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
 
@@ -259,5 +262,10 @@ tests/scripts/*.err
 tests/scripts/*.out
 tests/scripts/*.msg
 
+# Other tests
+tests/convergence/rates
+tests/convergence/prates
+tests/par-mesh-format/ex1p
+
 # VPATH builds
 build-*/*

.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
@@ -58,8 +65,14 @@ Improved GPU capabilities
   compute a global sparse matrix. All integrators supported by element assembly
   are also supported by full assembly. See the '-fa' option in Example 9.
 
+- Added CUDA support for sparse matrix-vector multiplication with cuSPARSE.
+
 - Added support for BlockOperator on GPU. See the updated Example 5.
 
+- Added partial assembly and GPU support for complex operators, including the
+  classes ComplexOperator, [Par]ComplexGridFunction, [Par]ComplexLinearForm, and
+  [Par]SesquilinearForm. See the updated Example 22.
+
 Discretization improvements
 ---------------------------
 - Added support for matrix-free interpolation and restriction operators between
@@ -88,6 +101,14 @@ Discretization improvements
 
 - Added support face integrals on the boundaries of NURBS meshes.
 
+- Added support for interpolation of functions in L2, H(div) and H(curl)
+  spaces using GSLIB-FindPoints.
+
+- Added support for computing asymptotic error estimates and convergence rates
+  for the whole de Rham sequence based on the new class ConvergenceStudy and new
+  member methods in GridFunction and ParGridFunction. See the rates.cpp file in
+  the tests/convergence directory for sample usage.
+
 Linear and nonlinear solvers
 ----------------------------
 - Added power method to iteratively estimate the largest eigenvalue and the
@@ -113,6 +134,12 @@ 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
@@ -149,6 +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.
 
@@ -163,28 +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
@@ -140,6 +141,7 @@ MFEM_USE_CEED          = NO
 MFEM_USE_UMPIRE        = NO
 MFEM_USE_SIMD          = NO
 MFEM_USE_ADIOS2        = NO
+MFEM_USE_MKL_CPARDISO  = NO
 
 # Compile and link options for zlib.
 ZLIB_DIR =
@@ -156,7 +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 =
@@ -232,7 +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:
@@ -240,6 +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 $(SCOTCH_OPT)
@@ -341,9 +348,9 @@ GSLIB_DIR = @MFEM_DIR@/../gslib/build
 GSLIB_OPT = -I$(GSLIB_DIR)/include
 GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs
 
-# CUDA library configuration (currently not needed)
+# CUDA library configuration
 CUDA_OPT =
-CUDA_LIB =
+CUDA_LIB = -lcusparse
 
 # HIP library configuration (currently not needed)
 HIP_OPT =
@@ -372,6 +379,15 @@ UMPIRE_DIR = @MFEM_DIR@/../umpire
 UMPIRE_OPT = -I$(UMPIRE_DIR)/include
 UMPIRE_LIB = -L$(UMPIRE_DIR)/lib -lumpire
 
+# 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
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+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
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 $EndNodes
 $Elements
-108
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-108 2 2 1 1 16 48 3
+38
+1 26 2 3 1 1 5 6 7
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+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
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+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
@@ -65,6 +66,7 @@ set(HDRS
   bilininteg.hpp
   coefficient.hpp
   complex_fem.hpp
+  convergence.hpp
   datacollection.hpp
   eltrans.hpp
   estimators.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_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
+         }
       }
    });
 }
@@ -170,47 +174,53 @@ static void PADiffusionSetup3D(const int Q1D,
                                const Vector &c,
                                Vector &d)
 {
-   const int NQ = Q1D*Q1D*Q1D;
    const bool const_c = c.Size() == 1;
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 6, NE);
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,Q1D,3,3,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D,Q1D, 6, NE);
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
    {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
       {
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J31 = J(q,2,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double J32 = J(q,2,1,e);
-         const double J13 = J(q,0,2,e);
-         const double J23 = J(q,1,2,e);
-         const double J33 = J(q,2,2,e);
-         const double detJ = J11 * (J22 * J33 - J32 * J23) -
-         /* */               J21 * (J12 * J33 - J32 * J13) +
-         /* */               J31 * (J12 * J23 - J22 * J13);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double c_detJ = W[q] * coeff / detJ;
-         // adj(J)
-         const double A11 = (J22 * J33) - (J23 * J32);
-         const double A12 = (J32 * J13) - (J12 * J33);
-         const double A13 = (J12 * J23) - (J22 * J13);
-         const double A21 = (J31 * J23) - (J21 * J33);
-         const double A22 = (J11 * J33) - (J13 * J31);
-         const double A23 = (J21 * J13) - (J11 * J23);
-         const double A31 = (J21 * J32) - (J31 * J22);
-         const double A32 = (J31 * J12) - (J11 * J32);
-         const double A33 = (J11 * J22) - (J12 * J21);
-         // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
-         D(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
-         D(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
-         D(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
-         D(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
-         D(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
-         D(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qz,z,Q1D)
+            {
+               const double J11 = J(qx,qy,qz,0,0,e);
+               const double J21 = J(qx,qy,qz,1,0,e);
+               const double J31 = J(qx,qy,qz,2,0,e);
+               const double J12 = J(qx,qy,qz,0,1,e);
+               const double J22 = J(qx,qy,qz,1,1,e);
+               const double J32 = J(qx,qy,qz,2,1,e);
+               const double J13 = J(qx,qy,qz,0,2,e);
+               const double J23 = J(qx,qy,qz,1,2,e);
+               const double J33 = J(qx,qy,qz,2,2,e);
+               const double detJ = J11 * (J22 * J33 - J32 * J23) -
+               /* */               J21 * (J12 * J33 - J32 * J13) +
+               /* */               J31 * (J12 * J23 - J22 * J13);
+               const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
+               const double c_detJ = W(qx,qy,qz) * coeff / detJ;
+               // adj(J)
+               const double A11 = (J22 * J33) - (J23 * J32);
+               const double A12 = (J32 * J13) - (J12 * J33);
+               const double A13 = (J12 * J23) - (J22 * J13);
+               const double A21 = (J31 * J23) - (J21 * J33);
+               const double A22 = (J11 * J33) - (J13 * J31);
+               const double A23 = (J21 * J13) - (J11 * J23);
+               const double A31 = (J21 * J32) - (J31 * J22);
+               const double A32 = (J31 * J12) - (J11 * J32);
+               const double A33 = (J11 * J22) - (J12 * J21);
+               // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
+               D(qx,qy,qz,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
+               D(qx,qy,qz,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
+               D(qx,qy,qz,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
+               D(qx,qy,qz,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
+               D(qx,qy,qz,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
+               D(qx,qy,qz,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+            }
+         }
       }
    });
 }
@@ -1670,7 +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)
    {

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

@@ -92,49 +92,64 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
    if (dim==2)
    {
       const int NE = ne;
-      const int NQ = nq;
+      const int Q1D = quad1D;
       const bool const_c = coeff.Size() == 1;
-      auto w = ir->GetWeights().Read();
-      auto J = Reshape(geom->J.Read(), NQ,2,2,NE);
-      auto C =
-         const_c ? Reshape(coeff.Read(), 1,1) : Reshape(coeff.Read(), NQ,NE);
-      auto v = Reshape(pa_data.Write(), NQ, NE);
-      MFEM_FORALL(e, NE,
+      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,2,2,NE);
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1) :
+                     Reshape(coeff.Read(), Q1D,Q1D,NE);
+      auto v = Reshape(pa_data.Write(), Q1D,Q1D, NE);
+      MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
       {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            const double J11 = J(q,0,0,e);
-            const double J12 = J(q,1,0,e);
-            const double J21 = J(q,0,1,e);
-            const double J22 = J(q,1,1,e);
-            const double detJ = (J11*J22)-(J21*J12);
-            const double coeff = const_c ? C(0,0) : C(q,e);
-            v(q,e) =  w[q] * coeff * detJ;
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               const double J11 = J(qx,qy,0,0,e);
+               const double J12 = J(qx,qy,1,0,e);
+               const double J21 = J(qx,qy,0,1,e);
+               const double J22 = J(qx,qy,1,1,e);
+               const double detJ = (J11*J22)-(J21*J12);
+               const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+               v(qx,qy,e) =  W(qx,qy) * coeff * detJ;
+            }
          }
       });
    }
    if (dim==3)
    {
       const int NE = ne;
-      const int NQ = nq;
+      const int Q1D = quad1D;
       const bool const_c = coeff.Size() == 1;
-      auto W = ir->GetWeights().Read();
-      auto J = Reshape(geom->J.Read(), NQ,3,3,NE);
-      auto C =
-         const_c ? Reshape(coeff.Read(), 1,1) : Reshape(coeff.Read(), NQ,NE);
-      auto v = Reshape(pa_data.Write(), NQ,NE);
-      MFEM_FORALL(e, NE,
+      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D,Q1D);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,Q1D,3,3,NE);
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1,1) :
+                     Reshape(coeff.Read(), Q1D,Q1D,Q1D,NE);
+      auto v = Reshape(pa_data.Write(), Q1D,Q1D,Q1D,NE);
+      MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
       {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            const double J11 = J(q,0,0,e), J12 = J(q,0,1,e), J13 = J(q,0,2,e);
-            const double J21 = J(q,1,0,e), J22 = J(q,1,1,e), J23 = J(q,1,2,e);
-            const double J31 = J(q,2,0,e), J32 = J(q,2,1,e), J33 = J(q,2,2,e);
-            const double detJ = J11 * (J22 * J33 - J32 * J23) -
-            /* */               J21 * (J12 * J33 - J32 * J13) +
-            /* */               J31 * (J12 * J23 - J22 * J13);
-            const double coeff = const_c ? C(0,0) : C(q,e);
-            v(q,e) = W[q] * coeff * detJ;
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qz,z,Q1D)
+               {
+                  const double J11 = J(qx,qy,qz,0,0,e);
+                  const double J21 = J(qx,qy,qz,1,0,e);
+                  const double J31 = J(qx,qy,qz,2,0,e);
+                  const double J12 = J(qx,qy,qz,0,1,e);
+                  const double J22 = J(qx,qy,qz,1,1,e);
+                  const double J32 = J(qx,qy,qz,2,1,e);
+                  const double J13 = J(qx,qy,qz,0,2,e);
+                  const double J23 = J(qx,qy,qz,1,2,e);
+                  const double J33 = J(qx,qy,qz,2,2,e);
+                  const double detJ = J11 * (J22 * J33 - J32 * J23) -
+                  /* */               J21 * (J12 * J33 - J32 * J13) +
+                  /* */               J31 * (J12 * J23 - J22 * J13);
+                  const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
+                  v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * detJ;
+               }
+            }
          }
       });
    }

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

@@ -319,6 +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

@@ -695,13 +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; }
@@ -718,6 +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
@@ -726,6 +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() { }
 };
 
@@ -753,6 +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;
@@ -790,10 +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++)
    {

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/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());
@@ -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/quadinterpolator.cpp

@@ -62,6 +62,7 @@ void QuadratureInterpolator::Eval2D(
    const int nq = maps.nqpt;
    const int ND = T_ND ? T_ND : nd;
    const int NQ = T_NQ ? T_NQ : nq;
+   const int NMAX = NQ > ND ? NQ : ND;
    const int VDIM = T_VDIM ? T_VDIM : vdim;
    MFEM_VERIFY(ND <= MAX_ND2D, "");
    MFEM_VERIFY(NQ <= MAX_NQ2D, "");
@@ -72,22 +73,24 @@ void QuadratureInterpolator::Eval2D(
    auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
    auto der = Reshape(q_der.Write(), NQ, VDIM, 2, NE);
    auto det = Reshape(q_det.Write(), NQ, NE);
-   MFEM_FORALL(e, NE,
+   MFEM_FORALL_2D(e, NE, NMAX, 1, 1,
    {
       const int ND = T_ND ? T_ND : nd;
       const int NQ = T_NQ ? T_NQ : nq;
       const int VDIM = T_VDIM ? T_VDIM : vdim;
       constexpr int max_ND = T_ND ? T_ND : MAX_ND2D;
       constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM2D;
-      double s_E[max_VDIM*max_ND];
-      for (int d = 0; d < ND; d++)
+      MFEM_SHARED double s_E[max_VDIM*max_ND];
+      MFEM_FOREACH_THREAD(d, x, ND)
       {
          for (int c = 0; c < VDIM; c++)
          {
             s_E[c+d*VDIM] = E(d,c,e);
          }
       }
-      for (int q = 0; q < NQ; ++q)
+      MFEM_SYNC_THREAD;
+
+      MFEM_FOREACH_THREAD(q, x, NQ)
       {
          if (eval_flags & VALUES)
          {
@@ -150,6 +153,7 @@ void QuadratureInterpolator::Eval3D(
    const int nq = maps.nqpt;
    const int ND = T_ND ? T_ND : nd;
    const int NQ = T_NQ ? T_NQ : nq;
+   const int NMAX = NQ > ND ? NQ : ND;
    const int VDIM = T_VDIM ? T_VDIM : vdim;
    MFEM_VERIFY(ND <= MAX_ND3D, "");
    MFEM_VERIFY(NQ <= MAX_NQ3D, "");
@@ -160,22 +164,24 @@ void QuadratureInterpolator::Eval3D(
    auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
    auto der = Reshape(q_der.Write(), NQ, VDIM, 3, NE);
    auto det = Reshape(q_det.Write(), NQ, NE);
-   MFEM_FORALL(e, NE,
+   MFEM_FORALL_2D(e, NE, NMAX, 1, 1,
    {
       const int ND = T_ND ? T_ND : nd;
       const int NQ = T_NQ ? T_NQ : nq;
       const int VDIM = T_VDIM ? T_VDIM : vdim;
       constexpr int max_ND = T_ND ? T_ND : MAX_ND3D;
       constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM3D;
-      double s_E[max_VDIM*max_ND];
-      for (int d = 0; d < ND; d++)
+      MFEM_SHARED double s_E[max_VDIM*max_ND];
+      MFEM_FOREACH_THREAD(d, x, ND)
       {
          for (int c = 0; c < VDIM; c++)
          {
             s_E[c+d*VDIM] = E(d,c,e);
          }
       }
-      for (int q = 0; q < NQ; ++q)
+      MFEM_SYNC_THREAD;
+
+      MFEM_FOREACH_THREAD(q, x, NQ)
       {
          if (eval_flags & VALUES)
          {

fem/tmop.cpp

@@ -1968,11 +1968,11 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
    Jpt.SetSize(dim);
    PMatI.UseExternalData(elfun.GetData(), dof, dim);
 
-   const IntegrationRule *ir = EnergyIntegrationRule(el);
+   const IntegrationRule &ir = EnergyIntegrationRule(el);
 
    energy = 0.0;
-   DenseTensor Jtr(dim, dim, ir->GetNPoints());
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+   DenseTensor Jtr(dim, dim, ir.GetNPoints());
+   targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);
 
    // Limited case.
    Vector shape, p, p0, d_vals;
@@ -1989,11 +1989,11 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       nodes0->GetSubVector(pos_dofs, pos0V);
       if (lim_dist)
       {
-         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+         lim_dist->GetValues(T.ElementNo, ir, d_vals);
       }
       else
       {
-         d_vals.SetSize(ir->GetNPoints()); d_vals = 1.0;
+         d_vals.SetSize(ir.GetNPoints()); d_vals = 1.0;
       }
    }
 
@@ -2019,13 +2019,13 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
    Vector zeta_q, zeta0_q;
    if (adaptive_limiting)
    {
-      zeta->GetValues(T.ElementNo, *ir, zeta_q);
-      zeta_0->GetValues(T.ElementNo, *ir, zeta0_q);
+      zeta->GetValues(T.ElementNo, ir, zeta_q);
+      zeta_0->GetValues(T.ElementNo, ir, zeta0_q);
    }
 
-   for (int i = 0; i < ir->GetNPoints(); i++)
+   for (int i = 0; i < ir.GetNPoints(); i++)
    {
-      const IntegrationPoint &ip = ir->IntPoint(i);
+      const IntegrationPoint &ip = ir.IntPoint(i);
       const DenseMatrix &Jtr_i = Jtr(i);
       metric->SetTargetJacobian(Jtr_i);
       CalcInverse(Jtr_i, Jrt);
@@ -2105,14 +2105,14 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
    elvect.SetSize(dof*dim);
    PMatO.UseExternalData(elvect.GetData(), dof, dim);
 
-   const IntegrationRule *ir = ActionIntegrationRule(el);
-   const int nqp = ir->GetNPoints();
+   const IntegrationRule &ir = ActionIntegrationRule(el);
+   const int nqp = ir.GetNPoints();
 
    elvect = 0.0;
    Vector weights(nqp);
    DenseTensor Jtr(dim, dim, nqp);
    DenseTensor dJtr(dim, dim, dim*nqp);
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);
 
    // Limited case.
    DenseMatrix pos0;
@@ -2129,7 +2129,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
       nodes0->GetSubVector(pos_dofs, pos0V);
       if (lim_dist)
       {
-         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+         lim_dist->GetValues(T.ElementNo, ir, d_vals);
       }
       else
       {
@@ -2149,7 +2149,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
       Tpr->GetPointMat().Transpose(PMatI); // PointMat = PMatI^T
       if (exact_action)
       {
-         targetC->ComputeElementTargetsGradient(*ir, elfun, *Tpr, dJtr);
+         targetC->ComputeElementTargetsGradient(ir, elfun, *Tpr, dJtr);
       }
    }
 
@@ -2159,7 +2159,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
 
    for (int q = 0; q < nqp; q++)
    {
-      const IntegrationPoint &ip = ir->IntPoint(q);
+      const IntegrationPoint &ip = ir.IntPoint(q);
       const DenseMatrix &Jtr_q = Jtr(q);
       metric->SetTargetJacobian(Jtr_q);
       CalcInverse(Jtr_q, Jrt);
@@ -2186,7 +2186,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
          DenseMatrix dwdx(dim);
          for (int d = 0; d < dim; d++)
          {
-            const DenseMatrix &dJtr_q = dJtr(q + d*ir->GetNPoints());
+            const DenseMatrix &dJtr_q = dJtr(q + d * nqp);
             Mult(Jrt, dJtr_q, dwdx );
             d_detW_dx(d) = dwdx.Trace();
          }
@@ -2221,7 +2221,7 @@ void TMOP_Integrator::AssembleElementVectorExact(const FiniteElement &el,
       }
    }
 
-   if (zeta) { AssembleElemVecAdaptLim(el, weights, *Tpr, *ir, PMatO); }
+   if (zeta) { AssembleElemVecAdaptLim(el, weights, *Tpr, ir, PMatO); }
 
    delete Tpr;
 }
@@ -2240,13 +2240,13 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
    PMatI.UseExternalData(elfun.GetData(), dof, dim);
    elmat.SetSize(dof*dim);
 
-   const IntegrationRule *ir = GradientIntegrationRule(el);
-   const int nqp = ir->GetNPoints();
+   const IntegrationRule &ir = GradientIntegrationRule(el);
+   const int nqp = ir.GetNPoints();
 
    elmat = 0.0;
    Vector weights(nqp);
    DenseTensor Jtr(dim, dim, nqp);
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);
 
    // Limited case.
    DenseMatrix pos0, grad_grad;
@@ -2263,7 +2263,7 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
       nodes0->GetSubVector(pos_dofs, pos0V);
       if (lim_dist)
       {
-         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+         lim_dist->GetValues(T.ElementNo, ir, d_vals);
       }
       else
       {
@@ -2285,7 +2285,7 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
 
    for (int q = 0; q < nqp; q++)
    {
-      const IntegrationPoint &ip = ir->IntPoint(q);
+      const IntegrationPoint &ip = ir.IntPoint(q);
       const DenseMatrix &Jtr_q = Jtr(q);
       metric->SetTargetJacobian(Jtr_q);
       CalcInverse(Jtr_q, Jrt);
@@ -2302,7 +2302,6 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
 
       // TODO: derivatives of adaptivity-based targets.
 
-      // TODO optimize by symmetry.
       if (coeff0)
       {
          el.CalcShape(ip, shape);
@@ -2328,7 +2327,7 @@ void TMOP_Integrator::AssembleElementGradExact(const FiniteElement &el,
       }
    }
 
-   if (zeta) { AssembleElemGradAdaptLim(el, weights, *Tpr, *ir, elmat); }
+   if (zeta) { AssembleElemGradAdaptLim(el, weights, *Tpr, ir, elmat); }
 
    delete Tpr;
 }
@@ -2499,10 +2498,10 @@ void TMOP_Integrator::AssembleElementVectorFD(const FiniteElement &el,
    // Contributions from adaptive limiting (exact derivatives).
    if (zeta)
    {
-      const IntegrationRule *ir = ActionIntegrationRule(el);
-      const int nqp = ir->GetNPoints();
+      const IntegrationRule &ir = ActionIntegrationRule(el);
+      const int nqp = ir.GetNPoints();
       DenseTensor Jtr(dim, dim, nqp);
-      targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+      targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);
 
       IsoparametricTransformation Tpr;
       Tpr.SetFE(&el);
@@ -2514,11 +2513,11 @@ void TMOP_Integrator::AssembleElementVectorFD(const FiniteElement &el,
       Vector weights(nqp);
       for (int q = 0; q < nqp; q++)
       {
-         weights(q) = ir->IntPoint(q).weight * Jtr(q).Det();
+         weights(q) = ir.IntPoint(q).weight * Jtr(q).Det();
       }
 
       PMatO.UseExternalData(elvect.GetData(), dof, dim);
-      AssembleElemVecAdaptLim(el, weights, Tpr, *ir, PMatO);
+      AssembleElemVecAdaptLim(el, weights, Tpr, ir, PMatO);
    }
 }
 
@@ -2595,10 +2594,10 @@ void TMOP_Integrator::AssembleElementGradFD(const FiniteElement &el,
    // Contributions from adaptive limiting.
    if (zeta)
    {
-      const IntegrationRule *ir = GradientIntegrationRule(el);
-      const int nqp = ir->GetNPoints();
+      const IntegrationRule &ir = GradientIntegrationRule(el);
+      const int nqp = ir.GetNPoints();
       DenseTensor Jtr(dim, dim, nqp);
-      targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
+      targetC->ComputeElementTargets(T.ElementNo, el, ir, elfun, Jtr);
 
       IsoparametricTransformation Tpr;
       Tpr.SetFE(&el);
@@ -2610,10 +2609,10 @@ void TMOP_Integrator::AssembleElementGradFD(const FiniteElement &el,
       Vector weights(nqp);
       for (int q = 0; q < nqp; q++)
       {
-         weights(q) = ir->IntPoint(q).weight * Jtr(q).Det();
+         weights(q) = ir.IntPoint(q).weight * Jtr(q).Det();
       }
 
-      AssembleElemGradAdaptLim(el, weights, Tpr, *ir, elmat);
+      AssembleElemGradAdaptLim(el, weights, Tpr, ir, elmat);
    }
 }
 
@@ -2643,33 +2642,32 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
    Array<int> vdofs;
    Vector x_vals;
    const FiniteElementSpace* const fes = x.FESpace();
-   const FiniteElement *fe = fes->GetFE(0);
 
-   const int dof = fes->GetFE(0)->GetDof(), dim = fes->GetFE(0)->GetDim();
-
-   DSh.SetSize(dof, dim);
+   const int dim = fes->GetMesh()->Dimension();
    Jrt.SetSize(dim);
    Jpr.SetSize(dim);
    Jpt.SetSize(dim);
 
-   const IntegrationRule *ir = EnergyIntegrationRule(*fe);
-   const int nqp =  ir->GetNPoints();
-   DenseTensor Jtr(dim, dim, nqp);
-
    metric_energy = 0.0;
    lim_energy = 0.0;
    for (int i = 0; i < fes->GetNE(); i++)
    {
-      fe = fes->GetFE(i);
+      const FiniteElement *fe = fes->GetFE(i);
+      const IntegrationRule &ir = EnergyIntegrationRule(*fe);
+      const int nqp = ir.GetNPoints();
+      DenseTensor Jtr(dim, dim, nqp);
+      const int dof = fe->GetDof();
+      DSh.SetSize(dof, dim);
+
       fes->GetElementVDofs(i, vdofs);
       x.GetSubVector(vdofs, x_vals);
       PMatI.UseExternalData(x_vals.GetData(), dof, dim);
 
-      targetC->ComputeElementTargets(i, *fe, *ir, x_vals, Jtr);
+      targetC->ComputeElementTargets(i, *fe, ir, x_vals, Jtr);
 
       for (int q = 0; q < nqp; q++)
       {
-         const IntegrationPoint &ip = ir->IntPoint(q);
+         const IntegrationPoint &ip = ir.IntPoint(q);
          metric->SetTargetJacobian(Jtr(q));
          CalcInverse(Jtr(q), Jrt);
          const double weight = ip.weight * Jtr(q).Det();
@@ -2693,9 +2691,9 @@ void TMOP_Integrator::ComputeMinJac(const Vector &x,
                                     const FiniteElementSpace &fes)
 {
    const FiniteElement *fe = fes.GetFE(0);
-   const IntegrationRule *ir = EnergyIntegrationRule(*fe);
+   const IntegrationRule &ir = EnergyIntegrationRule(*fe);
    const int NE = fes.GetMesh()->GetNE(), dim = fe->GetDim(),
-             dof = fe->GetDof(), nsp = ir->GetNPoints();
+             dof = fe->GetDof(), nsp = ir.GetNPoints();
 
    Array<int> xdofs(dof * dim);
    DenseMatrix Jpr(dim), dshape(dof, dim), pos(dof, dim);
@@ -2712,7 +2710,7 @@ void TMOP_Integrator::ComputeMinJac(const Vector &x,
       detv_sum = 0.;
       for (int j = 0; j < nsp; j++)
       {
-         fes.GetFE(i)->CalcDShape(ir->IntPoint(j), dshape);
+         fes.GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
          MultAtB(pos, dshape, Jpr);
          detv_sum += std::fabs(Jpr.Det());
       }

fem/tmop.hpp

@@ -890,6 +890,10 @@ protected:
    TMOP_QualityMetric *metric;        // not owned
    const TargetConstructor *targetC;  // not owned
 
+   // Custom integration rules.
+   IntegrationRules *IntegRules;
+   int integ_order;
+
    // Weight Coefficient multiplying the quality metric term.
    Coefficient *coeff1; // not owned, if NULL -> coeff1 is 1.
    // Normalization factor for the metric term.
@@ -988,17 +992,21 @@ protected:
       nodes0 = NULL; coeff0 = NULL; lim_dist = NULL; lim_func = NULL;
    }
 
-   const IntegrationRule *EnergyIntegrationRule(const FiniteElement &el) const
+   const IntegrationRule &EnergyIntegrationRule(const FiniteElement &el) const
    {
-      return (IntRule) ? IntRule
-             /*     */ : &(IntRules.Get(el.GetGeomType(), 2*el.GetOrder() + 3));
+      if (IntegRules)
+      {
+         return IntegRules->Get(el.GetGeomType(), integ_order);
+      }
+      return (IntRule) ? *IntRule
+             /*     */ : IntRules.Get(el.GetGeomType(), 2*el.GetOrder() + 3);
    }
-   const IntegrationRule *ActionIntegrationRule(const FiniteElement &el) const
+   const IntegrationRule &ActionIntegrationRule(const FiniteElement &el) const
    {
       // TODO the energy most likely needs less integration points.
       return EnergyIntegrationRule(el);
    }
-   const IntegrationRule *GradientIntegrationRule(const FiniteElement &el) const
+   const IntegrationRule &GradientIntegrationRule(const FiniteElement &el) const
    {
       // TODO the action and energy most likely need less integration points.
       return EnergyIntegrationRule(el);
@@ -1008,7 +1016,7 @@ public:
    /** @param[in] m  TMOP_QualityMetric that will be integrated (not owned).
        @param[in] tc Target-matrix construction algorithm to use (not owned). */
    TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc)
-      : metric(m), targetC(tc),
+      : metric(m), targetC(tc), IntegRules(NULL), integ_order(-1),
         coeff1(NULL), metric_normal(1.0),
         nodes0(NULL), coeff0(NULL),
         lim_dist(NULL), lim_func(NULL), lim_normal(1.0),
@@ -1019,6 +1027,14 @@ public:
 
    ~TMOP_Integrator();
 
+   /// Prescribe a set of integration rules; relevant for mixed meshes.
+   /** This function has priority over SetIntRule(), if both are called. */
+   void SetIntegrationRules(IntegrationRules &irules, int order)
+   {
+      IntegRules = &irules;
+      integ_order = order;
+   }
+
    /// Sets a scaling Coefficient for the quality metric term of the integrator.
    /** With this addition, the integrator becomes
           @f$ \int w1 W(Jpt) dx @f$.

fem/tmop_tools.cpp

@@ -176,8 +176,8 @@ SerialAdvectorCGOper::SerialAdvectorCGOper(const Vector &x_start,
 
    MassIntegrator *Minteg = new MassIntegrator;
    M.AddDomainIntegrator(Minteg);
-   M.Assemble();
-   M.Finalize();
+   M.Assemble(0);
+   M.Finalize(0);
 }
 
 void SerialAdvectorCGOper::Mult(const Vector &ind, Vector &di_dt) const
@@ -220,8 +220,8 @@ ParAdvectorCGOper::ParAdvectorCGOper(const Vector &x_start,
 
    MassIntegrator *Minteg = new MassIntegrator;
    M.AddDomainIntegrator(Minteg);
-   M.Assemble();
-   M.Finalize();
+   M.Assemble(0);
+   M.Finalize(0);
 }
 
 void ParAdvectorCGOper::Mult(const Vector &ind, Vector &di_dt) const
@@ -298,34 +298,12 @@ void InterpolatorFP::SetInitialField(const Vector &init_nodes,
    field0_gf = init_field;
 
    dim = f->GetFE(0)->GetDim();
-   const int pts_cnt = init_nodes.Size() / dim;
-   el_id_out.SetSize(pts_cnt);
-   code_out.SetSize(pts_cnt);
-   task_id_out.SetSize(pts_cnt);
-   pos_r_out.SetSize(pts_cnt*dim);
-   dist_p_out.SetSize(pts_cnt);
 }
 
 void InterpolatorFP::ComputeAtNewPosition(const Vector &new_nodes,
                                           Vector &new_field)
 {
-   const int pts_cnt = new_nodes.Size() / dim;
-
-   // The sizes may change between calls due to AMR.
-   if (el_id_out.Size() != pts_cnt)
-   {
-      el_id_out.SetSize(pts_cnt);
-      code_out.SetSize(pts_cnt);
-      task_id_out.SetSize(pts_cnt);
-      pos_r_out.SetSize(pts_cnt*dim);
-      dist_p_out(pts_cnt);
-   }
-
-   // Interpolate FE function values on the found points.
-   finder->FindPoints(new_nodes, code_out, task_id_out,
-                      el_id_out, pos_r_out, dist_p_out);
-   finder->Interpolate(code_out, task_id_out, el_id_out,
-                       pos_r_out, field0_gf, new_field);
+   finder->Interpolate(new_nodes, field0_gf, new_field);
 }
 
 #endif
@@ -353,13 +331,12 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
       energy_in = nlf->GetEnergy(x);
    }
 
-   const int NE = fes->GetMesh()->GetNE(), dim = fes->GetFE(0)->GetDim(),
-             dof = fes->GetFE(0)->GetDof(), nsp = ir.GetNPoints();
-   Array<int> xdofs(dof * dim);
-   DenseMatrix Jpr(dim), dshape(dof, dim), pos(dof, dim);
-   Vector posV(pos.Data(), dof * dim);
-   Vector x_out_loc(fes->GetVSize());
+   const int NE = fes->GetMesh()->GetNE(), dim = fes->GetMesh()->Dimension();
+   Array<int> xdofs;
+   DenseMatrix Jpr(dim);
 
+   // Get the local prolongation of the solution vector.
+   Vector x_out_loc(fes->GetVSize());
    if (serial)
    {
       const SparseMatrix *cP = fes->GetConformingProlongation();
@@ -373,15 +350,23 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
    }
 #endif
 
+   // Check if the starting mesh (given by x) is inverted.
+   // Note that x hasn't been modified by the Newton update yet.
    double min_detJ = infinity();
    for (int i = 0; i < NE; i++)
    {
+      const int dof = fes->GetFE(i)->GetDof();
+      DenseMatrix dshape(dof, dim), pos(dof, dim);
+      Vector posV(pos.Data(), dof * dim);
+
       fes->GetElementVDofs(i, xdofs);
       x_out_loc.GetSubVector(xdofs, posV);
 
+      const IntegrationRule &irule = GetIntegrationRule(*fes->GetFE(i));
+      const int nsp = irule.GetNPoints();
       for (int j = 0; j < nsp; j++)
       {
-         fes->GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
+         fes->GetFE(i)->CalcDShape(irule.IntPoint(j), dshape);
          MultAtB(pos, dshape, Jpr);
          min_detJ = std::min(min_detJ, Jpr.Det());
       }
@@ -394,18 +379,18 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
                     p_nlf->ParFESpace()->GetComm());
    }
 #endif
-   bool untangling = false;
-   if (min_detJ_all <= 0) { untangling = true; }
+   const bool untangling = (min_detJ_all <= 0) ? true : false;
 
    const bool have_b = (b.Size() == Height());
 
    Vector x_out(x.Size());
    bool x_out_ok = false;
    double scale = 1.0, energy_out = 0.0;
-   double norm0 = Norm(r);
+   const double norm0 = Norm(r);
 
    const double detJ_factor = (solver_type == 1) ? 0.25 : 0.5;
 
+   // Perform the line search.
    for (int i = 0; i < 12; i++)
    {
       add(x, -scale, c, x_out);
@@ -429,11 +414,18 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
          int jac_ok = 1;
          for (int i = 0; i < NE; i++)
          {
+            const int dof = fes->GetFE(i)->GetDof();
+            DenseMatrix dshape(dof, dim), pos(dof, dim);
+            Vector posV(pos.Data(), dof * dim);
+
             fes->GetElementVDofs(i, xdofs);
             x_out_loc.GetSubVector(xdofs, posV);
+
+            const IntegrationRule &irule = GetIntegrationRule(*fes->GetFE(i));
+            const int nsp = irule.GetNPoints();
             for (int j = 0; j < nsp; j++)
             {
-               fes->GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
+               fes->GetFE(i)->CalcDShape(irule.IntPoint(j), dshape);
                MultAtB(pos, dshape, Jpr);
                if (Jpr.Det() <= 0.0) { jac_ok = 0; goto break2; }
             }

fem/tmop_tools.hpp

@@ -49,8 +49,6 @@ private:
    Vector nodes0;
    GridFunction field0_gf;
    FindPointsGSLIB *finder;
-   Array<uint> el_id_out, code_out, task_id_out;
-   Vector pos_r_out, dist_p_out;
    int dim;
 public:
    InterpolatorFP() : finder(NULL) { }
@@ -118,16 +116,39 @@ protected:
 
    // Quadrature points that are checked for negative Jacobians etc.
    const IntegrationRule &ir;
+   // These fields are relevant for mixed meshes.
+   IntegrationRules *IntegRules;
+   int integ_order;
+
+   const IntegrationRule &GetIntegrationRule(const FiniteElement &el) const
+   {
+      if (IntegRules)
+      {
+         return IntegRules->Get(el.GetGeomType(), integ_order);
+      }
+      return ir;
+   }
 
    void UpdateDiscreteTC(const TMOP_Integrator &ti, const Vector &x_new) const;
 
 public:
 #ifdef MFEM_USE_MPI
    TMOPNewtonSolver(MPI_Comm comm, const IntegrationRule &irule, int type = 0)
-      : LBFGSSolver(comm), solver_type(type), parallel(true), ir(irule) { }
+      : LBFGSSolver(comm), solver_type(type), parallel(true),
+        ir(irule), IntegRules(NULL), integ_order(-1) { }
 #endif
    TMOPNewtonSolver(const IntegrationRule &irule, int type = 0)
-      : LBFGSSolver(), solver_type(type), parallel(false), ir(irule) { }
+      : LBFGSSolver(), solver_type(type), parallel(false),
+        ir(irule), IntegRules(NULL), integ_order(-1) { }
+
+   /// Prescribe a set of integration rules; relevant for mixed meshes.
+   /** If called, this function has priority over the IntegrationRule given to
+       the constructor of the class. */
+   void SetIntegrationRules(IntegrationRules &irules, int order)
+   {
+      IntegRules = &irules;
+      integ_order = order;
+   }
 
    virtual double ComputeScalingFactor(const Vector &x, const Vector &b) const;
 

general/adios2stream.cpp

@@ -235,8 +235,8 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
       }
 
       // format info
-      SafeDefineAttribute<std::string>(io, "format", "MFEM ADIOS2 BP v0.1" );
-      SafeDefineAttribute<std::string>(io, "format/version", "0.1" );
+      SafeDefineAttribute<std::string>(io, "format", "MFEM ADIOS2 BP v0.2" );
+      SafeDefineAttribute<std::string>(io, "format/version", "0.2" );
       std::string mesh_type = "Unknown";
       std::vector<std::string> viz_tools;
       viz_tools.reserve(2); //for now
@@ -298,6 +298,7 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
          element_nvertices = static_cast<size_t>(mesh.elements[0]->GetNVertices());
       }
       SafeDefineVariable<uint64_t>(io, "connectivity", {}, {}, {nelements, element_nvertices+1});
+      SafeDefineVariable<int32_t>(io, "material", {}, {}, {nelements});
 
       // vertices
       SafeDefineVariable<uint32_t>(io,"NumOfVertices", {adios2::LocalValueDim});
@@ -348,8 +349,15 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
          io.InquireVariable<uint64_t>("connectivity");
       adios2::Variable<uint64_t>::Span span_connectivity = engine.Put<uint64_t>
                                                            (var_connectivity);
+
+      adios2::Variable<int32_t> var_element_attribute =
+         io.InquireVariable<int32_t>("material");
+      adios2::Variable<int32_t>::Span span_element_attribute = engine.Put<int32_t>
+                                                               (var_element_attribute);
+
       size_t span_vertices_offset = 0;
       size_t span_connectivity_offset = 0;
+      size_t span_element_attribute_offset = 0;
       // use for setting absolute node id for each element
       size_t point_id = 0;
       DenseMatrix pmatrix;
@@ -370,6 +378,9 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
          }
          span_vertices_offset += static_cast<size_t>(pmatrix.Width()*pmatrix.Height());
 
+         // element attribute
+         const int element_attribute = mesh.GetAttribute(e);
+
          // connectivity
          const int nv = Geometries.GetVertices(type)->GetNPoints();
          const Array<int> &element_vertices = refined_geometry->RefGeoms;
@@ -379,6 +390,10 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
             span_connectivity[span_connectivity_offset] = static_cast<uint64_t>(nv);
             ++span_connectivity_offset;
 
+            span_element_attribute[span_element_attribute_offset] = static_cast<int32_t>
+                                                                    (element_attribute);
+            ++span_element_attribute_offset;
+
             for (int k =0; k < nv; k++, v++ )
             {
                span_connectivity[span_connectivity_offset] = static_cast<uint64_t>
@@ -419,9 +434,17 @@ void adios2stream::Print(const Mesh& mesh, const mode print_mode)
       adios2::Variable<uint64_t>::Span spanConnectivity =
          engine.Put<uint64_t>(varConnectivity);
 
+      adios2::Variable<int32_t> varElementAttribute =
+         io.InquireVariable<int32_t>("material");
+      // zero-copy access to adios2 buffer to put non-contiguous to contiguous memory
+      adios2::Variable<int32_t>::Span spanElementAttribute =
+         engine.Put<int32_t>(varElementAttribute);
+
       size_t elementPosition = 0;
       for (int e = 0; e < mesh.GetNE(); ++e)
       {
+         spanElementAttribute[e] = static_cast<int32_t>(mesh.GetAttribute(e));
+
          const int nVertices = mesh.elements[e]->GetNVertices();
          spanConnectivity[elementPosition] = nVertices;
          for (int v = 0; v < nVertices; ++v)
@@ -688,7 +711,7 @@ std::string adios2stream::VTKSchema() const noexcept
 {
    std::string vtkSchema = R"(
 <?xml version="1.0"?>
-<VTKFile type="UnstructuredGrid" version="0.1" byte_order="LittleEndian">
+<VTKFile type="UnstructuredGrid" version="0.2" byte_order="LittleEndian">
   <UnstructuredGrid>
     <Piece NumberOfPoints="NumOfVertices" NumberOfCells="NumOfElements">
       <Points>
@@ -696,6 +719,9 @@ std::string adios2stream::VTKSchema() const noexcept
 
    vtkSchema += R"(
       </Points>
+	  <CellData>
+        <DataArray Name="material" />
+	  </CellData>
       <Cells>
         <DataArray Name="connectivity" />
         <DataArray Name="types" />

general/device.cpp

@@ -12,9 +12,10 @@
 #include "forall.hpp"
 #include "occa.hpp"
 #ifdef MFEM_USE_CEED
-#include <ceed.h>
+#include "../fem/libceed/ceed.hpp"
 #endif
 
+#include <unordered_map>
 #include <string>
 #include <map>
 
@@ -33,13 +34,16 @@ occa::device occaDevice;
 
 #ifdef MFEM_USE_CEED
 Ceed ceed = NULL;
+
+CeedBasisMap ceed_basis_map;
+CeedRestrMap ceed_restr_map;
 #endif
 
 // Backends listed by priority, high to low:
 static const Backend::Id backend_list[Backend::NUM_BACKENDS] =
 {
    Backend::CEED_CUDA, Backend::OCCA_CUDA, Backend::RAJA_CUDA, Backend::CUDA,
-   Backend::HIP, Backend::DEBUG,
+   Backend::HIP, Backend::DEBUG_DEVICE,
    Backend::OCCA_OMP, Backend::RAJA_OMP, Backend::OMP,
    Backend::CEED_CPU, Backend::OCCA_CPU, Backend::RAJA_CPU, Backend::CPU
 };
@@ -154,6 +158,16 @@ Device::~Device()
    {
       free(device_option);
 #ifdef MFEM_USE_CEED
+      // Destroy FES -> CeedBasis, CeedElemRestriction hash table contents
+      for (auto entry : internal::ceed_basis_map)
+      {
+         CeedBasisDestroy(&entry.second);
+      }
+      for (auto entry : internal::ceed_restr_map)
+      {
+         CeedElemRestrictionDestroy(&entry.second);
+      }
+      // Destroy Ceed context
       CeedDestroy(&internal::ceed);
 #endif
       mm.Destroy();
@@ -266,7 +280,7 @@ void Device::Print(std::ostream &out)
 
 void Device::UpdateMemoryTypeAndClass()
 {
-   const bool debug = Device::Allows(Backend::DEBUG);
+   const bool debug = Device::Allows(Backend::DEBUG_DEVICE);
 
    const bool device = Device::Allows(Backend::DEVICE_MASK);
 
@@ -504,7 +518,7 @@ void Device::Setup(const int device)
          CeedDeviceSetup(device_option);
       }
    }
-   if (Allows(Backend::DEBUG)) { ngpu = 1; }
+   if (Allows(Backend::DEBUG_DEVICE)) { ngpu = 1; }
 }
 
 } // mfem

general/device.hpp

@@ -64,8 +64,9 @@ struct Backend
       /** @brief [device] Debug backend: host memory is READ/WRITE protected
           while a device is in use. It allows to test the "device" code-path
           (using separate host/device memory pools and host <-> device
-          transfers) without any GPU hardware. */
-      DEBUG = 1 << 12
+          transfers) without any GPU hardware. As 'DEBUG' is sometimes used
+          as a macro, `_DEVICE` has been added to avoid conflicts. */
+      DEBUG_DEVICE = 1 << 12
    };
 
    /** @brief Additional useful constants. For example, the *_MASK constants can
@@ -86,7 +87,7 @@ struct Backend
       /// Bitwise-OR of all CEED backends
       CEED_MASK = CEED_CPU | CEED_CUDA,
       /// Biwise-OR of all device backends
-      DEVICE_MASK = CUDA_MASK | HIP_MASK | DEBUG,
+      DEVICE_MASK = CUDA_MASK | HIP_MASK | DEBUG_DEVICE,
 
       /// Biwise-OR of all RAJA backends
       RAJA_MASK = RAJA_CPU | RAJA_OMP | RAJA_CUDA,
@@ -193,7 +194,8 @@ public:
        * The available backends are described by the Backend class.
        * The string name of a backend is the lowercase version of the
          Backend::Id enumeration constant with '_' replaced by '-', e.g. the
-         string name of 'RAJA_CPU' is 'raja-cpu'.
+         string name of 'RAJA_CPU' is 'raja-cpu'. The string name of the debug
+         backend (Backend::Id 'DEBUG_DEVICE') is exceptionally set to 'debug'.
        * The 'cpu' backend is always enabled with lowest priority.
        * The current backend priority from highest to lowest is:
          'ceed-cuda', 'occa-cuda', 'raja-cuda', 'cuda', 'hip', 'debug',

general/forall.hpp

@@ -343,7 +343,7 @@ inline void ForallWrap(const bool use_dev, const int N,
    { return HipWrap3D(N, d_body, X, Y, Z); }
 #endif
 
-   if (Device::Allows(Backend::DEBUG)) { goto backend_cpu; }
+   if (Device::Allows(Backend::DEBUG_DEVICE)) { goto backend_cpu; }
 
 #if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_OPENMP)
    // Handle all allowed OpenMP backends except Backend::OMP

general/mem_manager.cpp

@@ -136,8 +136,10 @@ struct Memory
    void *d_ptr;
    const size_t bytes;
    const MemoryType h_mt, d_mt;
+   mutable bool h_rw, d_rw;
    Memory(void *p, size_t b, MemoryType h, MemoryType d):
-      h_ptr(p), d_ptr(nullptr), bytes(b), h_mt(h), d_mt(d) { }
+      h_ptr(p), d_ptr(nullptr), bytes(b), h_mt(h), d_mt(d),
+      h_rw(true), d_rw(true) { }
 };
 
 /// Alias class that holds the base memory region and the offset
@@ -173,8 +175,8 @@ public:
    virtual ~HostMemorySpace() { }
    virtual void Alloc(void **ptr, size_t bytes) { *ptr = std::malloc(bytes); }
    virtual void Dealloc(void *ptr) { std::free(ptr); }
-   virtual void Protect(const void*, size_t) { }
-   virtual void Unprotect(const void*, size_t) { }
+   virtual void Protect(const Memory&, size_t) { }
+   virtual void Unprotect(const Memory&, size_t) { }
    virtual void AliasProtect(const void*, size_t) { }
    virtual void AliasUnprotect(const void*, size_t) { }
 };
@@ -352,8 +354,10 @@ public:
    MmuHostMemorySpace(): HostMemorySpace() { MmuInit(); }
    void Alloc(void **ptr, size_t bytes) { MmuAlloc(ptr, bytes); }
    void Dealloc(void *ptr) { MmuDealloc(ptr, maps->memories.at(ptr).bytes); }
-   void Protect(const void *ptr, size_t bytes) { MmuProtect(ptr, bytes); }
-   void Unprotect(const void *ptr, size_t bytes) { MmuAllow(ptr, bytes); }
+   void Protect(const Memory& mem, size_t bytes)
+   { if (mem.h_rw) { mem.h_rw = false; MmuProtect(mem.h_ptr, bytes); } }
+   void Unprotect(const Memory &mem, size_t bytes)
+   { if (!mem.h_rw) { mem.h_rw = true; MmuAllow(mem.h_ptr, bytes); } }
    /// Aliases need to be restricted during protection
    void AliasProtect(const void *ptr, size_t bytes)
    { MmuProtect(MmuAddrR(ptr), MmuLengthR(ptr, bytes)); }
@@ -442,8 +446,10 @@ public:
    MmuDeviceMemorySpace(): DeviceMemorySpace() { }
    void Alloc(Memory &m) { MmuAlloc(&m.d_ptr, m.bytes); }
    void Dealloc(Memory &m) { MmuDealloc(m.d_ptr, m.bytes); }
-   void Protect(const Memory &m) { MmuProtect(m.d_ptr, m.bytes); }
-   void Unprotect(const Memory &m) { MmuAllow(m.d_ptr, m.bytes); }
+   void Protect(const Memory &m)
+   { if (m.d_rw) { m.d_rw = false; MmuProtect(m.d_ptr, m.bytes); } }
+   void Unprotect(const Memory &m)
+   { if (!m.d_rw) { m.d_rw = true; MmuAllow(m.d_ptr, m.bytes); } }
    /// Aliases need to be restricted during protection
    void AliasProtect(const void *ptr, size_t bytes)
    { MmuProtect(MmuAddrR(ptr), MmuLengthR(ptr, bytes)); }
@@ -969,11 +975,8 @@ void MemoryManager::Copy_(void *dst_h_ptr, const void *src_h_ptr,
       {
          if (dst_h_ptr != src_d_ptr && bytes != 0)
          {
-            internal::Memory &dst_h_base = maps->memories.at(dst_h_ptr);
             internal::Memory &src_d_base = maps->memories.at(src_d_ptr);
-            MemoryType dst_h_mt = dst_h_base.h_mt;
             MemoryType src_d_mt = src_d_base.d_mt;
-            ctrl->Host(dst_h_mt)->Unprotect(dst_h_ptr, bytes);
             ctrl->Device(src_d_mt)->DtoH(dst_h_ptr, src_d_ptr, bytes);
          }
       }
@@ -1174,13 +1177,14 @@ void *MemoryManager::GetDevicePtr(const void *h_ptr, size_t bytes,
    const MemoryType &d_mt = mem.d_mt;
    MFEM_VERIFY_TYPES(h_mt, d_mt);
    if (!mem.d_ptr) { ctrl->Device(d_mt)->Alloc(mem); }
+   // Aliases might have done some protections
    ctrl->Device(d_mt)->Unprotect(mem);
    if (copy_data)
    {
       MFEM_ASSERT(bytes <= mem.bytes, "invalid copy size");
       ctrl->Device(d_mt)->HtoD(mem.d_ptr, h_ptr, bytes);
    }
-   ctrl->Host(h_mt)->Protect(h_ptr, bytes);
+   ctrl->Host(h_mt)->Protect(mem, bytes);
    return mem.d_ptr;
 }
 
@@ -1206,6 +1210,7 @@ void *MemoryManager::GetAliasDevicePtr(const void *alias_ptr, size_t bytes,
    void *alias_d_ptr = static_cast<char*>(mem.d_ptr) + offset;
    MFEM_ASSERT(alias_h_ptr == alias_ptr, "internal error");
    MFEM_ASSERT(bytes <= alias.bytes, "internal error");
+   mem.d_rw = false;
    ctrl->Device(d_mt)->AliasUnprotect(alias_d_ptr, bytes);
    ctrl->Host(h_mt)->AliasUnprotect(alias_ptr, bytes);
    if (copy) { ctrl->Device(d_mt)->HtoD(alias_d_ptr, alias_h_ptr, bytes); }
@@ -1221,8 +1226,8 @@ void *MemoryManager::GetHostPtr(const void *ptr, size_t bytes, bool copy)
    const MemoryType &h_mt = mem.h_mt;
    const MemoryType &d_mt = mem.d_mt;
    MFEM_VERIFY_TYPES(h_mt, d_mt);
-   ctrl->Host(h_mt)->Unprotect(mem.h_ptr, bytes);
    // Aliases might have done some protections
+   ctrl->Host(h_mt)->Unprotect(mem, bytes);
    if (mem.d_ptr) { ctrl->Device(d_mt)->Unprotect(mem); }
    if (copy && mem.d_ptr) { ctrl->Device(d_mt)->DtoH(mem.h_ptr, mem.d_ptr, bytes); }
    if (mem.d_ptr) { ctrl->Device(d_mt)->Protect(mem); }
@@ -1240,6 +1245,7 @@ void *MemoryManager::GetAliasHostPtr(const void *ptr, size_t bytes,
    void *alias_h_ptr = static_cast<char*>(mem->h_ptr) + alias.offset;
    void *alias_d_ptr = static_cast<char*>(mem->d_ptr) + alias.offset;
    MFEM_ASSERT(alias_h_ptr == ptr,  "internal error");
+   mem->h_rw = false;
    ctrl->Host(h_mt)->AliasUnprotect(alias_h_ptr, bytes);
    if (mem->d_ptr) { ctrl->Device(d_mt)->AliasUnprotect(alias_d_ptr, bytes); }
    if (copy_data && mem->d_ptr)

linalg/CMakeLists.txt

@@ -76,6 +76,13 @@ if (MFEM_USE_GINKGO)
   list(APPEND HDRS ginkgo.hpp)
 endif()
 
+if (MFEM_USE_MUMPS)
+  list(APPEND SRCS mumps.cpp)
+  # If this list (HDRS -> HEADERS) is used for install, we probably want the
+  # header added all the time.
+  list(APPEND HDRS mumps.hpp)
+endif()
+
 if (MFEM_USE_SUNDIALS)
   list(APPEND SRCS sundials.cpp)
   list(APPEND HDRS sundials.hpp)
@@ -98,6 +105,11 @@ if (MFEM_USE_HIOP)
   list(APPEND HDRS hiop.hpp)
 endif()
 
+if (MFEM_USE_MKL_CPARDISO)
+  list(APPEND SRCS cpardiso.cpp)
+  list(APPEND HDRS cpardiso.hpp)
+endif()
+
 convert_filenames_to_full_paths(SRCS)
 convert_filenames_to_full_paths(HDRS)
 

linalg/complex_operator.cpp

@@ -26,10 +26,10 @@ ComplexOperator::ComplexOperator(Operator * Op_Real, Operator * Op_Imag,
    , ownReal_(ownReal)
    , ownImag_(ownImag)
    , convention_(convention)
-   , x_r_(NULL, width / 2)
-   , x_i_(NULL, width / 2)
-   , y_r_(NULL, height / 2)
-   , y_i_(NULL, height / 2)
+   , x_r_()
+   , x_i_()
+   , y_r_()
+   , y_i_()
    , u_(NULL)
    , v_(NULL)
 {}
@@ -68,14 +68,26 @@ const Operator & ComplexOperator::imag() const
 
 void ComplexOperator::Mult(const Vector &x, Vector &y) const
 {
-   double * x_data = x.GetData();
-   x_r_.SetData(x_data);
-   x_i_.SetData(&x_data[width / 2]);
+   x.Read();
+   y.UseDevice(true); y = 0.0;
 
-   y_r_.SetData(&y[0]);
-   y_i_.SetData(&y[height / 2]);
+   x_r_.MakeRef(const_cast<Vector&>(x), 0, width/2);
+   x_i_.MakeRef(const_cast<Vector&>(x), width/2, width/2);
+
+   y_r_.MakeRef(y, 0, height/2);
+   y_i_.MakeRef(y, height/2, height/2);
 
    this->Mult(x_r_, x_i_, y_r_, y_i_);
+
+   y_r_.SyncAliasMemory(y);
+   y_i_.SyncAliasMemory(y);
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   x_r_.Destroy();
+   x_i_.Destroy();
+   y_r_.Destroy();
+   y_i_.Destroy();
 }
 
 void ComplexOperator::Mult(const Vector &x_r, const Vector &x_i,
@@ -91,31 +103,47 @@ void ComplexOperator::Mult(const Vector &x_r, const Vector &x_i,
       y_r = 0.0;
       y_i = 0.0;
    }
+
    if (Op_Imag_)
    {
-      if (!v_) { v_ = new Vector(Op_Imag_->Height()); }
+      if (!v_) { v_ = new Vector(); }
+      v_->UseDevice(true);
+      v_->SetSize(Op_Imag_->Height());
+
       Op_Imag_->Mult(x_i, *v_);
-      y_r_ -= *v_;
+      y_r.Add(-1.0, *v_);
       Op_Imag_->Mult(x_r, *v_);
-      y_i_ += *v_;
+      y_i.Add(1.0, *v_);
    }
 
    if (convention_ == BLOCK_SYMMETRIC)
    {
-      y_i_ *= -1.0;
+      y_i *= -1.0;
    }
 }
 
 void ComplexOperator::MultTranspose(const Vector &x, Vector &y) const
 {
-   double * x_data = x.GetData();
-   y_r_.SetData(x_data);
-   y_i_.SetData(&x_data[height / 2]);
+   x.Read();
+   y.UseDevice(true); y = 0.0;
 
-   x_r_.SetData(&y[0]);
-   x_i_.SetData(&y[width / 2]);
+   x_r_.MakeRef(const_cast<Vector&>(x), 0, height/2);
+   x_i_.MakeRef(const_cast<Vector&>(x), height/2, height/2);
 
-   this->MultTranspose(y_r_, y_i_, x_r_, x_i_);
+   y_r_.MakeRef(y, 0, width/2);
+   y_i_.MakeRef(y, width/2, width/2);
+
+   this->MultTranspose(x_r_, x_i_, y_r_, y_i_);
+
+   y_r_.SyncAliasMemory(y);
+   y_i_.SyncAliasMemory(y);
+
+   // Destroy alias vectors to prevent dangling aliases when the base vectors
+   // are deleted
+   x_r_.Destroy();
+   x_i_.Destroy();
+   y_r_.Destroy();
+   y_i_.Destroy();
 }
 
 void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
@@ -136,13 +164,17 @@ void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
       y_r = 0.0;
       y_i = 0.0;
    }
+
    if (Op_Imag_)
    {
-      if (!u_) { u_ = new Vector(Op_Imag_->Width()); }
+      if (!u_) { u_ = new Vector(); }
+      u_->UseDevice(true);
+      u_->SetSize(Op_Imag_->Width());
+
       Op_Imag_->MultTranspose(x_i, *u_);
-      y_r_.Add(convention_ == BLOCK_SYMMETRIC ? -1.0 : 1.0, *u_);
+      y_r.Add(convention_ == BLOCK_SYMMETRIC ? -1.0 : 1.0, *u_);
       Op_Imag_->MultTranspose(x_r, *u_);
-      y_i_ -= *u_;
+      y_i.Add(-1.0, *u_);
    }
 }
 

linalg/complex_operator.hpp

@@ -100,7 +100,7 @@ public:
    /** @brief Real or imaginary part accessor methods
 
        The following accessor methods should only be called if the requested
-       part of the opertor is known to exist.  This can be checked with
+       part of the operator is known to exist. This can be checked with
        hasRealPart() or hasImagPart().
    */
    virtual Operator & real();
@@ -166,7 +166,7 @@ public:
    /** Combine the blocks making up this complex operator into a single
        SparseMatrix. The resulting matrix can be passed to solvers which require
        access to the matrix entries themselves, such as sparse direct solvers,
-       rather than simply the action of the opertor. Note that this combined
+       rather than simply the action of the operator. Note that this combined
        operator requires roughly twice the memory of the block structured
        operator. */
    SparseMatrix * GetSystemMatrix() const;
@@ -269,7 +269,7 @@ public:
        HypreParMatrix. The resulting matrix can be passed to solvers which
        require access to the matrix entries themselves, such as sparse direct
        solvers or Hypre preconditioners, rather than simply the action of the
-       opertor. Note that this combined operator requires roughly twice the
+       operator. Note that this combined operator requires roughly twice the
        memory of the block structured operator. */
    HypreParMatrix * GetSystemMatrix() const;
 

linalg/cpardiso.cpp

@@ -0,0 +1,233 @@
+
+#include "../config/config.hpp"
+
+#ifdef MFEM_USE_MKL_CPARDISO
+#ifdef MFEM_USE_MPI
+
+#include "cpardiso.hpp"
+#include "hypre.hpp"
+#include <algorithm>
+#include <vector>
+#include <numeric>
+
+namespace mfem
+{
+CPardisoSolver::CPardisoSolver(MPI_Comm comm) : comm_(comm)
+{
+   // Solver default parameters overridden with provided by iparm
+   iparm[0] = 1;
+   // Use METIS for fill-in reordering
+   iparm[1] = 2;
+   // Write solution into x
+   iparm[5] = 0;
+   // Max number of iterative refinement steps
+   iparm[7] = 2;
+   // Perturb the pivot elements with 1E-13
+   iparm[9] = 13;
+   // Use non-symmetric permutation and scaling MPS
+   iparm[10] = 1;
+   // Switch on Maximum Weighted Matching algorithm (default for non-symmetric)
+   iparm[12] = 1;
+   // Output: Number of non-zeros in the factor LU
+   iparm[17] = -1;
+   // Output: Mflops for LU factorization
+   iparm[18] = -1;
+   // Check input data for correctness
+   iparm[26] = 1;
+   // 0-based indexing
+   iparm[34] = 1;
+   // All inputs are distributed between MPI processes
+   iparm[39] = 2;
+   // Maximum number of numerical factorizations
+   maxfct = 1;
+   // Which factorization to use
+   mnum = 1;
+   // Print statistical information in file
+   msglvl = 0;
+   // Initialize error flag
+   error = 0;
+   // Real unsymmetric matrix
+   mtype = MatType::REAL_UNSYMMETRIC;
+   // Number of right hand sides
+   nrhs = 1;
+};
+
+void CPardisoSolver::SetOperator(const Operator &op)
+{
+   auto hypreParMat = dynamic_cast<const HypreParMatrix &>(op);
+
+   MFEM_ASSERT(hypreParMat, "Must pass HypreParMatrix as Operator");
+
+   auto parcsr_op = static_cast<hypre_ParCSRMatrix *>(
+                       const_cast<HypreParMatrix &>(hypreParMat));
+
+   hypre_CSRMatrix *csr_op = hypre_MergeDiagAndOffd(parcsr_op);
+#if MFEM_HYPRE_VERSION >= 21600
+   hypre_CSRMatrixBigJtoJ(csr_op);
+#endif
+
+   m = parcsr_op->global_num_rows;
+   first_row = parcsr_op->first_row_index;
+   nnz_loc = csr_op->num_nonzeros;
+   m_loc = csr_op->num_rows;
+
+   height = m_loc;
+   width = m_loc;
+
+   double *csr_nzval = csr_op->data;
+   int *csr_colind = csr_op->j;
+
+   delete[] csr_rowptr;
+   delete[] reordered_csr_colind;
+   delete[] reordered_csr_nzval;
+   csr_rowptr = new int[m_loc + 1];
+   reordered_csr_colind = new int[nnz_loc];
+   reordered_csr_nzval = new double[nnz_loc];
+
+   for (int i = 0; i <= m_loc; i++)
+   {
+      csr_rowptr[i] = (csr_op->i)[i];
+   }
+
+   // CPardiso expects the column indices to be sorted for each row
+   std::vector<int> permutation_idx(nnz_loc);
+   std::iota(permutation_idx.begin(), permutation_idx.end(), 0);
+   for (int i = 0; i < m_loc; i++)
+   {
+      std::sort(permutation_idx.begin() + csr_rowptr[i],
+                permutation_idx.begin() + csr_rowptr[i + 1],
+                [csr_colind](int i1, int i2)
+      {
+         return csr_colind[i1] < csr_colind[i2];
+      });
+   }
+
+   for (int i = 0; i < nnz_loc; i++)
+   {
+      reordered_csr_colind[i] = csr_colind[permutation_idx[i]];
+      reordered_csr_nzval[i] = csr_nzval[permutation_idx[i]];
+   }
+
+   hypre_CSRMatrixDestroy(csr_op);
+
+   // The number of row in global matrix, rhs element and solution vector that
+   // begins the input domain belonging to this MPI process
+   iparm[40] = first_row;
+
+   // The number of row in global matrix, rhs element and solution vector that
+   // ends the input domain belonging to this MPI process
+   iparm[41] = first_row + m_loc - 1;
+
+   // Analyze inputs
+   phase = 11;
+   cluster_sparse_solver(pt,
+                         &maxfct,
+                         &mnum,
+                         &mtype,
+                         &phase,
+                         &m,
+                         reordered_csr_nzval,
+                         csr_rowptr,
+                         reordered_csr_colind,
+                         &idum,
+                         &nrhs,
+                         iparm,
+                         &msglvl,
+                         &ddum,
+                         &ddum,
+                         &comm_,
+                         &error);
+
+   MFEM_ASSERT(error == 0, "Pardiso analyze input error");
+
+   // Numerical factorization
+   phase = 22;
+   cluster_sparse_solver(pt,
+                         &maxfct,
+                         &mnum,
+                         &mtype,
+                         &phase,
+                         &m,
+                         reordered_csr_nzval,
+                         csr_rowptr,
+                         reordered_csr_colind,
+                         &idum,
+                         &nrhs,
+                         iparm,
+                         &msglvl,
+                         &ddum,
+                         &ddum,
+                         &comm_,
+                         &error);
+
+   MFEM_ASSERT(error == 0, "Pardiso factorization input error");
+}
+
+void CPardisoSolver::Mult(const Vector &b, Vector &x) const
+{
+   // Solve
+   phase = 33;
+   cluster_sparse_solver(pt,
+                         &maxfct,
+                         &mnum,
+                         &mtype,
+                         &phase,
+                         &m,
+                         reordered_csr_nzval,
+                         csr_rowptr,
+                         reordered_csr_colind,
+                         &idum,
+                         &nrhs,
+                         iparm,
+                         &msglvl,
+                         b.GetData(),
+                         x.GetData(),
+                         &comm_,
+                         &error);
+
+   MFEM_ASSERT(error == 0, "Pardiso solve error");
+}
+
+void CPardisoSolver::SetPrintLevel(int print_level)
+{
+   msglvl = print_level;
+}
+
+void CPardisoSolver::SetMatrixType(MatType mat_type)
+{
+   mtype = mat_type;
+}
+
+CPardisoSolver::~CPardisoSolver()
+{
+   // Release all internal memory
+   phase = -1;
+   cluster_sparse_solver(pt,
+                         &maxfct,
+                         &mnum,
+                         &mtype,
+                         &phase,
+                         &m,
+                         reordered_csr_nzval,
+                         csr_rowptr,
+                         reordered_csr_colind,
+                         &idum,
+                         &nrhs,
+                         iparm,
+                         &msglvl,
+                         &ddum,
+                         &ddum,
+                         &comm_,
+                         &error);
+
+   MFEM_ASSERT(error == 0, "Pardiso free error");
+
+   delete[] csr_rowptr;
+   delete[] reordered_csr_colind;
+   delete[] reordered_csr_nzval;
+}
+
+} // namespace mfem
+
+#endif // MFEM_USE_MKL_CPARDISO
+#endif // MFEM_USE_MPI

linalg/cpardiso.hpp

@@ -0,0 +1,125 @@
+// 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_CPARDISO
+#define MFEM_CPARDISO
+
+#include "../config/config.hpp"
+
+#ifdef MFEM_USE_MKL_CPARDISO
+#ifdef MFEM_USE_MPI
+#include "operator.hpp"
+#include <mpi.h>
+#include "mkl_cluster_sparse_solver.h"
+
+namespace mfem
+{
+/**
+ * @brief MKL Parallel Direct Sparse Solver for Clusters
+ *
+ * Interface to the MPI enabled MKL version of Pardiso
+ */
+class CPardisoSolver : public Solver
+{
+public:
+   enum MatType
+   {
+      REAL_STRUCTURE_SYMMETRIC = 1,
+      REAL_UNSYMMETRIC = 11
+   };
+
+   /**
+    * @brief Construct a new CPardisoSolver object
+    *
+    * @param comm MPI Communicator
+    */
+   CPardisoSolver(MPI_Comm comm);
+
+   /**
+    * @brief Set the Operator object and perform factorization
+    *
+    * @a op needs to be of type HypreParMatrix. The contents are copied and
+    * reordered in an internal CSR structure.
+    *
+    * @param op Operator to use in factorization and solve
+    */
+   void SetOperator(const Operator &op) override;
+
+   /**
+    * @brief Solve
+    *
+    * @param b RHS vector
+    * @param x Solution vector
+    */
+   void Mult(const Vector &b, Vector &x) const override;
+
+   /**
+    * @brief Set the print level for Pardiso
+    *
+    * Prints statistics after the factorization and after each solve.
+    *
+    * @param print_lvl Print level
+    */
+   void SetPrintLevel(int print_lvl);
+
+   /**
+    * @brief Set the matrix type
+    *
+    * The matrix type supported is either real and symmetric or real and
+    * non-symmetric.
+    *
+    * @param mat_type Matrix type
+    */
+   void SetMatrixType(MatType mat_type);
+
+   ~CPardisoSolver();
+
+private:
+   MPI_Comm comm_;
+
+   // Global number of rows
+   int m;
+
+   // First row index of the global matrix on the local MPI rank
+   int first_row;
+
+   // Local number of nonzero entries
+   int nnz_loc;
+
+   // Local number of rows, obtained from a ParCSR matrix
+   int m_loc;
+
+   // CSR data structure for the copy data of the local CSR matrix
+   int *csr_rowptr = nullptr;
+   double *reordered_csr_nzval = nullptr;
+   int *reordered_csr_colind = nullptr;
+
+   // Internal solver memory pointer pt,
+   // 32-bit: int pt[64]
+   // 64-bit: long int pt[64] or void *pt[64] should be OK on both architectures
+   mutable void *pt[64] = {0};
+
+   // Solver control parameters, detailed description can be found in the
+   // constructor.
+   mutable int iparm[64] = {0};
+   mutable int maxfct, mnum, msglvl, phase, error;
+   int mtype;
+   int nrhs;
+
+   // Dummy variables
+   mutable int idum;
+   mutable double ddum;
+};
+} // namespace mfem
+
+#endif
+#endif // MFEM_USE_MKL_CPARDISO
+#endif // MFEM_USE_MPI

linalg/densemat.cpp

@@ -373,7 +373,7 @@ void DenseMatrix::SymmetricScaling(const Vector & s)
 {
    if (height != width || s.Size() != height)
    {
-      mfem_error("DenseMatrix::SymmetricScaling");
+      mfem_error("DenseMatrix::SymmetricScaling: dimension mismatch");
    }
 
    double * ss = new double[width];
@@ -401,7 +401,7 @@ void DenseMatrix::InvSymmetricScaling(const Vector & s)
 {
    if (height != width || s.Size() != width)
    {
-      mfem_error("DenseMatrix::SymmetricScaling");
+      mfem_error("DenseMatrix::InvSymmetricScaling: dimension mismatch");
    }
 
    double * ss = new double[width];
@@ -528,7 +528,7 @@ double DenseMatrix::Weight() const
       double F = d[0] * d[3] + d[1] * d[4] + d[2] * d[5];
       return sqrt(E * G - F * F);
    }
-   mfem_error("DenseMatrix::Weight()");
+   mfem_error("DenseMatrix::Weight(): mismatched or unsupported dimensions");
    return 0.0;
 }
 
@@ -639,7 +639,7 @@ void DenseMatrix::Invert()
 #ifdef MFEM_DEBUG
    if (Height() <= 0 || Height() != Width())
    {
-      mfem_error("DenseMatrix::Invert()");
+      mfem_error("DenseMatrix::Invert(): dimension mismatch");
    }
 #endif
 
@@ -1083,7 +1083,7 @@ void DenseMatrix::Eigensystem(Vector &ev, DenseMatrix *evect)
 
    MFEM_CONTRACT_VAR(ev);
    MFEM_CONTRACT_VAR(evect);
-   mfem_error("DenseMatrix::Eigensystem");
+   mfem_error("DenseMatrix::Eigensystem: Compiled without LAPACK");
 
 #endif
 }
@@ -1164,7 +1164,7 @@ void DenseMatrix::Eigensystem(DenseMatrix &b, Vector &ev,
    MFEM_CONTRACT_VAR(b);
    MFEM_CONTRACT_VAR(ev);
    MFEM_CONTRACT_VAR(evect);
-   mfem_error("DenseMatrix::Eigensystem for generalized eigenvalues");
+   mfem_error("DenseMatrix::Eigensystem(generalized): Compiled without LAPACK");
 #endif
 }
 
@@ -1204,7 +1204,7 @@ void DenseMatrix::SingularValues(Vector &sv) const
 #else
    MFEM_CONTRACT_VAR(sv);
    // compiling without lapack
-   mfem_error("DenseMatrix::SingularValues");
+   mfem_error("DenseMatrix::SingularValues: Compiled without LAPACK");
 #endif
 }
 
@@ -1441,7 +1441,7 @@ void DenseMatrix::GradToCurl(DenseMatrix &curl)
    if ((Width() != 2 || curl.Width() != 1 || 2*n != curl.Height()) &&
        (Width() != 3 || curl.Width() != 3 || 3*n != curl.Height()))
    {
-      mfem_error("DenseMatrix::GradToCurl(...)");
+      mfem_error("DenseMatrix::GradToCurl(...): dimension mismatch");
    }
 #endif
 
@@ -1676,7 +1676,7 @@ void DenseMatrix::AddMatrix(DenseMatrix &A, int ro, int co)
 #ifdef MFEM_DEBUG
    if (co+aw > Width() || ro+ah > h)
    {
-      mfem_error("DenseMatrix::AddMatrix(...) 1");
+      mfem_error("DenseMatrix::AddMatrix(...) 1 : dimension mismatch");
    }
 #endif
 
@@ -1706,7 +1706,7 @@ void DenseMatrix::AddMatrix(double a, const DenseMatrix &A, int ro, int co)
 #ifdef MFEM_DEBUG
    if (co+aw > Width() || ro+ah > h)
    {
-      mfem_error("DenseMatrix::AddMatrix(...) 2");
+      mfem_error("DenseMatrix::AddMatrix(...) 2 : dimension mismatch");
    }
 #endif
 
@@ -1753,7 +1753,7 @@ void DenseMatrix::AdjustDofDirection(Array<int> &dofs)
 #ifdef MFEM_DEBUG
    if (dofs.Size() != n || Width() != n)
    {
-      mfem_error("DenseMatrix::AdjustDofDirection(...)");
+      mfem_error("DenseMatrix::AdjustDofDirection(...): dimension mismatch");
    }
 #endif
 
@@ -2093,11 +2093,11 @@ void CalcAdjugate(const DenseMatrix &a, DenseMatrix &adja)
 #ifdef MFEM_DEBUG
    if (a.Width() > a.Height() || a.Width() < 1 || a.Height() > 3)
    {
-      mfem_error("CalcAdjugate(...)");
+      mfem_error("CalcAdjugate(...): unsupported dimensions");
    }
    if (a.Width() != adja.Height() || a.Height() != adja.Width())
    {
-      mfem_error("CalcAdjugate(...)");
+      mfem_error("CalcAdjugate(...): dimension mismatch");
    }
 #endif
 
@@ -2166,7 +2166,7 @@ void CalcAdjugateTranspose(const DenseMatrix &a, DenseMatrix &adjat)
    if (a.Height() != a.Width() || adjat.Height() != adjat.Width() ||
        a.Width() != adjat.Width() || a.Width() < 1 || a.Width() > 3)
    {
-      mfem_error("CalcAdjugateTranspose(...)");
+      mfem_error("CalcAdjugateTranspose(...): dimension mismatch");
    }
 #endif
    if (a.Width() == 1)
@@ -2269,7 +2269,7 @@ void CalcInverseTranspose(const DenseMatrix &a, DenseMatrix &inva)
    if ( (a.Width() != a.Height()) || ( (a.Height()!= 1) && (a.Height()!= 2)
                                        && (a.Height()!= 3) ) )
    {
-      mfem_error("CalcInverseTranspose(...)");
+      mfem_error("CalcInverseTranspose(...): dimension mismatch");
    }
 #endif
 
@@ -2396,7 +2396,7 @@ void MultABt(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
    if (A.Height() != ABt.Height() || B.Height() != ABt.Width() ||
        A.Width() != B.Width())
    {
-      mfem_error("MultABt(...)");
+      mfem_error("MultABt(...): dimension mismatch");
    }
 #endif
 
@@ -2462,7 +2462,7 @@ void MultADBt(const DenseMatrix &A, const Vector &D,
    if (A.Height() != ADBt.Height() || B.Height() != ADBt.Width() ||
        A.Width() != B.Width() || A.Width() != D.Size())
    {
-      mfem_error("MultADBt(...)");
+      mfem_error("MultADBt(...): dimension mismatch");
    }
 #endif
 
@@ -2501,7 +2501,7 @@ void AddMultABt(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
    if (A.Height() != ABt.Height() || B.Height() != ABt.Width() ||
        A.Width() != B.Width())
    {
-      mfem_error("AddMultABt(...)");
+      mfem_error("AddMultABt(...): dimension mismatch");
    }
 #endif
 
@@ -2559,7 +2559,7 @@ void AddMultADBt(const DenseMatrix &A, const Vector &D,
    if (A.Height() != ADBt.Height() || B.Height() != ADBt.Width() ||
        A.Width() != B.Width() || A.Width() != D.Size())
    {
-      mfem_error("AddMultADBt(...)");
+      mfem_error("AddMultADBt(...): dimension mismatch");
    }
 #endif
 
@@ -2595,7 +2595,7 @@ void AddMult_a_ABt(double a, const DenseMatrix &A, const DenseMatrix &B,
    if (A.Height() != ABt.Height() || B.Height() != ABt.Width() ||
        A.Width() != B.Width())
    {
-      mfem_error("AddMult_a_ABt(...)");
+      mfem_error("AddMult_a_ABt(...): dimension mismatch");
    }
 #endif
 
@@ -2653,7 +2653,7 @@ void MultAtB(const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &AtB)
    if (A.Width() != AtB.Height() || B.Width() != AtB.Width() ||
        A.Height() != B.Height())
    {
-      mfem_error("MultAtB(...)");
+      mfem_error("MultAtB(...): dimension mismatch");
    }
 #endif
 
@@ -2761,7 +2761,7 @@ void MultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 #ifdef MFEM_DEBUG
    if (v.Size() != VWt.Height() || w.Size() != VWt.Width())
    {
-      mfem_error("MultVWt(...)");
+      mfem_error("MultVWt(...): dimension mismatch");
    }
 #endif
 
@@ -2782,7 +2782,7 @@ void AddMultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 #ifdef MFEM_DEBUG
    if (VWt.Height() != m || VWt.Width() != n)
    {
-      mfem_error("AddMultVWt(...)");
+      mfem_error("AddMultVWt(...): dimension mismatch");
    }
 #endif
 
@@ -2803,7 +2803,7 @@ void AddMultVVt(const Vector &v, DenseMatrix &VVt)
 #ifdef MFEM_DEBUG
    if (VVt.Height() != n || VVt.Width() != n)
    {
-      mfem_error("AddMultVVt(...)");
+      mfem_error("AddMultVVt(...): dimension mismatch");
    }
 #endif
 
@@ -2828,7 +2828,7 @@ void AddMult_a_VWt(const double a, const Vector &v, const Vector &w,
 #ifdef MFEM_DEBUG
    if (VWt.Height() != m || VWt.Width() != n)
    {
-      mfem_error("AddMult_a_VWt(...)");
+      mfem_error("AddMult_a_VWt(...): dimension mismatch");
    }
 #endif
 
@@ -3353,7 +3353,7 @@ void DenseMatrixEigensystem::Eval()
 #ifdef MFEM_DEBUG
    if (mat.Width() != n)
    {
-      mfem_error("DenseMatrixEigensystem::Eval()");
+      mfem_error("DenseMatrixEigensystem::Eval(): dimension mismatch");
    }
 #endif
 

linalg/hypre.cpp

@@ -1048,6 +1048,36 @@ HYPRE_Int HypreParMatrix::MultTranspose(HypreParVector & x, HypreParVector & y,
    return hypre_ParCSRMatrixMatvecT(a, A, x, b, y);
 }
 
+void HypreParMatrix::AbsMult(double a, const Vector &x,
+                             double b, Vector &y) const
+{
+   MFEM_ASSERT(x.Size() == Width(), "invalid x.Size() = " << x.Size()
+               << ", expected size = " << Width());
+   MFEM_ASSERT(y.Size() == Height(), "invalid y.Size() = " << y.Size()
+               << ", expected size = " << Height());
+
+   auto x_data = x.HostRead();
+   auto y_data = (b == 0.0) ? y.HostWrite() : y.HostReadWrite();
+
+   internal::hypre_ParCSRMatrixAbsMatvec(A, a, const_cast<double*>(x_data),
+                                         b, y_data);
+}
+
+void HypreParMatrix::AbsMultTranspose(double a, const Vector &x,
+                                      double b, Vector &y) const
+{
+   MFEM_ASSERT(x.Size() == Height(), "invalid x.Size() = " << x.Size()
+               << ", expected size = " << Height());
+   MFEM_ASSERT(y.Size() == Width(), "invalid y.Size() = " << y.Size()
+               << ", expected size = " << Width());
+
+   auto x_data = x.HostRead();
+   auto y_data = (b == 0.0) ? y.HostWrite() : y.HostReadWrite();
+
+   internal::hypre_ParCSRMatrixAbsMatvecT(A, a, const_cast<double*>(x_data),
+                                          b, y_data);
+}
+
 HypreParMatrix* HypreParMatrix::LeftDiagMult(const SparseMatrix &D,
                                              HYPRE_Int* row_starts) const
 {
@@ -3185,10 +3215,31 @@ void HypreBoomerAMG::SetOperator(const Operator &op)
    B = X = NULL;
 }
 
-void HypreBoomerAMG::SetSystemsOptions(int dim)
+void HypreBoomerAMG::SetSystemsOptions(int dim, bool order_bynodes)
 {
    HYPRE_BoomerAMGSetNumFunctions(amg_precond, dim);
 
+   // The default "system" ordering in hypre is Ordering::byVDIM. When we are
+   // using Ordering::byNODES, we have to specify the ordering explicitly with
+   // HYPRE_BoomerAMGSetDofFunc as in the following code.
+   if (order_bynodes)
+   {
+      // hypre actually deletes the following pointer in HYPRE_BoomerAMGDestroy,
+      // so we don't need to track it
+      HYPRE_Int *mapping = mfem_hypre_CTAlloc(HYPRE_Int, height);
+      int h_nnodes = height / dim; // nodes owned in linear algebra (not fem)
+      MFEM_VERIFY(height % dim == 0, "Ordering does not work as claimed!");
+      int k = 0;
+      for (int i = 0; i < dim; ++i)
+      {
+         for (int j = 0; j < h_nnodes; ++j)
+         {
+            mapping[k++] = i;
+         }
+      }
+      HYPRE_BoomerAMGSetDofFunc(amg_precond, mapping);
+   }
+
    // More robust options with respect to convergence
    HYPRE_BoomerAMGSetAggNumLevels(amg_precond, 0);
    HYPRE_BoomerAMGSetStrongThreshold(amg_precond, 0.5);

linalg/hypre.hpp

@@ -446,6 +446,12 @@ public:
    virtual void MultTranspose(const Vector &x, Vector &y) const
    { MultTranspose(1.0, x, 0.0, y); }
 
+   /// Computes y = a * |A| * x + b * y, using entry-wise absolute values of matrix A
+   void AbsMult(double a, const Vector &x, double b, Vector &y) const;
+
+   /// Computes y = a * |At| * x + b * y, using entry-wise absolute values of the transpose of matrix A
+   void AbsMultTranspose(double a, const Vector &x, double b, Vector &y) const;
+
    /** The "Boolean" analog of y = alpha * A * x + beta * y, where elements in
        the sparsity pattern of the matrix are treated as "true". */
    void BooleanMult(int alpha, const int *x, int beta, int *y)
@@ -986,16 +992,15 @@ public:
 
    virtual void SetOperator(const Operator &op);
 
-   /** More robust options for systems, such as elasticity. Note that BoomerAMG
-       assumes Ordering::byVDIM in the finite element space used to generate the
-       matrix A. */
-   void SetSystemsOptions(int dim);
+   /** More robust options for systems, such as elasticity. */
+   void SetSystemsOptions(int dim, bool order_bynodes=false);
 
    /** A special elasticity version of BoomerAMG that takes advantage of
        geometric rigid body modes and could perform better on some problems, see
        "Improving algebraic multigrid interpolation operators for linear
        elasticity problems", Baker, Kolev, Yang, NLAA 2009, DOI:10.1002/nla.688.
-       As with SetSystemsOptions(), this solver assumes Ordering::byVDIM. */
+       This solver assumes Ordering::byVDIM in the FiniteElementSpace used to
+       construct A. */
    void SetElasticityOptions(ParFiniteElementSpace *fespace);
 
    void SetPrintLevel(int print_level)

linalg/hypre_parcsr.cpp

@@ -16,6 +16,7 @@
 
 #include "hypre_parcsr.hpp"
 #include <limits>
+#include <cmath>
 
 namespace mfem
 {
@@ -977,6 +978,196 @@ void hypre_ParCSRMatrixSplit(hypre_ParCSRMatrix *A,
    }
 }
 
+/* Based on hypre_CSRMatrixMatvec in hypre's csr_matvec.c */
+void hypre_CSRMatrixAbsMatvec(hypre_CSRMatrix *A,
+                              HYPRE_Real alpha,
+                              HYPRE_Real *x,
+                              HYPRE_Real beta,
+                              HYPRE_Real *y)
+{
+   HYPRE_Real       *A_data   = hypre_CSRMatrixData(A);
+   HYPRE_Int        *A_i      = hypre_CSRMatrixI(A);
+   HYPRE_Int        *A_j      = hypre_CSRMatrixJ(A);
+   HYPRE_Int         num_rows = hypre_CSRMatrixNumRows(A);
+
+   HYPRE_Int        *A_rownnz = hypre_CSRMatrixRownnz(A);
+   HYPRE_Int         num_rownnz = hypre_CSRMatrixNumRownnz(A);
+
+   HYPRE_Real       *x_data = x;
+   HYPRE_Real       *y_data = y;
+
+   HYPRE_Real        temp, tempx;
+
+   HYPRE_Int         i, jj;
+
+   HYPRE_Int         m;
+
+   HYPRE_Real        xpar=0.7;
+
+   /*-----------------------------------------------------------------------
+    * Do (alpha == 0.0) computation - RDF: USE MACHINE EPS
+    *-----------------------------------------------------------------------*/
+
+   if (alpha == 0.0)
+   {
+      for (i = 0; i < num_rows; i++)
+      {
+         y_data[i] *= beta;
+      }
+      return;
+   }
+
+   /*-----------------------------------------------------------------------
+    * y = (beta/alpha)*y
+    *-----------------------------------------------------------------------*/
+
+   temp = beta / alpha;
+
+   if (temp != 1.0)
+   {
+      if (temp == 0.0)
+      {
+         for (i = 0; i < num_rows; i++)
+         {
+            y_data[i] = 0.0;
+         }
+      }
+      else
+      {
+         for (i = 0; i < num_rows; i++)
+         {
+            y_data[i] *= temp;
+         }
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y += abs(A)*x
+    *-----------------------------------------------------------------*/
+
+   /* use rownnz pointer to do the abs(A)*x multiplication
+      when num_rownnz is smaller than num_rows */
+
+   if (num_rownnz < xpar*(num_rows))
+   {
+      for (i = 0; i < num_rownnz; i++)
+      {
+         m = A_rownnz[i];
+
+         tempx = 0;
+         for (jj = A_i[m]; jj < A_i[m+1]; jj++)
+         {
+            tempx += std::abs(A_data[jj])*x_data[A_j[jj]];
+         }
+         y_data[m] += tempx;
+      }
+   }
+   else
+   {
+      for (i = 0; i < num_rows; i++)
+      {
+         tempx = 0;
+         for (jj = A_i[i]; jj < A_i[i+1]; jj++)
+         {
+            tempx += std::abs(A_data[jj])*x_data[A_j[jj]];
+         }
+         y_data[i] += tempx;
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y = alpha*y
+    *-----------------------------------------------------------------*/
+
+   if (alpha != 1.0)
+   {
+      for (i = 0; i < num_rows; i++)
+      {
+         y_data[i] *= alpha;
+      }
+   }
+
+}
+
+/* Based on hypre_CSRMatrixMatvecT in hypre's csr_matvec.c */
+void hypre_CSRMatrixAbsMatvecT(hypre_CSRMatrix *A,
+                               HYPRE_Real alpha,
+                               HYPRE_Real *x,
+                               HYPRE_Real beta,
+                               HYPRE_Real *y)
+{
+   HYPRE_Real       *A_data   = hypre_CSRMatrixData(A);
+   HYPRE_Int        *A_i      = hypre_CSRMatrixI(A);
+   HYPRE_Int        *A_j      = hypre_CSRMatrixJ(A);
+   HYPRE_Int         num_rows = hypre_CSRMatrixNumRows(A);
+   HYPRE_Int         num_cols = hypre_CSRMatrixNumCols(A);
+
+   HYPRE_Real       *x_data = x;
+   HYPRE_Real       *y_data = y;
+
+   HYPRE_Int         i, j, jj;
+
+   HYPRE_Real        temp;
+
+   if (alpha == 0.0)
+   {
+      for (i = 0; i < num_cols; i++)
+      {
+         y_data[i] *= beta;
+      }
+      return;
+   }
+
+   /*-----------------------------------------------------------------------
+    * y = (beta/alpha)*y
+    *-----------------------------------------------------------------------*/
+
+   temp = beta / alpha;
+
+   if (temp != 1.0)
+   {
+      if (temp == 0.0)
+      {
+         for (i = 0; i < num_cols; i++)
+         {
+            y_data[i] = 0.0;
+         }
+      }
+      else
+      {
+         for (i = 0; i < num_cols; i++)
+         {
+            y_data[i] *= temp;
+         }
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y += abs(A)^T*x
+    *-----------------------------------------------------------------*/
+
+   for (i = 0; i < num_rows; i++)
+   {
+      for (jj = A_i[i]; jj < A_i[i+1]; jj++)
+      {
+         j = A_j[jj];
+         y_data[j] += std::abs(A_data[jj]) * x_data[i];
+      }
+   }
+
+   /*-----------------------------------------------------------------
+    * y = alpha*y
+    *-----------------------------------------------------------------*/
+
+   if (alpha != 1.0)
+   {
+      for (i = 0; i < num_cols; i++)
+      {
+         y_data[i] *= alpha;
+      }
+   }
+}
+
 /* Based on hypre_CSRMatrixMatvec in hypre's csr_matvec.c */
 void hypre_CSRMatrixBooleanMatvec(hypre_CSRMatrix *A,
                                   HYPRE_Bool alpha,
@@ -1236,6 +1427,143 @@ hypre_ParCSRCommHandleCreate_bool(HYPRE_Int            job,
    return comm_handle;
 }
 
+/* Based on hypre_ParCSRMatrixMatvec in par_csr_matvec.c */
+void hypre_ParCSRMatrixAbsMatvec(hypre_ParCSRMatrix *A,
+                                 HYPRE_Real alpha,
+                                 HYPRE_Real *x,
+                                 HYPRE_Real beta,
+                                 HYPRE_Real *y)
+{
+   hypre_ParCSRCommHandle *comm_handle;
+   hypre_ParCSRCommPkg *comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   hypre_CSRMatrix   *diag   = hypre_ParCSRMatrixDiag(A);
+   hypre_CSRMatrix   *offd   = hypre_ParCSRMatrixOffd(A);
+
+   HYPRE_Int          num_cols_offd = hypre_CSRMatrixNumCols(offd);
+   HYPRE_Int          num_sends, i, j, index;
+
+   HYPRE_Real        *x_tmp, *x_buf;
+
+   x_tmp = mfem_hypre_CTAlloc(HYPRE_Real, num_cols_offd);
+
+   /*---------------------------------------------------------------------
+    * If there exists no CommPkg for A, a CommPkg is generated using
+    * equally load balanced partitionings
+    *--------------------------------------------------------------------*/
+   if (!comm_pkg)
+   {
+      hypre_MatvecCommPkgCreate(A);
+      comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   }
+
+   num_sends = hypre_ParCSRCommPkgNumSends(comm_pkg);
+   x_buf = mfem_hypre_CTAlloc(
+              HYPRE_Real, hypre_ParCSRCommPkgSendMapStart(comm_pkg, num_sends));
+
+   index = 0;
+   for (i = 0; i < num_sends; i++)
+   {
+      j = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i);
+      for ( ; j < hypre_ParCSRCommPkgSendMapStart(comm_pkg, i+1); j++)
+      {
+         x_buf[index++] = x[hypre_ParCSRCommPkgSendMapElmt(comm_pkg, j)];
+      }
+   }
+
+   comm_handle = hypre_ParCSRCommHandleCreate(1, comm_pkg, x_buf, x_tmp);
+
+   hypre_CSRMatrixAbsMatvec(diag, alpha, x, beta, y);
+
+   hypre_ParCSRCommHandleDestroy(comm_handle);
+
+   if (num_cols_offd)
+   {
+      hypre_CSRMatrixAbsMatvec(offd, alpha, x_tmp, 1.0, y);
+   }
+
+   mfem_hypre_TFree(x_buf);
+   mfem_hypre_TFree(x_tmp);
+}
+
+/* Based on hypre_ParCSRMatrixMatvecT in par_csr_matvec.c */
+void hypre_ParCSRMatrixAbsMatvecT(hypre_ParCSRMatrix *A,
+                                  HYPRE_Real alpha,
+                                  HYPRE_Real *x,
+                                  HYPRE_Real beta,
+                                  HYPRE_Real *y)
+{
+   hypre_ParCSRCommHandle *comm_handle;
+   hypre_ParCSRCommPkg    *comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   hypre_CSRMatrix        *diag = hypre_ParCSRMatrixDiag(A);
+   hypre_CSRMatrix        *offd = hypre_ParCSRMatrixOffd(A);
+   HYPRE_Real             *y_tmp;
+   HYPRE_Real             *y_buf;
+
+   HYPRE_Int               num_cols_offd = hypre_CSRMatrixNumCols(offd);
+
+   HYPRE_Int               i, j, jj, end, num_sends;
+
+   y_tmp = mfem_hypre_TAlloc(HYPRE_Real, num_cols_offd);
+
+   /*---------------------------------------------------------------------
+    * If there exists no CommPkg for A, a CommPkg is generated using
+    * equally load balanced partitionings
+    *--------------------------------------------------------------------*/
+   if (!comm_pkg)
+   {
+      hypre_MatvecCommPkgCreate(A);
+      comm_pkg = hypre_ParCSRMatrixCommPkg(A);
+   }
+
+   num_sends = hypre_ParCSRCommPkgNumSends(comm_pkg);
+   y_buf = mfem_hypre_CTAlloc(
+              HYPRE_Real, hypre_ParCSRCommPkgSendMapStart(comm_pkg, num_sends));
+
+   if (num_cols_offd)
+   {
+#if MFEM_HYPRE_VERSION >= 21100
+      if (A->offdT)
+      {
+         // offdT is optional. Used only if it's present.
+         hypre_CSRMatrixAbsMatvec(A->offdT, alpha, x, 0., y_tmp);
+      }
+      else
+#endif
+      {
+         hypre_CSRMatrixAbsMatvecT(offd, alpha, x, 0., y_tmp);
+      }
+   }
+
+   comm_handle = hypre_ParCSRCommHandleCreate(2, comm_pkg, y_tmp, y_buf);
+
+#if MFEM_HYPRE_VERSION >= 21100
+   if (A->diagT)
+   {
+      // diagT is optional. Used only if it's present.
+      hypre_CSRMatrixAbsMatvec(A->diagT, alpha, x, beta, y);
+   }
+   else
+#endif
+   {
+      hypre_CSRMatrixAbsMatvecT(diag, alpha, x, beta, y);
+   }
+
+   hypre_ParCSRCommHandleDestroy(comm_handle);
+
+   for (i = 0; i < num_sends; i++)
+   {
+      end = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i+1);
+      for (j = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i); j < end; j++)
+      {
+         jj = hypre_ParCSRCommPkgSendMapElmt(comm_pkg, j);
+         y[jj] += y_buf[j];
+      }
+   }
+
+   mfem_hypre_TFree(y_buf);
+   mfem_hypre_TFree(y_tmp);
+}
+
 /* Based on hypre_ParCSRMatrixMatvec in par_csr_matvec.c */
 void hypre_ParCSRMatrixBooleanMatvec(hypre_ParCSRMatrix *A,
                                      HYPRE_Bool alpha,

linalg/hypre_parcsr.hpp

@@ -118,6 +118,34 @@ void hypre_ParCSRMatrixSplit(hypre_ParCSRMatrix *A,
 typedef int HYPRE_Bool;
 #define HYPRE_MPI_BOOL MPI_INT
 
+/// Computes y = alpha * |A| * x + beta * y, using entry-wise absolute values of matrix A
+void hypre_CSRMatrixAbsMatvec(hypre_CSRMatrix *A,
+                              HYPRE_Real alpha,
+                              HYPRE_Real *x,
+                              HYPRE_Real beta,
+                              HYPRE_Real *y);
+
+/// Computes y = alpha * |At| * x + beta * y, using entry-wise absolute values of the transpose of matrix A
+void hypre_CSRMatrixAbsMatvecT(hypre_CSRMatrix *A,
+                               HYPRE_Real alpha,
+                               HYPRE_Real *x,
+                               HYPRE_Real beta,
+                               HYPRE_Real *y);
+
+/// Computes y = alpha * |A| * x + beta * y, using entry-wise absolute values of matrix A
+void hypre_ParCSRMatrixAbsMatvec(hypre_ParCSRMatrix *A,
+                                 HYPRE_Real alpha,
+                                 HYPRE_Real *x,
+                                 HYPRE_Real beta,
+                                 HYPRE_Real *y);
+
+/// Computes y = alpha * |At| * x + beta * y, using entry-wise absolute values of the transpose of matrix A
+void hypre_ParCSRMatrixAbsMatvecT(hypre_ParCSRMatrix *A,
+                                  HYPRE_Real alpha,
+                                  HYPRE_Real *x,
+                                  HYPRE_Real beta,
+                                  HYPRE_Real *y);
+
 /** The "Boolean" analog of y = alpha * A * x + beta * y, where elements in the
     sparsity pattern of the CSR matrix A are treated as "true". */
 void hypre_CSRMatrixBooleanMatvec(hypre_CSRMatrix *A,

linalg/linalg.hpp

@@ -45,6 +45,10 @@
 #include "hypre_parcsr.hpp"
 #include "hypre.hpp"
 
+#ifdef MFEM_USE_MUMPS
+#include "mumps.hpp"
+#endif
+
 #ifdef MFEM_USE_PETSC
 #include "petsc.hpp"
 #endif
@@ -61,6 +65,10 @@
 #include "strumpack.hpp"
 #endif
 
+#ifdef MFEM_USE_MKL_CPARDISO
+#include "cpardiso.hpp"
+#endif
+
 #endif // MFEM_USE_MPI
 
 #endif