
-
-   constexpr QVectorLayout L = QVectorLayout::byVDIM;
-
-   const int id = (dim<<12) | (vdim<<8) | (D1D<<4) | Q1D;
-
-   switch (id)
-   {
-      case 0x2134: return Grad2D<L,1,3,4,8>(NE,B,G,X,Y);
-      case 0x2146: return Grad2D<L,1,4,6,4>(NE,B,G,X,Y);
-      case 0x2158: return Grad2D<L,1,5,8,2>(NE,B,G,X,Y);
-
-      case 0x2234: return Grad2D<L,2,3,4,8>(NE,B,G,X,Y);
-      case 0x2246: return Grad2D<L,2,4,6,4>(NE,B,G,X,Y);
-      case 0x2258: return Grad2D<L,2,5,8,2>(NE,B,G,X,Y);
-
-      case 0x3134: return Grad3D<L,1,3,4>(NE,B,G,X,Y);
-      case 0x3146: return Grad3D<L,1,4,6>(NE,B,G,X,Y);
-      case 0x3158: return Grad3D<L,1,5,8>(NE,B,G,X,Y);
-
-      case 0x3334: return Grad3D<L,3,3,4>(NE,B,G,X,Y);
-      case 0x3346: return Grad3D<L,3,4,6>(NE,B,G,X,Y);
-      case 0x3358: return Grad3D<L,3,5,8>(NE,B,G,X,Y);
-      default:
-      {
-         constexpr int MD1 = 8;
-         constexpr int MQ1 = 8;
-         MFEM_VERIFY(D1D <= MD1, "Orders higher than " << MD1-1
-                     << " are not supported!");
-         MFEM_VERIFY(Q1D <= MQ1, "Quadrature rules with more than "
-                     << MQ1 << " 1D points are not supported!");
-         if (dim == 2) { Grad2D<L,0,0,0,0,MD1,MQ1>(NE,B,G,X,Y,vdim,D1D,Q1D); }
-         if (dim == 3) { Grad3D<L,0,0,0,MD1,MQ1>(NE,B,G,X,Y,vdim,D1D,Q1D); }
-         return;
-      }
-   }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
-   MFEM_ABORT("Kernel not supported yet");
-}
-
-} // namespace mfem