Adding BlockGSPreconditioner.

Bug fix for MixedVectorCurlIntegrator PA

.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 +65,16 @@ 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 AmgX solver class for simple integration with NVIDIA's multigrid library.
+
 - 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 +103,14 @@ 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 +136,9 @@ Linear and nonlinear solvers
 
 - Added support for the SLEPc eigensolver package.
 
+- Added partially assembled convergent diagonal preconditioner for adaptively
+  refined meshes (i.e. non-conforming finite element spaces), see Example 6/6p.
+
 New and updated examples and miniapps
 -------------------------------------
 - Added a new example, Example 25/25p, to demonstrate the use of a Perfectly
@@ -149,6 +175,9 @@ 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 +192,47 @@ 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)
@@ -265,6 +295,11 @@ if (MFEM_USE_CEED)
   find_package(libCEED REQUIRED)
 endif()
 
+if (MFEM_USE_AMGX)
+  include_directories(${AMGX_DIR}/include)
+  link_directories(${AMGX_DIR}/lib64 -L${AMGX_DIR}/lib -Xlinker=-rpath=${CUDA_HOME}/lib64)
+endif()
+
 if (MFEM_USE_CONDUIT)
     find_package(Conduit REQUIRED conduit relay blueprint )
 endif()
@@ -296,22 +331,6 @@ if (MFEM_USE_HIOP)
   # find_package updates HIOP_FOUND, HIOP_INCLUDE_DIRS, HIOP_LIBRARIES
 endif()
 
-# CUDA
-if (MFEM_USE_CUDA)
-   set(CMAKE_CUDA_STANDARD 11)
-   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
-   set(CMAKE_CUDA_EXTENSIONS OFF)
-   set(CMAKE_CUDA_FLAGS "-arch=${CUDA_ARCH} --expt-extended-lambda"
-       CACHE STRING "CUDA flags set for MFEM" FORCE)
-   if (MFEM_USE_MPI)
-      set(CUDA_CCBIN_COMPILER ${MPI_CXX_COMPILER})
-   else()
-      set(CUDA_CCBIN_COMPILER ${CMAKE_CXX_COMPILER})
-   endif()
-   string(APPEND CMAKE_CUDA_FLAGS " -ccbin ${CUDA_CCBIN_COMPILER}")
-   set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CUDA_CCBIN_COMPILER})
-endif()
-
 # OCCA
 if (MFEM_USE_OCCA)
    find_package(OCCA REQUIRED)
@@ -357,7 +376,8 @@ 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 AMGX)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")

INSTALL

@@ -350,6 +350,12 @@ MFEM_USE_STRUMPACK = YES/NO
    classes. When enabled, this option uses the STRUMPACK_* library options, see
    below.
 
+MFEM_USE_AMGX = YES/NO
+   Enable MFEM functionality based on the AMGX multigrid library from 
+   NVIDIA. When enabled, this options enables the user to use SparseMatrices
+   and HypreParMatrices to solve linear systems using routines from the AMGX
+   library.
+
 MFEM_USE_GINKGO = YES/NO
    Enable MFEM functionality based on the Ginkgo library, which provides
    iterative linear solvers and preconditioners with OpenMP, CUDA backends, see
@@ -650,6 +656,11 @@ The specific libraries and their options are:
   Options: CUDA_CXX, CUDA_ARCH, CUDA_OPT, CUDA_LIB.
   Versions: CUDA >= 9.1, older versions may work too.
 
+- AMGX (optional), used when MFEM_USE_AMGX = YES.
+  URL: https://github.com/NVIDIA/AMGX
+  Options: AMGX_OPT, AMGX_LIB.
+  Versions: AMGX >= 2.1, older versions may work too.
+
 - HIP (optional), used when MFEM_USE_HIP = YES.
   URL: https://rocm.github.io/ROCmInstall.html
   Options: HIP_CXX, HIP_ARCH, HIP_OPT, HIP_LIB.
@@ -663,7 +674,7 @@ 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.
@@ -806,6 +817,7 @@ MFEM_USE_MESQUITE
 MFEM_USE_SUITESPARSE
 MFEM_USE_SUPERLU
 MFEM_USE_STRUMPACK
+MFEM_USE_AMGX
 MFEM_USE_GINKGO
 MFEM_USE_GNUTLS
 MFEM_USE_NETCDF

config/cmake/config.hpp.in

@@ -126,6 +126,9 @@
 // Requires a CUDA compiler (nvcc).
 #cmakedefine MFEM_USE_CUDA
 
+// Enable MFEM functionality based on the AMGX library
+#cmakedefine MFEM_USE_AMGX
+
 // Enable MFEM functionality based on the RAJA library
 #cmakedefine MFEM_USE_RAJA
 

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/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.in

@@ -137,6 +137,9 @@
 // Requires a CUDA compiler (nvcc).
 // #define MFEM_USE_CUDA
 
+// Enable MFEM functionality based on the AMGX library.
+// #define MFEM_USE_AMGX
+
 // Build the AMD GPU/HIP-enabled version of the MFEM library.
 // Requires a HIP compiler (hipcc).
 // #define MFEM_USE_HIP

config/config.mk.in

@@ -45,6 +45,7 @@ MFEM_USE_PUMI          = @MFEM_USE_PUMI@
 MFEM_USE_HIOP          = @MFEM_USE_HIOP@
 MFEM_USE_GSLIB         = @MFEM_USE_GSLIB@
 MFEM_USE_CUDA          = @MFEM_USE_CUDA@
+MFEM_USE_AMGX          = @MFEM_USE_AMGX@
 MFEM_USE_HIP           = @MFEM_USE_HIP@
 MFEM_USE_RAJA          = @MFEM_USE_RAJA@
 MFEM_USE_OCCA          = @MFEM_USE_OCCA@

config/defaults.cmake

@@ -83,6 +83,11 @@ set(HYPRE_DIR "${MFEM_DIR}/../hypre/src/hypre" CACHE PATH
 # If hypre was compiled to depend on BLAS and LAPACK:
 # set(HYPRE_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
 #     "Packages that HYPRE depends on.")
+if (MFEM_USE_CUDA)
+   # This is only necessary when hypre is built with cuda:
+   set(HYPRE_REQUIRED_LIBRARIES "-lcusparse" "-lcurand" CACHE STRING
+       "Libraries that HYPRE depends on.")
+endif()
 
 set(METIS_DIR "${MFEM_DIR}/../metis-4.0" CACHE PATH "Path to the METIS library.")
 
@@ -182,6 +187,7 @@ set(HIOP_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
 
 set(OCCA_DIR "${MFEM_DIR}/../occa" CACHE PATH "Path to OCCA")
 set(RAJA_DIR "${MFEM_DIR}/../raja" CACHE PATH "Path to RAJA")
+set(AMGX_DIR "${MFEM_DIR}/../amgx" CACHE PATH "Path to AMGX")
 set(CEED_DIR "${MFEM_DIR}/../libCEED" CACHE PATH "Path to libCEED")
 set(UMPIRE_DIR "${MFEM_DIR}/../umpire" CACHE PATH "Path to Umpire")
 

config/defaults.mk

@@ -133,6 +133,7 @@ MFEM_USE_PUMI          = NO
 MFEM_USE_HIOP          = NO
 MFEM_USE_GSLIB         = NO
 MFEM_USE_CUDA          = NO
+MFEM_USE_AMGX          = NO
 MFEM_USE_HIP           = NO
 MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
@@ -154,6 +155,10 @@ LIBUNWIND_LIB = $(if $(NOTMAC),-lunwind -ldl,)
 HYPRE_DIR = @MFEM_DIR@/../hypre/src/hypre
 HYPRE_OPT = -I$(HYPRE_DIR)/include
 HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
+ifeq (YES,$(MFEM_USE_CUDA))
+   # This is only necessary when hypre is built with cuda:
+   HYPRE_LIB += -lcusparse -lcurand
+endif
 
 # METIS library configuration
 ifeq ($(MFEM_USE_SUPERLU)$(MFEM_USE_STRUMPACK),NONO)
@@ -341,9 +346,9 @@ 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 +377,11 @@ UMPIRE_DIR = @MFEM_DIR@/../umpire
 UMPIRE_OPT = -I$(UMPIRE_DIR)/include
 UMPIRE_LIB = -L$(UMPIRE_DIR)/lib -lumpire
 
+# AMGX library configuration
+AMGX_DIR = @MFEM_DIR@/../amgx
+AMGX_OPT = -I$(AMGX_DIR)/include
+AMGX_LIB = -L$(CUDA_HOME)/lib64 -lcusparse -lcusolver -lcublas -lnvToolsExt -L$(AMGX_DIR)/lib -lamgx -Xlinker=-rpath=$(CUDA_HOME)/lib64
+
 # If YES, enable some informational messages
 VERBOSE = NO
 

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

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 2.2 0 8
 $EndMeshFormat
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 $EndElements
 $Periodic
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 1 3
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 $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/amgx/amg_pcg.json

@@ -0,0 +1,38 @@
+{
+    "config_version": 2,
+    "solver": {
+        "preconditioner": {
+            "print_grid_stats": 1,
+            "print_vis_data": 0,
+            "solver": "AMG",
+            "smoother": {
+                "scope": "jacobi",
+                "solver": "BLOCK_JACOBI",
+                "relaxation_factor": 0.7,
+                "monitor_residual": 0,
+                "print_solve_stats": 0
+            },
+            "print_solve_stats": 0,
+            "presweeps": 1,
+            "interpolator": "D2",
+            "max_row_sum" : 0.9,
+            "strength_threshold" : 0.25,
+            "max_iters": 1,
+            "monitor_residual": 0,
+            "store_res_history": 0,
+            "scope": "amg",
+            "max_levels": 100,
+            "cycle": "V",
+            "postsweeps": 1
+        },
+        "solver": "PCG",
+        "print_solve_stats": 1,
+        "obtain_timings": 1,
+        "max_iters": 100,
+        "monitor_residual": 1,
+        "convergence": "RELATIVE_MAX",
+        "scope": "main",
+        "tolerance": 1e-12,
+        "norm": "L2"
+    }
+}

examples/amgx/ex1.cpp

@@ -0,0 +1,271 @@
+//                                MFEM Example 1
+//
+// Compile with: make ex1
+//
+// Sample runs:  ex1 -m ../../data/square-disc.mesh
+//               ex1 -m ../../data/star.mesh
+//               ex1 -m ../../data/star-mixed.mesh
+//               ex1 -m ../../data/escher.mesh
+//               ex1 -m ../../data/fichera.mesh
+//               ex1 -m ../../data/fichera-mixed.mesh
+//               ex1 -m ../../data/toroid-wedge.mesh
+//               ex1 -m ../../data/periodic-annulus-sector.msh
+//               ex1 -m ../../data/periodic-torus-sector.msh
+//               ex1 -m ../../data/square-disc-p2.vtk -o 2
+//               ex1 -m ../../data/square-disc-p3.mesh -o 3
+//               ex1 -m ../../data/square-disc-nurbs.mesh -o -1
+//               ex1 -m ../../data/star-mixed-p2.mesh -o 2
+//               ex1 -m ../../data/disc-nurbs.mesh -o -1
+//               ex1 -m ../../data/pipe-nurbs.mesh -o -1
+//               ex1 -m ../../data/fichera-mixed-p2.mesh -o 2
+//               ex1 -m ../../data/star-surf.mesh
+//               ex1 -m ../../data/square-disc-surf.mesh
+//               ex1 -m ../../data/inline-segment.mesh
+//               ex1 -m ../../data/amr-quad.mesh
+//               ex1 -m ../../data/amr-hex.mesh
+//               ex1 -m ../../data/fichera-amr.mesh
+//               ex1 -m ../../data/mobius-strip.mesh
+//               ex1 -m ../../data/mobius-strip.mesh -o -1 -sc
+//
+// Device sample runs:
+//               ex1 -pa -d cuda
+//               ex1 -pa -d raja-cuda
+//               ex1 -pa -d occa-cuda
+//               ex1 -pa -d raja-omp
+//               ex1 -pa -d occa-omp
+//               ex1 -pa -d ceed-cpu
+//             * ex1 -pa -d ceed-cuda
+//               ex1 -pa -d ceed-cuda:/gpu/cuda/shared
+//               ex1 -m ../../data/beam-hex.mesh -pa -d cuda
+//               ex1 -m ../../data/beam-tet.mesh -pa -d ceed-cpu
+//               ex1 -m ../../data/beam-tet.mesh -pa -d ceed-cuda:/gpu/cuda/ref
+//
+// AmgX sample runs:
+//               ./ex1 --amgx-file multi_gs.json --amgx-solver
+//               ./ex1 --amgx-file precon.json --amgx-preconditioner
+//               ./ex1 --amgx-file multi_gs.json --amgx-solver -d cuda
+//               ./ex1 --amgx-file precon.json --amgx-preconditioner -d cuda
+//
+// Description:  This example code demonstrates the use of MFEM to define a
+//               simple finite element discretization of the Laplace problem
+//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
+//               Specifically, we discretize using a FE space of the specified
+//               order, or if order < 1 using an isoparametric/isogeometric
+//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
+//               NURBS mesh, etc.)
+//
+//               The example highlights the use of mesh refinement, finite
+//               element grid functions, as well as linear and bilinear forms
+//               corresponding to the left-hand side and right-hand side of the
+//               discrete linear system. We also cover the explicit elimination
+//               of essential boundary conditions, static condensation, and the
+//               optional connection to the GLVis tool for visualization.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../../data/star.mesh";
+   int order = 1;
+   bool static_cond = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = true;
+   bool amgx_solver = true;
+   const char* amgx_json_file = ""; // jason file for amgx
+
+   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(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&amgx_json_file, "--amgx-file", "--amgx-file",
+                  "AMGX solver config file (overrides --amgx-solver, --amgx-verbose)");
+   args.AddOption(&amgx_solver, "--amgx-solver", "--amgx-solver",
+                  "--amgx-preconditioner",
+                  "--amgx-preconditioner",
+                  "Configure AMGX as solver or preconditioner.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   MFEM_VERIFY(!pa && strcmp(amgx_json_file,"") != 0,
+               "An AmgX json file is needed for this example \n");
+
+   // 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(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+
+   // 4. Refine the mesh 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 50,000
+   //    elements.
+   {
+      int ref_levels =
+         (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh.UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use continuous
+   //    Lagrange finite elements of the specified order. If order < 1, we
+   //    instead use an isoparametric/isogeometric space.
+   FiniteElementCollection *fec;
+   bool delete_fec;
+   if (order > 0)
+   {
+      fec = new H1_FECollection(order, dim);
+      delete_fec = true;
+   }
+   else if (mesh.GetNodes())
+   {
+      fec = mesh.GetNodes()->OwnFEC();
+      delete_fec = false;
+      cout << "Using isoparametric FEs: " << fec->Name() << endl;
+   }
+   else
+   {
+      fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
+   }
+   FiniteElementSpace fespace(&mesh, fec);
+   cout << "Number of finite element unknowns: "
+        << fespace.GetTrueVSize() << endl;
+
+   // 6. Determine the list of true (i.e. 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 (mesh.bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh.bdr_attributes.Max());
+      ess_bdr = 1;
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
+   //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
+   //    the basis functions in the finite element fespace.
+   LinearForm b(&fespace);
+   ConstantCoefficient one(1.0);
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
+
+   // 8. Define the solution vector x as a finite element grid function
+   //    corresponding to fespace. Initialize x with initial guess of zero,
+   //    which satisfies the boundary conditions.
+   GridFunction x(&fespace);
+   x = 0.0;
+
+   // 9. Set up the bilinear form a(.,.) on the finite element space
+   //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
+   //    domain integrator.
+   BilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));
+
+   // 10. Assemble the bilinear form and the corresponding linear system,
+   //     applying any necessary transformations such as: eliminating boundary
+   //     conditions, applying conforming constraints for non-conforming AMR,
+   //     static condensation, etc.
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();
+
+   OperatorPtr A;
+   Vector B, X;
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+   cout << "Size of linear system: " << A->Height() << endl;
+
+   // 11. Solve the linear system A X = B.
+   if (!pa)
+   {
+      AmgXSolver amgx;
+
+      amgx.ReadParameters(amgx_json_file, AmgXSolver::EXTERNAL);
+      amgx.InitSerial();
+      amgx.SetOperator(*A.As<SparseMatrix>());
+
+      if (amgx_solver)
+      {
+         amgx.Mult(B,X);
+      }
+      else
+      {
+         PCG(*A.As<SparseMatrix>(), amgx, B, X, 3, 40, 1e-12, 0.0);
+      }
+
+   }
+   else // Jacobi preconditioning in partial assembly mode
+   {
+      if (UsesTensorBasis(fespace))
+      {
+         OperatorJacobiSmoother M(a, ess_tdof_list);
+         PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
+      }
+      else
+      {
+         CG(*A, B, X, 1, 400, 1e-12, 0.0);
+      }
+   }
+
+   // 12. Recover the solution as a finite element grid function.
+   a.RecoverFEMSolution(X, b, x);
+
+   // 13. Save the refined mesh and the solution. This output can be viewed later
+   //     using GLVis: "glvis -m refined.mesh -g sol.gf".
+   ofstream mesh_ofs("refined.mesh");
+   mesh_ofs.precision(8);
+   mesh.Print(mesh_ofs);
+   ofstream sol_ofs("sol.gf");
+   sol_ofs.precision(8);
+   x.Save(sol_ofs);
+
+   // 14. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << mesh << x << flush;
+   }
+
+   // 15. Free the used memory.
+   if (delete_fec)
+   {
+      delete fec;
+   }
+
+   return 0;
+}

examples/amgx/ex1p.cpp

@@ -0,0 +1,322 @@
+//                       MFEM Example 1 - Parallel Version
+//
+// Compile with: make ex1p
+//
+// Sample runs:  mpirun -np 4 ex1p -m ../../data/square-disc.mesh
+//               mpirun -np 4 ex1p -m ../../data/star.mesh
+//               mpirun -np 4 ex1p -m ../../data/star-mixed.mesh
+//               mpirun -np 4 ex1p -m ../../data/escher.mesh
+//               mpirun -np 4 ex1p -m ../../data/fichera.mesh
+//               mpirun -np 4 ex1p -m ../../data/fichera-mixed.mesh
+//               mpirun -np 4 ex1p -m ../../data/toroid-wedge.mesh
+//               mpirun -np 4 ex1p -m ../../data/periodic-annulus-sector.msh
+//               mpirun -np 4 ex1p -m ../../data/periodic-torus-sector.msh
+//               mpirun -np 4 ex1p -m ../../data/square-disc-p2.vtk -o 2
+//               mpirun -np 4 ex1p -m ../../data/square-disc-p3.mesh -o 3
+//               mpirun -np 4 ex1p -m ../../data/square-disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../../data/star-mixed-p2.mesh -o 2
+//               mpirun -np 4 ex1p -m ../../data/disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../../data/pipe-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../../data/ball-nurbs.mesh -o 2
+//               mpirun -np 4 ex1p -m ../../data/fichera-mixed-p2.mesh -o 2
+//               mpirun -np 4 ex1p -m ../../data/star-surf.mesh
+//               mpirun -np 4 ex1p -m ../../data/square-disc-surf.mesh
+//               mpirun -np 4 ex1p -m ../../data/inline-segment.mesh
+//               mpirun -np 4 ex1p -m ../../data/amr-quad.mesh
+//               mpirun -np 4 ex1p -m ../../data/amr-hex.mesh
+//               mpirun -np 4 ex1p -m ../../data/mobius-strip.mesh
+//               mpirun -np 4 ex1p -m ../../data/mobius-strip.mesh -o -1 -sc
+//
+// Device sample runs:
+//               mpirun -np 4 ex1p -pa -d cuda
+//               mpirun -np 4 ex1p -pa -d occa-cuda
+//               mpirun -np 4 ex1p -pa -d raja-omp
+//               mpirun -np 4 ex1p -pa -d ceed-cpu
+//             * mpirun -np 4 ex1p -pa -d ceed-cuda
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared
+//               mpirun -np 4 ex1p -m ../../data/beam-tet.mesh -pa -d ceed-cpu
+//
+// AmgX sample runs:
+//
+//               mpirun -n 40 ./ex1p --amgx-file amg_pcg.json
+//               lrun -n 4 ./ex1p --amgx-file amg_pcg.json --amgx-mpi-gpu-exclusive
+//
+// Description:  This example code demonstrates the use of MFEM to define a
+//               simple finite element discretization of the Laplace problem
+//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
+//               Specifically, we discretize using a FE space of the specified
+//               order, or if order < 1 using an isoparametric/isogeometric
+//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
+//               NURBS mesh, etc.)
+//
+//               The example highlights the use of mesh refinement, finite
+//               element grid functions, as well as linear and bilinear forms
+//               corresponding to the left-hand side and right-hand side of the
+//               discrete linear system. We also cover the explicit elimination
+//               of essential boundary conditions, static condensation, and the
+//               optional connection to the GLVis tool for visualization.
+
+#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/star.mesh";
+   int order = 1;
+   bool static_cond = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = true;
+   bool amgx_mpi_teams = true;
+   const char* amgx_json_file = ""; // jason file for amgx
+   int ndevices = 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(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&amgx_json_file, "--amgx-file", "--amgx-file",
+                  "AMGX solver config file (overrides --amgx-solver, --amgx-verbose)");
+   args.AddOption(&amgx_mpi_teams, "--amgx-mpi-teams", "--amgx-mpi-teams",
+                  "--amgx-mpi-gpu-exclusive", "--amgx-mpi-gpu-exclusive",
+                  "Create MPI teams when using AMGX.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&ndevices, "-nd","--nd","Number of GPU devices.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+
+      MFEM_VERIFY(!pa == true && strcmp(amgx_json_file,"") != 0,
+                  "An AmgX json file is needed for this example \n");
+   }
+
+   // 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(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.
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; 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();
+   {
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; 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;
+   bool delete_fec;
+   if (order > 0)
+   {
+      fec = new H1_FECollection(order, dim);
+      delete_fec = true;
+   }
+   else if (pmesh.GetNodes())
+   {
+      fec = pmesh.GetNodes()->OwnFEC();
+      delete_fec = false;
+      if (myid == 0)
+      {
+         cout << "Using isoparametric FEs: " << fec->Name() << endl;
+      }
+   }
+   else
+   {
+      fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
+   }
+   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);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));
+
+   // 12. Assemble the parallel bilinear form and the corresponding linear
+   //     system, applying any necessary transformations such as: parallel
+   //     assembly, eliminating boundary conditions, applying conforming
+   //     constraints for non-conforming AMR, static condensation, etc.
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();
+
+   OperatorPtr 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.
+   Solver *prec = NULL;
+   if (!pa)
+   {
+
+      AmgXSolver amgx;
+
+      amgx.ReadParameters(amgx_json_file, AmgXSolver::EXTERNAL);
+
+      if (amgx_mpi_teams)
+      {
+         //Forms MPI teams to load balance between mpi ranks and gpus
+         amgx.InitMPITeams(MPI_COMM_WORLD, ndevices);
+      }
+      else
+      {
+         //Assumes MPI == number of devices
+         amgx.InitExclusiveGPU(MPI_COMM_WORLD);
+      }
+
+      amgx.SetOperator(*A.As<HypreParMatrix>());
+
+      amgx.Mult(B, X);
+
+   }
+   else
+   {
+
+      if (UsesTensorBasis(fespace))
+      {
+         prec = new OperatorJacobiSmoother(a, ess_tdof_list);
+      }
+
+      CGSolver cg(MPI_COMM_WORLD);
+      cg.SetRelTol(1e-12);
+      cg.SetMaxIter(2000);
+      cg.SetPrintLevel(1);
+      if (prec) { cg.SetPreconditioner(*prec); }
+      cg.SetOperator(*A);
+      cg.Mult(B, X);
+      delete prec;
+
+   }
+
+   // 14. Recover the parallel grid function corresponding to X. This is the
+   //     local finite element solution on each processor.
+   a.RecoverFEMSolution(X, b, x);
+
+   // 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_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh.Print(mesh_ofs);
+
+      ofstream sol_ofs(sol_name.str().c_str());
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+   }
+
+   // 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.
+   if (delete_fec)
+   {
+      delete fec;
+   }
+   MPI_Finalize();
+
+   return 0;
+}

examples/amgx/makefile

@@ -0,0 +1,72 @@
+# 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.
+
+# Use the MFEM build directory
+MFEM_DIR ?= ../..
+MFEM_BUILD_DIR ?= ../..
+SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/amgx/,)
+CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
+# Use the MFEM install directory
+# MFEM_INSTALL_DIR = ../../mfem
+# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+SEQ_EXAMPLES = ex1
+PAR_EXAMPLES = ex1p
+ifeq ($(MFEM_USE_MPI),NO)
+   EXAMPLES = $(SEQ_EXAMPLES)
+else
+   EXAMPLES = $(PAR_EXAMPLES) $(SEQ_EXAMPLES)
+endif
+
+.SUFFIXES:
+.SUFFIXES: .o .cpp .mk
+.PHONY: all clean clean-build clean-exec
+
+# Remove built-in rule
+%: %.cpp
+
+# Replace the default implicit rule for *.cpp files
+%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+
+all: $(EXAMPLES)
+
+ifeq ($(MFEM_USE_AMGX),NO)
+$(EXAMPLES):
+	$(error MFEM is not configured with AMGX)
+endif
+
+MFEM_TESTS = EXAMPLES
+include $(MFEM_TEST_MK)
+
+# Testing: Parallel vs. serial runs
+RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
+SERIAL_NAME := Serial AMGX example
+PARALLEL_NAME := Parallel AMGX example
+%-test-par: %
+	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME))
+%-test-seq: %
+	@$(call mfem-test,$<,, $(SERIAL_NAME))
+
+# Testing: "test" target and mfem-test* variables are defined in config/test.mk
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not build)
+
+clean: clean-build
+
+clean-build:
+	rm -f *.o *~ $(SEQ_EXAMPLES) $(PAR_EXAMPLES)
+	rm -rf *.dSYM *.TVD.*breakpoints

examples/amgx/multi_gs.json

@@ -0,0 +1,24 @@
+{
+    "config_version": 2,
+    "solver": {
+        "max_uncolored_percentage": 0.15,
+        "algorithm": "AGGREGATION",
+        "solver": "AMG",
+        "smoother": "MULTICOLOR_GS",
+        "presweeps": 1,
+        "symmetric_GS" : 1,
+        "selector": "SIZE_2",
+        "coarsest_sweeps": 10,
+        "max_iters": 10000,
+        "postsweeps": 1,
+        "scope": "main",
+        "max_levels": 1000,
+        "matrix_coloring_scheme" : "MIN_MAX",
+        "tolerance": 0.0000001,
+        "print_solve_stats": 1,
+        "obtain_timings": 1,
+        "monitor_residual": 1,
+        "norm": "L2",
+        "cycle": "V"
+    }
+}

examples/amgx/precon.json

@@ -0,0 +1,21 @@
+{
+    "config_version": 2,
+    "solver": {
+        "max_uncolored_percentage": 0.15,
+        "algorithm": "AGGREGATION",
+        "solver": "AMG",
+        "smoother": "MULTICOLOR_GS",
+        "presweeps": 1,
+        "symmetric_GS" : 1,
+        "selector": "SIZE_2",
+        "coarsest_sweeps": 10,
+        "max_iters": 2,
+        "postsweeps": 1,
+        "scope": "main",
+        "max_levels": 1000,
+        "matrix_coloring_scheme" : "MIN_MAX",
+        "tolerance": 0.0,
+        "norm": "L2",
+        "cycle": "V"
+    }
+}

examples/ex1.cpp

@@ -71,6 +71,7 @@ int main(int argc, char *argv[])
    bool pa = false;
    const char *device_config = "cpu";
    bool visualization = true;
+   bool amgx = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -82,6 +83,8 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&amgx, "-amgx", "--amgx-precon", "-no-amgx",
+                  "--no-amgx-precon", "Use AmgX V-cycle as preconditioner for CG.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -191,7 +194,31 @@ int main(int argc, char *argv[])
    cout << "Size of linear system: " << A->Height() << endl;
 
    // 11. Solve the linear system A X = B.
-   if (!pa)
+   if (pa)
+   {
+      // Jacobi preconditioning in partial assembly mode
+      if (UsesTensorBasis(fespace))
+      {
+         OperatorJacobiSmoother M(a, ess_tdof_list);
+         PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
+      }
+      else
+      {
+         CG(*A, B, X, 1, 400, 1e-12, 0.0);
+      }
+   }
+   else if (amgx)
+   {
+#if defined(MFEM_USE_AMGX)
+      bool amgx_verbose = false;
+      AmgXSolver amgx(AmgXSolver::PRECONDITIONER, amgx_verbose);
+      amgx.SetOperator(*A.As<SparseMatrix>());
+      PCG(*A, amgx, B, X, 1, 200, 1e-12, 0.0);
+#else
+      mfem_error("MFEM not configured with AMGX \n");
+#endif
+   }
+   else
    {
 #ifndef MFEM_USE_SUITESPARSE
       // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
@@ -205,18 +232,6 @@ int main(int argc, char *argv[])
       umf_solver.Mult(B, X);
 #endif
    }
-   else // Jacobi preconditioning in partial assembly mode
-   {
-      if (UsesTensorBasis(fespace))
-      {
-         OperatorJacobiSmoother M(a, ess_tdof_list);
-         PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
-      }
-      else
-      {
-         CG(*A, B, X, 1, 400, 1e-12, 0.0);
-      }
-   }
 
    // 12. Recover the solution as a finite element grid function.
    a.RecoverFEMSolution(X, b, x);

examples/ex1p.cpp

@@ -73,6 +73,7 @@ int main(int argc, char *argv[])
    bool pa = false;
    const char *device_config = "cpu";
    bool visualization = true;
+   bool amgx = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -84,6 +85,8 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&amgx, "-amgx", "--amgx-precon", "-no-amgx",
+                  "--no-amgx-precon", "Use AmgX V-cycle as preconditioner for CG.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -218,6 +221,7 @@ int main(int argc, char *argv[])
 
    // 13. Solve the linear system A X = B.
    //     * With full assembly, use the BoomerAMG preconditioner from hypre.
+   //     * If AmgX is available solve using amg preconditioner.
    //     * With partial assembly, use Jacobi smoothing, for now.
    Solver *prec = NULL;
    if (pa)
@@ -227,6 +231,16 @@ int main(int argc, char *argv[])
          prec = new OperatorJacobiSmoother(a, ess_tdof_list);
       }
    }
+   else if (amgx)
+   {
+#if defined(MFEM_USE_AMGX)
+      bool amgx_verbose = false;
+      prec = new AmgXSolver(MPI_COMM_WORLD, AmgXSolver::PRECONDITIONER,
+                            amgx_verbose);
+#else
+      mfem_error("MFEM not configured with AMGX \n");
+#endif
+   }
    else
    {
       prec = new HypreBoomerAMG;

examples/ex1p_helmholtz.cpp

@@ -0,0 +1,503 @@
+//                       MFEM Example 1 - Parallel Version
+//
+// Compile with: make ex1p
+//
+// Sample runs:  mpirun -np 4 ex1p -m ../data/square-disc.mesh
+//               mpirun -np 4 ex1p -m ../data/star.mesh
+//               mpirun -np 4 ex1p -m ../data/star-mixed.mesh
+//               mpirun -np 4 ex1p -m ../data/escher.mesh
+//               mpirun -np 4 ex1p -m ../data/fichera.mesh
+//               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
+//               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
+//               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
+//               mpirun -np 4 ex1p -m ../data/square-disc-p3.mesh -o 3
+//               mpirun -np 4 ex1p -m ../data/square-disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/star-mixed-p2.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/pipe-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/ball-nurbs.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/fichera-mixed-p2.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/star-surf.mesh
+//               mpirun -np 4 ex1p -m ../data/square-disc-surf.mesh
+//               mpirun -np 4 ex1p -m ../data/inline-segment.mesh
+//               mpirun -np 4 ex1p -m ../data/amr-quad.mesh
+//               mpirun -np 4 ex1p -m ../data/amr-hex.mesh
+//               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh
+//               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh -o -1 -sc
+//
+// Description:  This example code demonstrates the use of MFEM to define a
+//               simple finite element discretization of the Laplace problem
+//               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
+//               Specifically, we discretize using a FE space of the specified
+//               order, or if order < 1 using an isoparametric/isogeometric
+//               space (i.e. quadratic for quadratic curvilinear mesh, NURBS for
+//               NURBS mesh, etc.)
+//
+//               The example highlights the use of mesh refinement, finite
+//               element grid functions, as well as linear and bilinear forms
+//               corresponding to the left-hand side and right-hand side of the
+//               discrete linear system. We also cover the explicit elimination
+//               of essential boundary conditions, static condensation, and the
+//               optional connection to the GLVis tool for visualization.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+double u_exact(const Vector &x);
+double f_exact(const Vector &x);
+
+// #define FORM_DEFINITE
+#define USE_GMRES
+
+#define USE_CSL
+
+#define K2 250.0
+
+int dim;
+double kappa;
+
+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/beam-tet.mesh";
+   int order = 1;
+   bool static_cond = false;
+   bool visualization = 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(&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);
+   }
+
+   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
+   //    and volume meshes with the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+
+   kappa = 2.0 * M_PI;
+
+   // 4. 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.
+   {
+      int ref_levels =
+         (int)floor(log(100000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted.
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   {
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; l++)
+      {
+         pmesh->UniformRefinement();
+      }
+   }
+
+   {
+      double minsize = pmesh->GetElementSize(0);
+      double maxsize = minsize;
+      for (int i=1; i<pmesh->GetNE(); ++i)
+      {
+         const double size_i = pmesh->GetElementSize(i);
+         minsize = std::min(minsize, size_i);
+         maxsize = std::max(maxsize, size_i);
+      }
+
+      cout << myid << ": Element size range: (" << minsize << ", " << maxsize << ")"
+           << endl;
+   }
+
+   // 6. 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;
+   if (order > 0)
+   {
+      fec = new H1_FECollection(order, dim);
+   }
+   else if (pmesh->GetNodes())
+   {
+      fec = pmesh->GetNodes()->OwnFEC();
+      if (myid == 0)
+      {
+         cout << "Using isoparametric FEs: " << fec->Name() << endl;
+      }
+   }
+   else
+   {
+      fec = new H1_FECollection(order = 1, dim);
+   }
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+   if (myid == 0)
+   {
+      cout << "Number of finite element unknowns: " << size << endl;
+   }
+
+   // 7. Determine the list of true (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);
+   }
+
+   // 8. 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 = new ParLinearForm(fespace);
+
+   //ConstantCoefficient bcoef(1.0);
+   FunctionCoefficient bcoef(f_exact);
+
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient zero(0.0);
+   ConstantCoefficient neg(-K2);
+   ConstantCoefficient pos(K2);
+   b->AddDomainIntegrator(new DomainLFIntegrator(bcoef));
+   b->Assemble();
+
+   // 9. 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;
+
+   // 10. 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 = new ParBilinearForm(fespace);
+   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   a->AddDomainIntegrator(new MassIntegrator(neg));
+
+#ifdef FORM_DEFINITE
+   ParBilinearForm *adef = new ParBilinearForm(fespace);
+   adef->AddDomainIntegrator(new DiffusionIntegrator(one));
+   adef->AddDomainIntegrator(new MassIntegrator(pos));
+
+   if (static_cond) { adef->EnableStaticCondensation(); }
+   adef->Assemble();
+
+   ParGridFunction xdef(fespace);
+   xdef = 0.0;
+
+   ParLinearForm *bdef = new ParLinearForm(fespace);
+   bdef->AddDomainIntegrator(new DomainLFIntegrator(bcoef));
+   bdef->Assemble();
+
+   HypreParMatrix Adef;
+   Vector Bdef, Xdef;
+   adef->FormLinearSystem(ess_tdof_list, xdef, *bdef, Adef, Xdef, Bdef);
+#endif
+
+   // 11. Assemble the parallel bilinear form and the corresponding linear
+   //     system, applying any necessary transformations such as: parallel
+   //     assembly, eliminating boundary conditions, applying conforming
+   //     constraints for non-conforming AMR, static condensation, etc.
+   if (static_cond) { a->EnableStaticCondensation(); }
+   a->Assemble();
+
+   HypreParMatrix A;
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+
+   if (myid == 0)
+   {
+      cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
+   }
+
+   //A.Print("helmholtz");
+
+   // 12. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
+   //     preconditioner from hypre.
+#ifdef FORM_DEFINITE
+   HypreSolver *amg = new HypreBoomerAMG(Adef);
+#else
+   HypreSolver *amg = new HypreBoomerAMG(A);
+#endif
+
+   const bool fullDirect = true;
+
+   if (fullDirect)
+   {
+#ifdef USE_CSL
+      Vector Bdef, Xdef;
+
+      ParBilinearForm *Mform =  new ParBilinearForm(fespace);
+      Mform->AddDomainIntegrator(new MassIntegrator(pos));
+      Mform->Assemble();
+
+      HypreParMatrix Mmat, Smat, Mcopy;
+      Mform->FormLinearSystem(ess_tdof_list, x, *b, Mmat, Xdef, Bdef);
+      Mform->FormLinearSystem(ess_tdof_list, x, *b, Mcopy, Xdef,
+                              Bdef);  // There must be a better way than creating two identical matrices.
+
+      ParBilinearForm *Sform =  new ParBilinearForm(fespace);
+      Sform->AddDomainIntegrator(new DiffusionIntegrator(one));
+      Sform->Assemble();
+
+      Sform->FormLinearSystem(ess_tdof_list, x, *b, Smat, Xdef, Bdef);
+
+      const double beta1 = 1.0;
+      const double beta2 = 1.0;
+
+      Mmat *= -beta1;
+
+      HypreParMatrix * cslRe = ParAdd(&Smat, &Mmat);
+
+      Mcopy *= beta2;
+
+      ComplexHypreParMatrix chpm(cslRe, &Mcopy, false, false);
+
+      HypreParMatrix *cSysMat = chpm.GetSystemMatrix();
+
+      Array<int> block_trueOffsets(3); // number of variables + 1
+      block_trueOffsets[0] = 0;
+      block_trueOffsets[1] = fespace->TrueVSize();
+      block_trueOffsets[2] = fespace->TrueVSize();
+      block_trueOffsets.PartialSum();
+
+      // Note that B is of true size.
+      BlockVector trueY(block_trueOffsets), trueX(block_trueOffsets),
+                  trueRhs(block_trueOffsets);
+
+      trueRhs.GetBlock(0) = B;
+      trueRhs.GetBlock(1) = 0.0;
+
+      Operator * Arow = new STRUMPACKRowLocMatrix(*cSysMat);
+
+      STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+      strumpack->SetPrintFactorStatistics(true);
+      strumpack->SetPrintSolveStatistics(false);
+      strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      // strumpack->SetMC64Job(strumpack::MC64Job::NONE);
+      // strumpack->SetSymmetricPattern(true);
+      strumpack->SetOperator(*Arow);
+      strumpack->SetFromCommandLine();
+      //Solver * precond = strumpack;
+
+      // strumpack->Mult(B, X);
+
+      BlockOperator blockDiagA(block_trueOffsets);
+      for (int i=0; i<2; ++i)
+      {
+         blockDiagA.SetDiagonalBlock(i, &A);
+      }
+
+      ProductOperator prod(&blockDiagA, strumpack, false, false);
+      //GMRESSolver *gmres = new GMRESSolver(fespace->GetComm());
+      BiCGSTABSolver *gmres = new BiCGSTABSolver(fespace->GetComm());
+
+      gmres->SetOperator(prod);
+      gmres->SetRelTol(1e-8);
+      gmres->SetMaxIter(10000);
+      gmres->SetPrintLevel(1);
+
+      gmres->Mult(trueRhs, trueY);
+      strumpack->Mult(trueY, trueX);
+
+      X = trueX.GetBlock(0);
+      double xim2 = trueX.GetBlock(1).Norml2();
+      xim2 *= xim2;
+      double sumxim2 = 0.0;
+
+      MPI_Allreduce(&xim2, &sumxim2, 1, MPI_DOUBLE, MPI_SUM, fespace->GetComm());
+
+      if (myid == 0)
+      {
+         cout << myid << ": norm of Xim " << trueX.GetBlock(1).Norml2() << ", global " <<
+              sqrt(sumxim2) << endl;
+      }
+
+      delete gmres;
+      delete strumpack;
+      delete Arow;
+#else
+      Operator * Arow = new STRUMPACKRowLocMatrix(A);
+
+      STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+      strumpack->SetPrintFactorStatistics(true);
+      strumpack->SetPrintSolveStatistics(false);
+      strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      // strumpack->SetMC64Job(strumpack::MC64Job::NONE);
+      // strumpack->SetSymmetricPattern(true);
+      strumpack->SetOperator(*Arow);
+      strumpack->SetFromCommandLine();
+      //Solver * precond = strumpack;
+
+      strumpack->Mult(B, X);
+
+      delete strumpack;
+      delete Arow;
+#endif
+   }
+   else
+   {
+#ifdef USE_GMRES
+      HypreGMRES *gmres = new HypreGMRES(A);
+      gmres->SetTol(1e-12);
+      gmres->SetMaxIter(1000);
+      gmres->SetPrintLevel(10);
+      gmres->SetPreconditioner(*amg);
+      gmres->Mult(B, X);
+      delete gmres;
+#else
+      HyprePCG *pcg = new HyprePCG(A);
+      pcg->SetTol(1e-12);
+      pcg->SetMaxIter(100);
+      pcg->SetPrintLevel(2);
+      pcg->SetPreconditioner(*amg);
+      pcg->Mult(B, X);
+#endif
+   }
+
+   /*
+   HYPRE_ParCSRMatrix* amgP = amg->Get_Restriction();
+   HypreParMatrix P0(amgP[0], false);
+   HypreParMatrix P1(amgP[1], false);
+   HypreParMatrix P2(amgP[2], false);
+   //HypreParMatrix P3(amgP[3], false);
+
+   P0.Print("P0");
+   */
+
+   // 13. Recover the parallel grid function corresponding to X. This is the
+   //     local finite element solution on each processor.
+   a->RecoverFEMSolution(X, *b, x);
+
+   // Compute and print the L^2 norm of the error.
+   {
+      FunctionCoefficient uex(u_exact);
+
+      double err = x.ComputeL2Error(uex);
+      double xnrm = x.ComputeL2Error(zero);
+      ParGridFunction zerogf(fespace);
+      zerogf = 0.0;
+      double normE = zerogf.ComputeL2Error(uex);
+      if (myid == 0)
+      {
+         cout << "|| E_h - E ||_{L^2} = " << err << endl;
+         cout << "|| E_h ||_{L^2} = " << xnrm << endl;
+         cout << "|| E ||_{L^2} = " << normE << endl;
+      }
+   }
+
+   // 14. 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_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      ofstream sol_ofs(sol_name.str().c_str());
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+   }
+
+   // 15. 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;
+   }
+
+   // 16. Free the used memory.
+   //delete pcg;
+   delete amg;
+   delete a;
+   delete b;
+   delete fespace;
+   if (order > 0) { delete fec; }
+   delete pmesh;
+
+   MPI_Finalize();
+
+   return 0;
+}
+
+
+double u_exact(const Vector & x)
+{
+   double xi(x(0));
+   double yi(x(1));
+   double zi(1.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   return sin(kappa*xi)*sin(kappa*yi)*sin(kappa*zi);
+}
+
+double f_exact(const Vector &x)
+{
+   double xi(x(0));
+   double yi(x(1));
+   double zi(1.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   const double s = 1.0;
+
+   return ((3.0*kappa*kappa) - (s*K2)) * sin(kappa*xi)*sin(kappa*yi)*sin(
+             kappa*zi) / s;
+}

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 +82,27 @@ 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,
+
+   using VectorCoefficient::Eval;
+
+   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 +119,13 @@ 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 +368,19 @@ 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 +422,13 @@ 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 +766,7 @@ 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 +777,13 @@ 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 +794,13 @@ 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 +811,13 @@ 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 +831,18 @@ 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 +855,18 @@ 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 +879,13 @@ 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 +82,27 @@ 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,
+
+   using VectorCoefficient::Eval;
+
+   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 +119,13 @@ 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 +396,19 @@ 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 +456,13 @@ 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 +822,7 @@ 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 +833,13 @@ 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 +850,13 @@ 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 +867,13 @@ 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 +887,18 @@ 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 +911,18 @@ 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 +935,13 @@ 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/ex3p.cpp

@@ -158,9 +158,9 @@ int main(int argc, char *argv[])
    //    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;
+   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
    if (pmesh->bdr_attributes.Size())
    {
-      Array<int> ess_bdr(pmesh->bdr_attributes.Max());
       ess_bdr = 1;
       fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
@@ -207,18 +207,36 @@ int main(int argc, char *argv[])
    // 13. Solve the system AX=B using PCG with the AMS preconditioner from hypre
    //     (in the full assembly case) or CG with Jacobi preconditioner (in the
    //     partial assembly case).
-
-   if (pa) // Jacobi preconditioning in partial assembly mode
+   if (pa) // matrix-free auxiliary space solver with PA
    {
-      OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);
+      StopWatch sw;
+      sw.Clear();
+      sw.Start();
+
+      MatrixFreeAMS *ams = new MatrixFreeAMS(*a, *A, *fespace, muinv, sigma, NULL,
+                                             ess_bdr); //, 2, 2);
+
+      //OperatorJacobiSmoother jacobi(*a, ess_tdof_list);
 
       CGSolver cg(MPI_COMM_WORLD);
       cg.SetRelTol(1e-12);
       cg.SetMaxIter(1000);
       cg.SetPrintLevel(1);
       cg.SetOperator(*A);
-      cg.SetPreconditioner(Jacobi);
+      cg.SetPreconditioner(*ams);
+      //cg.SetPreconditioner(jacobi);
+      //cg.iterative_mode = false;
+      sw.Stop();
+      cout << myid << ": MatrixFreeAMS-CG setup time " << sw.RealTime() << endl;
+
+      sw.Clear();
+      sw.Start();
+
       cg.Mult(B, X);
+
+      sw.Stop();
+      cout << myid << ": MatrixFreeAMS-CG solve time " << sw.RealTime() << endl;
+      ams->PrintTimings(myid);
    }
    else
    {

examples/ex3p_airy.cpp

@@ -0,0 +1,425 @@
+//                       MFEM Example 3 - Parallel Version
+//
+// Compile with: make ex3p
+//
+// Sample runs:  mpirun -np 4 ex3p -m ../data/star.mesh
+//               mpirun -np 4 ex3p -m ../data/square-disc.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/beam-tet.mesh
+//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex3p -m ../data/escher.mesh
+//               mpirun -np 4 ex3p -m ../data/escher.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/fichera.mesh
+//               mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
+//               mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
+//               mpirun -np 4 ex3p -m ../data/square-disc-nurbs.mesh
+//               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
+//               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
+//               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
+//               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
+//
+// Description:  This example code solves a simple electromagnetic diffusion
+//               problem corresponding to the second order definite Maxwell
+//               equation curl curl E + E = f with boundary condition
+//               E x n = <given tangential field>. Here, we use a given exact
+//               solution E and compute the corresponding r.h.s. f.
+//               We discretize with Nedelec finite elements in 2D or 3D.
+//
+//               The example demonstrates the use of H(curl) finite element
+//               spaces with the curl-curl and the (vector finite element) mass
+//               bilinear form, as well as the computation of discretization
+//               error when the exact solution is known. Static condensation is
+//               also illustrated.
+//
+//               We recommend viewing examples 1-2 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+#define TEST_AIRY
+
+#ifdef TEST_AIRY
+#include "gsl_sf_airy.h"
+
+#define XSHIFT 0.0 // 0.25
+#endif
+
+// Exact solution, E, and r.h.s., f. See below for implementation.
+void E_exact(const Vector &, Vector &);
+void f_exact(const Vector &, Vector &);
+double freq = 1.0, kappa;
+int dim;
+
+//#define K2_VALUE 11.9
+//#define K2_VALUE 2.1
+//#define K2_VALUE 1500.9
+#define K2_VALUE 10981.41589009910  // 104.792251097584^2 or 5 GHz
+
+void test_Airy_epsilon(const Vector &x, Vector &e)
+{
+   e(0) = 1.0;
+   e(1) = 1.0;
+   e(2) = (4.0 * (x(0) + XSHIFT)) - 1.0;
+
+   e *= -K2_VALUE;
+}
+
+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/beam-tet.mesh";
+   const char *mesh_file = "../data/inline-tetHalf.mesh";
+   //const char *mesh_file = "inline-tetSlab.mesh";
+   //const char *mesh_file = "../data/inline-hexHalf.mesh";
+   //const char *mesh_file = "../data/inline-tet.mesh";
+   int order = 2;
+   bool static_cond = false;
+   bool visualization = 1;
+#ifdef MFEM_USE_STRUMPACK
+   bool use_strumpack = false;
+#endif
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
+                  " solution.");
+   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.");
+#ifdef MFEM_USE_STRUMPACK
+   args.AddOption(&use_strumpack, "-strumpack", "--strumpack-solver",
+                  "-no-strumpack", "--no-strumpack-solver",
+                  "Use STRUMPACK's double complex linear solver.");
+#endif
+
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+      cout << "Using k2 " << K2_VALUE << endl;
+   }
+   kappa = freq * M_PI;
+
+
+   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
+   //    and volume meshes with the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+   int sdim = mesh->SpaceDimension();
+
+   // 4. Refine the serial mesh on all processors to increase the resolution. In
+   //    this example we do 'ref_levels' of uniform refinement. We choose
+   //    'ref_levels' to be the largest number that gives a final mesh with no
+   //    more than 1,000 elements.
+   {
+      int ref_levels =
+         (int)floor(log(100000./mesh->GetNE())/log(2.)/dim);
+      ref_levels = 0;
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
+   //    meshes need to be reoriented before we can define high-order Nedelec
+   //    spaces on them.
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   {
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; l++)
+      {
+         pmesh->UniformRefinement();
+      }
+   }
+   pmesh->ReorientTetMesh();
+
+   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   //    use the Nedelec finite elements of the specified order.
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+   long globalNE = pmesh->GetGlobalNE();
+   if (myid == 0)
+   {
+      cout << "Number of finite element unknowns: " << size << endl;
+      cout << "Number of mesh elements: " << globalNE << endl;
+   }
+
+   // 7. 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);
+   }
+
+   // 8. Set up the parallel linear form b(.) which corresponds to the
+   //    right-hand side of the FEM linear system, which in this case is
+   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
+   //    basis functions in the finite element fespace.
+   VectorFunctionCoefficient f(sdim, f_exact);
+   ParLinearForm *b = new ParLinearForm(fespace);
+   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
+   b->Assemble();
+
+   // 9. Define the solution vector x as a parallel finite element grid function
+   //    corresponding to fespace. Initialize x by projecting the exact
+   //    solution. Note that only values from the boundary edges will be used
+   //    when eliminating the non-homogeneous boundary condition to modify the
+   //    r.h.s. vector b.
+   ParGridFunction x(fespace);
+   ParGridFunction solproj(fespace);
+   VectorFunctionCoefficient E(sdim, E_exact);
+   x.ProjectCoefficient(E);
+
+   solproj = x;
+
+   // 10. Set up the parallel bilinear form corresponding to the EM diffusion
+   //     operator curl muinv curl + sigma I, by adding the curl-curl and the
+   //     mass domain integrators.
+   Coefficient *muinv = new ConstantCoefficient(1.0);
+   Coefficient *sigma = new ConstantCoefficient(-K2_VALUE);
+   ParBilinearForm *a = new ParBilinearForm(fespace);
+   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+#ifdef TEST_AIRY
+   VectorFunctionCoefficient epsilon(3, test_Airy_epsilon);
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(epsilon));
+#else
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
+#endif
+
+   // 11. Assemble the parallel bilinear form and the corresponding linear
+   //     system, applying any necessary transformations such as: parallel
+   //     assembly, eliminating boundary conditions, applying conforming
+   //     constraints for non-conforming AMR, static condensation, etc.
+   if (static_cond) { a->EnableStaticCondensation(); }
+   a->Assemble();
+
+   HypreParMatrix A;
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+
+   if (myid == 0)
+   {
+      cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
+   }
+
+   StopWatch chrono;
+   chrono.Clear();
+   chrono.Start();
+
+#ifdef MFEM_USE_STRUMPACK
+   if (use_strumpack)
+   {
+      Operator * Arow = new STRUMPACKRowLocMatrix(A);
+
+      STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+      strumpack->SetPrintFactorStatistics(true);
+      strumpack->SetPrintSolveStatistics(false);
+      strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      // strumpack->SetMC64Job(strumpack::MC64Job::NONE);
+      // strumpack->SetSymmetricPattern(true);
+      strumpack->SetOperator(*Arow);
+      strumpack->SetFromCommandLine();
+      //Solver * precond = strumpack;
+
+      strumpack->Mult(B, X);
+      //X = 0.0;
+
+      {
+         // Check residual
+         Vector res(X.Size());
+         Vector ssol(X.Size());
+         ssol = X;
+
+         const double Bnrm = B.Norml2();
+         const double Bnrm2 = Bnrm*Bnrm;
+
+         A.Mult(ssol, res);
+         res -= B;
+
+         const double Rnrm = res.Norml2();
+         const double Rnrm2 = Rnrm*Rnrm;
+
+         double sumBnrm2 = 0.0;
+         double sumRnrm2 = 0.0;
+         MPI_Allreduce(&Bnrm2, &sumBnrm2, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+         MPI_Allreduce(&Rnrm2, &sumRnrm2, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+
+         if (myid == 0)
+         {
+            cout << myid << ": STRUMPACK residual norm " << sqrt(sumRnrm2) << ", B norm " <<
+                 sqrt(sumBnrm2) << endl;
+         }
+      }
+
+      delete strumpack;
+      delete Arow;
+   }
+   else
+#endif
+   {
+      // 12. Define and apply a parallel PCG solver for AX=B with the AMS
+      //     preconditioner from hypre.
+      ParFiniteElementSpace *prec_fespace =
+         (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
+      HypreSolver *ams = new HypreAMS(A, prec_fespace);
+      HyprePCG *pcg = new HyprePCG(A);
+      pcg->SetTol(1e-12);
+      pcg->SetMaxIter(500);
+      pcg->SetPrintLevel(2);
+      pcg->SetPreconditioner(*ams);
+      pcg->Mult(B, X);
+
+      delete pcg;
+      delete ams;
+   }
+
+   chrono.Stop();
+   if (myid == 0)
+   {
+      cout << "Solver time " << chrono.RealTime() << endl;
+   }
+
+   // 13. Recover the parallel grid function corresponding to X. This is the
+   //     local finite element solution on each processor.
+   a->RecoverFEMSolution(X, *b, x);
+
+   // 14. Compute and print the L^2 norm of the error.
+   {
+      double err = x.ComputeL2Error(E);
+      ParGridFunction x0(fespace);
+      x0 = 0.0;
+
+      double solnrm = x0.ComputeL2Error(E);
+
+      if (myid == 0)
+      {
+         cout << "\n|| E_h - E ||_{L^2} = " << err << ", relative error " << err / solnrm
+              << endl;
+      }
+   }
+
+   // 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_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      ofstream sol_ofs(sol_name.str().c_str());
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+      //solproj.Save(sol_ofs);
+   }
+
+   // 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 a;
+   delete sigma;
+   delete muinv;
+   delete b;
+   delete fespace;
+   delete fec;
+   delete pmesh;
+
+   MPI_Finalize();
+
+   return 0;
+}
+
+
+void E_exact(const Vector &x, Vector &E)
+{
+   if (dim == 3)
+   {
+#ifdef TEST_AIRY
+      const double y = (4.0 * (x(0) + XSHIFT)) - 1.0;
+      const double k = sqrt(K2_VALUE);
+      const double beta = pow(0.25 * k, 2.0/3.0);
+
+      E(0) = 0.0;
+      E(1) = 0.0;
+      E(2) = gsl_sf_airy_Ai(-beta * y, GSL_PREC_DOUBLE);
+#else
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(2));
+      E(2) = sin(kappa * x(0));
+#endif
+   }
+   else
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { E(2) = 0.0; }
+   }
+}
+
+void f_exact(const Vector &x, Vector &f)
+{
+   if (dim == 3)
+   {
+#ifdef TEST_AIRY
+      f = 0.0;
+#else
+      f(0) = (-K2_VALUE + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (-K2_VALUE + kappa * kappa) * sin(kappa * x(2));
+      f(2) = (-K2_VALUE + kappa * kappa) * sin(kappa * x(0));
+#endif
+   }
+   else
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}

examples/ex3p_cfosls.cpp

@@ -0,0 +1,848 @@
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+#include "gsl_sf_airy.h"
+
+#include "multigrid.hpp"
+
+using namespace std;
+using namespace mfem;
+
+
+//#define DIRECT_SOLVER
+
+// Define exact solution
+void E_exact(const Vector & x, Vector & E);
+void H_exact(const Vector & x, Vector & H);
+void f_exact_H(const Vector & x, Vector & f_H);
+void get_maxwell_solution(const Vector & x, double E[], double curlE[],
+                          double curl2E[]);
+void epsilon_func(const Vector &x, Vector &M);
+void epsilon2_func(const Vector &x, Vector &M);
+void epsilon_func_mat(const Vector &x, DenseMatrix &M);
+
+int dim;
+double omega;
+int sol = 3;
+
+
+class FOSLSSolver : public Solver
+{
+public:
+   FOSLSSolver(ParFiniteElementSpace *fespace_, std::vector<HypreParMatrix*>& P,
+               const int myid_)
+      : Solver(2 * fespace_->GetTrueVSize()), M_inv(MPI_COMM_WORLD),
+        fespace(fespace_),
+        n(fespace_->GetTrueVSize()), nfull(fespace_->GetVSize()), LSpcg(MPI_COMM_WORLD),
+        myid(myid_)
+   {
+      z.SetSize(n);
+      Minv_x.SetSize(n);
+
+      ParMesh *pmesh = fespace->GetParMesh();
+      int dim = pmesh->Dimension();
+      int sdim = pmesh->SpaceDimension();
+
+      VectorFunctionCoefficient epsilon(dim, epsilon_func);
+      VectorFunctionCoefficient epsilonT(epsilon);  // transpose of epsilon
+      VectorFunctionCoefficient epsilon2(dim,epsilon2_func);
+      ConstantCoefficient pos(omega);
+      ConstantCoefficient sigma(omega*omega);
+      ScalarVectorProductCoefficient coeff(pos,epsilon);
+      ScalarVectorProductCoefficient coeffT(pos,epsilonT);
+      ScalarVectorProductCoefficient coeff2(sigma,epsilon2);
+
+      bM = new ParBilinearForm(fespace);
+      bM->AddDomainIntegrator(new VectorFEMassIntegrator());
+      bM->Assemble();
+      bM->Finalize();
+
+      bM_eps = new ParBilinearForm(fespace);
+      bM_eps->AddDomainIntegrator(new VectorFEMassIntegrator(epsilonT));
+      bM_eps->Assemble();
+      bM_eps->Finalize();
+
+      bM_curl = new ParMixedBilinearForm(fespace,fespace);
+      bM_curl->AddDomainIntegrator(new MixedVectorWeakCurlIntegrator());
+      bM_curl->Assemble();
+      bM_curl->Finalize();
+
+      Array<int> ess_tdof_list;  // empty
+
+      bM->FormSystemMatrix(ess_tdof_list, M);
+      bM_eps->FormSystemMatrix(ess_tdof_list, M_eps);
+      //bM_curl->FormColSystemMatrix(ess_tdof_list, M_curl);
+      {
+         OperatorPtr M_curl_ptr;
+         bM_curl->FormRectangularSystemMatrix(ess_tdof_list, ess_tdof_list, M_curl_ptr);
+         M_curl = M_curl_ptr.As<HypreParMatrix>();
+      }
+
+      M_inv.SetAbsTol(1.0e-12);
+      M_inv.SetRelTol(1.0e-12);
+      M_inv.SetMaxIter(100);
+      M_inv.SetOperator(M);
+      M_inv.SetPrintLevel(0);
+
+      block_trueOffsets.SetSize(5);
+
+      block_trueOffsets[0] = 0;
+      block_trueOffsets[1] = n;
+      block_trueOffsets[2] = n;
+      block_trueOffsets[3] = n;
+      block_trueOffsets[4] = n;
+      block_trueOffsets.PartialSum();
+
+      trueRhs = new BlockVector(block_trueOffsets);
+      trueSol = new BlockVector(block_trueOffsets);
+
+      //    _           _    _  _       _  _
+      //   |             |  |    |     |    |
+      //   |  A00   A01  |  | E  |     |F_E |
+      //   |             |  |    |  =  |    |
+      //   |  A10   A11  |  | H  |     |F_G |
+      //   |_           _|  |_  _|     |_  _|
+      //
+      // A00 = (curl E, curl F) + \omega^2 (E,F)
+      // A01 = - \omega *( (curl E, F) + (E,curl F)
+      // A10 = - \omega *( (curl H, G) + (H,curl G)
+      // A11 = (curl H, curl G) + \omega^2 (H,G)
+
+      ParBilinearForm *a_EE = new ParBilinearForm(fespace);
+      a_EE->AddDomainIntegrator(new CurlCurlIntegrator());
+      a_EE->AddDomainIntegrator(new VectorFEMassIntegrator(coeff2));
+      a_EE->AddBoundaryIntegrator(new VectorFEMassIntegrator());
+      a_EE->Assemble();
+      a_EE->Finalize();
+      HypreParMatrix *A_EE = new HypreParMatrix;
+      a_EE->FormSystemMatrix(ess_tdof_list, *A_EE);
+
+      ParBilinearForm *a_HH = new ParBilinearForm(fespace);
+      a_HH->AddDomainIntegrator(new CurlCurlIntegrator());
+      a_HH->AddDomainIntegrator(new VectorFEMassIntegrator(sigma));
+      a_HH->AddBoundaryIntegrator(new VectorFEMassIntegrator());
+      a_HH->Assemble();
+      a_HH->Finalize();
+      HypreParMatrix *A_HH = new HypreParMatrix;
+      a_HH->FormSystemMatrix(ess_tdof_list, *A_HH);
+
+      ParBilinearForm *a_tang = new ParBilinearForm(fespace);
+      a_tang->AddBoundaryIntegrator(new VectorFEBoundaryTangentIntegrator(1.0));
+      a_tang->Assemble();
+      a_tang->Finalize();
+      OperatorHandle A_tang_ptr;
+      a_tang->FormSystemMatrix(ess_tdof_list, A_tang_ptr);
+      HypreParMatrix *A_tang = A_tang_ptr.As<HypreParMatrix>();
+
+      // (k curl u, eps v) + (k u, curl v)
+      ParMixedBilinearForm *a_mix1 = new ParMixedBilinearForm(fespace,fespace);
+      a_mix1->AddDomainIntegrator(new MixedVectorCurlIntegrator(coeffT));
+      a_mix1->AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(pos));
+      a_mix1->Assemble();
+      a_mix1->Finalize();
+      HypreParMatrix *A_mix1 = NULL; // new HypreParMatrix;
+      //a_mix1->FormColSystemMatrix(ess_tdof_list, *A_mix1);
+      {
+         OperatorPtr A_mix1_ptr;
+         a_mix1->FormRectangularSystemMatrix(ess_tdof_list, ess_tdof_list, A_mix1_ptr);
+         A_mix1 = A_mix1_ptr.As<HypreParMatrix>();
+      }
+
+      // (k curl u, v) + (k eps u, curl v)
+      ParMixedBilinearForm *a_mix2 = new ParMixedBilinearForm(fespace,fespace);
+      a_mix2->AddDomainIntegrator(new MixedVectorCurlIntegrator(pos));
+      a_mix2->AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(coeff));
+      a_mix2->Assemble();
+      a_mix2->Finalize();
+      HypreParMatrix *A_mix2 = NULL; // new HypreParMatrix;
+      //a_mix2->FormColSystemMatrix(ess_tdof_list, *A_mix2);
+      {
+         OperatorPtr A_mix2_ptr;
+         a_mix2->FormRectangularSystemMatrix(ess_tdof_list, ess_tdof_list, A_mix2_ptr);
+         A_mix2 = A_mix2_ptr.As<HypreParMatrix>();
+      }
+
+      BlockOperator *LS_Maxwellop = new BlockOperator(block_trueOffsets);
+      const int numBlocks = 4;
+
+      LS_Maxwellop->SetBlock(0, 0, A_EE);
+      LS_Maxwellop->SetBlock(1, 0, A_mix2, -1.0); // no bc
+      LS_Maxwellop->SetBlock(3, 0, A_tang, -1.0);
+      LS_Maxwellop->SetBlock(0, 1, A_mix1, -1.0);  // no bc
+      LS_Maxwellop->SetBlock(1, 1, A_HH);
+      LS_Maxwellop->SetBlock(2, 1, A_tang, -1.0);  // other rotation
+      LS_Maxwellop->SetBlock(1, 2, A_tang);
+      LS_Maxwellop->SetBlock(2, 2, A_EE);
+      LS_Maxwellop->SetBlock(3, 2, A_mix2, -1.0);  // no bc
+      LS_Maxwellop->SetBlock(0, 3, A_tang);  // other rotation
+      LS_Maxwellop->SetBlock(2, 3, A_mix1, -1.0);  // no bc
+      LS_Maxwellop->SetBlock(3, 3, A_HH);
+
+      // Set up the preconditioner
+      Array2D<HypreParMatrix*> blockA(numBlocks, numBlocks);
+      Array2D<double> blockAcoef(numBlocks, numBlocks);
+
+      for (int i=0; i<numBlocks; ++i)
+      {
+         for (int j=0; j<numBlocks; ++j)
+         {
+            if (LS_Maxwellop->IsZeroBlock(i,j) == 0)
+            {
+               blockA(i,j) = static_cast<HypreParMatrix *>(&LS_Maxwellop->GetBlock(i,j));
+               blockAcoef(i,j) = LS_Maxwellop->GetBlockCoef(i,j);
+            }
+            else
+            {
+               blockA(i,j) = NULL;
+               blockAcoef(i,j) = 1.0;
+            }
+         }
+      }
+
+      LSpcg.SetAbsTol(1.0e-12);
+      LSpcg.SetRelTol(1.0e-8);
+      LSpcg.SetMaxIter(2000);
+      LSpcg.SetOperator(*LS_Maxwellop);
+      LSpcg.SetPrintLevel(1);
+
+      BlockMGSolver * precMG = NULL;
+
+#ifdef DIRECT_SOLVER
+      std::vector<std::vector<int> > blockProcOffsets(numBlocks);
+      std::vector<std::vector<int> > all_block_num_loc_rows(numBlocks);
+      Array2D<SparseMatrix*> Asp;
+      Asp.SetSize(numBlocks,numBlocks);
+
+      {
+         int nprocs, rank;
+         MPI_Comm_rank(MPI_COMM_WORLD, &rank);
+         MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
+
+         std::vector<int> allnumrows(nprocs);
+         const int blockNumRows = n;
+         MPI_Allgather(&blockNumRows, 1, MPI_INT, allnumrows.data(), 1, MPI_INT,
+                       MPI_COMM_WORLD);
+
+         for (int b=0; b<numBlocks; ++b)
+         {
+            blockProcOffsets[b].resize(nprocs);
+            all_block_num_loc_rows[b].resize(nprocs);
+
+            for (int j=0; j<numBlocks; ++j)
+            {
+               Asp(b,j) = NULL;
+            }
+         }
+
+         blockProcOffsets[0][0] = 0;
+         for (int i=0; i<nprocs-1; ++i)
+         {
+            blockProcOffsets[0][i+1] = blockProcOffsets[0][i] + allnumrows[i];
+         }
+
+         for (int i=0; i<nprocs; ++i)
+         {
+            for (int b=0; b<numBlocks; ++b)
+            {
+               all_block_num_loc_rows[b][i] = allnumrows[i];
+            }
+
+            for (int b=1; b<numBlocks; ++b)
+            {
+               blockProcOffsets[b][i] = blockProcOffsets[0][i];
+            }
+         }
+      }
+
+      LSH = CreateHypreParMatrixFromBlocks(MPI_COMM_WORLD, block_trueOffsets, blockA,
+                                           Asp,
+                                           blockAcoef, blockProcOffsets, all_block_num_loc_rows);
+
+      invLSH = CreateStrumpackSolver(new STRUMPACKRowLocMatrix(*LSH), MPI_COMM_WORLD);
+#else
+      precMG = new BlockMGSolver(LS_Maxwellop->Height(), LS_Maxwellop->Width(),
+                                 blockA, blockAcoef, P);
+      precMG->SetTheta(0.5);
+      LSpcg.SetPreconditioner(*precMG);
+#endif
+   }
+
+   void SetOperator(const Operator &op) { }
+
+   void Mult(const Vector &x, Vector &y) const
+   {
+      // Solve (curl E, curl v) - k^2 (eps E, v) + ik <pi(u), pi(v)> = (x, v), with no BC,
+      // where x is complex, using FOSLS. This is the Galerkin discretization of
+      // curl curl u - k^2 eps u = x, with ik n x u x n - n x curl u = 0 on the boundary.
+
+      MFEM_VERIFY(x.Size() == 2*n, "");
+
+      (*trueRhs) = 0.0;
+
+      for (int i=0; i<n; ++i)
+      {
+         z[i] = x[i];   // Set z = x_Re
+      }
+
+      M_inv.Mult(z, Minv_x);
+      M_eps.Mult(Minv_x, z);
+
+      trueRhs->GetBlock(0) -= z;
+
+      M_curl->Mult(Minv_x, z);
+      z *= 1.0 / omega;
+
+      trueRhs->GetBlock(1) = z;
+
+      for (int i=0; i<n; ++i)
+      {
+         z[i] = x[n + i];   // Set z = x_Im
+      }
+
+      M_inv.Mult(z, Minv_x);
+      M_eps.Mult(Minv_x, z);
+
+      trueRhs->GetBlock(2) -= z;
+
+      M_curl->Mult(Minv_x, z);
+      z *= 1.0 / omega;
+
+      trueRhs->GetBlock(3) += z;
+
+#ifdef DIRECT_SOLVER
+      invLSH->Mult(*trueRhs, *trueSol);
+#else
+      LSpcg.Mult(*trueRhs, *trueSol);
+#endif
+
+      for (int i=0; i<n; ++i)
+      {
+         y[i] = trueSol->GetBlock(0)[i];   // Set y_Re = E_Re
+      }
+
+      for (int i=0; i<n; ++i)
+      {
+         y[n + i] = trueSol->GetBlock(2)[i];   // Set y_Im = E_Im
+      }
+   }
+
+   void ComplexFOSLSTest()
+   {
+      Array<int> block_offsets;
+
+      block_offsets.SetSize(5);
+
+      block_offsets[0] = 0;
+      block_offsets[1] = nfull;
+      block_offsets[2] = nfull;
+      block_offsets[3] = nfull;
+      block_offsets[4] = nfull;
+      block_offsets.PartialSum();
+
+      BlockVector rhs(block_offsets);
+      BlockVector rhsIm(block_offsets);
+
+      rhs = 0.0;
+      rhsIm = 0.0;
+
+      const double ci = 0.0; // 3.3;
+
+      // Exact complex solution: E = Er + i Ei = Epw + ci i Epw, where Epw is E_exact.
+
+      // Set up the linear form with the real part Fr only.
+      const int sdim = 3;
+      VectorFunctionCoefficient Eex(sdim, E_exact);
+      VectorFunctionCoefficient Hex(sdim, H_exact);
+      ConstantCoefficient negOne(-1.0);
+      VectorFunctionCoefficient mEex(sdim, E_exact, &negOne);
+      VectorFunctionCoefficient mHex(sdim, H_exact, &negOne);
+
+      ConstantCoefficient neg(-omega);
+      ConstantCoefficient pos(omega);
+      VectorFunctionCoefficient f_H(3,f_exact_H);  // f / omega
+      ScalarVectorProductCoefficient sf_H(neg,f_H);
+      ScalarVectorProductCoefficient spf_H(pos,f_H);
+      ScalarVectorProductCoefficient mf_H(negOne,f_H);
+
+      VectorFunctionCoefficient epsilon(3, epsilon_func);
+      VectorFunctionCoefficient epsilonT(3, epsilon_func);  // transpose of epsilon
+      MatrixFunctionCoefficient epsilonTmat(3,
+                                            epsilon_func_mat);  // transpose of epsilon
+
+      MatVecCoefficient epsT_spf_H(epsilonTmat, spf_H);
+      MatVecCoefficient epsT_sf_H(epsilonTmat, sf_H);
+
+      ParLinearForm *b_E = new ParLinearForm;
+      b_E->Update(fespace, rhs.GetBlock(0), 0);
+      b_E->AddDomainIntegrator(new VectorFEDomainLFIntegrator(
+                                  epsT_sf_H)); // (k^{-1} Fr, -k eps Qr)
+      b_E->AddBoundaryIntegrator(new VectorFEDomainLFIntegrator(
+                                    Eex));  // <n x E_Re x n, n x Q_Re x n>
+      b_E->Assemble();
+
+      ParLinearForm *b_H = new ParLinearForm;
+      b_H->Update(fespace, rhs.GetBlock(1), 0);
+      b_H->AddDomainIntegrator(new VectorFEDomainLFCurlIntegrator(
+                                  f_H));  // (k^{-1} Fr, curl Rr)
+      b_H->AddBoundaryIntegrator(new VectorFEDomainLFIntegrator(
+                                    Hex));  // <n x H_Re, n x R_Re>
+      b_H->Assemble();
+
+      ParLinearForm *b_E_Im = new ParLinearForm;
+      b_E_Im->Update(fespace, rhs.GetBlock(2), 0);
+      b_E_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(
+                                       mHex));  // <n x H_Re, n x Q_Im x n>
+      b_E_Im->Assemble();
+
+      ParLinearForm *b_H_Im = new ParLinearForm;
+      b_H_Im->Update(fespace, rhs.GetBlock(3), 0);
+      b_H_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(
+                                       mEex));  // -<n x E_Re x n, n x R_Im>
+      b_H_Im->Assemble();
+
+      // Add the imaginary part Fi.
+
+      ParLinearForm *b_Ei = new ParLinearForm;
+      b_Ei->Update(fespace, rhsIm.GetBlock(0), 0);
+      b_Ei->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(
+                                     Hex));  // -<n x H_Im, n x Q_Re x n>
+      b_Ei->Assemble();
+
+      ParLinearForm *b_Hi = new ParLinearForm;
+      b_Hi->Update(fespace, rhsIm.GetBlock(1), 0);
+      b_Hi->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(
+                                     Eex));  // <n x E_Im x n, n x R_Re>
+      b_Hi->Assemble();
+
+      ParLinearForm *b_Ei_Im = new ParLinearForm;
+      b_Ei_Im->Update(fespace, rhsIm.GetBlock(2), 0);
+      b_Ei_Im->AddDomainIntegrator(new VectorFEDomainLFIntegrator(
+                                      epsT_sf_H)); // -(k^{-1} Fi, k eps Qi)
+      b_Ei_Im->AddBoundaryIntegrator(new VectorFEDomainLFIntegrator(
+                                        Eex));  // <n x E_Im x n, n x Q_Im x n>
+      b_Ei_Im->Assemble();
+
+      ParLinearForm *b_Hi_Im = new ParLinearForm;
+      b_Hi_Im->Update(fespace, rhsIm.GetBlock(3), 0);
+      b_Hi_Im->AddDomainIntegrator(new VectorFEDomainLFCurlIntegrator(
+                                      f_H)); // (k^{-1} Fi, curl Ri)
+      b_Hi_Im->AddBoundaryIntegrator(new VectorFEDomainLFIntegrator(
+                                        Hex));  // <n x H_Im, n x R_Im>
+      b_Hi_Im->Assemble();
+
+      rhsIm *= ci;
+      rhs += rhsIm;
+
+      for (int i=0; i<4; ++i)
+      {
+         fespace->GetProlongationMatrix()->MultTranspose(rhs.GetBlock(i),
+                                                         trueRhs->GetBlock(i));
+      }
+
+#ifdef DIRECT_SOLVER
+      invLSH->Mult(*trueRhs, *trueSol);
+#else
+      LSpcg.Mult(*trueRhs, *trueSol);
+#endif
+
+      // Check error
+      ParGridFunction E_gf(fespace);
+      int order = 2;
+      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));
+      }
+
+      ParMesh *pmesh = fespace->GetParMesh();
+
+      // Check error of real part
+
+      E_gf.SetFromTrueDofs(trueSol->GetBlock(0));
+      double Error_E = E_gf.ComputeL2Error(Eex, irs);
+      double norm_E = ComputeGlobalLpNorm(2, Eex, *pmesh, irs);
+
+      cout << myid << ": real error " << Error_E << " relative to " << norm_E << endl;
+
+      {
+         ostringstream mesh_name, sol_name;
+         mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+         sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+         ofstream mesh_ofs(mesh_name.str().c_str());
+         mesh_ofs.precision(8);
+         pmesh->Print(mesh_ofs);
+
+         ofstream sol_ofs(sol_name.str().c_str());
+         sol_ofs.precision(8);
+         E_gf.Save(sol_ofs);
+      }
+
+      // Check error of imaginary part
+      E_gf.SetFromTrueDofs(trueSol->GetBlock(2));
+      const double iml2 = E_gf.Norml2();
+      E_gf *= ci == 0.0 ? 0.0 : (1.0 / ci);
+      Error_E = E_gf.ComputeL2Error(Eex, irs);
+
+      cout << myid << ": imag error " << Error_E << " relative to " << norm_E <<
+           ", l2 norm " << iml2 << endl;
+   }
+
+private:
+
+   BlockVector *trueRhs, *trueSol;
+
+   Array<int> block_trueOffsets;
+
+   ParBilinearForm *bM, *bM_eps;
+   ParMixedBilinearForm *bM_curl;
+
+   HypreParMatrix M, M_eps;
+   HypreParMatrix *M_curl;
+
+   CGSolver M_inv;
+
+   const int n;
+   const int nfull;
+   const int myid;
+
+   mutable Vector z, Minv_x;
+
+   CGSolver LSpcg;
+
+   STRUMPACKSolver *invLSH;
+   HypreParMatrix *LSH;
+
+   ParFiniteElementSpace *fespace;
+};
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Initialize MPI
+   int num_procs, myid;
+   MPI_Init(&argc, &argv); // Initialize MPI
+   MPI_Comm_size(MPI_COMM_WORLD,
+                 &num_procs); //total number of processors available
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid); // Determine process identifier
+   // 1. Parse command-line options.
+   // geometry file
+   const char *mesh_file = "../data/inline-hex.mesh";
+   // finite element order of approximation
+   int order = 1;
+   // static condensation flag
+   bool static_cond = false;
+   // visualization flag
+   bool visualization = 1;
+   // number of wavelengths
+   double k = 1.0;
+   // number of mg levels
+   int ref_levels = 1;
+   // number of initial ref
+   int initref = 1;
+
+   // optional command line inputs
+   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(&k, "-k", "--wavelengths",
+                  "Number of wavelengths.");
+   args.AddOption(&ref_levels, "-ref", "--ref_levels",
+                  "Number of Refinements.");
+   args.AddOption(&initref, "-initref", "--initref",
+                  "Number of initial refinements.");
+   args.AddOption(&sol, "-sol", "--exact",
+                  "Exact solution flag - "
+                  " 1:sinusoidal, 2: point source, 3: plane wave");
+   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();
+   // check if the inputs are correct
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // Angular frequency
+   //omega = 2.0*k*M_PI;
+   omega = k;
+
+   // 2. Read the mesh from the given mesh file.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+
+   if (sol == 4)
+   {
+      mesh->EnsureNodes();
+      GridFunction *nodes = mesh->GetNodes();
+      (*nodes) *= 0.5;
+   }
+
+   dim = mesh->Dimension();
+   int sdim = mesh->SpaceDimension();
+
+   // 3. Executing uniform h-refinement
+   for (int i = 0; i < initref; i++ )
+   {
+      mesh->UniformRefinement();
+   }
+
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+
+   // 4. Define a finite element space on the mesh.
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   std::vector<ParFiniteElementSpace * > fespaces(ref_levels+1);
+   std::vector<ParMesh * > ParMeshes(ref_levels+1);
+   std::vector<HypreParMatrix*> P(ref_levels);
+
+   for (int i = 0; i < ref_levels; i++)
+   {
+      ParMeshes[i] =new ParMesh(*pmesh);
+      fespaces[i] = new ParFiniteElementSpace(*fespace, *ParMeshes[i]);
+      pmesh->UniformRefinement();
+      // Update fespace
+      fespace->Update();
+      OperatorHandle Tr(Operator::Hypre_ParCSR);
+      fespace->GetTrueTransferOperator(*fespaces[i], Tr);
+      Tr.SetOperatorOwner(false);
+      Tr.Get(P[i]);
+   }
+   fespaces[ref_levels] = new ParFiniteElementSpace(*fespace);
+
+   FOSLSSolver fosls(fespace, P, myid);
+
+   fosls.ComplexFOSLSTest();
+
+   for (auto p: ParMeshes) { delete p; }
+   for (auto p: fespaces) { delete p; }
+   for (auto p: P) { delete p; }
+   ParMeshes.clear();
+   fespaces.clear();
+   P.clear();
+   delete fec;
+   delete fespace;
+   delete pmesh;
+
+   MPI_Finalize();
+   return 0;
+}
+
+//define exact solution
+void E_exact(const Vector &x, Vector &E)
+{
+   double curlE[3], curl2E[3];
+   get_maxwell_solution(x, E, curlE, curl2E);
+}
+
+void H_exact(const Vector &x, Vector &H)
+{
+   double E[3], curlE[3], curl2E[3];
+   get_maxwell_solution(x, E, curlE, curl2E);
+   for (int i = 0; i<3; i++) { H(i) = curlE[i]/omega; }
+}
+
+
+void f_exact_H(const Vector &x, Vector &f)
+{
+   // curl H - omega E = f
+   // = curl (curl E / omega) - omega E
+   f = 0.0;
+   if (sol !=4)
+   {
+      double E[3], curlE[3], curl2E[3];
+      get_maxwell_solution(x, E, curlE, curl2E);
+      f(0) = curl2E[0] / omega - omega * E[0];
+      f(1) = curl2E[1] / omega - omega * E[1];
+      f(2) = curl2E[2] / omega - omega * E[2];
+   }
+}
+
+void get_maxwell_solution(const Vector &X, double E[], double curlE[],
+                          double curl2E[])
+{
+   double x = X[0];
+   double y = X[1];
+   double z = X[2];
+
+   if (sol ==-1)
+   {
+      E[0] = y * z * (1.0 - y) * (1.0 - z);
+      E[1] = x * y * z * (1.0 - x) * (1.0 - z);
+      E[2] = x * y * (1.0 - x) * (1.0 - y);
+
+      curlE[0] = -(x-1.0) * x * (y*(2.0*z-3.0)+1.0);
+      curlE[1] = -2.0*(y-1.0)*y*(x-z);
+      curlE[2] = (z-1)*z*(1.0+y*(2.0*x-3.0));
+
+      curl2E[0] = 2.0 * y * (1.0 - y) - (2.0 * x - 3.0) * z * (1 - z);
+      curl2E[1] = 2.0 * y * (x * (1.0 - x) + (1.0 - z) * z);
+      curl2E[2] = 2.0 * y * (1.0 - y) + x * (3.0 - 2.0 * z) * (1.0 - x);
+   }
+   else if (sol == 0) // polynomial
+   {
+      // Polynomial vanishing on the boundary
+      E[0] = y * z * (1.0 - y) * (1.0 - z);
+      E[1] = (1.0 - x) * x * y * (1.0 - z) * z;
+      E[2] = (1.0 - x) * x * (1.0 - y) * y;
+      //
+      curlE[0] = -(-1.0 + x) * x * (1.0 + y * (-3.0 + 2.0 * z));
+      curlE[1] = -2.0 * (-1.0 + y) * y * (x - z);
+      curlE[2] = (1.0 + (-3.0 + 2.0 * x) * y) * (-1.0 + z) * z;
+
+      curl2E[0] = -2.0 * (-1.0 + y) * y + (-3.0 + 2.0 * x) * (-1.0 + z) * z;
+      curl2E[1] = -2.0 * y * (-x + x * x + (-1.0 + z) * z);
+      curl2E[2] = -2.0 * (-1.0 + y) * y + (-1.0 + x) * x * (-3.0 + 2.0 * z);
+   }
+   else if (sol == 1) // sinusoidal
+   {
+      E[0] = sin(omega * y);
+      E[1] = sin(omega * z);
+      E[2] = sin(omega * x);
+
+      curlE[0] = -omega * cos(omega * z);
+      curlE[1] = -omega * cos(omega * x);
+      curlE[2] = -omega * cos(omega * y);
+
+      curl2E[0] = omega * omega * E[0];
+      curl2E[1] = omega * omega * E[1];
+      curl2E[2] = omega * omega * E[2];
+   }
+   else if (sol == 2) // point source
+   {
+      // shift to avoid singularity
+      double x0 = x + 0.1;
+      double x1 = y + 0.1;
+      double x2 = z + 0.1;
+      double r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
+
+      E[0] = cos(omega * r);
+      E[1] = 0.0;
+      E[2] = 0.0;
+
+      double r_x = x0 / r;
+      double r_y = x1 / r;
+      double r_z = x2 / r;
+      double r_xy = -(r_x / r) * r_y;
+      double r_xz = -(r_x / r) * r_z;
+      double r_yx = r_xy;
+      double r_yy = (1.0 / r) * (1.0 - r_y * r_y);
+      double r_zx = r_xz;
+      double r_zz = (1.0 / r) * (1.0 - r_z * r_z);
+
+      curlE[0] = 0.0;
+      curlE[1] = -omega * r_z * sin(omega * r);
+      curlE[2] =  omega * r_y * sin(omega * r);
+
+      curl2E[0] = omega * ((r_yy + r_zz) * sin(omega * r) +
+                           (omega * r_y * r_y + omega * r_z * r_z) * cos(omega * r));
+      curl2E[1] = -omega * (r_yx * sin(omega * r) + omega * r_y * r_x * cos(
+                               omega * r));
+      curl2E[2] = -omega * (r_zx * sin(omega * r) + omega * r_z * r_x * cos(
+                               omega * r));
+   }
+   else if (sol == 3) // plane wave
+   {
+      double coeff = omega / sqrt(3.0);
+      E[0] = cos(coeff * (x + y + z));
+      E[1] = 0.0;
+      E[2] = 0.0;
+
+      curlE[0] = 0.0;
+      curlE[1] = -coeff * sin(coeff * (x + y + z));
+      curlE[2] = coeff * sin(coeff * (x + y + z));
+
+      curl2E[0] = 2.0 * coeff * coeff * E[0];
+      curl2E[1] = -coeff * coeff * E[0];
+      curl2E[2] = -coeff * coeff * E[0];
+   }
+   else if (sol == -1)
+   {
+      E[0] = cos(omega * y);
+      E[1] = 0.0;
+
+      curlE[0] = 0.0;
+      curlE[1] = 0.0;
+      curlE[2] = -omega * sin(omega * y);
+
+      curl2E[0] = omega*omega * cos(omega*y);
+      curl2E[1] = 0.0;
+      curl2E[2] = 0.0;
+   }
+   else if (sol == 4) // Airy function
+   {
+      E[0] = 0;
+      E[1] = 0;
+      // double b = -pow(omega/4.0,2.0/3.0)*(4.0*x(0)-1.0);
+      double b = -pow(omega/4.0,2.0/3.0)*(4.0*x-1.0);
+      //E[2] = boost::math::airy_ai(b);
+      E[2] = gsl_sf_airy_Ai(b, GSL_PREC_DOUBLE);
+
+      curlE[0] = 0.0;
+      curlE[1] = 4.0 * pow(omega/4.0,2.0/3.0) * gsl_sf_airy_Ai_deriv(b,
+                                                                     GSL_PREC_DOUBLE);
+      curlE[2] = 0.0;
+
+      // not used
+      curl2E[0] = 0.0;
+      curl2E[1] = 0.0;
+      curl2E[2] = 0.0;
+   }
+}
+
+void epsilon_func(const Vector &x, Vector &M)
+{
+   M.SetSize(3);
+
+   M = 1.0;
+   if (sol == 4)
+   {
+      M[2] = 4.0*x(0)-1.0;
+   }
+}
+
+void epsilon2_func(const Vector &x, Vector &M)
+{
+   M.SetSize(3);
+
+   M = 1.0;
+   if (sol == 4)
+   {
+      M[2] = (4.0*x(0)-1.0) * (4.0*x(0)-1.0);
+   }
+}
+
+void epsilon_func_mat(const Vector &x, DenseMatrix &M)
+{
+   M.SetSize(3);
+
+   M = 0.0;
+   M(0,0) = 1.0;
+   M(1,1) = 1.0;
+   if (sol != 4)
+   {
+      M(2,2) = 1.0;
+   }
+   else
+   {
+      M(2,2) = 4.0*x(0)-1.0;
+   }
+}

examples/ex3p_fosls.cpp

@@ -0,0 +1,764 @@
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+#include "gsl_sf_airy.h"
+
+#include "multigrid.hpp"
+
+using namespace std;
+using namespace mfem;
+
+#define COMPLEX_IMPEDANCE  // Whether to use impedance BC and solve a complex system
+
+// Define exact solution
+void E_exact(const Vector & x, Vector & E);
+void H_exact(const Vector & x, Vector & H);
+void f_exact_H(const Vector & x, Vector & f_H);
+void get_maxwell_solution(const Vector & x, double E[], double curlE[],
+                          double curl2E[]);
+void epsilon_func(const Vector &x, DenseMatrix &M);
+void epsilon2_func(const Vector &x, DenseMatrix &M);
+
+int dim;
+double omega;
+int sol = 4;
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Initialize MPI
+   int num_procs, myid;
+   MPI_Init(&argc, &argv); // Initialize MPI
+   MPI_Comm_size(MPI_COMM_WORLD,
+                 &num_procs); //total number of processors available
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid); // Determine process identifier
+   // 1. Parse command-line options.
+   // geometry file
+   const char *mesh_file = "../data/inline-hex.mesh";
+   // finite element order of approximation
+   int order = 1;
+   // static condensation flag
+   bool static_cond = false;
+   // visualization flag
+   bool visualization = 1;
+   // number of wavelengths
+   double k = 1.0;
+   // number of mg levels
+   int ref_levels = 1;
+   // number of initial ref
+   int initref = 1;
+
+   // optional command line inputs
+   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(&k, "-k", "--wavelengths",
+                  "Number of wavelengths.");
+   args.AddOption(&ref_levels, "-ref", "--ref_levels",
+                  "Number of Refinements.");
+   args.AddOption(&initref, "-initref", "--initref",
+                  "Number of initial refinements.");
+   args.AddOption(&sol, "-sol", "--exact",
+                  "Exact solution flag - "
+                  " 1:sinusoidal, 2: point source, 3: plane wave");
+   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();
+   // check if the inputs are correct
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // Angular frequency
+   //omega = 2.0*k*M_PI;
+   omega = k;
+
+   // 2. Read the mesh from the given mesh file.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+
+   if (sol == 4)
+   {
+      mesh->EnsureNodes();
+      GridFunction *nodes = mesh->GetNodes();
+      (*nodes) *= 0.5;
+   }
+
+   dim = mesh->Dimension();
+   int sdim = mesh->SpaceDimension();
+
+   // 3. Executing uniform h-refinement
+   for (int i = 0; i < initref; i++ )
+   {
+      mesh->UniformRefinement();
+   }
+
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+
+   // 4. Define a finite element space on the mesh.
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   std::vector<ParFiniteElementSpace * > fespaces(ref_levels+1);
+   std::vector<ParMesh * > ParMeshes(ref_levels+1);
+   std::vector<HypreParMatrix*> P(ref_levels);
+
+   for (int i = 0; i < ref_levels; i++)
+   {
+      ParMeshes[i] =new ParMesh(*pmesh);
+      fespaces[i] = new ParFiniteElementSpace(*fespace, *ParMeshes[i]);
+      pmesh->UniformRefinement();
+      // Update fespace
+      fespace->Update();
+      OperatorHandle Tr(Operator::Hypre_ParCSR);
+      fespace->GetTrueTransferOperator(*fespaces[i], Tr);
+      Tr.SetOperatorOwner(false);
+      Tr.Get(P[i]);
+   }
+   fespaces[ref_levels] = new ParFiniteElementSpace(*fespace);
+
+   Array<int> ess_tdof_listE;
+   Array<int> ess_tdof_listH;
+   Array<int> ess_bdrE(pmesh->bdr_attributes.Max());
+   Array<int> ess_bdrH(pmesh->bdr_attributes.Max());
+#ifdef COMPLEX_IMPEDANCE
+   ess_bdrE = 0;
+   ess_bdrH = 0;  // Neumann
+#else
+   ess_bdrE = 1;
+   ess_bdrH = 0;  // Neumann
+#endif
+   fespace->GetEssentialTrueDofs(ess_bdrE, ess_tdof_listE);
+   fespace->GetEssentialTrueDofs(ess_bdrH, ess_tdof_listH);
+
+#ifdef COMPLEX_IMPEDANCE
+   Array<int> bdr_attr(pmesh->bdr_attributes.Max());
+   bdr_attr = 1;
+   ConstantCoefficient impedance(omega);
+   RestrictedCoefficient imp_rest(impedance, bdr_attr);
+   Array<int> block_offsets(5);
+   Array<int> block_trueOffsets(5);
+#else
+   Array<int> block_offsets(3);
+   Array<int> block_trueOffsets(3);
+#endif
+   block_offsets[0] = 0;
+   block_offsets[1] = fespace->GetVSize();
+   block_offsets[2] = fespace->GetVSize();
+#ifdef COMPLEX_IMPEDANCE
+   block_offsets[3] = fespace->GetVSize();
+   block_offsets[4] = fespace->GetVSize();
+#endif
+   block_offsets.PartialSum();
+
+   block_trueOffsets[0] = 0;
+   block_trueOffsets[1] = fespace->TrueVSize();
+   block_trueOffsets[2] = fespace->TrueVSize();
+#ifdef COMPLEX_IMPEDANCE
+   block_trueOffsets[3] = fespace->TrueVSize();
+   block_trueOffsets[4] = fespace->TrueVSize();
+#endif
+   block_trueOffsets.PartialSum();
+
+   //    _           _    _  _       _  _
+   //   |             |  |    |     |    |
+   //   |  A00   A01  |  | E  |     |F_E |
+   //   |             |  |    |  =  |    |
+   //   |  A10   A11  |  | H  |     |F_G |
+   //   |_           _|  |_  _|     |_  _|
+   //
+   // A00 = (curl E, curl F) + \omega^2 (E,F)
+   // A01 = - \omega *( (curl E, F) + (E,curl F)
+   // A10 = - \omega *( (curl H, G) + (H,curl G)
+   // A11 = (curl H, curl G) + \omega^2 (H,G)
+
+   BlockVector x(block_offsets), rhs(block_offsets);
+   BlockVector trueX(block_trueOffsets), trueRhs(block_trueOffsets);
+
+   x = 0.0;
+   rhs = 0.0;
+   trueX = 0.0;
+   trueRhs = 0.0;
+
+   VectorFunctionCoefficient Eex(sdim, E_exact);
+   ConstantCoefficient negOne(-1.0);
+   VectorFunctionCoefficient mEex(sdim, E_exact, &negOne);
+
+   ParGridFunction * E_gf = new ParGridFunction;
+   ParGridFunction * Exact_gf = new ParGridFunction(fespace);
+   E_gf->MakeRef(fespace, x.GetBlock(0));
+   E_gf->ProjectCoefficient(Eex);
+   Exact_gf->ProjectCoefficient(Eex);
+
+   VectorFunctionCoefficient Hex(sdim, H_exact);
+   ParGridFunction * H_gf = new ParGridFunction;
+   H_gf->MakeRef(fespace, x.GetBlock(1));
+   H_gf->ProjectCoefficient(Hex);
+
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient sigma(pow(omega, 2));
+   ConstantCoefficient neg(-abs(omega));
+   ConstantCoefficient pos(abs(omega));
+
+   MatrixFunctionCoefficient epsilon(dim,epsilon_func);
+   TransposeMatrixCoefficient epsilonT(epsilon);  // transpose of epsilon
+   MatrixFunctionCoefficient epsilon2(dim,epsilon2_func);
+   ScalarMatrixProductCoefficient coeff(neg,epsilon);
+   ScalarMatrixProductCoefficient coeff2(sigma,epsilon2);
+
+   // 6. Set up the linear form
+   VectorFunctionCoefficient f_H(sdim,f_exact_H);
+   ScalarVectorProductCoefficient sf_H(neg,f_H);
+
+   MatVecCoefficient epsT_sf_H(epsilonT, sf_H);
+
+   ParLinearForm *b_E = new ParLinearForm;
+   b_E->Update(fespace, rhs.GetBlock(0), 0);
+   b_E->AddDomainIntegrator(new VectorFEDomainLFIntegrator(epsT_sf_H));
+#ifdef COMPLEX_IMPEDANCE
+   b_E->AddBoundaryIntegrator(new VectorFEDomainLFIntegrator(
+                                 Eex));  // <g_Im, n x Q x n> = <n x E_Re x n, n x Q x n>
+
+   ParLinearForm *b_E_Im = new ParLinearForm;
+   b_E_Im->Update(fespace, rhs.GetBlock(2), 0);
+   b_E_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(
+                                    Hex));  // -<g_Re, n x Q x n> = <n x H_Re, n x Q x n>
+   b_E_Im->Assemble();
+#endif
+   b_E->Assemble();
+
+   ParLinearForm *b_H = new ParLinearForm;
+   b_H->Update(fespace, rhs.GetBlock(1), 0);
+   b_H->AddDomainIntegrator(new VectorFEDomainLFCurlIntegrator(f_H));
+#ifdef COMPLEX_IMPEDANCE
+   b_H->AddBoundaryIntegrator(new VectorFEDomainLFIntegrator(
+                                 Hex));  // -<g_Re, n x R> = <n x H_Re, n x R>
+
+   ParLinearForm *b_H_Im = new ParLinearForm;
+   b_H_Im->Update(fespace, rhs.GetBlock(3), 0);
+   b_H_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentLFIntegrator(
+                                    mEex));  // -<g_Im, n x R> = -<n x E_Re x n, n x R>
+   b_H_Im->Assemble();
+#endif
+   b_H->Assemble();
+
+#ifdef COMPLEX_IMPEDANCE
+   fespace->GetProlongationMatrix()->MultTranspose(rhs.GetBlock(2),
+                                                   trueRhs.GetBlock(2));
+   fespace->GetProlongationMatrix()->MultTranspose(rhs.GetBlock(3),
+                                                   trueRhs.GetBlock(3));
+#endif
+
+   // 7. Bilinear form a(.,.) on the finite element space
+   ParBilinearForm *a_EE = new ParBilinearForm(fespace);
+   a_EE->AddDomainIntegrator(new CurlCurlIntegrator(one));
+   a_EE->AddDomainIntegrator(new VectorFEMassIntegrator(coeff2));
+
+#ifdef COMPLEX_IMPEDANCE
+   a_EE->AddBoundaryIntegrator(new VectorFEMassIntegrator());
+   //a_EE->AddBoundaryIntegrator(new VectorFEMassIntegrator(imp_rest));
+   //a_EE->AddBoundaryIntegrator(new BoundaryMassIntegrator(imp_rest));
+   //a_EE->AddBdrFaceIntegrator(new BoundaryMassIntegrator(imp_rest));
+#endif
+
+   a_EE->Assemble();
+   a_EE->Finalize();
+   HypreParMatrix *A_EE = new HypreParMatrix;
+   a_EE->FormLinearSystem(ess_tdof_listE, x.GetBlock(0), rhs.GetBlock(0), *A_EE,
+                          trueX.GetBlock(0), trueRhs.GetBlock(0));
+
+   ParBilinearForm *a_HH = new ParBilinearForm(fespace);
+   a_HH->AddDomainIntegrator(new CurlCurlIntegrator(one)); // one is the coeff
+   a_HH->AddDomainIntegrator(new VectorFEMassIntegrator(sigma));
+
+#ifdef COMPLEX_IMPEDANCE
+   a_HH->AddBoundaryIntegrator(new VectorFEMassIntegrator());
+   //a_HH->AddBoundaryIntegrator(new VectorFEMassIntegrator(imp_rest));
+   //a_HH->AddBoundaryIntegrator(new BoundaryMassIntegrator(imp_rest));
+#endif
+
+   a_HH->Assemble();
+   a_HH->Finalize();
+   HypreParMatrix *A_HH = new HypreParMatrix;
+   a_HH->FormLinearSystem(ess_tdof_listH, x.GetBlock(1), rhs.GetBlock(1), *A_HH,
+                          trueX.GetBlock(1), trueRhs.GetBlock(1));
+
+   ParMixedBilinearForm *a_HE = new ParMixedBilinearForm(fespace,fespace);
+   a_HE->AddDomainIntegrator(new MixedVectorCurlIntegrator(neg));
+   a_HE->AddDomainIntegrator(new MixedVectorWeakCurlIntegrator(coeff));
+   a_HE->Assemble();
+   a_HE->Finalize();
+   HypreParMatrix *A_HE = new HypreParMatrix;
+   a_HE->FormColLinearSystem(ess_tdof_listE,x.GetBlock(0),rhs.GetBlock(1),*A_HE,
+                             trueX.GetBlock(0),trueRhs.GetBlock(1));
+
+   HypreParMatrix *A_EH = A_HE->Transpose();
+
+#ifdef COMPLEX_IMPEDANCE
+   ParBilinearForm *a_EH_Im = new ParBilinearForm(fespace);
+   //a_EH_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentIntegrator(imp_rest));
+   //a_EH_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentIntegrator(impedance));
+   //a_EH_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentIntegrator(omega));
+   a_EH_Im->AddBoundaryIntegrator(new VectorFEBoundaryTangentIntegrator());
+   a_EH_Im->Assemble();
+   a_EH_Im->Finalize();
+
+   OperatorHandle A_EH_Im_ptr;
+   a_EH_Im->FormSystemMatrix(ess_tdof_listE,
+                             A_EH_Im_ptr);  // empty ess_tdof_list for impedance
+
+   HypreParMatrix *A_EH_Im = A_EH_Im_ptr.As<HypreParMatrix>();
+
+   HypreParMatrix *A_HE_Im = A_EH_Im->Transpose();
+#endif
+
+   BlockOperator *LS_Maxwellop = new BlockOperator(block_trueOffsets);
+#ifdef COMPLEX_IMPEDANCE
+   const int numBlocks = 4;
+#else
+   const int numBlocks = 2;
+#endif
+
+   LS_Maxwellop->SetBlock(0, 0, A_EE);
+   LS_Maxwellop->SetBlock(0, 1, A_EH);
+   LS_Maxwellop->SetBlock(1, 0, A_HE);
+   LS_Maxwellop->SetBlock(1, 1, A_HH);
+
+#ifdef COMPLEX_IMPEDANCE
+   LS_Maxwellop->SetBlock(0, 3, A_EH_Im);
+   LS_Maxwellop->SetBlock(1, 2, A_HE_Im, -1.0);
+
+   LS_Maxwellop->SetBlock(2, 1, A_EH_Im, -1.0);
+   LS_Maxwellop->SetBlock(3, 0, A_HE_Im);
+
+   LS_Maxwellop->SetBlock(2, 2, A_EE);
+   LS_Maxwellop->SetBlock(2, 3, A_EH);
+   LS_Maxwellop->SetBlock(3, 2, A_HE);
+   LS_Maxwellop->SetBlock(3, 3, A_HH);
+#endif
+
+   if (myid == 0)
+   {
+      cout << "Size of fine grid system: "
+           << 2.0 * A_EE->GetGlobalNumRows() << " x " << 2.0* A_EE->GetGlobalNumCols() <<
+           endl;
+   }
+
+   // Set up the preconditioner
+   Array2D<HypreParMatrix*> blockA(numBlocks, numBlocks);
+   Array2D<double> blockAcoef(numBlocks, numBlocks);
+
+   for (int i=0; i<numBlocks; ++i)
+   {
+      for (int j=0; j<numBlocks; ++j)
+      {
+         if (LS_Maxwellop->IsZeroBlock(i,j) == 0)
+         {
+            blockA(i,j) = static_cast<HypreParMatrix *>(&LS_Maxwellop->GetBlock(i,j));
+            blockAcoef(i,j) = LS_Maxwellop->GetBlockCoef(i,j);
+         }
+         else
+         {
+            blockA(i,j) = NULL;
+            blockAcoef(i,j) = 1.0;
+         }
+      }
+   }
+
+   // // double nnz = A_HH->NNZ();
+   // // double ndof = A_HH->GetGlobalNumRows();
+   // // double est_mem_b = nnz*12.0 + (ndof+1.0)*4;
+   // // double gb = est_mem_b*4.0/pow(1024.0,3);
+
+   // // mfem::out << "Estimated memory taken by the global matrix: " <<  gb << endl;
+
+   int maxit(2000);
+   double rtol(1.e-8);
+   double atol(1.e-12);
+
+   // trueX = 0.0;
+   CGSolver pcg(MPI_COMM_WORLD);
+   pcg.SetAbsTol(atol);
+   pcg.SetRelTol(rtol);
+   pcg.SetMaxIter(maxit);
+   pcg.SetOperator(*LS_Maxwellop);
+   pcg.SetPrintLevel(1);
+   chrono.Clear();
+   chrono.Start();
+   BlockMGSolver * precMG = new BlockMGSolver(LS_Maxwellop->Height(),
+                                              LS_Maxwellop->Width(), blockA, blockAcoef, P);
+   //precMG->SetTheta(0.5);
+   // // int lv_coarse = min(ref_levels,ref_levels-1);
+   // // int levels = ref_levels - lv_coarse;
+   // // BlkParSchwarzSmoother * precAS = new BlkParSchwarzSmoother(fespaces[lv_coarse]->GetParMesh(),levels,fespaces[ref_levels],LS_Maxwellop);
+   chrono.Stop();
+   if (myid == 0)
+   {
+      cout << "MG Setup time: " << chrono.RealTime() << endl;
+   }
+
+   // Randomize H RHS
+   //trueRhs = 1.0;
+   /*
+   for (int i=block_trueOffsets[1]; i<block_trueOffsets[2]; ++i)
+     trueRhs[i] = i % 53;
+   */
+
+   chrono.Clear();
+   chrono.Start();
+   pcg.SetPreconditioner(*precMG);
+   // // pcg.SetPreconditioner(*precAS);
+   pcg.Mult(trueRhs, trueX);
+   chrono.Stop();
+   delete precMG;
+   // // delete precAS;
+
+   // // trueX = 0.0;
+   // // invA->Mult(trueRhs,trueX);
+
+   if (myid == 0)
+   {
+      cout << "MG Solution time time: " << chrono.RealTime() << endl;
+   }
+   // // cin.get();
+   // //  if(myid == 0)
+   // //    cout << "MG prec Solution time: " << chrono.RealTime() << endl;
+
+
+   // // chrono.Clear();
+   // // chrono.Start();
+   // // Block_AMSSolver * precAMS = new Block_AMSSolver(block_trueOffsets,fespaces);
+   // // precAMS->SetSmootherType(Block_AMS::BlkSmootherType::SCHWARZ);
+   // // precAMS->SetSmootherType(Block_AMS::BlkSmootherType::HYPRE);
+   // // precAMS->SetOperator(LS_Maxwellop);
+   // // precAMS->SetTheta(1.0/5.0);
+   // // // 0-Smoother, 1-Grad, 2,3,4-Pix,Piy,Piz
+   // // precAMS->SetCycleType("023414320");
+   // // precAMS->SetNumberofCycles(1);
+   // // chrono.Stop();
+   // // if(myid == 0)
+   // //    cout << "BlkAMS Setup time: " << chrono.RealTime() << endl;
+
+   // // // resolve with block AMS
+   // // trueX = 0;
+   // // chrono.Clear();
+   // // chrono.Start();
+   // // pcg.SetPreconditioner(*precAMS);
+   // // pcg.Mult(trueRhs, trueX);
+   // // chrono.Stop();
+   // // delete precAMS;
+
+   // // if(myid == 0)
+   // //    cout << "BlockAMS Solution time: " << chrono.RealTime() << endl;
+
+
+   a_EE->RecoverFEMSolution(trueX.GetBlock(0), *b_E, *E_gf);
+   a_HH->RecoverFEMSolution(trueX.GetBlock(1), *b_H, *H_gf);
+
+
+   int order_quad = 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));
+   }
+
+   double Error_E = E_gf->ComputeL2Error(Eex, irs);
+   double norm_E = ComputeGlobalLpNorm(2, Eex, *pmesh, irs);
+
+   double Error_H = H_gf->ComputeL2Error(Hex, irs);
+   double norm_H = ComputeGlobalLpNorm(2, Hex , *pmesh, irs);
+
+   if (myid == 0)
+   {
+      cout << "|| E_h - E || = " << Error_E  << "\n";
+      cout << "|| E_h - E ||/||E|| = " << Error_E/norm_E  << "\n";
+      cout << "|| H_h - H || = " << Error_H  << "\n";
+      cout << "|| H_h - H ||/||H|| = " << Error_H/norm_H  << "\n";
+      cout << "Total error = " << setprecision(15) << sqrt(Error_H*Error_H
+                                                           +Error_E*Error_E) << "\n";
+   }
+
+   {
+      ostringstream mesh_name, sol_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      ofstream sol_ofs(sol_name.str().c_str());
+      sol_ofs.precision(8);
+      E_gf->Save(sol_ofs);
+   }
+
+   //ParGridFunction ExactE(fespace);
+   /*
+   if (visualization)
+     {
+       // 8. Connect to GLVis.
+       char vishost[] = "localhost";
+       int  visport   = 19916;
+       // socketstream E_sock(vishost, visport);
+       // E_sock << "parallel " << num_procs << " " << myid << "\n";
+       // E_sock.precision(8);
+       // E_sock << "solution\n" << *pmesh << *E_gf << "window_title 'Electric field'" << endl;
+       socketstream Exact_sock(vishost, visport);
+       Exact_sock << "parallel " << num_procs << " " << myid << "\n";
+       Exact_sock.precision(8);
+       Exact_sock << "solution\n" << *pmesh << *Exact_gf << "window_title 'Electric field'" << endl;
+
+       // MPI_Barrier(pmesh->GetComm());
+       // socketstream Eex_sock(vishost, visport);
+       // Eex_sock << "parallel " << num_procs << " " << myid << "\n";
+       // Eex_sock.precision(8);
+       // Eex_sock << "solution\n" << *pmesh << *Exact_gf << "window_title 'Exact Electric field'" << endl;
+     }
+   */
+   // delete A_EE;
+   // delete A_HE;
+   // delete A_EH;
+   // delete A_HH;
+   // delete LS_Maxwellop;
+   // delete a_EE;
+   // delete a_HE;
+   // delete a_HH;
+   // delete b_E;
+   // delete b_H;
+   delete E_gf;
+   delete Exact_gf;
+   for (auto p: ParMeshes) { delete p; }
+   for (auto p: fespaces) { delete p; }
+   for (auto p: P) { delete p; }
+   ParMeshes.clear();
+   fespaces.clear();
+   P.clear();
+   delete fec;
+   delete fespace;
+   delete pmesh;
+
+   // cout << "Freed memory: " << endl;
+   // cin.get();
+   MPI_Finalize();
+   return 0;
+}
+
+//define exact solution
+void E_exact(const Vector &x, Vector &E)
+{
+   double curlE[3], curl2E[3];
+   get_maxwell_solution(x, E, curlE, curl2E);
+}
+
+void H_exact(const Vector &x, Vector &H)
+{
+   double E[3], curlE[3], curl2E[3];
+   get_maxwell_solution(x, E, curlE, curl2E);
+   for (int i = 0; i<3; i++) { H(i) = curlE[i]/omega; }
+}
+
+
+void f_exact_H(const Vector &x, Vector &f)
+{
+   // curl H - omega E = f
+   // = curl (curl E / omega) - omega E
+   f = 0.0;
+   if (sol !=4)
+   {
+      double E[3], curlE[3], curl2E[3];
+      get_maxwell_solution(x, E, curlE, curl2E);
+      f(0) = curl2E[0] / omega - omega * E[0];
+      f(1) = curl2E[1] / omega - omega * E[1];
+      f(2) = curl2E[2] / omega - omega * E[2];
+   }
+}
+
+void get_maxwell_solution(const Vector &X, double E[], double curlE[],
+                          double curl2E[])
+{
+   double x = X[0];
+   double y = X[1];
+   double z = X[2];
+
+
+
+   if (sol ==-1)
+   {
+      E[0] = y * z * (1.0 - y) * (1.0 - z);
+      E[1] = x * y * z * (1.0 - x) * (1.0 - z);
+      E[2] = x * y * (1.0 - x) * (1.0 - y);
+
+      curlE[0] = -(x-1.0) * x * (y*(2.0*z-3.0)+1.0);
+      curlE[1] = -2.0*(y-1.0)*y*(x-z);
+      curlE[2] = (z-1)*z*(1.0+y*(2.0*x-3.0));
+
+      curl2E[0] = 2.0 * y * (1.0 - y) - (2.0 * x - 3.0) * z * (1 - z);
+      curl2E[1] = 2.0 * y * (x * (1.0 - x) + (1.0 - z) * z);
+      curl2E[2] = 2.0 * y * (1.0 - y) + x * (3.0 - 2.0 * z) * (1.0 - x);
+   }
+   else if (sol == 0) // polynomial
+   {
+      // Polynomial vanishing on the boundary
+      E[0] = y * z * (1.0 - y) * (1.0 - z);
+      E[1] = (1.0 - x) * x * y * (1.0 - z) * z;
+      E[2] = (1.0 - x) * x * (1.0 - y) * y;
+      //
+      curlE[0] = -(-1.0 + x) * x * (1.0 + y * (-3.0 + 2.0 * z));
+      curlE[1] = -2.0 * (-1.0 + y) * y * (x - z);
+      curlE[2] = (1.0 + (-3.0 + 2.0 * x) * y) * (-1.0 + z) * z;
+
+      curl2E[0] = -2.0 * (-1.0 + y) * y + (-3.0 + 2.0 * x) * (-1.0 + z) * z;
+      curl2E[1] = -2.0 * y * (-x + x * x + (-1.0 + z) * z);
+      curl2E[2] = -2.0 * (-1.0 + y) * y + (-1.0 + x) * x * (-3.0 + 2.0 * z);
+   }
+   else if (sol == 1) // sinusoidal
+   {
+      E[0] = sin(omega * y);
+      E[1] = sin(omega * z);
+      E[2] = sin(omega * x);
+
+      curlE[0] = -omega * cos(omega * z);
+      curlE[1] = -omega * cos(omega * x);
+      curlE[2] = -omega * cos(omega * y);
+
+      curl2E[0] = omega * omega * E[0];
+      curl2E[1] = omega * omega * E[1];
+      curl2E[2] = omega * omega * E[2];
+   }
+   else if (sol == 2) // point source
+   {
+      // shift to avoid singularity
+      double x0 = x + 0.1;
+      double x1 = y + 0.1;
+      double x2 = z + 0.1;
+      //
+      double r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
+
+      E[0] = cos(omega * r);
+      E[1] = 0.0;
+      E[2] = 0.0;
+
+      double r_x = x0 / r;
+      double r_y = x1 / r;
+      double r_z = x2 / r;
+      double r_xy = -(r_x / r) * r_y;
+      double r_xz = -(r_x / r) * r_z;
+      double r_yx = r_xy;
+      double r_yy = (1.0 / r) * (1.0 - r_y * r_y);
+      double r_zx = r_xz;
+      double r_zz = (1.0 / r) * (1.0 - r_z * r_z);
+
+      curlE[0] = 0.0;
+      curlE[1] = -omega * r_z * sin(omega * r);
+      curlE[2] =  omega * r_y * sin(omega * r);
+
+      curl2E[0] = omega * ((r_yy + r_zz) * sin(omega * r) +
+                           (omega * r_y * r_y + omega * r_z * r_z) * cos(omega * r));
+      curl2E[1] = -omega * (r_yx * sin(omega * r) + omega * r_y * r_x * cos(
+                               omega * r));
+      curl2E[2] = -omega * (r_zx * sin(omega * r) + omega * r_z * r_x * cos(
+                               omega * r));
+   }
+   else if (sol == 3) // plane wave
+   {
+      double coeff = omega / sqrt(3.0);
+      E[0] = cos(coeff * (x + y + z));
+      E[1] = 0.0;
+      E[2] = 0.0;
+
+      curlE[0] = 0.0;
+      curlE[1] = -coeff * sin(coeff * (x + y + z));
+      curlE[2] = coeff * sin(coeff * (x + y + z));
+
+      curl2E[0] = 2.0 * coeff * coeff * E[0];
+      curl2E[1] = -coeff * coeff * E[0];
+      curl2E[2] = -coeff * coeff * E[0];
+   }
+   else if (sol == -1)
+   {
+      E[0] = cos(omega * y);
+      E[1] = 0.0;
+
+      curlE[0] = 0.0;
+      curlE[1] = 0.0;
+      curlE[2] = -omega * sin(omega * y);
+
+      curl2E[0] = omega*omega * cos(omega*y);
+      curl2E[1] = 0.0;
+      curl2E[2] = 0.0;
+   }
+   else if (sol == 4) // Airy function
+   {
+      E[0] = 0;
+      E[1] = 0;
+      // double b = -pow(omega/4.0,2.0/3.0)*(4.0*x(0)-1.0);
+      double b = -pow(omega/4.0,2.0/3.0)*(4.0*x-1.0);
+      //E[2] = boost::math::airy_ai(b);
+      E[2] = gsl_sf_airy_Ai(b, GSL_PREC_DOUBLE);
+
+      curlE[0] = 0.0;
+      curlE[1] = 4.0 * pow(omega/4.0,2.0/3.0) * gsl_sf_airy_Ai_deriv(b,
+                                                                     GSL_PREC_DOUBLE);
+      curlE[2] = 0.0;
+
+      //  not used
+      curl2E[0] = 0.0;
+      curl2E[1] = 0.0;
+      curl2E[2] = 0.0;
+   }
+}
+
+
+void epsilon_func(const Vector &x, DenseMatrix &M)
+{
+   M.SetSize(3);
+
+   M = 0.0;
+   M(0,0) = 1.0;
+   M(1,1) = 1.0;
+   if (sol != 4)
+   {
+      M(2,2) = 1.0;
+   }
+   else
+   {
+      M(2,2) = 4.0*x(0)-1.0;
+      // M(2,2) = 2.0;
+   }
+}
+
+void epsilon2_func(const Vector &x, DenseMatrix &M)
+{
+   M.SetSize(3);
+
+   M = 0.0;
+   M(0,0) = 1.0;
+   M(1,1) = 1.0;
+   if (sol != 4)
+   {
+      M(2,2) = 1.0;
+   }
+   else
+   {
+      M(2,2) = (4.0*x(0)-1.0) * (4.0*x(0)-1.0);
+      // M(2,2) = 4.0;
+   }
+}

examples/ex3p_sp.cpp

@@ -0,0 +1,915 @@
+//                       MFEM Example 3 - Parallel Version
+//
+// Compile with: make ex3p
+//
+// Sample runs:  mpirun -np 4 ex3p -m ../data/star.mesh
+//               mpirun -np 4 ex3p -m ../data/square-disc.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/beam-tet.mesh
+//               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex3p -m ../data/escher.mesh
+//               mpirun -np 4 ex3p -m ../data/escher.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/fichera.mesh
+//               mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
+//               mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
+//               mpirun -np 4 ex3p -m ../data/square-disc-nurbs.mesh
+//               mpirun -np 4 ex3p -m ../data/beam-hex-nurbs.mesh
+//               mpirun -np 4 ex3p -m ../data/amr-quad.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/amr-hex.mesh
+//               mpirun -np 4 ex3p -m ../data/star-surf.mesh -o 2
+//               mpirun -np 4 ex3p -m ../data/mobius-strip.mesh -o 2 -f 0.1
+//               mpirun -np 4 ex3p -m ../data/klein-bottle.mesh -o 2 -f 0.1
+//
+// Description:  This example code solves a simple electromagnetic diffusion
+//               problem corresponding to the second order definite Maxwell
+//               equation curl curl E + E = f with boundary condition
+//               E x n = <given tangential field>. Here, we use a given exact
+//               solution E and compute the corresponding r.h.s. f.
+//               We discretize with Nedelec finite elements in 2D or 3D.
+//
+//               The example demonstrates the use of H(curl) finite element
+//               spaces with the curl-curl and the (vector finite element) mass
+//               bilinear form, as well as the computation of discretization
+//               error when the exact solution is known. Static condensation is
+//               also illustrated.
+//
+//               We recommend viewing examples 1-2 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+// Exact solution, E, and r.h.s., f. See below for implementation.
+void E_exact(const Vector &, Vector &);
+void f_exact(const Vector &, Vector &);
+double freq = 1.0, kappa;
+int dim;
+
+#define SIGMAVAL -250.0
+//#define FORM_DEFINITE
+//#define SOLVE_A2
+//#define ITER_A2
+
+//#define USE_CSL
+
+//#define USE_HELMHOLTZ
+
+//#define TEST_MULTIPLE_SP
+
+#ifdef USE_HELMHOLTZ
+void GetHelmholtzMatrix(ParMesh *pmesh, const int dir, HypreParMatrix *A)
+{
+   const int order = 1;
+   FiniteElementCollection *fec;
+   fec = new H1_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+
+   Array<int> ess_tdof_list;
+
+   const bool homogeneousBCeverywhere = false;
+   if (homogeneousBCeverywhere)
+   {
+      if (pmesh->bdr_attributes.Size())
+      {
+         Array<int> ess_bdr(pmesh->bdr_attributes.Max());
+         ess_bdr = 1;
+         fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      }
+   }
+   else
+   {
+      // Set boundary conditions, depending on dir.
+      MFEM_VERIFY(dim == 3, "");
+      for (int i=0; i<pmesh->GetNBE(); ++i)
+      {
+         Element *elem = pmesh->GetBdrElement(i);
+         MFEM_VERIFY(elem->GetNVertices() >= 3, "");
+         const int *vertices = elem->GetVertices();
+         double *v[3];
+         for (int j=0; j<3; ++j)
+         {
+            v[j] = pmesh->GetVertex(vertices[j]);
+         }
+
+         double u[3];
+         double w[3];
+         for (int j=0; j<3; ++j)
+         {
+            u[j] = v[1][j] - v[0][j];  // An edge tangent
+            w[j] = v[2][j] - v[1][j];  // Another edge tangent, not parallel to u.
+         }
+
+         double n[3];  // normal vector, taken as the cross product u x v
+         n[0] = (u[1]*w[2]) - (u[2]*w[1]);
+         n[1] = (u[2]*w[0]) - (u[0]*w[2]);
+         n[2] = (u[0]*w[1]) - (u[1]*w[0]);
+
+         double t = sqrt((n[0]*n[0]) + (n[1]*n[1]) + (n[2]*n[2]));
+
+         int d = -1;
+         for (int j=0; j<3; ++j)
+         {
+            n[j] /= t;  // normalize
+            if (fabs(fabs(n[j]) - 1.0) < 1.0e-8)
+            {
+               d = j;
+            }
+         }
+
+         MFEM_VERIFY(d >= 0, "");
+
+         if (d != dir)  // face has essential BC at all DOF's.
+         {
+            elem->SetAttribute(1);
+         }
+         else
+         {
+            elem->SetAttribute(0);
+         }
+      }
+
+      Array<int> ess_bdr(2);
+      ess_bdr = 0;
+      ess_bdr[1] = 1;
+      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   ParBilinearForm *a = new ParBilinearForm(fespace);
+   ConstantCoefficient one(1.0);
+   ConstantCoefficient neg(SIGMAVAL);
+
+   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   a->AddDomainIntegrator(new MassIntegrator(neg));
+
+   ParLinearForm *b = new ParLinearForm(fespace);
+   ConstantCoefficient zero(0.0);
+   b->AddDomainIntegrator(new DomainLFIntegrator(zero));
+   b->Assemble();
+
+   bool static_cond = false;
+
+   if (static_cond) { a->EnableStaticCondensation(); }
+   a->Assemble();
+
+   ParGridFunction x(fespace);
+   x = 0.0;
+
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, *A, X, B);
+}
+#endif
+
+
+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/beam-tet.mesh";
+   int order = 2;
+   bool static_cond = false;
+   bool visualization = 1;
+#ifdef MFEM_USE_STRUMPACK
+   bool use_strumpack = false;
+#endif
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
+                  " solution.");
+   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.");
+#ifdef MFEM_USE_STRUMPACK
+   args.AddOption(&use_strumpack, "-strumpack", "--strumpack-solver",
+                  "-no-strumpack", "--no-strumpack-solver",
+                  "Use STRUMPACK's double complex linear solver.");
+#endif
+
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+   kappa = freq * M_PI;
+
+   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
+   //    and volume meshes with the same code.
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   dim = mesh->Dimension();
+   int sdim = mesh->SpaceDimension();
+
+   // 4. Refine the serial mesh on all processors to increase the resolution. In
+   //    this example we do 'ref_levels' of uniform refinement. We choose
+   //    'ref_levels' to be the largest number that gives a final mesh with no
+   //    more than 1,000 elements.
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      //(int)floor(log(100000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted. Tetrahedral
+   //    meshes need to be reoriented before we can define high-order Nedelec
+   //    spaces on them.
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   {
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; l++)
+      {
+         pmesh->UniformRefinement();
+      }
+   }
+   pmesh->ReorientTetMesh();
+
+   {
+      double minsize = pmesh->GetElementSize(0);
+      double maxsize = minsize;
+      for (int i=1; i<pmesh->GetNE(); ++i)
+      {
+         const double size_i = pmesh->GetElementSize(i);
+         minsize = std::min(minsize, size_i);
+         maxsize = std::max(maxsize, size_i);
+      }
+
+      cout << myid << ": Element size range: (" << minsize << ", " << maxsize << ")"
+           << endl;
+   }
+
+   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   //    use the Nedelec finite elements of the specified order.
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+   long globalNE = pmesh->GetGlobalNE();
+   if (myid == 0)
+   {
+      cout << "Number of mesh elements: " << globalNE << endl;
+      cout << "Number of finite element unknowns: " << size << endl;
+      cout << "Root local number of finite element unknowns: " << fespace->TrueVSize()
+           << endl;
+   }
+
+   // 7. 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);
+   }
+
+   // 8. Set up the parallel linear form b(.) which corresponds to the
+   //    right-hand side of the FEM linear system, which in this case is
+   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
+   //    basis functions in the finite element fespace.
+   VectorFunctionCoefficient f(sdim, f_exact);
+   ParLinearForm *b = new ParLinearForm(fespace);
+   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
+   b->Assemble();
+
+   // 9. Define the solution vector x as a parallel finite element grid function
+   //    corresponding to fespace. Initialize x by projecting the exact
+   //    solution. Note that only values from the boundary edges will be used
+   //    when eliminating the non-homogeneous boundary condition to modify the
+   //    r.h.s. vector b.
+   ParGridFunction x(fespace);
+   VectorFunctionCoefficient E(sdim, E_exact);
+   x.ProjectCoefficient(E);
+
+   // 10. Set up the parallel bilinear form corresponding to the EM diffusion
+   //     operator curl muinv curl + sigma I, by adding the curl-curl and the
+   //     mass domain integrators.
+   Coefficient *muinv = new ConstantCoefficient(1.0);
+   Coefficient *sigma = new ConstantCoefficient(SIGMAVAL);
+   Coefficient *sigmaAbs = new ConstantCoefficient(fabs(SIGMAVAL));
+   ParBilinearForm *a = new ParBilinearForm(fespace);
+   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
+
+   //cout << myid << ": NBE " << pmesh->GetNBE() << endl;
+
+#ifdef FORM_DEFINITE
+   ParBilinearForm *adef = new ParBilinearForm(fespace);
+   adef->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   adef->AddDomainIntegrator(new VectorFEMassIntegrator(*sigmaAbs));
+
+   if (static_cond) { adef->EnableStaticCondensation(); }
+   adef->Assemble();
+
+   HypreParMatrix Adef;
+   Vector Bdef, Xdef;
+   adef->FormLinearSystem(ess_tdof_list, x, *b, Adef, Xdef, Bdef);
+#endif
+
+#ifdef USE_CSL
+   Vector Bdef, Xdef;
+
+   ParBilinearForm *Mform =  new ParBilinearForm(fespace);
+   Mform->AddDomainIntegrator(new VectorFEMassIntegrator(*sigmaAbs));
+   Mform->Assemble();
+
+   // Mform->Finalize();
+
+   HypreParMatrix Mmat, Smat, Mcopy;
+   Mform->FormLinearSystem(ess_tdof_list, x, *b, Mmat, Xdef, Bdef);
+   Mform->FormLinearSystem(ess_tdof_list, x, *b, Mcopy, Xdef,
+                           Bdef);  // There must be a better way than creating two identical matrices.
+
+   ParBilinearForm *Sform =  new ParBilinearForm(fespace);
+   Sform->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   Sform->Assemble();
+
+   Sform->FormLinearSystem(ess_tdof_list, x, *b, Smat, Xdef, Bdef);
+
+   ParBilinearForm *agrad = new ParBilinearForm(fespace);
+   //agrad->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   agrad->AddDomainIntegrator(new VectorFEMassIntegrator(*muinv));
+
+   if (static_cond) { agrad->EnableStaticCondensation(); }
+   agrad->Assemble();
+   HypreParMatrix Agrad;
+   agrad->FormLinearSystem(ess_tdof_list, x, *b, Agrad, Xdef, Bdef);
+#endif
+
+#ifdef ITER_A2
+   Vector Bdef, Xdef;
+
+   ParBilinearForm *Mform =  new ParBilinearForm(fespace);
+   Mform->AddDomainIntegrator(new VectorFEMassIntegrator(*sigmaAbs));
+   Mform->Assemble();
+
+   Mform->Finalize();
+
+   HypreParMatrix Mmat, Mcopy;
+   Mform->FormLinearSystem(ess_tdof_list, x, *b, Mmat, Xdef, Bdef);
+   Mform->FormLinearSystem(ess_tdof_list, x, *b, Mcopy, Xdef,
+                           Bdef);  // There must be a better way to implement M^2.
+
+   /*
+   HypreParMatrix *Mmat = Mform->ParallelAssemble();
+   HypreParMatrix *Mcopy = Mform->ParallelAssemble();  // There must be a better way to implement M^2.
+   */
+
+   ParBilinearForm *Sform =  new ParBilinearForm(fespace);
+   Sform->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
+   Sform->Assemble();
+
+   HypreParMatrix Smat, Scopy;
+   Sform->FormLinearSystem(ess_tdof_list, x, *b, Smat, Xdef, Bdef);
+   Sform->FormLinearSystem(ess_tdof_list, x, *b, Scopy, Xdef, Bdef);
+#endif
+
+   // 11. Assemble the parallel bilinear form and the corresponding linear
+   //     system, applying any necessary transformations such as: parallel
+   //     assembly, eliminating boundary conditions, applying conforming
+   //     constraints for non-conforming AMR, static condensation, etc.
+   if (static_cond) { a->EnableStaticCondensation(); }
+   a->Assemble();
+
+   HypreParMatrix A;
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+
+#ifdef SOLVE_A2
+   HypreParMatrix Acopy;
+   {
+      Vector Bdum, Xdum;
+      a->FormLinearSystem(ess_tdof_list, x, *b, Acopy, Xdum, Bdum);
+   }
+#endif
+
+   if (myid == 0)
+   {
+      cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
+   }
+
+   StopWatch chrono;
+   chrono.Clear();
+   chrono.Start();
+
+   //A.Print("maxwell1000_2");
+
+#ifdef MFEM_USE_STRUMPACK
+   if (use_strumpack)
+   {
+      const bool fullDirect = true;
+
+#ifdef USE_CSL
+      const double beta1 = 1.0;
+      const double beta2 = 0.5;
+
+      Mmat *= -beta1;
+
+      // HypreParMatrix *cslRe = Add(1.0, Smat, -beta1, Mmat);
+      HypreParMatrix * cslRe = ParAdd(&Smat, &Mmat);
+
+      Mcopy *= beta2;
+
+      //ComplexHypreParMatrix chpm(cslRe, &Mcopy, false, false);
+      ComplexHypreParMatrix chpm(&A, &Mcopy, false,
+                                 false);  // For the case beta1 = 1.
+
+      HypreParMatrix *cSysMat = chpm.GetSystemMatrix();
+
+      Array<int> block_offsets(3); // number of variables + 1
+      block_offsets[0] = 0;
+      block_offsets[1] = fespace->GetVSize();
+      block_offsets[2] = fespace->GetVSize();
+      block_offsets.PartialSum();
+
+      Array<int> block_trueOffsets(3); // number of variables + 1
+      block_trueOffsets[0] = 0;
+      block_trueOffsets[1] = fespace->TrueVSize();
+      block_trueOffsets[2] = fespace->TrueVSize();
+      block_trueOffsets.PartialSum();
+
+      //cout << myid << ": V size " << fespace->GetVSize() << ", true " << fespace->TrueVSize() << ", global true " << size << ", B size "
+      //<< B.Size() << ", X size " << X.Size() << endl;
+
+      // Note that B is of true size.
+      BlockVector trueY(block_trueOffsets), trueX(block_trueOffsets),
+                  trueRhs(block_trueOffsets);
+
+      trueRhs.GetBlock(0) = B;
+      trueRhs.GetBlock(1) = 0.0;
+
+      Operator * Arow = new STRUMPACKRowLocMatrix(*cSysMat);
+
+      STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+      strumpack->SetPrintFactorStatistics(true);
+      strumpack->SetPrintSolveStatistics(false);
+      strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      // strumpack->SetMC64Job(strumpack::MC64Job::NONE);
+      // strumpack->SetSymmetricPattern(true);
+      strumpack->SetOperator(*Arow);
+      strumpack->SetFromCommandLine();
+#endif
+
+      if (fullDirect)
+      {
+#ifdef USE_CSL
+         //Solver * precond = strumpack;
+
+         // strumpack->Mult(B, X);
+
+         BlockOperator blockDiagA(block_trueOffsets);
+         for (int i=0; i<2; ++i)
+         {
+            blockDiagA.SetDiagonalBlock(i, &A);
+         }
+
+         ParFiniteElementSpace *prec_fespace =
+            (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
+         HypreSolver *amsgrad = new HypreAMS(Agrad, prec_fespace);
+
+#ifdef HYPRE_DYLAN
+         {
+            Vector Xtmp(X);
+            amsgrad->Mult(B,
+                          Xtmp);  // Just a hack to get ams to run its setup function. There should be a better way.
+         }
+
+         HypreAMSG *amsg = new HypreAMSG((HypreAMS*) amsgrad, argc, argv);
+         BlockOperator blockDiagP(block_trueOffsets);
+         for (int i=0; i<2; ++i)
+         {
+            blockDiagP.SetDiagonalBlock(i, amsg);
+         }
+
+         TripleProductOperator strumpackProj(&blockDiagP, strumpack, &blockDiagP, false,
+                                             false, false);
+         ProductOperator prod(&blockDiagA, &strumpackProj, false, false);
+#else
+         ProductOperator prod(&blockDiagA, strumpack, false, false);
+#endif
+
+         GMRESSolver *gmres = new GMRESSolver(fespace->GetComm());
+         //BiCGSTABSolver *gmres = new BiCGSTABSolver(fespace->GetComm());
+
+         gmres->SetOperator(prod);
+         gmres->SetRelTol(1e-12);
+         gmres->SetMaxIter(1000);
+         gmres->SetPrintLevel(1);
+
+         gmres->Mult(trueRhs, trueY);
+         strumpack->Mult(trueY, trueX);
+
+         X = trueX.GetBlock(0);
+         double xim2 = trueX.GetBlock(1).Norml2();
+         xim2 *= xim2;
+         double sumxim2 = 0.0;
+
+         MPI_Allreduce(&xim2, &sumxim2, 1, MPI_DOUBLE, MPI_SUM, fespace->GetComm());
+
+         if (myid == 0)
+         {
+            cout << myid << ": norm of Xim " << trueX.GetBlock(1).Norml2() << ", global " <<
+                 sqrt(sumxim2) << endl;
+         }
+
+         delete gmres;
+         delete strumpack;
+         delete Arow;
+#else
+         cout << "Solving with STRUMPACK" << endl;
+
+#ifdef TEST_MULTIPLE_SP
+         const int Ns = 2;
+         std::vector<Operator*> Arows(Ns);
+         std::vector<STRUMPACKSolver*> strumpacks(Ns);
+
+         //Operator * Arow = new STRUMPACKRowLocMatrix(A);
+
+         for (int m=0; m<Ns; ++m)
+         {
+            Arows[m] = new STRUMPACKRowLocMatrix(A);
+
+            //STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+            strumpacks[m] = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+            strumpacks[m]->SetPrintFactorStatistics(true);
+            strumpacks[m]->SetPrintSolveStatistics(false);
+            strumpacks[m]->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+            strumpacks[m]->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+            // strumpack->SetMC64Job(strumpack::MC64Job::NONE);
+            // strumpack->SetSymmetricPattern(true);
+            strumpacks[m]->SetOperator(*Arows[m]);
+            strumpacks[m]->SetFromCommandLine();
+            //Solver * precond = strumpack;
+
+            strumpacks[m]->Mult(B, X);
+
+            //delete strumpack;
+            //delete Arow;
+         }
+#else
+         Operator * Arow = new STRUMPACKRowLocMatrix(A);
+
+         STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+         strumpack->SetPrintFactorStatistics(true);
+         strumpack->SetPrintSolveStatistics(false);
+         strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+         strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+         // strumpack->SetMC64Job(strumpack::MC64Job::NONE);
+         // strumpack->SetSymmetricPattern(true);
+         strumpack->SetOperator(*Arow);
+         strumpack->SetFromCommandLine();
+         //Solver * precond = strumpack;
+
+         cout << "Solving with strumpack one time" << endl;
+
+         strumpack->Mult(B, X);
+
+         delete strumpack;
+         delete Arow;
+#endif
+#endif
+      }
+      else
+      {
+         ParFiniteElementSpace *prec_fespace =
+            (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
+         HypreSolver *ams = new HypreAMS(A, prec_fespace);
+
+#ifdef HYPRE_DYLAN
+         {
+            Vector Xtmp(X);
+            ams->Mult(B,
+                      Xtmp);  // Just a hack to get ams to run its setup function. There should be a better way.
+         }
+
+         HypreParMatrix H[3];
+#ifdef USE_HELMHOLTZ
+         for (int i=0; i<3; ++i)
+         {
+            GetHelmholtzMatrix(pmesh, i, &(H[i]));
+         }
+#endif
+
+#ifdef USE_CSL
+         HypreIAMS *iams = new HypreIAMS(A, H, strumpack, &trueX, &trueY,
+                                         (HypreAMS*) ams, argc, argv);
+#else
+         HypreIAMS *iams = new HypreIAMS(A, H, strumpack, NULL, NULL, (HypreAMS*) ams,
+                                         argc, argv);
+#endif
+
+         GMRESSolver *gmres = new GMRESSolver(fespace->GetComm());
+         //FGMRESSolver *gmres = new FGMRESSolver(fespace->GetComm());
+         //BiCGSTABSolver *gmres = new BiCGSTABSolver(fespace->GetComm());
+         //MINRESSolver *gmres = new MINRESSolver(fespace->GetComm());
+
+         gmres->SetOperator(A);
+         gmres->SetRelTol(1e-16);
+         gmres->SetMaxIter(1000);
+         gmres->SetPrintLevel(1);
+
+#ifdef SOLVE_A2
+         {
+            StopWatch chronoA2;
+            chronoA2.Clear();
+            chronoA2.Start();
+
+            HypreParMatrix * A2 = ParMult(&A, &Acopy);
+
+            chronoA2.Stop();
+            cout << "A2 setup time " << chronoA2.RealTime() << endl;
+
+            Vector AB(B);
+            A.Mult(B, AB);
+            gmres->SetOperator(*A2);
+
+            HypreSolver *ams2 = new HypreAMS(A, prec_fespace);
+            {
+               Vector Xtmp(X);
+               ams2->Mult(B,
+                          Xtmp);  // Just a hack to get ams to run its setup function. There should be a better way.
+            }
+
+#ifdef ITER_A2
+            // Iteratively solve 0.5 (A^2 + S^2 + M^2) u^{k+1} = 0.5 (SM + MS) u^k + Ab
+
+            StopWatch chronoIterA2;
+            chronoIterA2.Clear();
+            chronoIterA2.Start();
+
+            HypreParMatrix * M2 = ParMult(&Mmat, &Mcopy);
+            HypreParMatrix * S2 = ParMult(&Smat, &Scopy);
+
+            HypreParMatrix * MS = ParMult(&Mmat, &Scopy);
+            HypreParMatrix * SM = ParMult(&Smat, &Mcopy);
+
+            HypreParMatrix * Bmat = ParAdd(SM, MS);
+            (*Bmat) *= 0.5;
+
+            // TODO: there must be a better way to form a sum of three matrices. Of course, we could define an operator that does 3 mat-vecs.
+            //HypreParMatrix * S2M2 = ParAdd(S2, M2);
+            //HypreParMatrix * iterMat = ParAdd(A2, S2M2);
+            HypreParMatrix * iterMat = ParAdd(A2, Bmat);
+
+            chronoIterA2.Stop();
+            cout << "Iter A2 setup time " << chronoIterA2.RealTime() << endl;
+
+            /*
+            HypreSolver *ams3 = new HypreAMS(*iterMat, prec_fespace);
+            {
+              Vector Xtmp(X);
+              ams3->Mult(B, Xtmp);  // Just a hack to get ams to run its setup function. There should be a better way.
+            }
+            */
+
+            /*
+            // GMRES
+            gmres->SetOperator(*iterMat);
+            gmres->SetPreconditioner(*ams2);
+            */
+
+
+            //HypreBoomerAMG *amg = new HypreBoomerAMG(*iterMat);
+            HypreBoomerAMG *amg = new HypreBoomerAMG(*A2);
+
+            // PCG
+            HyprePCG *pcg = new HyprePCG(*iterMat);
+            //HyprePCG *pcg = new HyprePCG(*A2);
+            pcg->SetTol(1e-12);
+            pcg->SetMaxIter(10);
+            pcg->SetPrintLevel(2);
+            pcg->SetPreconditioner(*amg);
+
+            /*
+            // Strumpack linear solver
+            Operator * Arow = new STRUMPACKRowLocMatrix(*iterMat);
+
+            STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+            strumpack->SetPrintFactorStatistics(true);
+            strumpack->SetPrintSolveStatistics(false);
+            strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+            strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+            strumpack->SetOperator(*Arow);
+            strumpack->SetFromCommandLine();
+            */
+
+            Vector iterRHS(AB);
+            Vector iterU(AB);
+            Vector iterU0(AB);
+
+            iterU = 0.0;
+            iterU0 = 0.0;
+
+            bool iterate = true;
+            int numIter = 0;
+            while (iterate)
+            {
+               iterRHS = iterU;
+               iterRHS.Add(-1.0, iterU0);
+
+               cout << "Iteration " << numIter + 1 << ": diff norm " << iterRHS.Norml2() <<
+                    endl;
+
+               iterU0 = iterU;
+
+               Bmat->Mult(iterU0, iterRHS);
+               //iterRHS.Add(2.0, AB);
+               iterRHS.Add(1.0, AB);
+
+               //gmres->Mult(iterRHS, iterU);
+               pcg->Mult(iterRHS, iterU);
+               //strumpack->Mult(iterRHS, iterU);
+
+               numIter++;
+
+               if (numIter > 100)
+               {
+                  iterate = false;
+               }
+            }
+
+            //delete strumpack;
+            //delete Arow;
+
+            delete pcg;
+
+            X = iterU;
+#else
+            //HypreIAMS *iams2 = new HypreIAMS(*A2, (HypreAMS*) ams2, argc, argv);
+            //gmres->SetPreconditioner(*iams2);
+            cout << myid << ": Solving" << endl;
+            gmres->SetPreconditioner(*ams2);
+            gmres->Mult(AB, X);
+            cout << myid << ": Solved" << endl;
+            return 3;
+#endif
+         }
+#else
+         gmres->SetPreconditioner(*iams);
+         gmres->Mult(B, X);
+#endif
+#else
+         HypreGMRES *gmres = new HypreGMRES(A);
+         gmres->SetTol(1e-12);
+         gmres->SetMaxIter(100);
+         gmres->SetPrintLevel(10);
+
+#ifdef FORM_DEFINITE
+         HypreSolver *amsdef = new HypreAMS(Adef, prec_fespace);
+         gmres->SetPreconditioner(*amsdef);
+#else
+         gmres->SetPreconditioner(*ams);
+#endif
+         gmres->Mult(B, X);
+#endif
+
+         delete gmres;
+         //delete iams;
+         //delete ams;
+      }
+   }
+   else
+#endif
+   {
+      // 12. Define and apply a parallel PCG solver for AX=B with the AMS
+      //     preconditioner from hypre.
+      ParFiniteElementSpace *prec_fespace =
+         (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
+      HypreSolver *ams = new HypreAMS(A, prec_fespace);
+      HyprePCG *pcg = new HyprePCG(A);
+      pcg->SetTol(1e-12);
+      pcg->SetMaxIter(500);
+      pcg->SetPrintLevel(2);
+      pcg->SetPreconditioner(*ams);
+      pcg->Mult(B, X);
+
+      delete pcg;
+      delete ams;
+   }
+
+   chrono.Stop();
+   cout << myid << ": Solver time " << chrono.RealTime() << endl;
+
+   // 13. Recover the parallel grid function corresponding to X. This is the
+   //     local finite element solution on each processor.
+   a->RecoverFEMSolution(X, *b, x);
+
+   // 14. Compute and print the L^2 norm of the error.
+   {
+      double err = x.ComputeL2Error(E);
+      Vector zeroVec(3);
+      zeroVec = 0.0;
+      VectorConstantCoefficient vzero(zeroVec);
+      ParGridFunction zerogf(fespace);
+      zerogf = 0.0;
+      double normE = zerogf.ComputeL2Error(E);
+      double normX = x.ComputeL2Error(vzero);
+      if (myid == 0)
+      {
+         cout << "|| E_h - E ||_{L^2} = " << err << endl;
+         cout << "|| E_h ||_{L^2} = " << normX << endl;
+         cout << "|| E ||_{L^2} = " << normE << endl;
+      }
+   }
+
+   // 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_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "sol." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      ofstream sol_ofs(sol_name.str().c_str());
+      sol_ofs.precision(8);
+      x.Save(sol_ofs);
+   }
+
+   // 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 a;
+   delete sigma;
+   delete muinv;
+   delete b;
+   delete fespace;
+   delete fec;
+   delete pmesh;
+
+   MPI_Finalize();
+
+   return 0;
+}
+
+
+void E_exact(const Vector &x, Vector &E)
+{
+   if (dim == 3)
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(2));
+      E(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { E(2) = 0.0; }
+   }
+}
+
+void f_exact(const Vector &x, Vector &f)
+{
+   if (dim == 3)
+   {
+      f(0) = (SIGMAVAL + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (SIGMAVAL + kappa * kappa) * sin(kappa * x(2));
+      f(2) = (SIGMAVAL + kappa * kappa) * sin(kappa * x(0));
+   }
+   else
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}

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/multigrid.hpp

@@ -0,0 +1,517 @@
+#pragma once
+
+#include "mfem.hpp"
+
+using namespace std;
+
+namespace mfem
+{
+
+STRUMPACKSolver* CreateStrumpackSolver(Operator *Arow, MPI_Comm comm)
+{
+   //STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, comm);
+   STRUMPACKSolver * strumpack = new STRUMPACKSolver(0, NULL, comm);
+   strumpack->SetPrintFactorStatistics(true);
+   strumpack->SetPrintSolveStatistics(false);
+   strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+   strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+   strumpack->SetOperator(*Arow);
+   strumpack->SetFromCommandLine();
+   return strumpack;
+}
+
+hypre_CSRMatrix* GetHypreParMatrixData(const HypreParMatrix & hypParMat)
+{
+   // First cast the parameter to a hypre_ParCSRMatrix
+   hypre_ParCSRMatrix * parcsr_op =
+      (hypre_ParCSRMatrix *)const_cast<HypreParMatrix&>(hypParMat);
+
+   MFEM_ASSERT(parcsr_op != NULL,"STRUMPACK: const_cast failed in SetOperator");
+
+   // Create the CSRMatrixMPI A_ by borrowing the internal data from a hypre_CSRMatrix.
+   return hypre_MergeDiagAndOffd(parcsr_op);
+}
+
+// Row and column offsets are assumed to be the same, for each process.
+// Array offsets stores process-local offsets with respect to the blocks. Process offsets are not included.
+HypreParMatrix* CreateHypreParMatrixFromBlocks(MPI_Comm comm,
+                                               Array<int> const& offsets, Array2D<HypreParMatrix*> const& blocks,
+                                               Array2D<SparseMatrix*> const& blocksSp,
+                                               Array2D<double> const& coefficient,
+                                               std::vector<std::vector<int> > const& blockProcOffsets,
+                                               std::vector<std::vector<int> > const& all_block_num_loc_rows)
+{
+   const int numBlocks = offsets.Size() - 1;
+   const int num_loc_rows = offsets[numBlocks];
+
+   int nprocs, rank;
+   MPI_Comm_rank(comm, &rank);
+   MPI_Comm_size(comm, &nprocs);
+
+   std::vector<int> all_num_loc_rows(nprocs);
+   std::vector<int> procOffsets(nprocs);
+   std::vector<std::vector<int> > procBlockOffsets(nprocs);
+
+   MPI_Allgather(&num_loc_rows, 1, MPI_INT, all_num_loc_rows.data(), 1, MPI_INT,
+                 comm);
+
+   int first_loc_row = 0;
+   int glob_nrows = 0;
+   procOffsets[0] = 0;
+   for (int i=0; i<nprocs; ++i)
+   {
+      glob_nrows += all_num_loc_rows[i];
+      if (i < rank)
+      {
+         first_loc_row += all_num_loc_rows[i];
+      }
+
+      if (i < nprocs-1)
+      {
+         procOffsets[i+1] = procOffsets[i] + all_num_loc_rows[i];
+      }
+
+      if (numBlocks > 0)
+      {
+         procBlockOffsets[i].resize(numBlocks);
+         procBlockOffsets[i][0] = 0;
+      }
+
+      for (int j=1; j<numBlocks; ++j)
+      {
+         procBlockOffsets[i][j] = procBlockOffsets[i][j-1] + all_block_num_loc_rows[j
+                                                                                    -1][i];
+      }
+   }
+
+   const int glob_ncols = glob_nrows;
+
+   std::vector<int> opI(num_loc_rows+1);
+   std::vector<int> cnt(num_loc_rows);
+
+   for (int i=0; i<num_loc_rows; ++i)
+   {
+      opI[i] = 0;
+      cnt[i] = 0;
+   }
+
+   opI[num_loc_rows] = 0;
+
+   Array2D<hypre_CSRMatrix*> csr_blocks(numBlocks, numBlocks);
+
+   // Loop over all blocks, to determine nnz for each row.
+   for (int i=0; i<numBlocks; ++i)
+   {
+      for (int j=0; j<numBlocks; ++j)
+      {
+         if (blocks(i, j) == NULL)
+         {
+            csr_blocks(i, j) = NULL;
+
+            if (blocksSp(i, j) != NULL)
+            {
+               const int nrows = blocksSp(i, j)->Height();
+               for (int k=0; k<nrows; ++k)
+               {
+                  const int rowg = offsets[i] + k;
+                  opI[rowg + 1] += blocksSp(i, j)->GetI()[k+1] - blocksSp(i, j)->GetI()[k];
+               }
+            }
+         }
+         else
+         {
+            MFEM_VERIFY(blocksSp(i, j) == NULL, "");
+
+            csr_blocks(i, j) = GetHypreParMatrixData(*(blocks(i, j)));
+
+            const int nrows = csr_blocks(i, j)->num_rows;
+
+            for (int k=0; k<nrows; ++k)
+            {
+               const int rowg = offsets[i] + k;
+               //(*(leftInjection(i, j)))[k]
+               opI[rowg + 1] += csr_blocks(i, j)->i[k+1] - csr_blocks(i, j)->i[k];
+            }
+         }
+      }
+   }
+
+   // Now opI[i] is nnz for row i-1. Do a partial sum to get offsets.
+   for (int i=0; i<num_loc_rows; ++i)
+   {
+      opI[i+1] += opI[i];
+   }
+
+   const int nnz = opI[num_loc_rows];
+
+   std::vector<HYPRE_Int> opJ(nnz);
+   std::vector<double> data(nnz);
+
+   // Loop over all blocks, to set matrix data.
+   for (int i=0; i<numBlocks; ++i)
+   {
+      for (int j=0; j<numBlocks; ++j)
+      {
+         if (csr_blocks(i, j) != NULL || blocksSp(i, j) != NULL)
+         {
+            const bool useCSR = (csr_blocks(i, j) != NULL);
+
+            const int nrows = useCSR ? csr_blocks(i, j)->num_rows : blocksSp(i,
+                                                                             j)->Height();
+            const double coef = coefficient(i, j);
+
+            int *Iarray = useCSR ? csr_blocks(i, j)->i : blocksSp(i, j)->GetI();
+
+            //const bool failure = (nrows != offsets[i+1] - offsets[i]);
+
+            MFEM_VERIFY(nrows == offsets[i+1] - offsets[i], "");
+
+            for (int k=0; k<nrows; ++k)
+            {
+               const int rowg = offsets[i] + k;  // process-local row
+               const int nnz_k = Iarray[k+1] - Iarray[k];
+               const int osk = Iarray[k];
+
+               for (int l=0; l<nnz_k; ++l)
+               {
+                  // Find the column process offset for the block.
+                  const int bcol = useCSR ? csr_blocks(i, j)->j[osk + l] : blocksSp(i,
+                                                                                    j)->GetJ()[osk + l];
+                  int bcolproc = 0;
+
+                  for (int p=1; p<nprocs; ++p)
+                  {
+                     if (blockProcOffsets[j][p] > bcol)
+                     {
+                        bcolproc = p-1;
+                        break;
+                     }
+                  }
+
+                  if (blockProcOffsets[j][nprocs - 1] <= bcol)
+                  {
+                     bcolproc = nprocs - 1;
+                  }
+
+                  const int colg = procOffsets[bcolproc] + procBlockOffsets[bcolproc][j] +
+                                   (bcol - blockProcOffsets[j][bcolproc]);
+
+                  if (colg < 0)
+                  {
+                     cout << "BUG, negative global column index" << endl;
+                  }
+
+                  opJ[opI[rowg] + cnt[rowg]] = colg;
+                  data[opI[rowg] + cnt[rowg]] = useCSR ? coef * csr_blocks(i,
+                                                                           j)->data[osk + l] : coef * blocksSp(i, j)->GetData()[osk + l];
+                  cnt[rowg]++;
+               }
+            }
+         }
+      }
+   }
+
+   bool cntCheck = true;
+   for (int i=0; i<num_loc_rows; ++i)
+   {
+      if (cnt[i] != opI[i+1] - opI[i])
+      {
+         cntCheck = false;
+      }
+   }
+
+   MFEM_VERIFY(cntCheck, "");
+
+   for (int i=0; i<numBlocks; ++i)
+   {
+      for (int j=0; j<numBlocks; ++j)
+      {
+         if (csr_blocks(i, j) != NULL)
+         {
+            hypre_CSRMatrixDestroy(csr_blocks(i, j));
+         }
+      }
+   }
+
+   std::vector<HYPRE_Int> rowStarts2(2);
+   rowStarts2[0] = first_loc_row;
+   rowStarts2[1] = first_loc_row + all_num_loc_rows[rank];
+
+   if (nnz > 0)
+   {
+      HYPRE_Int minJ = opJ[0];
+      HYPRE_Int maxJ = opJ[0];
+      for (int i=0; i<nnz; ++i)
+      {
+         minJ = std::min(minJ, opJ[i]);
+         maxJ = std::max(maxJ, opJ[i]);
+
+         if (opJ[i] >= glob_ncols)
+         {
+            cout << "Column indices out of range" << endl;
+         }
+      }
+   }
+
+   HypreParMatrix *hmat = new HypreParMatrix(comm, num_loc_rows, glob_nrows,
+                                             glob_ncols, (int*) opI.data(), (HYPRE_Int*) opJ.data(), (double*) data.data(),
+                                             (HYPRE_Int*) rowStarts2.data(), (HYPRE_Int*) rowStarts2.data());
+
+   return hmat;
+}
+
+class BlockMGSolver : public Solver
+{
+private:
+   /// The linear system matrix
+   Array2D<HypreParMatrix *>&
+   Af;  // TODO: remove this, as it is used only in the constructor
+   Array2D<double>&
+   Acoef;  // TODO: remove this, as it is used only in the constructor
+   vector<Array<int>> Aoffsets;
+   vector<Array<int>> Poffsets_i;
+   vector<Array<int>> Poffsets_j;
+   std::vector<Array2D<HypreParMatrix *>> A;
+   std::vector<HypreParMatrix *>& P;
+   std::vector<BlockOperator *> BlkP;
+   std::vector<BlockOperator *> BlkA;
+   std::vector<BlockOperator *> S;
+   HypreParMatrix * Ac;
+   int numGrids, numBlocks;
+   STRUMPACKSolver *invAc = nullptr;
+   double theta = 0.5;
+
+public:
+   BlockMGSolver(const int height, const int width, Array2D<HypreParMatrix *>& Af_,
+                 Array2D<double>& Acoef_, std::vector<HypreParMatrix *>& P_);
+
+   virtual void SetOperator(const Operator &op) {}
+
+   virtual void SetTheta(const double a) { theta = a; }
+
+   virtual void Mult(const Vector &r, Vector &z) const;
+   virtual ~BlockMGSolver();
+};
+
+BlockMGSolver::BlockMGSolver(const int height, const int width,
+                             Array2D<HypreParMatrix *>& Af_, Array2D<double>& Acoef_,
+                             std::vector<HypreParMatrix *>& P_)
+   : Solver(height, width), Af(Af_), Acoef(Acoef_), P(P_)
+{
+   numBlocks = Af.NumRows();
+   MFEM_VERIFY(Af.NumCols() == numBlocks, "");
+   numGrids = P.size();
+   BlkP.resize(numGrids);
+   BlkA.resize(numGrids+1);
+   S.resize(numGrids);
+   A.resize(numGrids + 1);
+   A[numGrids] = Af;
+   Aoffsets.resize(numGrids+1);
+   Poffsets_i.resize(numGrids);
+   Poffsets_j.resize(numGrids);
+   // Construct Bilinear form Matrices on each level
+   for (int k = numGrids ; k > 0; k--)
+   {
+      A[k - 1].SetSize(numBlocks,numBlocks);
+      Aoffsets[k].SetSize(numBlocks+1); Aoffsets[k][0] = 0;
+      for (int i=0; i<numBlocks; i++)
+      {
+         Aoffsets[k][i+1] = A[k](i,i)->Height();
+      }
+
+      Aoffsets[k].PartialSum();
+      BlkA[k] = new BlockOperator(Aoffsets[k]);
+      S[k-1] = new BlockOperator(Aoffsets[k]);  // Smoother
+
+      for (int i=0; i<numBlocks; i++)
+      {
+         for (int j=0; j<numBlocks; j++)
+         {
+            if (A[k](i,j) == NULL)
+            {
+               A[k - 1](i,j) = NULL;
+            }
+            else
+            {
+               A[k - 1](i,j) = RAP(A[k](i,j), P[k - 1]);
+               BlkA[k]->SetBlock(i, j, A[k](i,j), Acoef(i,j));
+            }
+         }
+
+         HypreSmoother *S_i = new HypreSmoother;
+         S_i->SetType(HypreSmoother::Jacobi);
+         S_i->SetOperator(*(A[k](i,i)));
+
+         S[k - 1]->SetBlock(i,i,S_i);
+      }
+
+      Poffsets_i[k-1].SetSize(numBlocks+1); Poffsets_i[k-1][0] = 0;
+      Poffsets_j[k-1].SetSize(numBlocks+1); Poffsets_j[k-1][0] = 0;
+      for (int i=0; i<numBlocks; i++)
+      {
+         Poffsets_i[k-1][i+1] = P[k-1]->Height();
+         Poffsets_j[k-1][i+1] = P[k-1]->Width();
+      }
+      Poffsets_i[k-1].PartialSum();
+      Poffsets_j[k-1].PartialSum();
+
+      BlkP[k-1] = new BlockOperator(Poffsets_i[k-1],Poffsets_j[k-1]);
+      for (int i=0; i<numBlocks; i++)
+      {
+         BlkP[k-1]->SetBlock(i,i,P[k-1]);
+      }
+   }
+   // Set up coarse solve operator
+   // Convert the coarse grid blockmatrix to a HypreParMatrix
+   Array<int> offsets(numBlocks+1);
+   offsets[0]=0;
+   for (int i=0; i<numBlocks; i++)
+   {
+      offsets[i+1]=A[0](i,i)->Height();
+   }
+
+   offsets.PartialSum();
+
+   BlkA[0] = new BlockOperator(offsets);
+
+   Array2D<SparseMatrix*> Asp;
+   //Array2D<double> Acoef;
+   Asp.SetSize(numBlocks,numBlocks);
+   //Acoef.SetSize(numBlocks,numBlocks);
+   for (int i=0; i<numBlocks; i++)
+   {
+      for (int j=0; j<numBlocks; j++)
+      {
+         if (A[0](i,j) != NULL)
+         {
+            BlkA[0]->SetBlock(i, j, A[0](i,j), Acoef(i,j));
+         }
+
+         Asp(i,j) = NULL;
+         //Acoef(i,j) = 1.0;
+      }
+   }
+
+   // Convert to HypreParMatrix
+   HypreParMatrix * Ac;
+
+   std::vector<std::vector<int> > blockProcOffsets(numBlocks);
+   std::vector<std::vector<int> > all_block_num_loc_rows(numBlocks);
+
+   {
+      int nprocs, rank;
+      MPI_Comm_rank(MPI_COMM_WORLD, &rank);
+      MPI_Comm_size(MPI_COMM_WORLD, &nprocs);
+
+      std::vector<int> allnumrows(nprocs);
+      const int blockNumRows = A[0](0,0)->Height();
+      MPI_Allgather(&blockNumRows, 1, MPI_INT, allnumrows.data(), 1, MPI_INT,
+                    MPI_COMM_WORLD);
+
+      for (int b=0; b<numBlocks; ++b)
+      {
+         blockProcOffsets[b].resize(nprocs);
+         all_block_num_loc_rows[b].resize(nprocs);
+      }
+
+      blockProcOffsets[0][0] = 0;
+      for (int i=0; i<nprocs-1; ++i)
+      {
+         blockProcOffsets[0][i+1] = blockProcOffsets[0][i] + allnumrows[i];
+      }
+
+      for (int i=0; i<nprocs; ++i)
+      {
+         for (int b=0; b<numBlocks; ++b)
+         {
+            all_block_num_loc_rows[b][i] = allnumrows[i];
+         }
+
+         for (int b=1; b<numBlocks; ++b)
+         {
+            blockProcOffsets[b][i] = blockProcOffsets[0][i];
+         }
+      }
+   }
+
+   Ac = CreateHypreParMatrixFromBlocks(MPI_COMM_WORLD, offsets, A[0], Asp,
+                                       Acoef, blockProcOffsets, all_block_num_loc_rows);
+
+   invAc = CreateStrumpackSolver(new STRUMPACKRowLocMatrix(*Ac), MPI_COMM_WORLD);
+
+   delete Ac;
+}
+
+void BlockMGSolver::Mult(const Vector &r, Vector &z) const
+{
+   // Residual vectors
+   std::vector<Vector> rv(numGrids + 1);
+   // correction vectors
+   std::vector<Vector> zv(numGrids + 1);
+   // allocation
+   for (int i = 0; i <= numGrids ; i++)
+   {
+      int n = (i==0) ? invAc->Height(): BlkA[i]->Width();
+      rv[i].SetSize(n);
+      zv[i].SetSize(n);
+   }
+   // Initial residual
+   rv[numGrids] = r;
+
+   // smooth and update residuals down to the coarsest level
+   for (int i = numGrids; i > 0 ; i--)
+   {
+      // Pre smooth
+      S[i - 1]->Mult(rv[i], zv[i]); zv[i] *= theta;
+      // compute residual
+      int n = BlkA[i]->Width();
+      Vector w(n);
+      BlkA[i]->Mult(zv[i], w);
+      rv[i] -= w;
+      // Restrict
+      BlkP[i - 1]->MultTranspose(rv[i], rv[i - 1]);
+   }
+
+   // Coarse grid Solve
+   invAc->Mult(rv[0], zv[0]);
+   //
+   for (int i = 1; i <= numGrids ; i++)
+   {
+      // Prolong correction
+      Vector u(BlkP[i - 1]->Height());
+      BlkP[i - 1]->Mult(zv[i - 1], u);
+      // Update correction
+      zv[i] += u;
+      // Update residual
+      Vector v(BlkA[i]->Height());
+      BlkA[i]->Mult(u, v); rv[i] -= v;
+      // Post smooth
+      S[i - 1]->Mult(rv[i], v); v *= theta;
+      // Update correction
+      zv[i] += v;
+   }
+   z = zv[numGrids];
+}
+
+BlockMGSolver::~BlockMGSolver()
+{
+   for (int i = numGrids - 1; i >= 0 ; i--)
+   {
+      delete S[i];
+      delete BlkP[i];
+      delete BlkA[i];
+      for (int j=0; j<numBlocks; j++)
+      {
+         for (int k=0; k<numBlocks; k++)
+         {
+            delete A[i](j,k);
+         }
+      }
+      A[i].DeleteAll();
+   }
+   delete BlkA[numGrids];
+   delete invAc;
+   A.clear();
+}
+
+} // namespace mfem

examples/multigriddd.hpp

@@ -0,0 +1,869 @@
+#ifndef BGMULTIGRID
+#define BGMULTIGRID
+
+#include "mfem.hpp"
+
+using namespace std;
+
+//namespace mfem {
+namespace blockgmg
+{
+
+// Row and column offsets are assumed to be the same, for each process.
+// Array offsets stores process-local offsets with respect to the blocks. Process offsets are not included.
+HypreParMatrix* CreateHypreParMatrixFromBlocks2(MPI_Comm comm,
+                                                Array<int> const& offsets, Array2D<HypreParMatrix*> const& blocks,
+                                                Array2D<SparseMatrix*> const& blocksSp,
+                                                Array2D<double> const& coefficient,
+                                                std::vector<std::vector<int> > const& blockProcOffsets,
+                                                std::vector<std::vector<int> > const& all_block_num_loc_rows);
+
+class BlockMGSolver : public Solver
+{
+private:
+   /// The linear system matrix
+   Array2D<HypreParMatrix *>&
+   Af;  // TODO: remove this, as it is used only in the constructor
+   Array2D<double>&
+   Acoef;  // TODO: remove this, as it is used only in the constructor
+   vector<Array<int>> Aoffsets;
+   vector<Array<int>> Poffsets_i;
+   vector<Array<int>> Poffsets_j;
+   std::vector<Array2D<HypreParMatrix *>> A;
+   std::vector<HypreParMatrix *> const& P;
+   std::vector<BlockOperator *> BlkP;
+   std::vector<BlockOperator *> BlkA;
+   std::vector<BlockOperator *> S;
+   HypreParMatrix * Ac;
+   SparseMatrix AcSp;
+   int numGrids, numBlocks;
+   //STRUMPACKSolver *invAc = nullptr;
+   Operator *invAc = nullptr;
+   double theta = 0.5;
+
+public:
+   BlockMGSolver(MPI_Comm comm, const int height, const int width,
+                 Array2D<HypreParMatrix *>& Af_,
+                 Array2D<double>& Acoef_, std::vector<HypreParMatrix *> const& P_)
+      : Solver(height, width), Af(Af_), Acoef(Acoef_), P(P_)
+   {
+      numBlocks = Af.NumRows();
+      MFEM_VERIFY(Af.NumCols() == numBlocks, "");
+      numGrids = P.size();
+      BlkP.resize(numGrids);
+      BlkA.resize(numGrids+1);
+      S.resize(numGrids);
+      A.resize(numGrids + 1);
+      A[numGrids] = Af;
+      Aoffsets.resize(numGrids+1);
+      Poffsets_i.resize(numGrids);
+      Poffsets_j.resize(numGrids);
+      // Construct Bilinear form Matrices on each level
+      for (int k = numGrids ; k > 0; k--)
+      {
+         A[k - 1].SetSize(numBlocks,numBlocks);
+         Aoffsets[k].SetSize(numBlocks+1); Aoffsets[k][0] = 0;
+         for (int i=0; i<numBlocks; i++)
+         {
+            Aoffsets[k][i+1] = A[k](i,i)->Height();
+         }
+
+         Aoffsets[k].PartialSum();
+         BlkA[k] = new BlockOperator(Aoffsets[k]);
+         S[k-1] = new BlockOperator(Aoffsets[k]);  // Smoother
+
+         for (int i=0; i<numBlocks; i++)
+         {
+            for (int j=0; j<numBlocks; j++)
+            {
+               if (A[k](i,j) == NULL)
+               {
+                  A[k - 1](i,j) = NULL;
+               }
+               else
+               {
+                  A[k - 1](i,j) = RAP(A[k](i,j), P[k - 1]);
+                  BlkA[k]->SetBlock(i, j, A[k](i,j), Acoef(i,j));
+               }
+            }
+
+            HypreSmoother *S_i = new HypreSmoother;
+            S_i->SetType(HypreSmoother::Jacobi);
+            S_i->SetOperator(*(A[k](i,i)));
+
+            S[k - 1]->SetBlock(i,i,S_i);
+         }
+
+         Poffsets_i[k-1].SetSize(numBlocks+1); Poffsets_i[k-1][0] = 0;
+         Poffsets_j[k-1].SetSize(numBlocks+1); Poffsets_j[k-1][0] = 0;
+         for (int i=0; i<numBlocks; i++)
+         {
+            Poffsets_i[k-1][i+1] = P[k-1]->Height();
+            Poffsets_j[k-1][i+1] = P[k-1]->Width();
+         }
+         Poffsets_i[k-1].PartialSum();
+         Poffsets_j[k-1].PartialSum();
+
+         BlkP[k-1] = new BlockOperator(Poffsets_i[k-1],Poffsets_j[k-1]);
+         for (int i=0; i<numBlocks; i++)
+         {
+            BlkP[k-1]->SetBlock(i,i,P[k-1]);
+         }
+      }
+      // Set up coarse solve operator
+      // Convert the coarse grid blockmatrix to a HypreParMatrix
+      Array<int> offsets(numBlocks+1);
+      offsets[0]=0;
+      for (int i=0; i<numBlocks; i++)
+      {
+         offsets[i+1]=A[0](i,i)->Height();
+      }
+
+      offsets.PartialSum();
+
+      BlkA[0] = new BlockOperator(offsets);
+
+      Array2D<SparseMatrix*> Asp;
+      //Array2D<double> Acoef;
+      Asp.SetSize(numBlocks,numBlocks);
+      //Acoef.SetSize(numBlocks,numBlocks);
+      for (int i=0; i<numBlocks; i++)
+      {
+         for (int j=0; j<numBlocks; j++)
+         {
+            if (A[0](i,j) != NULL)
+            {
+               BlkA[0]->SetBlock(i, j, A[0](i,j), Acoef(i,j));
+            }
+
+            Asp(i,j) = NULL;
+            //Acoef(i,j) = 1.0;
+         }
+      }
+
+      // Convert to HypreParMatrix
+      //HypreParMatrix * Ac;
+
+      std::vector<std::vector<int> > blockProcOffsets(numBlocks);
+      std::vector<std::vector<int> > all_block_num_loc_rows(numBlocks);
+
+      {
+         int nprocs, rank;
+         MPI_Comm_rank(comm, &rank);
+         MPI_Comm_size(comm, &nprocs);
+
+         std::vector<int> allnumrows(nprocs);
+         const int blockNumRows = A[0](0,
+                                       0)->Height();    // TODO: Not valid if blocks are of different size
+         MPI_Allgather(&blockNumRows, 1, MPI_INT, allnumrows.data(), 1, MPI_INT, comm);
+
+         for (int b=0; b<numBlocks; ++b)
+         {
+            blockProcOffsets[b].resize(nprocs);
+            all_block_num_loc_rows[b].resize(nprocs);
+         }
+
+         blockProcOffsets[0][0] = 0;
+         for (int i=0; i<nprocs-1; ++i)
+         {
+            blockProcOffsets[0][i+1] = blockProcOffsets[0][i] + allnumrows[i];
+         }
+
+         for (int i=0; i<nprocs; ++i)
+         {
+            for (int b=0; b<numBlocks; ++b)
+            {
+               all_block_num_loc_rows[b][i] = allnumrows[i];
+            }
+
+            for (int b=1; b<numBlocks; ++b)
+            {
+               blockProcOffsets[b][i] = blockProcOffsets[0][i];
+            }
+         }
+      }
+
+      Ac = CreateHypreParMatrixFromBlocks2(comm, offsets, A[0], Asp,
+                                           Acoef, blockProcOffsets, all_block_num_loc_rows);
+
+#ifdef MFEM_USE_STRUMPACK
+      invAc = CreateStrumpackSolver(new STRUMPACKRowLocMatrix(*Ac), comm);
+      delete Ac;
+#else
+      Ac->GetDiag(AcSp);  // AcSp does not own the data
+      UMFPackSolver *umf_solver = new UMFPackSolver();
+      umf_solver->Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      umf_solver->SetOperator(AcSp);
+      invAc = umf_solver;
+#endif
+   }
+
+   virtual void SetOperator(const Operator &op) {}
+
+   virtual void SetTheta(const double a) { theta = a; }
+
+   virtual void Mult(const Vector &r, Vector &z) const
+   {
+      // Residual vectors
+      std::vector<Vector> rv(numGrids + 1);
+      // correction vectors
+      std::vector<Vector> zv(numGrids + 1);
+      // allocation
+      for (int i = 0; i <= numGrids ; i++)
+      {
+         int n = (i==0) ? invAc->Height(): BlkA[i]->Width();
+         rv[i].SetSize(n);
+         zv[i].SetSize(n);
+      }
+      // Initial residual
+      rv[numGrids] = r;
+
+      // smooth and update residuals down to the coarsest level
+      for (int i = numGrids; i > 0 ; i--)
+      {
+         // Pre smooth
+         S[i - 1]->Mult(rv[i], zv[i]); zv[i] *= theta;
+         // compute residual
+         int n = BlkA[i]->Width();
+         Vector w(n);
+         BlkA[i]->Mult(zv[i], w);
+         rv[i] -= w;
+         // Restrict
+         BlkP[i - 1]->MultTranspose(rv[i], rv[i - 1]);
+      }
+
+      // Coarse grid Solve
+      invAc->Mult(rv[0], zv[0]);
+      //
+      for (int i = 1; i <= numGrids ; i++)
+      {
+         // Prolong correction
+         Vector u(BlkP[i - 1]->Height());
+         BlkP[i - 1]->Mult(zv[i - 1], u);
+         // Update correction
+         zv[i] += u;
+         // Update residual
+         Vector v(BlkA[i]->Height());
+         BlkA[i]->Mult(u, v); rv[i] -= v;
+         // Post smooth
+         S[i - 1]->Mult(rv[i], v); v *= theta;
+         // Update correction
+         zv[i] += v;
+      }
+      z = zv[numGrids];
+   }
+
+   virtual ~BlockMGSolver()
+   {
+      for (int i = numGrids - 1; i >= 0 ; i--)
+      {
+         delete S[i];
+         delete BlkP[i];
+         delete BlkA[i];
+         for (int j=0; j<numBlocks; j++)
+         {
+            for (int k=0; k<numBlocks; k++)
+            {
+               delete A[i](j,k);
+            }
+         }
+         A[i].DeleteAll();
+      }
+      delete BlkA[numGrids];
+      delete invAc;
+      A.clear();
+   }
+
+#ifdef MFEM_USE_STRUMPACK
+   STRUMPACKSolver* CreateStrumpackSolver(Operator *Arow, MPI_Comm comm)
+   {
+      //STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, comm);
+      STRUMPACKSolver * strumpack = new STRUMPACKSolver(0, NULL, comm);
+      strumpack->SetPrintFactorStatistics(true);
+      strumpack->SetPrintSolveStatistics(false);
+      strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      strumpack->SetOperator(*Arow);
+      strumpack->SetFromCommandLine();
+      return strumpack;
+   }
+#endif
+
+};
+
+#define SWTIMING
+#define SERIAL_PROLONGATION
+#define ITERATIVE_COARSE_SOLVE
+#define SPARSE_JACOBI
+//#define SPARSE_ICHOLESKY
+//#define SPARSE_ILU
+//#define COARSE_PA
+//#define BLOCK_DIAG
+
+//#define COARSE_AMS
+
+class BlockMGPASolver : public Solver
+{
+private:
+   /// The linear system matrix
+   Array2D<Operator*>&
+   Af;  // TODO: remove this, as it is used only in the constructor
+   Array2D<double>&
+   Acoef;  // TODO: remove this, as it is used only in the constructor
+   vector<Array<int>> Aoffsets;
+   vector<Array<int>> Poffsets_i;
+   vector<Array<int>> Poffsets_j;
+   Array<int> Coffsets;
+
+   std::vector<Array2D<Operator*>> A;
+#ifdef SERIAL_PROLONGATION
+   std::vector<SparseMatrix *> P;
+#else
+   std::vector<HypreParMatrix *> const& P;
+#endif
+   std::vector<Vector*> const& diag;
+   std::vector<Operator*> Pt;
+   std::vector<BlockOperator *> BlkP;
+   std::vector<BlockOperator *> BlkA;
+   std::vector<BlockOperator *> S;
+   std::vector<OperatorJacobiSmoother*> Jacobi;
+
+   HypreParMatrix * Ac;
+   SparseMatrix AcSp;
+   int numGrids, numBlocks;
+   //STRUMPACKSolver *invAc = nullptr;
+   Operator *invAc = nullptr;
+   double theta = 0.5;
+
+   mutable std::vector<Vector> rv, zv;
+   mutable Vector u, v, w;
+
+   Vector diagAc;
+   Array<int> emptyEssDof;
+   OperatorJacobiSmoother *JacobiAc;
+#ifdef SPARSE_ICHOLESKY
+   Solver *iCholAc;
+#endif
+#ifdef SPARSE_ILU
+   Solver *iluAc;
+#endif
+
+#ifdef BLOCK_DIAG
+   HypreParMatrix *AcDiag;
+   SparseMatrix AcDiagSp;
+#endif
+
+public:
+   BlockMGPASolver(MPI_Comm comm, const int height, const int width,
+                   Array2D<Operator*>& Af_, Array2D<double>& Acoef_,
+#ifdef COARSE_PA
+                   BlockOperator *BlkAc,
+#else
+                   Array2D<HypreParMatrix*> const& BlkAc,
+#endif
+#ifdef COARSE_AMS
+                   ParFiniteElementSpace* coarseFespace,
+#endif
+                   std::vector<HypreParMatrix *> const& P_, std::vector<Vector*> const& diag_,
+                   Array<int>& ess_tdof_list)
+#ifdef SERIAL_PROLONGATION
+      : Solver(height, width), Af(Af_), Acoef(Acoef_), diag(diag_)
+#else
+      : Solver(height, width), Af(Af_), Acoef(Acoef_), P(P_), diag(diag_)
+#endif
+   {
+      timeMult = 0.0;
+      timeMultAc = 0.0;
+      timeMultPresmooth = 0.0;
+      timeMultResidual = 0.0;
+      timeMultRestrict = 0.0;
+
+#ifdef SERIAL_PROLONGATION
+      P.resize(P_.size());
+      for (int i=0; i<P_.size(); ++i)
+      {
+         P[i] = new SparseMatrix();
+         P_[i]->GetDiag(*P[i]);
+         P[i]->BuildTranspose();
+      }
+#endif
+
+      numBlocks = Af.NumRows();
+      MFEM_VERIFY(Af.NumCols() == numBlocks, "");
+#ifndef COARSE_PA
+      MFEM_VERIFY(BlkAc.NumCols() == numBlocks && BlkAc.NumRows() == numBlocks, "");
+#endif
+      numGrids = P.size();
+      MFEM_VERIFY(diag.size() == numBlocks, "");
+      BlkP.resize(numGrids);
+      BlkA.resize(numGrids+1);
+      Pt.resize(numGrids);
+      S.resize(numGrids);
+      A.resize(numGrids + 1);
+      A[numGrids] = Af;
+      Aoffsets.resize(numGrids+1);
+      Poffsets_i.resize(numGrids);
+      Poffsets_j.resize(numGrids);
+
+      Jacobi.resize(numBlocks);
+      for (int i=0; i<numBlocks; ++i)
+      {
+         Jacobi[i] = new OperatorJacobiSmoother(*(diag[i]), ess_tdof_list, 1.0);
+      }
+
+      // Construct Bilinear form Matrices on each level
+      for (int k = numGrids ; k > 0; k--)
+      {
+         A[k - 1].SetSize(numBlocks,numBlocks);
+         Aoffsets[k].SetSize(numBlocks+1); Aoffsets[k][0] = 0;
+         for (int i=0; i<numBlocks; i++)
+         {
+            Aoffsets[k][i+1] = A[k](i,i)->Height();
+         }
+
+         Aoffsets[k].PartialSum();
+         BlkA[k] = new BlockOperator(Aoffsets[k]);
+         S[k-1] = new BlockOperator(Aoffsets[k]);  // Smoother
+         Pt[k - 1] = new TransposeOperator(P[k - 1]);
+
+         for (int i=0; i<numBlocks; i++)
+         {
+            for (int j=0; j<numBlocks; j++)
+            {
+               if (A[k](i,j) == NULL)
+               {
+                  A[k - 1](i,j) = NULL;
+               }
+               else
+               {
+                  //A[k - 1](i,j) = RAP(A[k](i,j), P[k - 1]);
+                  A[k - 1](i,j) = new TripleProductOperator(Pt[k - 1], A[k](i,j), P[k - 1], false,
+                                                            false, false);
+                  BlkA[k]->SetBlock(i, j, A[k](i,j), Acoef(i,j));
+               }
+            }
+
+            if (k == numGrids)  // finest level
+            {
+               S[k - 1]->SetBlock(i,i,Jacobi[i]);
+            }
+            else
+            {
+               S[k - 1]->SetBlock(i,i, new TripleProductOperator(Pt[k], &(S[k]->GetBlock(i,i)),
+                                                                 P[k], false,
+                                                                 false, false));   // TODO: get a diagonal on each level
+            }
+         }
+
+         Poffsets_i[k-1].SetSize(numBlocks+1); Poffsets_i[k-1][0] = 0;
+         Poffsets_j[k-1].SetSize(numBlocks+1); Poffsets_j[k-1][0] = 0;
+         for (int i=0; i<numBlocks; i++)
+         {
+            Poffsets_i[k-1][i+1] = P[k-1]->Height();
+            Poffsets_j[k-1][i+1] = P[k-1]->Width();
+         }
+         Poffsets_i[k-1].PartialSum();
+         Poffsets_j[k-1].PartialSum();
+
+         BlkP[k-1] = new BlockOperator(Poffsets_i[k-1],Poffsets_j[k-1]);
+         for (int i=0; i<numBlocks; i++)
+         {
+            BlkP[k-1]->SetBlock(i,i,P[k-1]);
+         }
+      }
+      // Set up coarse solve operator
+      // Convert the coarse grid blockmatrix to a HypreParMatrix
+      Coffsets.SetSize(numBlocks+1);
+      Coffsets[0]=0;
+      for (int i=0; i<numBlocks; i++)
+      {
+         Coffsets[i+1]=A[0](i,i)->Height();
+#ifndef COARSE_PA
+         MFEM_VERIFY(BlkAc(i,i)->Height() == A[0](i,i)->Height(), "");
+         MFEM_VERIFY(BlkAc(i,i)->Width() == A[0](i,i)->Width(), "");
+#endif
+      }
+      Coffsets.PartialSum();
+
+#ifdef COARSE_PA
+      BlkA[0] = BlkAc;
+#else
+      BlkA[0] = new BlockOperator(Coffsets);
+#endif
+
+      Array2D<SparseMatrix*> Asp;
+      //Array2D<double> Acoef;
+      Asp.SetSize(numBlocks,numBlocks);
+      //Acoef.SetSize(numBlocks,numBlocks);
+      for (int i=0; i<numBlocks; i++)
+      {
+         for (int j=0; j<numBlocks; j++)
+         {
+#ifndef COARSE_PA
+            MFEM_VERIFY((A[0](i,j) == NULL) == (BlkAc(i,j) == NULL), "");
+
+            if (BlkAc(i,j) != NULL)
+            {
+               BlkA[0]->SetBlock(i, j, BlkAc(i,j), Acoef(i,j));
+            }
+#endif
+
+            Asp(i,j) = NULL;
+            //Acoef(i,j) = 1.0;
+         }
+      }
+
+#ifdef COARSE_PA
+      CGSolver *cg_solver = new CGSolver();
+      cg_solver->SetAbsTol(1.0e-6);
+      cg_solver->SetRelTol(1.0e-6);
+      cg_solver->SetMaxIter(1000);
+      cg_solver->SetOperator(*BlkAc);
+      cg_solver->SetPrintLevel(0);
+      cg_solver->iterative_mode = false;
+      invAc = cg_solver;
+#else
+      // Convert to HypreParMatrix
+      HypreParMatrix * Ac;
+
+      std::vector<std::vector<int> > blockProcOffsets(numBlocks);
+      std::vector<std::vector<int> > all_block_num_loc_rows(numBlocks);
+
+      {
+         int nprocs, rank;
+         MPI_Comm_rank(comm, &rank);
+         MPI_Comm_size(comm, &nprocs);
+
+         std::vector<int> allnumrows(nprocs);
+         // TODO: Not valid if blocks are of different size
+         const int blockNumRows = BlkAc(0,0)->Height();
+
+         MPI_Allgather(&blockNumRows, 1, MPI_INT, allnumrows.data(), 1, MPI_INT, comm);
+
+         for (int b=0; b<numBlocks; ++b)
+         {
+            blockProcOffsets[b].resize(nprocs);
+            all_block_num_loc_rows[b].resize(nprocs);
+         }
+
+         blockProcOffsets[0][0] = 0;
+         for (int i=0; i<nprocs-1; ++i)
+         {
+            blockProcOffsets[0][i+1] = blockProcOffsets[0][i] + allnumrows[i];
+         }
+
+         for (int i=0; i<nprocs; ++i)
+         {
+            for (int b=0; b<numBlocks; ++b)
+            {
+               all_block_num_loc_rows[b][i] = allnumrows[i];
+            }
+
+            for (int b=1; b<numBlocks; ++b)
+            {
+               blockProcOffsets[b][i] = blockProcOffsets[0][i];
+            }
+         }
+      }
+
+      Ac = CreateHypreParMatrixFromBlocks2(comm, Coffsets, BlkAc, Asp,
+                                           Acoef, blockProcOffsets, all_block_num_loc_rows);
+
+#ifdef BLOCK_DIAG
+      {
+         Array2D<HypreParMatrix*> BlkAcDiag(numBlocks, numBlocks);
+         Array2D<double> DiagCoef(numBlocks, numBlocks);
+         DiagCoef = 0.0;
+         for (int i=0; i<numBlocks; ++i)
+         {
+            DiagCoef(i,i) = Acoef(i,i);
+            for (int j=0; j<numBlocks; ++j)
+            {
+               BlkAcDiag(i,j) = NULL;
+            }
+
+            BlkAcDiag(i,i) = BlkAc(i,i);
+         }
+
+         AcDiag = CreateHypreParMatrixFromBlocks2(comm, Coffsets, BlkAcDiag, Asp,
+                                                  DiagCoef, blockProcOffsets, all_block_num_loc_rows);
+
+         AcDiag->GetDiag(AcDiagSp);
+         //delete AcDiag;
+      }
+#endif
+
+#ifdef MFEM_USE_STRUMPACK
+      invAc = CreateStrumpackSolver(new STRUMPACKRowLocMatrix(*Ac), comm);
+      delete Ac;
+#else
+      Ac->GetDiag(AcSp);  // AcSp does not own the data
+      delete Ac;
+
+#ifdef ITERATIVE_COARSE_SOLVE
+      //CGSolver *cg_solver = new CGSolver(comm);
+      CGSolver *cg_solver = new CGSolver();
+      cg_solver->SetAbsTol(1.0e-6);
+      cg_solver->SetRelTol(1.0e-6);
+      cg_solver->SetMaxIter(1000);
+      cg_solver->SetOperator(AcSp);
+      cg_solver->SetPrintLevel(0);
+      cg_solver->iterative_mode = false;
+#ifdef SPARSE_JACOBI
+      AcSp.GetDiag(diagAc);
+      JacobiAc = new OperatorJacobiSmoother(diagAc, emptyEssDof);
+      cg_solver->SetPreconditioner(*JacobiAc);
+#endif
+#ifdef SPARSE_ICHOLESKY
+      {
+         Vector tmpX(AcSp.Height());
+         Vector tmpY(AcSp.Height());
+         tmpX = 1.0;
+         tmpY = 0.0;
+#ifdef BLOCK_DIAG
+         AcDiagSp.Finalize();
+         AcDiagSp.SortColumnIndices();
+
+         AcDiagSp.Mult(tmpX, tmpY);
+#else
+         AcSp.Finalize();
+         AcSp.SortColumnIndices();
+
+         AcSp.Mult(tmpX, tmpY);
+#endif
+      }
+#ifdef BLOCK_DIAG
+      iCholAc = new IncompleteCholesky(AcDiagSp);
+#else
+      iCholAc = new IncompleteCholesky(AcSp);
+#endif
+      cg_solver->SetPreconditioner(*iCholAc);
+      cg_solver->SetPrintLevel(-1);
+#endif // SPARSE_ICHOLESKY
+
+#ifdef SPARSE_ILU
+      {
+         Vector tmpX(AcSp.Height());
+         Vector tmpY(AcSp.Height());
+         tmpX = 1.0;
+         tmpY = 0.0;
+#ifdef BLOCK_DIAG
+         AcDiagSp.Finalize();
+         AcDiagSp.SortColumnIndices();
+
+         AcDiagSp.Mult(tmpX, tmpY);
+#else
+         AcSp.Finalize();
+         AcSp.SortColumnIndices();
+
+         AcSp.Mult(tmpX, tmpY);
+#endif
+      }
+#ifdef BLOCK_DIAG
+      iluAc = new ILUcusparse(AcDiagSp);
+#else
+      iluAc = new ILUcusparse(AcSp);
+#endif
+      cg_solver->SetPreconditioner(*iluAc);
+      cg_solver->SetPrintLevel(0);
+#endif // SPARSE_ILU
+
+#ifdef COARSE_AMS
+#ifndef COARSE_PA
+      MFEM_VERIFY(numBlocks == 4, "");
+      // TODO: just set 2 AMS solvers for E and H.
+
+      if (coarseFespace != NULL)
+      {
+         BlockDiagonalPreconditioner *blkAMS = new BlockDiagonalPreconditioner(Coffsets);
+
+         for (int i=0; i<numBlocks; ++i)
+         {
+            HypreAMS *ams = new HypreAMS(*BlkAc(i,i), coarseFespace);
+            blkAMS->SetDiagonalBlock(i, ams);
+         }
+
+         cg_solver->SetPreconditioner(*blkAMS);
+      }
+#endif
+#endif
+
+      invAc = cg_solver;
+#else
+      UMFPackSolver *umf_solver = new UMFPackSolver();
+      umf_solver->Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      umf_solver->SetOperator(AcSp);
+      invAc = umf_solver;
+#endif
+#endif
+#endif  // COARSE_PA
+
+      // Residual vectors
+      rv.resize(numGrids + 1);
+      // correction vectors
+      zv.resize(numGrids + 1);
+      // allocation
+      for (int i = 0; i <= numGrids ; i++)
+      {
+         int n = (i==0) ? invAc->Height(): BlkA[i]->Width();
+
+         rv[i].SetSize(n);
+         zv[i].SetSize(n);
+         rv[i].UseDevice(true);
+         zv[i].UseDevice(true);
+      }
+   }
+
+   virtual void SetOperator(const Operator &op) {}
+
+   virtual void SetTheta(const double a) { theta = a; }
+
+   virtual void Mult(const Vector &r, Vector &z) const
+   {
+#ifdef SWTIMING
+      StopWatch sw;
+      sw.Clear();
+      sw.Start();
+#endif
+
+      // Initial residual
+      rv[numGrids] = r;
+
+      // smooth and update residuals down to the coarsest level
+      for (int i = numGrids; i > 0 ; i--)
+      {
+         // Pre smooth
+#ifdef SWTIMING
+         StopWatch sws;
+         sws.Clear();
+         sws.Start();
+#endif
+
+         S[i - 1]->Mult(rv[i], zv[i]); zv[i] *= theta;
+
+#ifdef SWTIMING
+         sws.Stop();
+         timeMultPresmooth += sws.RealTime();
+#endif
+
+         // compute residual
+         int n = BlkA[i]->Width();
+         w.SetSize(n);
+         w.UseDevice(true);
+#ifdef SWTIMING
+         StopWatch swop;
+         swop.Clear();
+         swop.Start();
+#endif
+         BlkA[i]->Mult(zv[i], w);
+         rv[i] -= w;
+#ifdef SWTIMING
+         swop.Stop();
+         timeMultResidual += swop.RealTime();
+#endif
+         // Restrict
+#ifdef SWTIMING
+         StopWatch swr;
+         swr.Clear();
+         swr.Start();
+#endif
+         BlkP[i - 1]->MultTranspose(rv[i], rv[i - 1]);
+#ifdef SWTIMING
+         swr.Stop();
+         timeMultRestrict += swr.RealTime();
+#endif
+      }
+
+#ifdef SWTIMING
+      StopWatch swAc;
+      swAc.Clear();
+      swAc.Start();
+#endif
+
+      // Coarse grid Solve
+      invAc->Mult(rv[0], zv[0]);
+      //
+
+#ifdef SWTIMING
+      swAc.Stop();
+      timeMultAc += swAc.RealTime();
+#endif
+
+      for (int i = 1; i <= numGrids ; i++)
+      {
+         // Prolong correction
+         u.SetSize(BlkP[i - 1]->Height());
+         u.UseDevice(true);
+
+         BlkP[i - 1]->Mult(zv[i - 1], u);
+         // Update correction
+         zv[i] += u;
+         // Update residual
+         v.SetSize(BlkA[i]->Height());
+         v.UseDevice(true);
+
+         BlkA[i]->Mult(u, v); rv[i] -= v;
+         // Post smooth
+         S[i - 1]->Mult(rv[i], v); v *= theta;
+         // Update correction
+         zv[i] += v;
+      }
+      z = zv[numGrids];
+
+#ifdef SWTIMING
+      sw.Stop();
+      timeMult += sw.RealTime();
+#endif
+   }
+
+   virtual ~BlockMGPASolver()
+   {
+      for (int i = numGrids - 1; i >= 0 ; i--)
+      {
+         delete S[i];
+         delete BlkP[i];
+         delete BlkA[i];
+         for (int j=0; j<numBlocks; j++)
+         {
+            for (int k=0; k<numBlocks; k++)
+            {
+               delete A[i](j,k);
+            }
+         }
+         A[i].DeleteAll();
+      }
+      delete BlkA[numGrids];
+      delete invAc;
+      A.clear();
+
+#ifdef SPARSE_ICHOLESKY
+      delete iCholAc;
+#endif
+#ifdef SPARSE_ILU
+      delete iluAc;
+#endif
+   }
+
+#ifdef MFEM_USE_STRUMPACK
+   STRUMPACKSolver* CreateStrumpackSolver(Operator *Arow, MPI_Comm comm)
+   {
+      //STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, comm);
+      STRUMPACKSolver * strumpack = new STRUMPACKSolver(0, NULL, comm);
+      strumpack->SetPrintFactorStatistics(true);
+      strumpack->SetPrintSolveStatistics(false);
+      strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      strumpack->SetOperator(*Arow);
+      strumpack->SetFromCommandLine();
+      return strumpack;
+   }
+#endif
+
+   mutable double timeMult, timeMultAc, timeMultPresmooth, timeMultResidual,
+   timeMultRestrict;
+};
+
+}
+//} // namespace mfem
+
+#endif // BGMULTIGRID

examples/remapBlockMatrix.cpp

@@ -0,0 +1,363 @@
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <vector>
+#include <cstdlib>
+#include <cmath>
+
+using namespace std;
+
+class HypreMat
+{
+private:
+   std::vector<int> I, J;
+   std::vector<double> d;
+   int size;
+
+public:
+   HypreMat() : size(0)
+   {
+
+   }
+
+   int Size() const { return size; }
+
+   void ReadMatrixParallel(std::string filename, const int np)
+   {
+      int lastRow = 0;
+      int count = 0;
+
+      std::vector<int> R;
+
+      for (int p=0; p<np; ++p)
+      {
+         std::ifstream f(filename.c_str() + std::to_string(p), std::ifstream::in);
+
+         int rowFirst, rowLast, colFirst, colLast, row, col;
+         double v;
+
+         f >> rowFirst >> rowLast >> colFirst >> colLast;
+
+         I.resize(rowLast+2);
+
+         for (row=rowFirst+1; row<=rowLast+1; ++row)
+         {
+            I[row] = 0;
+         }
+
+         while (f.good())
+         {
+            f >> row >> col >> v;
+
+            if (row >= 2485)
+            {
+               abort();
+            }
+
+            //if (row < lastRow)  // verify ascending order of rows
+            //  abort();
+
+            lastRow = row;
+
+            I[row+1]++;
+            R.push_back(row);
+            J.push_back(col);
+            d.push_back(v);
+
+            count++;
+         }
+
+         f.close();
+      }
+
+      // Partial sum of I
+
+      size = I.size() - 1;
+
+      I[0] = 0;
+      for (int j=1; j<size; ++j)
+      {
+         I[j+1] += I[j];
+      }
+
+      //int *Idata = I.data();
+
+      if (I[size] != J.size() || I[size] != d.size())
+      {
+         abort();
+      }
+
+      {
+         // Reorder J and d
+         const int nnz = J.size();
+         if (nnz != d.size() || nnz != R.size())
+         {
+            abort();
+         }
+
+         std::vector<int> JJ(nnz);
+         std::vector<double> dd(nnz);
+         std::vector<int> cnt;
+
+         JJ = J;
+         dd = d;
+
+         cnt.assign(I.size(), 0); // slightly larger than necessary
+
+         for (int j=0; j<nnz; ++j)
+         {
+            J[I[R[j]] + cnt[R[j]]] = JJ[j];
+            d[I[R[j]] + cnt[R[j]]] = dd[j];
+            cnt[R[j]]++;
+         }
+      }
+   }
+
+   void CopyReorder(HypreMat const& A, std::vector<int> const& permRow,
+                    std::vector<int> const& permCol)
+   {
+      if (permRow.size() != A.Size() || permCol.size() != A.Size())
+      {
+         abort();
+      }
+
+      size = A.Size();
+      I.resize(size+1);
+
+      I[0] = 0;
+
+      for (int j=0; j<size; ++j)
+      {
+         const std::size_t nnz_j = A.I[j+1] - A.I[j];
+         I[permRow[j]+1] = nnz_j;
+      }
+
+      for (int j=1; j<size; ++j)
+      {
+         I[j+1] += I[j];
+      }
+
+      const std::size_t nnz = I[size];
+      J.resize(nnz);
+      d.resize(nnz);
+
+      std::vector<std::size_t> cnt;
+      cnt.assign(size, 0);
+
+      for (int j=0; j<size; ++j)
+      {
+         const int pj = permRow[j];
+         const std::size_t nnz_j = A.I[j+1] - A.I[j];
+
+         for (int k=0; k<nnz_j; ++k, cnt[pj]++)
+         {
+            J[I[pj] + cnt[pj]] = permCol[A.J[A.I[j] + k]];
+            d[I[pj] + cnt[pj]] = A.d[A.I[j] + k];
+         }
+      }
+   }
+
+   void Print(std::string filename)
+   {
+      std::ofstream f(filename.c_str());
+
+      for (int j=0; j<size; ++j)
+      {
+         for (int k=I[j]; k<I[j+1]; ++k)
+         {
+            f << j << " " << J[k] << " " << d[k] << endl;
+         }
+      }
+
+      f.close();
+   }
+
+   void Compare(HypreMat const& A)
+   {
+      if (size != A.Size())
+      {
+         abort();
+      }
+
+      for (int j=0; j<size; ++j)
+      {
+         for (int k=I[j]; k<I[j+1]; ++k)
+         {
+            int m = -1;
+
+            for (int l=A.I[j]; l<A.I[j+1]; ++l)
+            {
+               if (A.J[l] == J[k])
+               {
+                  m = l;
+               }
+            }
+
+            if (m < 0)
+            {
+               cout << "row " << j << " column " << J[k] << " not found" << endl;
+            }
+            //else if (fabs(A.d[m] - d[k]) > 1.0e-8)
+            else if (fabs(fabs(A.d[m]) - fabs(d[k])) > 0.0)
+            {
+               cout << "entry (" << j << ", " << J[k] << ") " << d[k] << " != " << A.d[m] <<
+                    endl;
+            }
+         }
+      }
+   }
+};
+
+void ReadCrd(std::string filename, std::vector<double>& crd)
+{
+   std::ifstream f(filename.c_str(), std::ifstream::in);
+
+   double c;
+
+   while (f.good())
+   {
+      f >> c;
+      crd.push_back(c);
+   }
+
+   // for some reason, the last value gets pushed twice
+   crd.pop_back();
+
+   f.close();
+}
+
+void ReadCrdParallel(std::string filenamebase, const int np,
+                     std::vector<double>& crd)
+{
+   for (int p=0; p<np; ++p)
+   {
+      ReadCrd(filenamebase + std::to_string(p),
+              crd);  // results get concatenated in crd
+   }
+}
+
+// crd is the DOF coordinates in serial, crdp in parallel.
+void SerialToParallelDOFMap(std::vector<double> const& crd,
+                            std::vector<double> const& crdp,
+                            std::vector<int>& sp)
+{
+   if (crdp.size() != crd.size())
+   {
+      abort();
+   }
+
+   const int dim = 3;
+   const int n = crd.size() / dim;  // number of DOF's
+
+   sp.resize(n);
+
+   const double tol = 1.0e-8;
+
+   // Simple O(n^2) search
+
+   for (int i=0; i<n; ++i)
+   {
+      sp[i] = -1;
+
+      for (int j=0; j<n; ++j)
+      {
+         bool eq = true;
+         for (int l=0; l<dim; ++l)
+         {
+            if (fabs(crd[(dim*i)+l] - crdp[(dim*j)+l]) > tol)
+            {
+               eq = false;
+            }
+         }
+
+         if (eq)
+         {
+            if (sp[i] != -1)
+            {
+               abort();
+            }
+
+            sp[i] = j;
+         }
+      }
+
+      if (sp[i] < 0)
+      {
+         abort();
+      }
+   }
+}
+
+int main()
+{
+   const int np = 2;
+
+   std::vector<double> crd0, crdp0, crd1, crdp1;
+
+   ReadCrd("dofcrd0Ser", crd0);
+   ReadCrd("dofcrd1Ser", crd1);
+
+   const int numCrd = crd0.size() / 3;
+
+   if (3*numCrd != crd0.size())
+   {
+      abort();
+   }
+
+   //for (int i=7440; i<crd.size(); ++i)
+   //cout << "crd[" << i << "] " << crd[i] << endl;
+
+   ReadCrdParallel("dofcrd0Par", np, crdp0);
+   ReadCrdParallel("dofcrd1Par", np, crdp1);
+
+   if (3*numCrd != crdp0.size())
+   {
+      abort();
+   }
+
+   std::vector<int> sp0, sp1;  // serial to parallel DOF map for a subdomain
+   SerialToParallelDOFMap(crd0, crdp0, sp0);
+   SerialToParallelDOFMap(crd1, crdp1, sp1);
+
+   /*
+   for (int i=0; i<sp.size(); ++i)
+     cout << i << " " << sp[i] << endl;
+   */
+
+   cout << "sp0" << endl;
+   for (int i=0; i<sp0.size(); ++i)
+   {
+      cout << i << " " << sp0[i] << endl;
+   }
+
+   cout << "sp1" << endl;
+   for (int i=0; i<sp1.size(); ++i)
+   {
+      cout << i << " " << sp1[i] << endl;
+   }
+
+   HypreMat Aser, Apar, AserToPar;
+
+   /*
+   Aser.ReadMatrixParallel("HypreAsdComplexIm1_Serial.0000", 1);
+   Apar.ReadMatrixParallel("HypreAsdComplexIm1_Par5.0000", np);
+   */
+
+   Aser.ReadMatrixParallel("ifopSer.0000", 1);
+   Apar.ReadMatrixParallel("ifopPar.0000", np);
+
+   //AserToPar.CopyReorder(Aser, sp, sp);
+   AserToPar.CopyReorder(Aser, sp0, sp1);
+
+   /*
+   Aser.Print("rbSer");
+   AserToPar.Print("rbSerToPar");
+   Apar.Print("rbPar");
+   */
+
+   cout << "Comparing " << endl;
+
+   AserToPar.Compare(Apar);
+
+   return 0;
+}

examples/testStrumpack.hpp

@@ -0,0 +1,105 @@
+#ifndef TESTSTRUMPACK_HPP
+#define TESTSTRUMPACK_HPP
+
+#include "mfem.hpp"
+
+using namespace mfem;
+using namespace std;
+
+
+void TestStrumpackConstructor()
+{
+   int num_procs, rank;
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &rank);
+
+   const int num_loc_rows = 100;
+   const int first_loc_row = num_loc_rows * rank;
+   const int glob_nrows = num_loc_rows * num_procs;
+   const int glob_ncols = glob_nrows;
+
+   int *opI = new int[num_loc_rows+1];
+
+   for (int i=0; i<num_loc_rows+1; ++i)
+   {
+      opI[i] = 0;
+   }
+
+   for (int i=0; i<num_loc_rows; ++i)
+   {
+      int nnz_i = 3;
+
+      if ((first_loc_row + i) == 0 ||
+          (first_loc_row + i) == glob_nrows-1)  // if first or last row
+      {
+         nnz_i = 2;
+      }
+
+      opI[i+1] = opI[i] + nnz_i;
+   }
+
+   const int nnz = opI[num_loc_rows];
+
+   int *opJ = new int[nnz];
+   double *data = new double[nnz];
+
+   int cnt = 0;
+   for (int i=0; i<num_loc_rows; ++i)
+   {
+      const int globalRow = first_loc_row + i;
+
+      // Diagonal entry
+
+      opJ[cnt] = first_loc_row + i;
+
+      if (globalRow == 0 || globalRow == glob_nrows-1)
+      {
+         data[cnt] = 2.0;
+      }
+      else
+      {
+         data[cnt] = 3.0;
+      }
+
+      cnt++;
+
+      // Upper diagonal
+      if (globalRow < glob_nrows-1)
+      {
+         opJ[cnt] = first_loc_row + i + 1;
+         data[cnt] = -1.0;
+         cnt++;
+      }
+
+      // Lower diagonal
+      if (globalRow > 0)
+      {
+         opJ[cnt] = first_loc_row + i - 1;
+         data[cnt] = -1.0;
+         cnt++;
+      }
+   }
+
+   Operator *op = new STRUMPACKRowLocMatrix(MPI_COMM_WORLD, num_loc_rows,
+                                            first_loc_row, glob_nrows, glob_ncols, opI, opJ, data);
+
+   STRUMPACKSolver * strumpack = new STRUMPACKSolver(0, NULL, MPI_COMM_WORLD);
+   strumpack->SetPrintFactorStatistics(true);
+   strumpack->SetPrintSolveStatistics(false);
+   strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+   strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+   strumpack->SetOperator(*op);
+   strumpack->SetFromCommandLine();
+
+   Vector x(num_loc_rows);
+   Vector y(num_loc_rows);
+
+   x = 1.0;
+   strumpack->Mult(x, y);
+
+   delete opI;
+   delete opJ;
+   delete data;
+}
+
+#endif // TESTSTRUMPACK_HPP

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());
@@ -1744,9 +1771,40 @@ MixedBilinearForm::~MixedBilinearForm()
    delete ext;
 }
 
+void DiscreteLinearOperator::SetAssemblyLevel(AssemblyLevel assembly_level)
+{
+   if (ext)
+   {
+      MFEM_ABORT("the assembly level has already been set!");
+   }
+   assembly = assembly_level;
+   switch (assembly)
+   {
+      case AssemblyLevel::FULL:
+         // Use the original BilinearForm implementation for now
+         break;
+      case AssemblyLevel::ELEMENT:
+         mfem_error("Element assembly not supported yet... stay tuned!");
+         break;
+      case AssemblyLevel::PARTIAL:
+         ext = new PADiscreteLinearOperatorExtension(this);
+         break;
+      case AssemblyLevel::NONE:
+         mfem_error("Matrix-free action not supported yet... stay tuned!");
+         break;
+      default:
+         mfem_error("Unknown assembly level");
+   }
+}
 
 void DiscreteLinearOperator::Assemble(int skip_zeros)
 {
+   if (ext)
+   {
+      ext->Assemble();
+      return;
+   }
+
    Array<int> dom_vdofs, ran_vdofs;
    ElementTransformation *T;
    const FiniteElement *dom_fe, *ran_fe;

fem/bilinearform.hpp

@@ -375,6 +375,9 @@ public:
    /// Get the output finite element space prolongation matrix
    virtual const Operator *GetOutputProlongation() const
    { return GetProlongation(); }
+   /// Get the output finite element space prolongation matrix (local diagonal)
+   virtual const Operator *GetLocalOutputProlongation() const
+   { return GetOutputProlongation(); }
    /// Get the output finite element space restriction matrix
    virtual const Operator *GetOutputRestriction() const
    { return GetRestriction(); }
@@ -591,6 +594,18 @@ public:
    /// Indicate that integrators are not owned by the BilinearForm
    void UseExternalIntegrators() { extern_bfs = 1; };
 
+   void GetTimings(double& t1, double& t2)
+   {
+      t1 = 0.0;
+      t2 = 0.0;
+      PABilinearFormExtension *paext = dynamic_cast<PABilinearFormExtension*>(ext);
+      if (paext != NULL)
+      {
+         t1 = paext->timingDomain;
+         t2 = paext->timingBoundary;
+      }
+   }
+
    /// Destroys bilinear form.
    virtual ~BilinearForm();
 };
@@ -984,9 +999,17 @@ public:
    /// Access all interpolators added with AddDomainInterpolator().
    Array<BilinearFormIntegrator*> *GetDI() { return &dbfi; }
 
+   /// Set the desired assembly level. The default is AssemblyLevel::FULL.
+   /** This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level);
+
    /** @brief Construct the internal matrix representation of the discrete
        linear operator. */
    virtual void Assemble(int skip_zeros = 1);
+
+   /// Get the output finite element space prolongation matrix (local diagonal)
+   virtual const Operator *GetLocalOutputProlongation() const
+   { return test_fes->GetLocalProlongationMatrix(); }
 };
 
 }

fem/bilinearform_ext.cpp

@@ -17,6 +17,8 @@
 #include "libceed/ceed.hpp"
 #include "pgridfunc.hpp"
 
+#include "../general/tic_toc.hpp"
+
 namespace mfem
 {
 
@@ -46,6 +48,9 @@ PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
    elem_restrict = NULL;
    int_face_restrict_lex = NULL;
    bdr_face_restrict_lex = NULL;
+
+   timingDomain = 0.0;
+   timingBoundary = 0.0;
 }
 
 void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
@@ -96,6 +101,13 @@ void PABilinearFormExtension::Assemble()
       integrators[i]->AssemblePA(*a->FESpace());
    }
 
+   Array<BilinearFormIntegrator*> &bdryIntegrators = *a->GetBBFI();
+   const int bdryIntegratorCount = bdryIntegrators.Size();
+   for (int i = 0; i < bdryIntegratorCount; ++i)
+   {
+      bdryIntegrators[i]->AssemblePA(*a->FESpace());
+   }
+
    Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
    const int intFaceIntegratorCount = intFaceIntegrators.Size();
    for (int i = 0; i < intFaceIntegratorCount; ++i)
@@ -109,6 +121,96 @@ void PABilinearFormExtension::Assemble()
    {
       bdrFaceIntegrators[i]->AssemblePABoundaryFaces(*a->FESpace());
    }
+
+   timingDomain = 0.0;
+   timingBoundary = 0.0;
+
+   if (bdryIntegratorCount > 0)
+   {
+      FiniteElementSpace *fes = a->GetFES();
+      const int nbe = fes->GetNBE();
+      const int bedofs = nbe > 0 ? nbe * fes->GetVDim() * fes->GetBE(0)->GetDof() : 0;
+      gatherMap.SetSize(bedofs);
+      indices.SetSize(bedofs);
+
+      ndofs = fes->GetNDofs();
+      offsets.SetSize(ndofs+1);
+      for (int i = 0; i <= ndofs; ++i)
+      {
+         offsets[i] = 0;
+      }
+
+      for (int i = 0; i < nbe; i++)
+      {
+         const FiniteElement &be = *fes->GetBE(i);
+         Array<int> vdofs;
+         fes -> GetBdrElementVDofs (i, vdofs);
+
+         const TensorBasisElement* el =
+            dynamic_cast<const TensorBasisElement*>(&be);
+
+         MFEM_VERIFY(el != NULL, "");
+
+         const Array<int> &fe_dof_map = el->GetDofMap();
+
+         MFEM_VERIFY(fe_dof_map.Size() == fes->GetBE(i)->GetDof(), "");
+         MFEM_VERIFY(vdofs.Size() == fes->GetBE(i)->GetDof(), "");
+
+         for (int j=0; j<vdofs.Size(); ++j)
+         {
+            const int sidj = fe_dof_map[j];
+            const int idj = sidj >= 0 ? sidj : -1 - sidj;
+            const int dof_j = vdofs[idj];
+            const int d = dof_j >= 0 ? dof_j : -1-dof_j;
+            offsets[d+1]++;
+         }
+      }
+
+      for (int i = 1; i <= ndofs; ++i)
+      {
+         // Partial sum
+         offsets[i] += offsets[i - 1];
+      }
+
+      int os = 0;
+      Array<int> cnt(ndofs);
+      cnt = 0;
+      indices = 0;
+
+      for (int i = 0; i < nbe; i++)
+      {
+         const FiniteElement &be = *fes->GetBE(i);
+         Array<int> vdofs;
+         fes -> GetBdrElementVDofs (i, vdofs);
+
+         const TensorBasisElement* el =
+            dynamic_cast<const TensorBasisElement*>(&be);
+
+         MFEM_VERIFY(el != NULL, "");
+
+         const Array<int> &fe_dof_map = el->GetDofMap();
+
+         MFEM_VERIFY(fe_dof_map.Size() == fes->GetBE(i)->GetDof(), "");
+         MFEM_VERIFY(vdofs.Size() == fes->GetBE(i)->GetDof(), "");
+
+         for (int j=0; j<vdofs.Size(); ++j)
+         {
+            const int sidj = fe_dof_map[j];
+            const int idj = sidj >= 0 ? sidj : -1 - sidj;
+            const int dof_j = vdofs[idj];
+            const bool plus = (sidj >= 0 && dof_j >= 0) || (sidj < 0 && dof_j < 0);
+            const int d = dof_j >= 0 ? dof_j : -1-dof_j;
+            const int lid = os + j;
+            gatherMap[lid] = plus ? d : -1-d;
+            indices[offsets[d] + cnt[d]] = plus ? lid : -1-lid;
+            cnt[d]++;
+         }
+
+         os += vdofs.Size();
+      }
+
+      MFEM_VERIFY(os == bedofs, "");
+   }
 }
 
 void PABilinearFormExtension::AssembleDiagonal(Vector &y) const
@@ -176,10 +278,18 @@ void PABilinearFormExtension::FormLinearSystem(const Array<int> &ess_tdof_list,
    A.Reset(oper); // A will own oper
 }
 
+//#define SWTIMING
+
 void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
 
+#ifdef SWTIMING
+   StopWatch swd;
+   swd.Clear();
+   swd.Start();
+#endif
+
    const int iSz = integrators.Size();
    if (DeviceCanUseCeed() || !elem_restrict)
    {
@@ -201,6 +311,93 @@ void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
       elem_restrict->MultTranspose(localY, y);
    }
 
+#ifdef SWTIMING
+   swd.Stop();
+   timingDomain += swd.RealTime();
+
+   StopWatch swb;
+   swb.Clear();
+   swb.Start();
+#endif
+
+   Array<BilinearFormIntegrator*> &bdryIntegrators = *a->GetBBFI();
+
+   const int biSz = bdryIntegrators.Size();
+   if (DeviceCanUseCeed() || !elem_restrict)
+   {
+      MFEM_ABORT("Not implemented");
+   }
+   else if (biSz > 0)
+   {
+      FiniteElementSpace *fes = a->GetFES();
+
+      const int nbe = fes->GetNBE();
+      const int bedofs = nbe > 0 ? nbe * fes->GetVDim() * fes->GetBE(0)->GetDof() : 0;
+      bdryX.SetSize(bedofs);
+      bdryY.SetSize(bedofs);
+      bdryX.UseDevice(true);
+      bdryY.UseDevice(true);
+      bdryX = 0.0;
+      bdryY = 0.0;
+
+      {
+         MFEM_VERIFY(gatherMap.Size() == bedofs, "");
+         auto d_gatherMap = gatherMap.Read();
+         auto d_x = x.Read();
+         auto d_bdryX = bdryX.Write();
+
+         MFEM_FORALL(i, bedofs,
+         {
+            const int gid = d_gatherMap[i];
+            const bool plus = gid >= 0;
+            const int j = plus ? gid : -1-gid;
+
+            d_bdryX[i] = plus ? d_x[j] : -d_x[j];
+         });
+      }
+
+      for (int i = 0; i < biSz; ++i)
+      {
+         bdryIntegrators[i]->AddMultPA(bdryX, bdryY);
+      }
+      //elem_restrict->MultTranspose(bdryY, y);
+
+      // bdryY contains quantities on all boundary elements. Now add them to y.
+
+      {
+         const int xsize = x.Size();
+         MFEM_VERIFY(y.Size() == xsize, "");
+         MFEM_VERIFY(gatherMap.Size() == bedofs, "");
+         auto d_offsets = offsets.Read();
+         auto d_indices = indices.Read();
+         auto d_y = y.ReadWrite();
+         auto d_bdryY = bdryY.Read();
+
+         MFEM_FORALL(i, ndofs,
+         {
+            const int offset = d_offsets[i];
+            const int nextOffset = d_offsets[i + 1];
+
+            double val = 0.0;
+            for (int j = offset; j < nextOffset; ++j)
+            {
+               const int id = d_indices[j];
+               const bool plus = id >= 0;
+               const int idj = plus ? id : -1-id;
+               const double yval = d_bdryY[idj];
+               val += plus ? yval : -yval;
+            }
+
+            d_y[i] += val;
+         });
+      }
+   }
+
+#ifdef SWTIMING
+   swb.Stop();
+   timingBoundary += swb.RealTime();
+#endif
+
    Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
    const int iFISz = intFaceIntegrators.Size();
    if (int_face_restrict_lex && iFISz>0)
@@ -258,6 +455,10 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
       }
    }
 
+   Array<BilinearFormIntegrator*> &bdryIntegrators = *a->GetBBFI();
+   const int biSz = bdryIntegrators.Size();
+   MFEM_VERIFY(biSz == 0, "TODO");
+
    Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
    const int iFISz = intFaceIntegrators.Size();
    if (int_face_restrict_lex && iFISz>0)
@@ -307,19 +508,21 @@ 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 +530,13 @@ 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 +549,7 @@ 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 +996,12 @@ 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()
@@ -811,7 +1019,6 @@ void PAMixedBilinearFormExtension::Update()
       localTrial.UseDevice(true);
       localTrial.SetSize(elem_restrict_trial->Height(),
                          Device::GetMemoryType());
-
    }
    if (elem_restrict_test)
    {
@@ -1011,4 +1218,133 @@ void PAMixedBilinearFormExtension::AssembleDiagonal_ADAt(const Vector &D,
    }
 }
 
+PADiscreteLinearOperatorExtension::PADiscreteLinearOperatorExtension(
+   DiscreteLinearOperator *linop) :
+   PAMixedBilinearFormExtension(linop)
+{
+}
+
+const Operator *PADiscreteLinearOperatorExtension::GetLocalOutputProlongation()
+const
+{
+   return a->GetLocalOutputProlongation();
+}
+
+void PADiscreteLinearOperatorExtension::Assemble()
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+   const int integratorCount = integrators.Size();
+   for (int i = 0; i < integratorCount; ++i)
+   {
+      integrators[i]->AssemblePA(*trialFes, *testFes);
+   }
+
+   test_multiplicity.UseDevice(true);
+   test_multiplicity.SetSize(elem_restrict_test->Width()); // l-vector
+   Vector ones(elem_restrict_test->Height()); // e-vector
+   ones = 1.0;
+
+   const ElementRestriction* elem_restrict =
+      dynamic_cast<const ElementRestriction*>(elem_restrict_test);
+   if (elem_restrict)
+   {
+      elem_restrict->MultTransposeUnsigned(ones, test_multiplicity);
+   }
+   else
+   {
+      mfem_error("A real ElementRestriction is required in this setting!");
+   }
+
+   auto tm = test_multiplicity.ReadWrite();
+   MFEM_FORALL(i, test_multiplicity.Size(),
+   {
+      tm[i] = 1.0 / tm[i];
+   });
+}
+
+void PADiscreteLinearOperatorExtension::AddMult(
+   const Vector &x, Vector &y, const double c) const
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+   const int iSz = integrators.Size();
+
+   // * G operation
+   SetupMultInputs(elem_restrict_trial, x, localTrial,
+                   elem_restrict_test, y, localTest, c);
+
+   // * B^TDB operation
+   for (int i = 0; i < iSz; ++i)
+   {
+      integrators[i]->AddMultPA(localTrial, localTest);
+   }
+
+   // do a kind of "set" rather than "add" in the below
+   // operation as compared to the BilinearForm case
+   // * G^T operation (kind of...)
+   const ElementRestriction* elem_restrict =
+      dynamic_cast<const ElementRestriction*>(elem_restrict_test);
+   if (elem_restrict)
+   {
+      tempY.SetSize(y.Size());
+      elem_restrict->MultLeftInverse(localTest, tempY);
+      y += tempY;
+   }
+   else
+   {
+      mfem_error("In this setting you need a real ElementRestriction!");
+   }
+}
+
+void PADiscreteLinearOperatorExtension::AddMultTranspose(
+   const Vector &x, Vector &y, const double c) const
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+   const int iSz = integrators.Size();
+
+   // do a kind of "set" rather than "add" in the below
+   // operation as compared to the BilinearForm case
+   // * G operation (kinda)
+   Vector xscaled(x);
+   MFEM_VERIFY(x.Size() == test_multiplicity.Size(), "Input vector of wrong size");
+   auto xs = xscaled.ReadWrite();
+   auto tm = test_multiplicity.Read();
+   MFEM_FORALL(i, x.Size(),
+   {
+      xs[i] *= tm[i];
+   });
+   SetupMultInputs(elem_restrict_test, xscaled, localTest,
+                   elem_restrict_trial, y, localTrial, c);
+
+   // * B^TD^TB operation
+   for (int i = 0; i < iSz; ++i)
+   {
+      integrators[i]->AddMultTransposePA(localTest, localTrial);
+   }
+
+   // * G^T operation
+   if (elem_restrict_trial)
+   {
+      tempY.SetSize(y.Size());
+      elem_restrict_trial->MultTranspose(localTrial, tempY);
+      y += tempY;
+   }
+   else
+   {
+      mfem_error("Trial ElementRestriction not defined");
+   }
+}
+
+void PADiscreteLinearOperatorExtension::FormRectangularSystemOperator(
+   const Array<int>& ess1, const Array<int>& ess2, OperatorHandle &A)
+{
+   const Operator *Pi = this->GetProlongation();
+   const Operator *Po = this->GetLocalOutputProlongation();
+   Operator *rap = SetupRAP(Pi, Po);
+
+   RectangularConstrainedOperator *Arco
+      = new RectangularConstrainedOperator(rap, ess1, ess2, rap != this);
+
+   A.Reset(Arco);
+}
+
 } // namespace mfem

fem/bilinearform_ext.hpp

@@ -21,6 +21,7 @@ namespace mfem
 
 class BilinearForm;
 class MixedBilinearForm;
+class DiscreteLinearOperator;
 
 /// Class extending the BilinearForm class to support different AssemblyLevels.
 /**  FA - Full Assembly
@@ -68,11 +69,16 @@ class PABilinearFormExtension : public BilinearFormExtension
 protected:
    const FiniteElementSpace *trialFes, *testFes; // Not owned
    mutable Vector localX, localY;
+   mutable Vector bdryX, bdryY;
    mutable Vector faceIntX, faceIntY;
    mutable Vector faceBdrX, faceBdrY;
    const Operator *elem_restrict; // Not owned
    const Operator *int_face_restrict_lex; // Not owned
    const Operator *bdr_face_restrict_lex; // Not owned
+   Array<int> gatherMap;
+   Array<int> indices;
+   Array<int> offsets;
+   int ndofs;
 
 public:
    PABilinearFormExtension(BilinearForm*);
@@ -88,6 +94,8 @@ public:
    void MultTranspose(const Vector &x, Vector &y) const;
    void Update();
 
+   mutable double timingDomain, timingBoundary;
+
 protected:
    void SetupRestrictionOperators(const L2FaceValues m);
 };
@@ -205,7 +213,7 @@ protected:
    mutable Vector localTrial, localTest, tempY;
    const Operator *elem_restrict_trial; // Not owned
    const Operator *elem_restrict_test;  // Not owned
-private:
+
    /// Helper function to set up inputs/outputs for Mult or MultTranspose
    void SetupMultInputs(const Operator *elem_restrict_x,
                         const Vector &x, Vector &localX,
@@ -251,6 +259,33 @@ public:
    void Update();
 };
 
+
+/**
+   This acts very much like PAMixedBilinearFormExtension, but its
+   FormRectangularSystemOperator implementation emulates 'Set' rather than
+   'Add' in the assembly case.
+*/
+class PADiscreteLinearOperatorExtension : public PAMixedBilinearFormExtension
+{
+public:
+   PADiscreteLinearOperatorExtension(DiscreteLinearOperator *linop);
+
+   /// Partial assembly of all internal integrators
+   void Assemble();
+
+   void AddMult(const Vector &x, Vector &y, const double c) const;
+
+   void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;
+
+   void FormRectangularSystemOperator(const Array<int>&, const Array<int>&,
+                                      OperatorHandle& A);
+
+   const Operator * GetLocalOutputProlongation() const;
+
+private:
+   Vector test_multiplicity;
+};
+
 }
 
 #endif

fem/bilininteg.cpp

@@ -22,14 +22,14 @@ namespace mfem
 
 void BilinearFormIntegrator::AssemblePA(const FiniteElementSpace&)
 {
-   mfem_error ("BilinearFormIntegrator::AssemblePA(...)\n"
+   mfem_error ("BilinearFormIntegrator::AssemblePA(fes)\n"
                "   is not implemented for this class.");
 }
 
 void BilinearFormIntegrator::AssemblePA(const FiniteElementSpace&,
                                         const FiniteElementSpace&)
 {
-   mfem_error ("BilinearFormIntegrator::AssemblePA(...)\n"
+   mfem_error ("BilinearFormIntegrator::AssemblePA(fes, fes)\n"
                "   is not implemented for this class.");
 }
 
@@ -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.");
@@ -89,7 +92,7 @@ void BilinearFormIntegrator::AddMultPA(const Vector &, Vector &) const
 
 void BilinearFormIntegrator::AddMultTransposePA(const Vector &, Vector &) const
 {
-   mfem_error ("BilinearFormIntegrator::MultAssembledTranspose(...)\n"
+   mfem_error ("BilinearFormIntegrator::AddMultTransposePA(...)\n"
                "   is not implemented for this class.");
 }
 
@@ -897,6 +900,44 @@ const IntegrationRule &MassIntegrator::GetRule(const FiniteElement &trial_fe,
    return IntRules.Get(trial_fe.GetGeomType(), order);
 }
 
+/// alpha (n x u, v)
+void VectorFEBoundaryTangentIntegrator::AssembleElementMatrix
+(const FiniteElement &el, ElementTransformation &Trans,
+ DenseMatrix &elmat)
+{
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, Trans);
+
+   const int nd1 = el.GetDof();
+
+   DenseMatrix vshape(nd1, 3);
+   DenseMatrix vshapeRotated(nd1, 3);
+
+   elmat.SetSize(nd1);
+
+   elmat = 0.0;
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+      Trans.SetIntPoint (&ip);
+
+      Vector n(3);
+      CalcOrtho(Trans.Jacobian(), n);
+
+      el.CalcVShape(Trans, vshape);
+
+      for (int j=0; j<nd1; ++j)
+      {
+         // Set vshapeRotated(j) = n x vshape
+         vshapeRotated(j, 0) = (n[1] * vshape(j, 2)) - (n[2] * vshape(j, 1));
+         vshapeRotated(j, 1) = (n[2] * vshape(j, 0)) - (n[0] * vshape(j, 2));
+         vshapeRotated(j, 2) = (n[0] * vshape(j, 1)) - (n[1] * vshape(j, 0));
+      }
+
+      const double w = alpha * ip.weight; // Trans.Weight() is included in n
+
+      AddMult_a_ABt(w, vshape, vshapeRotated, elmat);
+   }
+}
 
 void BoundaryMassIntegrator::AssembleFaceMatrix(
    const FiniteElement &el1, const FiniteElement &el2,
@@ -1522,6 +1563,7 @@ 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 +1571,7 @@ 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 +1615,12 @@ 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

@@ -17,9 +17,18 @@
 #include "fespace.hpp"
 #include "libceed/ceed.hpp"
 
+//#define SETUPONHOST
+
 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 +88,10 @@ 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 +99,12 @@ 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,
@@ -197,6 +209,9 @@ public:
    { return 0.0; }
 
    virtual ~BilinearFormIntegrator() { }
+
+   bool isBdryInteg = false;
+   Array<int> *el_marker = NULL;
 };
 
 /** Wraps a given @a BilinearFormIntegrator and transposes the resulting element
@@ -255,14 +270,17 @@ 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; } }
 };
@@ -1796,8 +1814,10 @@ protected:
 };
 
 /** Class for integrating the bilinear form a(u,v) := (Q grad u, v) where Q is a
-    scalar coefficient, and v is a vector with components v_i in the same space
-    as u. */
+    scalar coefficient, and v is a vector with components v_i in the same (H1) space
+    as u.
+
+    See also MixedVectorGradientIntegrator when v is in H(curl). */
 class GradientIntegrator : public BilinearFormIntegrator
 {
 protected:
@@ -1945,7 +1965,8 @@ 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 +2041,8 @@ 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);
 
@@ -2047,6 +2069,20 @@ public:
                                    DenseMatrix &elmat);
 };
 
+/// alpha (n x u, v)
+class VectorFEBoundaryTangentIntegrator : public MassIntegrator
+{
+private:
+   double alpha;
+
+public:
+   VectorFEBoundaryTangentIntegrator(double a = 1.0) : alpha(a)
+   { }
+
+   void AssembleElementMatrix(const FiniteElement &el,
+                              ElementTransformation &Trans, DenseMatrix &elmat);
+};
+
 /// alpha (q . grad u, v)
 class ConvectionIntegrator : public BilinearFormIntegrator
 {
@@ -2076,7 +2112,8 @@ 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 +2330,14 @@ 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 +2346,17 @@ 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 +2434,11 @@ 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 +2459,8 @@ 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 +2690,12 @@ 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);
@@ -2848,11 +2899,33 @@ class DiscreteInterpolator : public BilinearFormIntegrator { };
 class GradientInterpolator : public DiscreteInterpolator
 {
 public:
+   GradientInterpolator() : fake_fe(NULL) { }
+   virtual ~GradientInterpolator() { delete fake_fe; }
+
    virtual void AssembleElementMatrix2(const FiniteElement &h1_fe,
                                        const FiniteElement &nd_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat)
    { nd_fe.ProjectGrad(h1_fe, Trans, elmat); }
+
+   using BilinearFormIntegrator::AssemblePA;
+   /**
+      trial_fes should be H1 Lagrange
+      test_fes should be Nedelec
+   */
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector &x, Vector &y) const;
+   virtual void AddMultTransposePA(const Vector &x, Vector &y) const;
+
+private:
+   /// 1D finit element that generates and owns the 1D DofToQuad maps below
+   FiniteElement * fake_fe;
+
+   const DofToQuad *maps_C_C; // one-d map with Lobatto rows, Lobatto columns
+   const DofToQuad *maps_O_C; // one-d map with Legendre rows, Lobatto columns
+   int dim, ne, o_dofs1D, c_dofs1D;
 };
 
 
@@ -2867,6 +2940,24 @@ public:
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat)
    { ran_fe.Project(dom_fe, Trans, elmat); }
+
+   using BilinearFormIntegrator::AssemblePA;
+
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector &x, Vector &y) const;
+   virtual void AddMultTransposePA(const Vector &x, Vector &y) const;
+
+private:
+   /// 1D finit element that generates and owns the 1D DofToQuad maps below
+   FiniteElement * fake_fe;
+
+   const DofToQuad *maps_C_C; // one-d map with Lobatto rows, Lobatto columns
+   const DofToQuad *maps_O_C; // one-d map with Legendre rows, Lobatto columns
+   int dim, ne, o_dofs1D, c_dofs1D;
+
+   Vector pa_data;
 };
 
 

fem/bilininteg_convection_ea.cpp

@@ -22,6 +22,7 @@ static void EAConvectionAssemble1D(const int NE,
                                    const Array<double> &g,
                                    const Vector &padata,
                                    Vector &eadata,
+                                   const bool add,
                                    const int d1d = 0,
                                    const int q1d = 0)
 {
@@ -54,7 +55,14 @@ static void EAConvectionAssemble1D(const int NE,
             {
                val += r_Bj[k1] * D(k1, e) * r_Gi[k1];
             }
-            A(i1, j1, e) += val;
+            if (add)
+            {
+               A(i1, j1, e) += val;
+            }
+            else
+            {
+               A(i1, j1, e) = val;
+            }
          }
       }
    });
@@ -66,6 +74,7 @@ static void EAConvectionAssemble2D(const int NE,
                                    const Array<double> &g,
                                    const Vector &padata,
                                    Vector &eadata,
+                                   const bool add,
                                    const int d1d = 0,
                                    const int q1d = 0)
 {
@@ -121,7 +130,14 @@ static void EAConvectionAssemble2D(const int NE,
                                * r_B[k1][j1]* r_B[k2][j2];
                      }
                   }
-                  A(i1, i2, j1, j2, e) += val;
+                  if (add)
+                  {
+                     A(i1, i2, j1, j2, e) += val;
+                  }
+                  else
+                  {
+                     A(i1, i2, j1, j2, e) = val;
+                  }
                }
             }
          }
@@ -135,6 +151,7 @@ static void EAConvectionAssemble3D(const int NE,
                                    const Array<double> &g,
                                    const Vector &padata,
                                    Vector &eadata,
+                                   const bool add,
                                    const int d1d = 0,
                                    const int q1d = 0)
 {
@@ -191,7 +208,14 @@ static void EAConvectionAssemble3D(const int NE,
                               }
                            }
                         }
-                        A(i1, i2, i3, j1, j2, j3, e) += val;
+                        if (add)
+                        {
+                           A(i1, i2, i3, j1, j2, j3, e) += val;
+                        }
+                        else
+                        {
+                           A(i1, i2, i3, j1, j2, j3, e) = val;
+                        }
                      }
                   }
                }
@@ -202,7 +226,8 @@ static void EAConvectionAssemble3D(const int NE,
 }
 
 void ConvectionIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                      Vector &ea_data)
+                                      Vector &ea_data,
+                                      const bool add)
 {
    AssemblePA(fes);
    const int ne = fes.GetMesh()->GetNE();
@@ -212,44 +237,47 @@ void ConvectionIntegrator::AssembleEA(const FiniteElementSpace &fes,
    {
       switch ((dofs1D << 4 ) | quad1D)
       {
-         case 0x22: return EAConvectionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EAConvectionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EAConvectionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EAConvectionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EAConvectionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EAConvectionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EAConvectionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EAConvectionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EAConvectionAssemble1D<2,2>(ne,B,G,pa_data,ea_data,add);
+         case 0x33: return EAConvectionAssemble1D<3,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x44: return EAConvectionAssemble1D<4,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x55: return EAConvectionAssemble1D<5,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x66: return EAConvectionAssemble1D<6,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x77: return EAConvectionAssemble1D<7,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x88: return EAConvectionAssemble1D<8,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x99: return EAConvectionAssemble1D<9,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EAConvectionAssemble1D(ne,B,G,pa_data,ea_data,add,
+                                                     dofs1D,quad1D);
       }
    }
    else if (dim == 2)
    {
       switch ((dofs1D << 4 ) | quad1D)
       {
-         case 0x22: return EAConvectionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EAConvectionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EAConvectionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EAConvectionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EAConvectionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EAConvectionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EAConvectionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EAConvectionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x22: return EAConvectionAssemble2D<2,2>(ne,B,G,pa_data,ea_data,add);
+         case 0x33: return EAConvectionAssemble2D<3,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x44: return EAConvectionAssemble2D<4,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x55: return EAConvectionAssemble2D<5,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x66: return EAConvectionAssemble2D<6,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x77: return EAConvectionAssemble2D<7,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x88: return EAConvectionAssemble2D<8,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x99: return EAConvectionAssemble2D<9,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EAConvectionAssemble2D(ne,B,G,pa_data,ea_data,add,
+                                                     dofs1D,quad1D);
       }
    }
    else if (dim == 3)
    {
       switch ((dofs1D << 4 ) | quad1D)
       {
-         case 0x23: return EAConvectionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
-         case 0x34: return EAConvectionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
-         case 0x45: return EAConvectionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
-         case 0x56: return EAConvectionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
-         case 0x67: return EAConvectionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
-         case 0x78: return EAConvectionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
-         case 0x89: return EAConvectionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
+         case 0x23: return EAConvectionAssemble3D<2,3>(ne,B,G,pa_data,ea_data,add);
+         case 0x34: return EAConvectionAssemble3D<3,4>(ne,B,G,pa_data,ea_data,add);
+         case 0x45: return EAConvectionAssemble3D<4,5>(ne,B,G,pa_data,ea_data,add);
+         case 0x56: return EAConvectionAssemble3D<5,6>(ne,B,G,pa_data,ea_data,add);
+         case 0x67: return EAConvectionAssemble3D<6,7>(ne,B,G,pa_data,ea_data,add);
+         case 0x78: return EAConvectionAssemble3D<7,8>(ne,B,G,pa_data,ea_data,add);
+         case 0x89: return EAConvectionAssemble3D<8,9>(ne,B,G,pa_data,ea_data,add);
+         default:   return EAConvectionAssemble3D(ne,B,G,pa_data,ea_data,add,
+                                                     dofs1D,quad1D);
       }
    }
    MFEM_ABORT("Unknown kernel.");

fem/bilininteg_convection_pa.cpp

@@ -806,16 +806,16 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    {
       vel.SetSize(dim * nq * ne);
       auto C = Reshape(vel.HostWrite(), dim, nq, ne);
-      Vector Vq(dim);
+      DenseMatrix Q_ir;
       for (int e = 0; e < ne; ++e)
       {
          ElementTransformation& T = *fes.GetElementTransformation(e);
+         Q->Eval(Q_ir, T, *ir);
          for (int q = 0; q < nq; ++q)
          {
-            Q->Eval(Vq, T, ir->IntPoint(q));
             for (int i = 0; i < dim; ++i)
             {
-               C(i,q,e) = Vq(i);
+               C(i,q,e) = Q_ir(i,q);
             }
          }
       }

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_dgtrace_pa.cpp

@@ -43,7 +43,7 @@ static void PADGTraceSetup2D(const int Q1D,
    auto W = w.Read();
    auto qd = Reshape(op.Write(), Q1D, 2, 2, NF);
 
-   MFEM_FORALL(f, NF,//can be optimized with Q1D thread for NF blocks
+   MFEM_FORALL(f, NF, // can be optimized with Q1D thread for NF blocks
    {
       for (int q = 0; q < Q1D; ++q)
       {
@@ -85,7 +85,7 @@ static void PADGTraceSetup3D(const int Q1D,
    auto W = w.Read();
    auto qd = Reshape(op.Write(), Q1D, Q1D, 2, 2, NF);
 
-   MFEM_FORALL(f, NF,//can be optimized with Q1D*Q1D threads for NF blocks
+   MFEM_FORALL(f, NF, // can be optimized with Q1D*Q1D threads for NF blocks
    {
       for (int q1 = 0; q1 < Q1D; ++q1)
       {
@@ -156,57 +156,6 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
    pa_data.SetSize(symmDims * nq * nf, Device::GetMemoryType());
-   Vector r;
-   if (rho==nullptr)
-   {
-      r.SetSize(1);
-      r(0) = 1.0;
-   }
-   else if (ConstantCoefficient *c_rho = dynamic_cast<ConstantCoefficient*>(rho))
-   {
-      r.SetSize(1);
-      r(0) = c_rho->constant;
-   }
-   else if (QuadratureFunctionCoefficient* c_rho =
-               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
-   {
-      const QuadratureFunction &qFun = c_rho->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == nq * nf,
-                  "Incompatible QuadratureFunction dimension \n");
-
-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      r.SetSize(nq * nf);
-      auto C = Reshape(r.HostWrite(), nq, nf);
-      int f_ind = 0;
-      for (int f = 0; f < fes.GetNF(); ++f)
-      {
-         int e1, e2;
-         int inf1, inf2;
-         fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-         fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
-         int face_id = inf1 / 64;
-         if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
-             (type==FaceType::Boundary && e2<0 && inf2<0) )
-         {
-            ElementTransformation& T = *fes.GetMesh()->GetFaceTransformation(f);
-            for (int q = 0; q < nq; ++q)
-            {
-               // Convert to lexicographic ordering
-               int iq = ToLexOrdering(dim, face_id, quad1D, q);
-               C(iq,f_ind) = rho->Eval(T, ir->IntPoint(q));
-            }
-            f_ind++;
-         }
-      }
-      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
-   }
    Vector vel;
    if (VectorConstantCoefficient *c_u = dynamic_cast<VectorConstantCoefficient*>
                                         (u))
@@ -243,12 +192,15 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
          if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
              (type==FaceType::Boundary && e2<0 && inf2<0) )
          {
-            ElementTransformation& T = *fes.GetMesh()->GetFaceTransformation(f);
+            FaceElementTransformations &T =
+               *fes.GetMesh()->GetFaceElementTransformations(f);
             for (int q = 0; q < nq; ++q)
             {
                // Convert to lexicographic ordering
                int iq = ToLexOrdering(dim, face_id, quad1D, q);
-               u->Eval(Vq, T, ir->IntPoint(q));
+               T.SetAllIntPoints(&ir->IntPoint(q));
+               const IntegrationPoint &eip1 = T.GetElement1IntPoint();
+               u->Eval(Vq, *T.Elem1, eip1);
                for (int i = 0; i < dim; ++i)
                {
                   C(i,iq,f_ind) = Vq(i);
@@ -259,6 +211,80 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
       }
       MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
    }
+   Vector r;
+   if (rho==nullptr)
+   {
+      r.SetSize(1);
+      r(0) = 1.0;
+   }
+   else if (ConstantCoefficient *c_rho = dynamic_cast<ConstantCoefficient*>(rho))
+   {
+      r.SetSize(1);
+      r(0) = c_rho->constant;
+   }
+   else if (QuadratureFunctionCoefficient* c_rho =
+               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
+   {
+      const QuadratureFunction &qFun = c_rho->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == nq * nf,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
+   else
+   {
+      r.SetSize(nq * nf);
+      auto C_vel = Reshape(vel.HostRead(), dim, nq, nf);
+      auto n = Reshape(geom->normal.HostRead(), nq, dim, nf);
+      auto C = Reshape(r.HostWrite(), nq, nf);
+      int f_ind = 0;
+      for (int f = 0; f < fes.GetNF(); ++f)
+      {
+         int e1, e2;
+         int inf1, inf2;
+         fes.GetMesh()->GetFaceElements(f, &e1, &e2);
+         fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+         int face_id = inf1 / 64;
+         if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
+             (type==FaceType::Boundary && e2<0 && inf2<0) )
+         {
+            FaceElementTransformations &T =
+               *fes.GetMesh()->GetFaceElementTransformations(f);
+            for (int q = 0; q < nq; ++q)
+            {
+               // Convert to lexicographic ordering
+               int iq = ToLexOrdering(dim, face_id, quad1D, q);
+
+               T.SetAllIntPoints(&ir->IntPoint(q));
+               const IntegrationPoint &eip1 = T.GetElement1IntPoint();
+               const IntegrationPoint &eip2 = T.GetElement2IntPoint();
+               double r;
+
+               if (inf2 < 0)
+               {
+                  r = rho->Eval(*T.Elem1, eip1);
+               }
+               else
+               {
+                  double udotn = 0.0;
+                  for (int d=0; d<dim; ++d)
+                  {
+                     udotn += C_vel(d,iq,f_ind)*n(iq,d,f_ind);
+                  }
+                  if (udotn >= 0.0) { r = rho->Eval(*T.Elem2, eip2); }
+                  else { r = rho->Eval(*T.Elem1, eip1); }
+               }
+               C(iq,f_ind) = r;
+            }
+            f_ind++;
+         }
+      }
+      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
+   }
    PADGTraceSetup(dim, dofs1D, quad1D, nf, ir->GetWeights(),
                   geom->detJ, geom->normal, r, vel,
                   alpha, beta, pa_data);

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_gradient.cpp

@@ -334,7 +334,7 @@ static void PAGradientApplyTranspose2D(const int NE,
                                        const int q1d = 0)
 {
    // TODO
-   MFEM_ASSERT(false, "GradientPAApplyTranspose 3D not implemented.");
+   MFEM_ASSERT(false, "PAGradientApplyTranspose2D not implemented.");
 }
 
 // PA Gradient Apply 3D kernel

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

@@ -1,13 +1,13 @@
-// 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.
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
 //
 // This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
+// availability see http://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.
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
 
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
@@ -50,7 +50,7 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
    maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
-   pa_data.SetSize(ne*nq, Device::GetDeviceMemoryType());
+   pa_data.SetSize(ne*nq, Device::GetMemoryType());
    Vector coeff;
    if (Q == nullptr)
    {
@@ -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;
+               }
+            }
          }
       });
    }
@@ -935,8 +950,9 @@ static void SmemPAMassApply3D(const int NE,
    auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, NE);
    auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
    auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, 1,
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
    {
+      const int tidz = MFEM_THREAD_ID(z);
       const int D1D = T_D1D ? T_D1D : d1d;
       const int Q1D = T_Q1D ? T_Q1D : q1d;
       constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
@@ -953,188 +969,130 @@ static void SmemPAMassApply3D(const int NE,
       double (*QQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm1;
       double (*QQD)[MQ1][MD1] = (double (*)[MQ1][MD1]) sm0;
       double (*QDD)[MD1][MD1] = (double (*)[MD1][MD1]) sm1;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
+      MFEM_FOREACH_THREAD(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
+         MFEM_FOREACH_THREAD(dy,y,D1D)
          {
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
+            MFEM_FOREACH_THREAD(dx,x,D1D)
             {
                X[dz][dy][dx] = x(dx,dy,dz,e);
             }
          }
-         MFEM_FOREACH_THREAD(dx,x,Q1D)
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
          {
-            B[dx][dy] = b(dx,dy);
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+            }
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
+      MFEM_FOREACH_THREAD(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         MFEM_FOREACH_THREAD(dy,y,D1D)
          {
-            double u[D1D];
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; dz++)
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
             {
-               u[dz] = 0;
+               double u = 0.0;
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  u += X[dz][dy][dx] * B[qx][dx];
+               }
+               DDQ[dz][dy][qx] = u;
             }
-            MFEM_UNROLL(MD1)
-            for (int dx = 0; dx < D1D; ++dx)
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
             {
-               MFEM_UNROLL(MD1)
+               double u = 0.0;
+               for (int dy = 0; dy < D1D; ++dy)
+               {
+                  u += DDQ[dz][dy][qx] * B[qy][dy];
+               }
+               DQQ[dz][qy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
                for (int dz = 0; dz < D1D; ++dz)
                {
-                  u[dz] += X[dz][dy][dx] * B[qx][dx];
+                  u += DQQ[dz][qy][qx] * B[qz][dz];
                }
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               DDQ[dz][dy][qx] = u[dz];
+               QQQ[qz][qy][qx] = u * d(qx,qy,qz,e);
             }
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      if (tidz == 0)
       {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         MFEM_FOREACH_THREAD(d,y,D1D)
          {
-            double u[D1D];
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; dz++)
+            MFEM_FOREACH_THREAD(q,x,Q1D)
             {
-               u[dz] = 0;
+               Bt[d][q] = b(q,d);
             }
-            MFEM_UNROLL(MD1)
-            for (int dy = 0; dy < D1D; ++dy)
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
             {
-               MFEM_UNROLL(MD1)
-               for (int dz = 0; dz < D1D; dz++)
+               double u = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
                {
-                  u[dz] += DDQ[dz][dy][qx] * B[qy][dy];
+                  u += QQQ[qz][qy][qx] * Bt[dx][qx];
                }
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; dz++)
-            {
-               DQQ[dz][qy][qx] = u[dz];
+               QQD[qz][qy][dx] = u;
             }
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
       {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         MFEM_FOREACH_THREAD(dy,y,D1D)
          {
-            double u[Q1D];
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; qz++)
+            MFEM_FOREACH_THREAD(dx,x,D1D)
             {
-               u[qz] = 0;
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               MFEM_UNROLL(MQ1)
-               for (int qz = 0; qz < Q1D; qz++)
+               double u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
                {
-                  u[qz] += DQQ[dz][qy][qx] * B[qz][dz];
+                  u += QQD[qz][qy][dx] * Bt[dy][qy];
                }
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; qz++)
-            {
-               QQQ[qz][qy][qx] = u[qz] * d(qx,qy,qz,e);
+               QDD[qz][dy][dx] = u;
             }
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(d,y,D1D)
+      MFEM_FOREACH_THREAD(dz,z,D1D)
       {
-         MFEM_FOREACH_THREAD(q,x,Q1D)
+         MFEM_FOREACH_THREAD(dy,y,D1D)
          {
-            Bt[d][q] = b(q,d);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double u[Q1D];
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
+            MFEM_FOREACH_THREAD(dx,x,D1D)
             {
-               u[qz] = 0;
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               MFEM_UNROLL(MQ1)
+               double u = 0.0;
                for (int qz = 0; qz < Q1D; ++qz)
                {
-                  u[qz] += QQQ[qz][qy][qx] * Bt[dx][qx];
+                  u += QDD[qz][dy][dx] * Bt[dz][qz];
                }
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               QQD[qz][qy][dx] = u[qz];
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double u[Q1D];
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               u[qz] = 0;
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               MFEM_UNROLL(MQ1)
-               for (int qz = 0; qz < Q1D; ++qz)
-               {
-                  u[qz] += QQD[qz][qy][dx] * Bt[dy][qy];
-               }
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               QDD[qz][dy][dx] = u[qz];
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double u[D1D];
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               u[dz] = 0;
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               MFEM_UNROLL(MD1)
-               for (int dz = 0; dz < D1D; ++dz)
-               {
-                  u[dz] += QDD[qz][dy][dx] * Bt[dz][qz];
-               }
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               y(dx,dy,dz,e) += u[dz];
+               y(dx,dy,dz,e) += u;
             }
          }
       }
@@ -1165,20 +1123,14 @@ static void PAMassApply(const int dim,
       MFEM_ABORT("OCCA PA Mass Apply unknown kernel!");
    }
 #endif // MFEM_USE_OCCA
-   const int id = (D1D << 4) | Q1D;
    if (dim == 2)
    {
-      switch (id)
+      switch ((D1D << 4) | Q1D)
       {
          case 0x22: return SmemPAMassApply2D<2,2,16>(NE,B,Bt,D,X,Y);
-         case 0x24: return SmemPAMassApply2D<2,4,16>(NE,B,Bt,D,X,Y);
          case 0x33: return SmemPAMassApply2D<3,3,16>(NE,B,Bt,D,X,Y);
-         case 0x34: return SmemPAMassApply2D<3,4,16>(NE,B,Bt,D,X,Y);
-         case 0x36: return SmemPAMassApply2D<3,6,16>(NE,B,Bt,D,X,Y);
          case 0x44: return SmemPAMassApply2D<4,4,8>(NE,B,Bt,D,X,Y);
-         case 0x48: return SmemPAMassApply2D<4,8,4>(NE,B,Bt,D,X,Y);
          case 0x55: return SmemPAMassApply2D<5,5,8>(NE,B,Bt,D,X,Y);
-         case 0x58: return SmemPAMassApply2D<5,8,2>(NE,B,Bt,D,X,Y);
          case 0x66: return SmemPAMassApply2D<6,6,4>(NE,B,Bt,D,X,Y);
          case 0x77: return SmemPAMassApply2D<7,7,4>(NE,B,Bt,D,X,Y);
          case 0x88: return SmemPAMassApply2D<8,8,2>(NE,B,Bt,D,X,Y);
@@ -1188,25 +1140,18 @@ static void PAMassApply(const int dim,
    }
    else if (dim == 3)
    {
-      switch (id)
+      switch ((D1D << 4) | Q1D)
       {
          case 0x23: return SmemPAMassApply3D<2,3>(NE,B,Bt,D,X,Y);
-         case 0x24: return SmemPAMassApply3D<2,4>(NE,B,Bt,D,X,Y);
          case 0x34: return SmemPAMassApply3D<3,4>(NE,B,Bt,D,X,Y);
-         case 0x36: return SmemPAMassApply3D<3,6>(NE,B,Bt,D,X,Y);
          case 0x45: return SmemPAMassApply3D<4,5>(NE,B,Bt,D,X,Y);
-         case 0x46: return SmemPAMassApply3D<4,6>(NE,B,Bt,D,X,Y);
-         case 0x48: return SmemPAMassApply3D<4,8>(NE,B,Bt,D,X,Y);
          case 0x56: return SmemPAMassApply3D<5,6>(NE,B,Bt,D,X,Y);
-         case 0x58: return SmemPAMassApply3D<5,8>(NE,B,Bt,D,X,Y);
          case 0x67: return SmemPAMassApply3D<6,7>(NE,B,Bt,D,X,Y);
          case 0x78: return SmemPAMassApply3D<7,8>(NE,B,Bt,D,X,Y);
          case 0x89: return SmemPAMassApply3D<8,9>(NE,B,Bt,D,X,Y);
-         case 0x9A: return SmemPAMassApply3D<9,10>(NE,B,Bt,D,X,Y);
          default:   return PAMassApply3D(NE,B,Bt,D,X,Y,D1D,Q1D);
       }
    }
-   mfem::out << "Unknown kernel 0x" << std::hex << id << std::endl;
    MFEM_ABORT("Unknown kernel.");
 }
 

fem/bilininteg_transpose_ea.cpp

@@ -16,88 +16,171 @@ namespace mfem
 {
 
 void TransposeIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                     Vector &ea_data)
+                                     Vector &ea_data, const bool add)
 {
-   Vector ea_data_tmp(ea_data.Size());
-   ea_data_tmp = 0.0;
-   bfi->AssembleEA(fes, ea_data_tmp);
-   const int ne = fes.GetNE();
-   if (ne == 0) { return; }
-   const int dofs = fes.GetFE(0)->GetDof();
-   auto A = Reshape(ea_data_tmp.Write(), dofs, dofs, ne);
-   auto AT = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
-   MFEM_FORALL(e, ne,
+   if (add)
    {
-      for (int i = 0; i < dofs; i++)
+      Vector ea_data_tmp(ea_data.Size());
+      bfi->AssembleEA(fes, ea_data_tmp, false);
+      const int ne = fes.GetNE();
+      if (ne == 0) { return; }
+      const int dofs = fes.GetFE(0)->GetDof();
+      auto A = Reshape(ea_data_tmp.Read(), dofs, dofs, ne);
+      auto AT = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
+      MFEM_FORALL(e, ne,
       {
-         for (int j = 0; j < dofs; j++)
+         for (int i = 0; i < dofs; i++)
          {
-            const double a = A(i, j, e);
-            AT(j, i, e) += a;
+            for (int j = 0; j < dofs; j++)
+            {
+               const double a = A(i, j, e);
+               AT(j, i, e) += a;
+            }
          }
-      }
-   });
+      });
+   }
+   else
+   {
+      bfi->AssembleEA(fes, ea_data, false);
+      const int ne = fes.GetNE();
+      if (ne == 0) { return; }
+      const int dofs = fes.GetFE(0)->GetDof();
+      auto A = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
+      MFEM_FORALL(e, ne,
+      {
+         for (int i = 0; i < dofs; i++)
+         {
+            for (int j = i+1; j < dofs; j++)
+            {
+               const double aij = A(i, j, e);
+               const double aji = A(j, i, e);
+               A(j, i, e) = aij;
+               A(i, j, e) = aji;
+            }
+         }
+      });
+   }
 }
 
 void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
                                                   Vector &ea_data_int,
-                                                  Vector &ea_data_ext)
+                                                  Vector &ea_data_ext,
+                                                  const bool add)
 {
    const int nf = fes.GetNFbyType(FaceType::Interior);
    if (nf == 0) { return; }
-   Vector ea_data_int_tmp(ea_data_int.Size());
-   Vector ea_data_ext_tmp(ea_data_ext.Size());
-   ea_data_int_tmp = 0.0;
-   ea_data_ext_tmp = 0.0;
-   bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp);
-   const int faceDofs = fes.GetTraceElement(0,
-                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
-   auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
-   auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
-   auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
-   auto AT_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
-   MFEM_FORALL(f, nf,
+   if (add)
    {
-      for (int i = 0; i < faceDofs; i++)
+      Vector ea_data_int_tmp(ea_data_int.Size());
+      Vector ea_data_ext_tmp(ea_data_ext.Size());
+      bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
+      auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
+      auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      auto AT_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      MFEM_FORALL(f, nf,
       {
-         for (int j = 0; j < faceDofs; j++)
+         for (int i = 0; i < faceDofs; i++)
          {
-            const double a_int0 = A_int(i, j, 0, f);
-            const double a_int1 = A_int(i, j, 1, f);
-            const double a_ext0 = A_ext(i, j, 0, f);
-            const double a_ext1 = A_ext(i, j, 1, f);
-            AT_int(j, i, 0, f) += a_int0;
-            AT_int(j, i, 1, f) += a_int1;
-            AT_ext(j, i, 0, f) += a_ext1;
-            AT_ext(j, i, 1, f) += a_ext0;
+            for (int j = 0; j < faceDofs; j++)
+            {
+               const double a_int0 = A_int(i, j, 0, f);
+               const double a_int1 = A_int(i, j, 1, f);
+               const double a_ext0 = A_ext(i, j, 0, f);
+               const double a_ext1 = A_ext(i, j, 1, f);
+               AT_int(j, i, 0, f) += a_int0;
+               AT_int(j, i, 1, f) += a_int1;
+               AT_ext(j, i, 0, f) += a_ext1;
+               AT_ext(j, i, 1, f) += a_ext0;
+            }
          }
-      }
-   });
+      });
+   }
+   else
+   {
+      bfi->AssembleEAInteriorFaces(fes, ea_data_int, ea_data_ext, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      auto A_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
+      MFEM_FORALL(f, nf,
+      {
+         for (int i = 0; i < faceDofs; i++)
+         {
+            for (int j = i+1; j < faceDofs; j++)
+            {
+               const double aij_int0 = A_int(i, j, 0, f);
+               const double aij_int1 = A_int(i, j, 1, f);
+               const double aji_int0 = A_int(j, i, 0, f);
+               const double aji_int1 = A_int(j, i, 1, f);
+               A_int(j, i, 0, f) = aij_int0;
+               A_int(j, i, 1, f) = aij_int1;
+               A_int(i, j, 0, f) = aji_int0;
+               A_int(i, j, 1, f) = aji_int1;
+            }
+         }
+         for (int i = 0; i < faceDofs; i++)
+         {
+            for (int j = 0; j < faceDofs; j++)
+            {
+               const double aij_ext0 = A_ext(i, j, 0, f);
+               const double aji_ext1 = A_ext(j, i, 1, f);
+               A_ext(j, i, 1, f) = aij_ext0;
+               A_ext(i, j, 0, f) = aji_ext1;
+            }
+         }
+      });
+   }
 }
 
 void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                                  Vector &ea_data_bdr)
+                                                  Vector &ea_data_bdr,
+                                                  const bool add)
 {
    const int nf = fes.GetNFbyType(FaceType::Boundary);
    if (nf == 0) { return; }
-   Vector ea_data_bdr_tmp(ea_data_bdr.Size());
-   ea_data_bdr_tmp = 0.0;
-   bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp);
-   const int faceDofs = fes.GetTraceElement(0,
-                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
-   auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
-   auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
-   MFEM_FORALL(f, nf,
+   if (add)
    {
-      for (int i = 0; i < faceDofs; i++)
+      Vector ea_data_bdr_tmp(ea_data_bdr.Size());
+      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
+      auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
+      MFEM_FORALL(f, nf,
       {
-         for (int j = 0; j < faceDofs; j++)
+         for (int i = 0; i < faceDofs; i++)
          {
-            const double a_bdr = A_bdr(i, j, f);
-            AT_bdr(j, i, f) += a_bdr;
+            for (int j = 0; j < faceDofs; j++)
+            {
+               const double a_bdr = A_bdr(i, j, f);
+               AT_bdr(j, i, f) += a_bdr;
+            }
          }
-      }
-   });
+      });
+   }
+   else
+   {
+      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr, false);
+      const int faceDofs = fes.GetTraceElement(0,
+                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+      auto A_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
+      MFEM_FORALL(f, nf,
+      {
+         for (int i = 0; i < faceDofs; i++)
+         {
+            for (int j = i+1; j < faceDofs; j++)
+            {
+               const double aij_bdr = A_bdr(i, j, f);
+               const double aji_bdr = A_bdr(j, i, f);
+               A_bdr(j, i, f) = aij_bdr;
+               A_bdr(i, j, f) = aji_bdr;
+            }
+         }
+      });
+   }
 }
 
 }

fem/coefficient.cpp

@@ -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);
+   ((Vector*) tv)->Write(true);
+   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), d2shape_z(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+   basis1d.Eval(ip.y, shape_y, dshape_y, d2shape_y);
+   basis1d.Eval(ip.z, shape_z, dshape_z, d2shape_z);
+
+   for (int o = 0, k = 0; k <= p; k++)
+      for (int j = 0; j <= p; j++)
+         for (int i = 0; i <= p; i++)
+         {
+            Hessian(dof_map[o],0) = d2shape_x(i)*  shape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],1) =  dshape_x(i)* dshape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],2) =  dshape_x(i)*  shape_y(j)* dshape_z(k);
+            Hessian(dof_map[o],3) =   shape_x(i)*d2shape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],4) =   shape_x(i)* dshape_y(j)* dshape_z(k);
+            Hessian(dof_map[o],5) =   shape_x(i)*  shape_y(j)*d2shape_z(k);
+            o++;
+         }
+}
+
 void H1_HexahedronElement::ProjectDelta(int vertex, Vector &dofs) const
 {
    const int p = order;

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/fespace.hpp

@@ -330,6 +330,11 @@ public:
    virtual const Operator *GetProlongationMatrix() const
    { return GetConformingProlongation(); }
 
+   /// Return a prolongation operator that only acts on local dofs
+   /** The returned operator is owned by the FiniteElementSpace. */
+   virtual const Operator *GetLocalProlongationMatrix() const
+   { return GetConformingProlongation(); }
+
    /// The returned SparseMatrix is owned by the FiniteElementSpace.
    virtual const SparseMatrix *GetRestrictionMatrix() const
    { return GetConformingRestriction(); }
@@ -984,7 +989,6 @@ inline bool UsesTensorBasis(const FiniteElementSpace& fes)
 {
    return dynamic_cast<const mfem::TensorBasisElement *>(fes.GetFE(0))!=nullptr;
 }
-
 }
 
 #endif

fem/gridfunc.cpp

@@ -199,8 +199,7 @@ void GridFunction::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
    if (f != fes) { Destroy(); }
    fes = f;
    v.UseDevice(true);
-   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, fes->GetVSize()),
-                    fes->GetVSize(), true);
+   this->Vector::MakeRef(v, v_offset, fes->GetVSize());
    sequence = fes->GetSequence();
 }
 
@@ -1834,6 +1833,19 @@ void GridFunction::ImposeBounds(int i, const Vector &weights,
    ImposeBounds(i, weights, minv, maxv);
 }
 
+void GridFunction::RestrictConforming()
+{
+   const SparseMatrix *R = fes->GetRestrictionMatrix();
+   const Operator *P = fes->GetProlongationMatrix();
+
+   if (P && R)
+   {
+      Vector tmp(R->Height());
+      R->Mult(*this, tmp);
+      P->Mult(tmp, *this);
+   }
+}
+
 void GridFunction::GetNodalValues(Vector &nval, int vdim) const
 {
    int i, j;
@@ -2602,11 +2614,7 @@ double GridFunction::ComputeL2Error(
       }
    }
 
-   if (error < 0.0)
-   {
-      return -sqrt(-error);
-   }
-   return sqrt(error);
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
 }
 
 double GridFunction::ComputeL2Error(
@@ -2647,94 +2655,199 @@ double GridFunction::ComputeL2Error(
       }
    }
 
-   if (error < 0.0)
-   {
-      return -sqrt(-error);
-   }
-   return sqrt(error);
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
 }
 
-double GridFunction::ComputeH1Error(
-   Coefficient *exsol, VectorCoefficient *exgrad,
-   Coefficient *ell_coeff, double Nu, int norm_type) const
+double GridFunction::ComputeGradError(VectorCoefficient *exgrad,
+                                      const IntegrationRule *irs[]) const
 {
-   // assuming vdim is 1
-   int i, fdof, dim, intorder, j, k;
+   double error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *Tr;
+   Array<int> dofs;
+   Vector grad;
+   int intorder;
+   int dim = fes->GetMesh()->SpaceDimension();
+   Vector vec(dim);
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      Tr = fes->GetElementTransformation(i);
+      intorder = 2*fe->GetOrder() + 3; // <--------
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      fes->GetElementDofs(i, dofs);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         Tr->SetIntPoint(&ip);
+         GetGradient(*Tr,grad);
+         exgrad->Eval(vec,*Tr,ip);
+         vec-=grad;
+         error += ip.weight * Tr->Weight() * (vec * vec);
+      }
+   }
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeCurlError(VectorCoefficient *excurl,
+                                      const IntegrationRule *irs[]) const
+{
+   double error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *Tr;
+   Array<int> dofs;
+   Vector curl;
+   int intorder;
+   int dim = fes->GetMesh()->SpaceDimension();
+   int n = (dim == 3) ? dim : 1;
+   Vector vec(n);
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      Tr = fes->GetElementTransformation(i);
+      intorder = 2*fe->GetOrder() + 3;
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      fes->GetElementDofs(i, dofs);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         Tr->SetIntPoint(&ip);
+         GetCurl(*Tr,curl);
+         excurl->Eval(vec,*Tr,ip);
+         vec-=curl;
+         error += ip.weight * Tr->Weight() * ( vec * vec );
+      }
+   }
+
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeDivError(
+   Coefficient *exdiv, const IntegrationRule *irs[]) const
+{
+   double error = 0.0, a;
+   const FiniteElement *fe;
+   ElementTransformation *Tr;
+   Array<int> dofs;
+   int intorder;
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      Tr = fes->GetElementTransformation(i);
+      intorder = 2*fe->GetOrder() + 3;
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      fes->GetElementDofs(i, dofs);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         Tr->SetIntPoint (&ip);
+         a = GetDivergence(*Tr) - exdiv->Eval(*Tr, ip);
+         error += ip.weight * Tr->Weight() * a * a;
+      }
+   }
+
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeDGFaceJumpError(Coefficient *exsol,
+                                            Coefficient *ell_coeff, double Nu,
+                                            const IntegrationRule *irs[])  const
+{
+   int fdof, dim, intorder, k;
    Mesh *mesh;
    const FiniteElement *fe;
    ElementTransformation *transf;
    FaceElementTransformations *face_elem_transf;
-   Vector e_grad, a_grad, shape, el_dofs, err_val, ell_coeff_val;
-   DenseMatrix dshape, dshapet, Jinv;
+   Vector shape, el_dofs, err_val, ell_coeff_val;
    Array<int> vdofs;
    IntegrationPoint eip;
    double error = 0.0;
 
    mesh = fes->GetMesh();
    dim = mesh->Dimension();
-   e_grad.SetSize(dim);
-   a_grad.SetSize(dim);
-   Jinv.SetSize(dim);
 
-   if (norm_type & 1)
-      for (i = 0; i < mesh->GetNE(); i++)
-      {
-         fe = fes->GetFE(i);
-         fdof = fe->GetDof();
-         transf = mesh->GetElementTransformation(i);
-         el_dofs.SetSize(fdof);
-         dshape.SetSize(fdof, dim);
-         dshapet.SetSize(fdof, dim);
-         intorder = 2 * fe->GetOrder(); // <----------
-         const IntegrationRule &ir = IntRules.Get(fe->GetGeomType(), intorder);
-         fes->GetElementVDofs(i, vdofs);
-         for (k = 0; k < fdof; k++)
-            if (vdofs[k] >= 0)
-            {
-               el_dofs(k) =   (*this)(vdofs[k]);
-            }
-            else
-            {
-               el_dofs(k) = - (*this)(-1-vdofs[k]);
-            }
-         for (j = 0; j < ir.GetNPoints(); j++)
+   for (int i = 0; i < mesh->GetNumFaces(); i++)
+   {
+      face_elem_transf = mesh->GetFaceElementTransformations(i, 5);
+      int i1 = face_elem_transf->Elem1No;
+      int i2 = face_elem_transf->Elem2No;
+      intorder = fes->GetFE(i1)->GetOrder();
+      if (i2 >= 0)
+         if ( (k = fes->GetFE(i2)->GetOrder()) > intorder )
          {
-            const IntegrationPoint &ip = ir.IntPoint(j);
-            fe->CalcDShape(ip, dshape);
-            transf->SetIntPoint(&ip);
-            exgrad->Eval(e_grad, *transf, ip);
-            CalcInverse(transf->Jacobian(), Jinv);
-            Mult(dshape, Jinv, dshapet);
-            dshapet.MultTranspose(el_dofs, a_grad);
-            e_grad -= a_grad;
-            error += (ip.weight * transf->Weight() *
-                      ell_coeff->Eval(*transf, ip) *
-                      (e_grad * e_grad));
+            intorder = k;
          }
-      }
-
-   if (norm_type & 2)
-      for (i = 0; i < mesh->GetNFaces(); i++)
+      intorder = 2 * intorder;  // <-------------
+      const IntegrationRule *ir;
+      if (irs)
       {
-         face_elem_transf = mesh->GetFaceElementTransformations(i, 5);
-         int i1 = face_elem_transf->Elem1No;
-         int i2 = face_elem_transf->Elem2No;
-         intorder = fes->GetFE(i1)->GetOrder();
-         if (i2 >= 0)
-            if ( (k = fes->GetFE(i2)->GetOrder()) > intorder )
-            {
-               intorder = k;
-            }
-         intorder = 2 * intorder;  // <-------------
-         const IntegrationRule &ir =
-            IntRules.Get(face_elem_transf->GetGeometryType(), intorder);
-         err_val.SetSize(ir.GetNPoints());
-         ell_coeff_val.SetSize(ir.GetNPoints());
-         // side 1
-         transf = face_elem_transf->Elem1;
-         fe = fes->GetFE(i1);
+         ir = irs[face_elem_transf->GetGeometryType()];
+      }
+      else
+      {
+         ir = &(IntRules.Get(face_elem_transf->GetGeometryType(), intorder));
+      }
+      err_val.SetSize(ir->GetNPoints());
+      ell_coeff_val.SetSize(ir->GetNPoints());
+      // side 1
+      transf = face_elem_transf->Elem1;
+      fe = fes->GetFE(i1);
+      fdof = fe->GetDof();
+      fes->GetElementVDofs(i1, vdofs);
+      shape.SetSize(fdof);
+      el_dofs.SetSize(fdof);
+      for (k = 0; k < fdof; k++)
+         if (vdofs[k] >= 0)
+         {
+            el_dofs(k) =   (*this)(vdofs[k]);
+         }
+         else
+         {
+            el_dofs(k) = - (*this)(-1-vdofs[k]);
+         }
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         face_elem_transf->Loc1.Transform(ir->IntPoint(j), eip);
+         fe->CalcShape(eip, shape);
+         transf->SetIntPoint(&eip);
+         ell_coeff_val(j) = ell_coeff->Eval(*transf, eip);
+         err_val(j) = exsol->Eval(*transf, eip) - (shape * el_dofs);
+      }
+      if (i2 >= 0)
+      {
+         // side 2
+         face_elem_transf = mesh->GetFaceElementTransformations(i, 10);
+         transf = face_elem_transf->Elem2;
+         fe = fes->GetFE(i2);
          fdof = fe->GetDof();
-         fes->GetElementVDofs(i1, vdofs);
+         fes->GetElementVDofs(i2, vdofs);
          shape.SetSize(fdof);
          el_dofs.SetSize(fdof);
          for (k = 0; k < fdof; k++)
@@ -2746,60 +2859,69 @@ double GridFunction::ComputeH1Error(
             {
                el_dofs(k) = - (*this)(-1-vdofs[k]);
             }
-         for (j = 0; j < ir.GetNPoints(); j++)
+         for (int j = 0; j < ir->GetNPoints(); j++)
          {
-            face_elem_transf->Loc1.Transform(ir.IntPoint(j), eip);
+            face_elem_transf->Loc2.Transform(ir->IntPoint(j), eip);
             fe->CalcShape(eip, shape);
             transf->SetIntPoint(&eip);
-            ell_coeff_val(j) = ell_coeff->Eval(*transf, eip);
-            err_val(j) = exsol->Eval(*transf, eip) - (shape * el_dofs);
-         }
-         if (i2 >= 0)
-         {
-            // side 2
-            face_elem_transf = mesh->GetFaceElementTransformations(i, 10);
-            transf = face_elem_transf->Elem2;
-            fe = fes->GetFE(i2);
-            fdof = fe->GetDof();
-            fes->GetElementVDofs(i2, vdofs);
-            shape.SetSize(fdof);
-            el_dofs.SetSize(fdof);
-            for (k = 0; k < fdof; k++)
-               if (vdofs[k] >= 0)
-               {
-                  el_dofs(k) =   (*this)(vdofs[k]);
-               }
-               else
-               {
-                  el_dofs(k) = - (*this)(-1-vdofs[k]);
-               }
-            for (j = 0; j < ir.GetNPoints(); j++)
-            {
-               face_elem_transf->Loc2.Transform(ir.IntPoint(j), eip);
-               fe->CalcShape(eip, shape);
-               transf->SetIntPoint(&eip);
-               ell_coeff_val(j) += ell_coeff->Eval(*transf, eip);
-               ell_coeff_val(j) *= 0.5;
-               err_val(j) -= (exsol->Eval(*transf, eip) - (shape * el_dofs));
-            }
-         }
-         face_elem_transf = mesh->GetFaceElementTransformations(i, 16);
-         transf = face_elem_transf;
-         for (j = 0; j < ir.GetNPoints(); j++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(j);
-            transf->SetIntPoint(&ip);
-            error += (ip.weight * Nu * ell_coeff_val(j) *
-                      pow(transf->Weight(), 1.0-1.0/(dim-1)) *
-                      err_val(j) * err_val(j));
+            ell_coeff_val(j) += ell_coeff->Eval(*transf, eip);
+            ell_coeff_val(j) *= 0.5;
+            err_val(j) -= (exsol->Eval(*transf, eip) - (shape * el_dofs));
          }
       }
-
-   if (error < 0.0)
-   {
-      return -sqrt(-error);
+      face_elem_transf = mesh->GetFaceElementTransformations(i, 16);
+      transf = face_elem_transf;
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         transf->SetIntPoint(&ip);
+         error += (ip.weight * Nu * ell_coeff_val(j) *
+                   pow(transf->Weight(), 1.0-1.0/(dim-1)) *
+                   err_val(j) * err_val(j));
+      }
    }
-   return sqrt(error);
+
+   return (error < 0.0) ? -sqrt(-error) : sqrt(error);
+}
+
+double GridFunction::ComputeH1Error(Coefficient *exsol,
+                                    VectorCoefficient *exgrad,
+                                    Coefficient *ell_coef, double Nu,
+                                    int norm_type) const
+{
+   double error1 = 0.0;
+   double error2 = 0.0;
+   if (norm_type & 1) { error1 = GridFunction::ComputeGradError(exgrad); }
+   if (norm_type & 2) { error2 = GridFunction::ComputeDGFaceJumpError(exsol,ell_coef,Nu); }
+
+   return sqrt(error1 * error1 + error2 * error2);
+}
+
+double GridFunction::ComputeH1Error(Coefficient *exsol,
+                                    VectorCoefficient *exgrad,
+                                    const IntegrationRule *irs[]) const
+{
+   double L2error = GridFunction::ComputeLpError(2.0,*exsol,NULL,irs);
+   double GradError = ComputeGradError(exgrad,irs);
+   return sqrt(L2error*L2error + GradError*GradError);
+}
+
+double GridFunction::ComputeHDivError(VectorCoefficient *exsol,
+                                      Coefficient *exdiv,
+                                      const IntegrationRule *irs[]) const
+{
+   double L2error = GridFunction::ComputeLpError(2.0,*exsol,NULL,NULL,irs);
+   double DivError = ComputeDivError(exdiv,irs);
+   return sqrt(L2error*L2error + DivError*DivError);
+}
+
+double GridFunction::ComputeHCurlError(VectorCoefficient *exsol,
+                                       VectorCoefficient *excurl,
+                                       const IntegrationRule *irs[]) const
+{
+   double L2error = GridFunction::ComputeLpError(2.0,*exsol,NULL,NULL,irs);
+   double CurlError = ComputeCurlError(excurl,irs);
+   return sqrt(L2error*L2error + CurlError*CurlError);
 }
 
 double GridFunction::ComputeMaxError(
@@ -2855,7 +2977,6 @@ double GridFunction::ComputeMaxError(
          }
       }
    }
-
    return error;
 }
 

fem/gridfunc.hpp

@@ -334,6 +334,11 @@ public:
    void ImposeBounds(int i, const Vector &weights,
                      double _min = 0.0, double _max = infinity());
 
+   /** On a non-conforming mesh, make sure the function lies in the conforming
+       space by multiplying with R and then with P, the conforming restriction
+       and prolongation matrices of the space, respectively. */
+   void RestrictConforming();
+
    /** @brief Project the @a src GridFunction to @a this GridFunction, both of
        which must be on the same mesh. */
    /** The current implementation assumes that all elements use the same
@@ -422,6 +427,7 @@ public:
    virtual void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
                                              Array<int> &bdr_attr);
 
+
    virtual double ComputeL2Error(Coefficient &exsol,
                                  const IntegrationRule *irs[] = NULL) const
    { return ComputeLpError(2.0, exsol, NULL, irs); }
@@ -433,10 +439,50 @@ public:
                                  const IntegrationRule *irs[] = NULL,
                                  Array<int> *elems = NULL) const;
 
+   /// Returns ||grad u_ex - grad u_h||_L2 for H1 or L2 elements
+   virtual double ComputeGradError(VectorCoefficient *exgrad,
+                                   const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns ||curl u_ex - curl u_h||_L2 for ND elements
+   virtual double ComputeCurlError(VectorCoefficient *excurl,
+                                   const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns ||div u_ex - div u_h||_L2 for RT elements
+   virtual double ComputeDivError(Coefficient *exdiv,
+                                  const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns the Face Jumps error for L2 elements
+   virtual double ComputeDGFaceJumpError(Coefficient *exsol,
+                                         Coefficient *ell_coeff,
+                                         double Nu,
+                                         const IntegrationRule *irs[] = NULL)
+   const;
+
+   /** This method is kept for backward compatibility.
+
+       Returns either the H1-seminorm, or the DG face jumps error, or both
+       depending on norm_type = 1, 2, 3. Additional arguments for the DG face
+       jumps norm: ell_coeff: mesh-depended coefficient (weight) Nu: scalar
+       constant weight */
    virtual double ComputeH1Error(Coefficient *exsol, VectorCoefficient *exgrad,
                                  Coefficient *ell_coef, double Nu,
                                  int norm_type) const;
 
+   /// Returns the error measured in H1-norm for H1 elements or in "broken"
+   /// H1-norm for L2 elements
+   virtual double ComputeH1Error(Coefficient *exsol, VectorCoefficient *exgrad,
+                                 const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns the error measured in H(div)-norm for RT elements
+   virtual double ComputeHDivError(VectorCoefficient *exsol,
+                                   Coefficient *exdiv,
+                                   const IntegrationRule *irs[] = NULL) const;
+
+   /// Returns the error measured in H(curl)-norm for ND elements
+   virtual double ComputeHCurlError(VectorCoefficient *exsol,
+                                    VectorCoefficient *excurl,
+                                    const IntegrationRule *irs[] = NULL) const;
+
    virtual double ComputeMaxError(Coefficient &exsol,
                                   const IntegrationRule *irs[] = NULL) const
    {

fem/gslib.cpp

@@ -29,10 +29,13 @@ namespace mfem
 {
 
 FindPointsGSLIB::FindPointsGSLIB()
-   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
-     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
+   : mesh(NULL), meshsplit(NULL), ir_simplex(NULL),
+     fdata2D(NULL), fdata3D(NULL), cr(NULL), gsl_comm(NULL),
+     dim(-1), points_cnt(0), setupflag(false), default_interp_value(0),
+     avgtype(AvgType::ARITHMETIC)
 {
    gsl_comm = new comm;
+   cr       = new crystal;
 #ifdef MFEM_USE_MPI
    int initialized;
    MPI_Initialized(&initialized);
@@ -47,15 +50,20 @@ FindPointsGSLIB::FindPointsGSLIB()
 FindPointsGSLIB::~FindPointsGSLIB()
 {
    delete gsl_comm;
+   delete cr;
    delete ir_simplex;
+   delete meshsplit;
 }
 
 #ifdef MFEM_USE_MPI
 FindPointsGSLIB::FindPointsGSLIB(MPI_Comm _comm)
-   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
-     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
+   : mesh(NULL), meshsplit(NULL), ir_simplex(NULL),
+     fdata2D(NULL), fdata3D(NULL), cr(NULL), gsl_comm(NULL),
+     dim(-1), points_cnt(0), setupflag(false), default_interp_value(0),
+     avgtype(AvgType::ARITHMETIC)
 {
    gsl_comm = new comm;
+   cr      = new crystal;
    comm_init(gsl_comm, _comm);
 }
 #endif
@@ -70,6 +78,7 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
    // call FreeData if FindPointsGSLIB::Setup has been called already
    if (setupflag) { FreeData(); }
 
+   crystal_init(cr, gsl_comm);
    mesh = &m;
    dim  = mesh->Dimension();
    const FiniteElement *fe = mesh->GetNodalFESpace()->GetFE(0);
@@ -113,14 +122,16 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
    setupflag = true;
 }
 
-void FindPointsGSLIB::FindPoints(const Vector &point_pos,
-                                 Array<unsigned int> &codes,
-                                 Array<unsigned int> &proc_ids,
-                                 Array<unsigned int> &elem_ids,
-                                 Vector &ref_pos, Vector &dist)
+void FindPointsGSLIB::FindPoints(const Vector &point_pos)
 {
    MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
-   const int points_cnt = point_pos.Size() / dim;
+   points_cnt = point_pos.Size() / dim;
+   gsl_code.SetSize(points_cnt);
+   gsl_proc.SetSize(points_cnt);
+   gsl_elem.SetSize(points_cnt);
+   gsl_ref.SetSize(points_cnt * dim);
+   gsl_dist.SetSize(points_cnt);
+
    if (dim == 2)
    {
       const double *xv_base[2];
@@ -129,11 +140,11 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
       unsigned xv_stride[2];
       xv_stride[0] = sizeof(double);
       xv_stride[1] = sizeof(double);
-      findpts_2(codes.GetData(), sizeof(unsigned int),
-                proc_ids.GetData(), sizeof(unsigned int),
-                elem_ids.GetData(), sizeof(unsigned int),
-                ref_pos.GetData(), sizeof(double) * dim,
-                dist.GetData(), sizeof(double),
+      findpts_2(gsl_code.GetData(), sizeof(unsigned int),
+                gsl_proc.GetData(), sizeof(unsigned int),
+                gsl_elem.GetData(), sizeof(unsigned int),
+                gsl_ref.GetData(),  sizeof(double) * dim,
+                gsl_dist.GetData(), sizeof(double),
                 xv_base, xv_stride, points_cnt, fdata2D);
    }
    else
@@ -146,25 +157,27 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
       xv_stride[0] = sizeof(double);
       xv_stride[1] = sizeof(double);
       xv_stride[2] = sizeof(double);
-      findpts_3(codes.GetData(), sizeof(unsigned int),
-                proc_ids.GetData(), sizeof(unsigned int),
-                elem_ids.GetData(), sizeof(unsigned int),
-                ref_pos.GetData(), sizeof(double) * dim,
-                dist.GetData(), sizeof(double),
+      findpts_3(gsl_code.GetData(), sizeof(unsigned int),
+                gsl_proc.GetData(), sizeof(unsigned int),
+                gsl_elem.GetData(), sizeof(unsigned int),
+                gsl_ref.GetData(),  sizeof(double) * dim,
+                gsl_dist.GetData(), sizeof(double),
                 xv_base, xv_stride, points_cnt, fdata3D);
    }
-}
 
-void FindPointsGSLIB::FindPoints(const Vector &point_pos)
-{
-   const int points_cnt = point_pos.Size() / dim;
-   gsl_code.SetSize(points_cnt);
-   gsl_proc.SetSize(points_cnt);
-   gsl_elem.SetSize(points_cnt);
-   gsl_ref.SetSize(points_cnt * dim);
-   gsl_dist.SetSize(points_cnt);
+   // Set the element number and reference position to 0 for points not found
+   for (int i = 0; i < points_cnt; i++)
+   {
+      if (gsl_code[i] == 2)
+      {
+         gsl_elem[i] = 0;
+         for (int d = 0; d < dim; d++) { gsl_ref(i*dim + d) = -1.; }
+      }
+   }
 
-   FindPoints(point_pos, gsl_code, gsl_proc, gsl_elem, gsl_ref, gsl_dist);
+   // Map element number for simplices, and ref_pos from [-1,1] to [0,1] for
+   // both simplices and quads.
+   MapRefPosAndElemIndices();
 }
 
 void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
@@ -178,72 +191,24 @@ void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
    FindPoints(point_pos);
 }
 
-void FindPointsGSLIB::Interpolate(Array<unsigned int> &codes,
-                                  Array<unsigned int> &proc_ids,
-                                  Array<unsigned int> &elem_ids,
-                                  Vector &ref_pos, const GridFunction &field_in,
-                                  Vector &field_out)
-{
-
-   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
-   GridFunction field_in_scalar(&ind_fes);
-   Vector node_vals;
-
-   const int ncomp      = field_in.FESpace()->GetVDim(),
-             points_fld = field_in.Size() / ncomp,
-             points_cnt = codes.Size();
-   field_out.SetSize(points_cnt*ncomp);
-
-   for (int i = 0; i < ncomp; i++)
-   {
-      const int dataptrin  = i*points_fld,
-                dataptrout = i*points_cnt;
-      field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
-      GetNodeValues(field_in_scalar, node_vals);
-
-      if (dim==2)
-      {
-         findpts_eval_2(field_out.GetData()+dataptrout, sizeof(double),
-                        codes.GetData(),       sizeof(unsigned int),
-                        proc_ids.GetData(),    sizeof(unsigned int),
-                        elem_ids.GetData(),    sizeof(unsigned int),
-                        ref_pos.GetData(),     sizeof(double) * dim,
-                        points_cnt, node_vals.GetData(), fdata2D);
-      }
-      else
-      {
-         findpts_eval_3(field_out.GetData()+dataptrout, sizeof(double),
-                        codes.GetData(),       sizeof(unsigned int),
-                        proc_ids.GetData(),    sizeof(unsigned int),
-                        elem_ids.GetData(),    sizeof(unsigned int),
-                        ref_pos.GetData(),     sizeof(double) * dim,
-                        points_cnt, node_vals.GetData(), fdata3D);
-      }
-   }
-}
-
-void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
-                                  Vector &field_out)
-{
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
-}
-
 void FindPointsGSLIB::Interpolate(const Vector &point_pos,
                                   const GridFunction &field_in, Vector &field_out)
 {
    FindPoints(point_pos);
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+   Interpolate(field_in, field_out);
 }
 
 void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
                                   const GridFunction &field_in, Vector &field_out)
 {
    FindPoints(m, point_pos);
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
+   Interpolate(field_in, field_out);
 }
 
 void FindPointsGSLIB::FreeData()
 {
+   if (!setupflag) { return; }
+   crystal_free(cr);
    if (dim == 2)
    {
       findpts_free_2(fdata2D);
@@ -252,13 +217,13 @@ void FindPointsGSLIB::FreeData()
    {
       findpts_free_3(fdata3D);
    }
-   setupflag = false;
    gsl_code.DeleteAll();
    gsl_proc.DeleteAll();
    gsl_elem.DeleteAll();
    gsl_mesh.Destroy();
    gsl_ref.Destroy();
    gsl_dist.Destroy();
+   setupflag = false;
 }
 
 void FindPointsGSLIB::GetNodeValues(const GridFunction &gf_in,
@@ -358,9 +323,8 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
    const FiniteElement *fe   = mesh->GetNodalFESpace()->GetFE(0);
    const Geometry::Type gt   = fe->GetGeomType();
    const GridFunction *nodes = mesh->GetNodes();
-   Mesh *meshsplit           = NULL;
    const int NE              = mesh->GetNE();
-   int NEsplit = -1;
+   int NEsplit = 0;
 
    // Split the reference element into a reference submesh of quads or hexes.
    if (gt == Geometry::TRIANGLE)
@@ -516,8 +480,361 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
          pt_id++;
       }
    }
+}
 
-   delete meshsplit;
+void FindPointsGSLIB::MapRefPosAndElemIndices()
+{
+   gsl_mfem_ref = gsl_ref;
+   gsl_mfem_elem = gsl_elem;
+   const FiniteElement *fe = mesh->GetNodalFESpace()->GetFE(0);
+   const Geometry::Type gt = fe->GetGeomType();
+   int NEsplit = 0;
+
+   gsl_mfem_ref -= -1.;  // map  [-1, 1] to
+   gsl_mfem_ref *= 0.5;  //      [0,  1]
+   if (gt == Geometry::SQUARE || gt == Geometry::CUBE) { return; }
+
+   H1_FECollection feclin(1, dim);
+   FiniteElementSpace nodal_fes_lin(meshsplit, &feclin, dim);
+   GridFunction gf_lin(&nodal_fes_lin);
+
+   if (gt == Geometry::TRIANGLE)
+   {
+      const double quad_v[7][2] =
+      {
+         {0, 0}, {0.5, 0}, {1, 0}, {0, 0.5},
+         {1./3., 1./3.}, {0.5, 0.5}, {0, 1}
+      };
+      for (int k = 0; k < dim; k++)
+      {
+         for (int j = 0; j < gf_lin.Size()/dim; j++)
+         {
+            gf_lin(j+k*gf_lin.Size()/dim) = quad_v[j][k];
+         }
+      }
+      NEsplit = 3;
+   }
+   else if (gt == Geometry::TETRAHEDRON)
+   {
+      const double hex_v[15][3] =
+      {
+         {0, 0, 0.}, {1, 0., 0.}, {0., 1., 0.}, {0, 0., 1.},
+         {0.5, 0., 0.}, {0.5, 0.5, 0.}, {0., 0.5, 0.},
+         {0., 0., 0.5}, {0.5, 0., 0.5}, {0., 0.5, 0.5},
+         {1./3., 0., 1./3.}, {1./3., 1./3., 1./3.}, {0, 1./3., 1./3.},
+         {1./3., 1./3., 0}, {0.25, 0.25, 0.25}
+      };
+      for (int k = 0; k < dim; k++)
+      {
+         for (int j = 0; j < gf_lin.Size()/dim; j++)
+         {
+            gf_lin(j+k*gf_lin.Size()/dim) = hex_v[j][k];
+         }
+      }
+      NEsplit = 4;
+   }
+   else if (gt == Geometry::PRISM)
+   {
+      const double hex_v[14][3] =
+      {
+         {0, 0, 0}, {0.5, 0, 0}, {1, 0, 0}, {0, 0.5, 0},
+         {1./3., 1./3., 0}, {0.5, 0.5, 0}, {0, 1, 0},
+         {0, 0, 1}, {0.5, 0, 1}, {1, 0, 1}, {0, 0.5, 1},
+         {1./3., 1./3., 1}, {0.5, 0.5, 1}, {0, 1, 1}
+      };
+      for (int k = 0; k < dim; k++)
+      {
+         for (int j = 0; j < gf_lin.Size()/dim; j++)
+         {
+            gf_lin(j+k*gf_lin.Size()/dim) = hex_v[j][k];
+         }
+      }
+      NEsplit = 3;
+   }
+   else
+   {
+      MFEM_ABORT("Element type not currently supported.");
+   }
+
+   // Simplices are split into quads/hexes for GSLIB. For MFEM, we need to find
+   // the original element number and map the rst from micro to macro element.
+   for (int i = 0; i < points_cnt; i++)
+   {
+      if (gsl_code[i] == 2) { continue; }
+      int local_elem   = gsl_elem[i]%NEsplit;
+      gsl_mfem_elem[i] = (gsl_elem[i] - local_elem)/NEsplit; // macro element number
+
+      IntegrationPoint ip;
+      Vector mfem_ref(gsl_mfem_ref.GetData()+i*dim, dim);
+      ip.Set2(mfem_ref.GetData());
+      if (dim == 3) { ip.z = mfem_ref(2); }
+      gf_lin.GetVectorValue(local_elem, ip, mfem_ref); // map to rst of macro element
+   }
+}
+
+void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
+                                  Vector &field_out)
+{
+   const int  gf_order   = field_in.FESpace()->GetFE(0)->GetOrder(),
+              mesh_order = mesh->GetNodalFESpace()->GetFE(0)->GetOrder();
+
+   const FiniteElementCollection *fec_in =  field_in.FESpace()->FEColl();
+   const H1_FECollection *fec_h1 = dynamic_cast<const H1_FECollection *>(fec_in);
+   const L2_FECollection *fec_l2 = dynamic_cast<const L2_FECollection *>(fec_in);
+
+   if (fec_h1 && gf_order == mesh_order &&
+       fec_h1->GetBasisType() == BasisType::GaussLobatto)
+   {
+      InterpolateH1(field_in, field_out);
+      return;
+   }
+   else
+   {
+      InterpolateGeneral(field_in, field_out);
+      if (!fec_l2 || avgtype == AvgType::NONE) { return; }
+   }
+
+   // For points on element borders, project the L2 GridFunction to H1 and
+   // re-interpolate.
+   if (fec_l2)
+   {
+      Array<int> indl2;
+      for (int i = 0; i < points_cnt; i++)
+      {
+         if (gsl_code[i] == 1) { indl2.Append(i); }
+      }
+      if (indl2.Size() == 0) { return; } // no points on element borders
+
+      Vector field_out_l2(field_out.Size());
+      VectorGridFunctionCoefficient field_in_dg(&field_in);
+      int gf_order_h1 = std::max(gf_order, 1); // H1 should be at least order 1
+      H1_FECollection fec(gf_order_h1, dim);
+      const int ncomp = field_in.FESpace()->GetVDim();
+      FiniteElementSpace fes(mesh, &fec, ncomp);
+      GridFunction field_in_h1(&fes);
+
+      if (avgtype == AvgType::ARITHMETIC)
+      {
+         field_in_h1.ProjectDiscCoefficient(field_in_dg, GridFunction::ARITHMETIC);
+      }
+      else if (avgtype == AvgType::HARMONIC)
+      {
+         field_in_h1.ProjectDiscCoefficient(field_in_dg, GridFunction::HARMONIC);
+      }
+      else
+      {
+         MFEM_ABORT("Invalid averaging type.");
+      }
+
+      if (gf_order_h1 == mesh_order) // basis is GaussLobatto by default
+      {
+         InterpolateH1(field_in_h1, field_out_l2);
+      }
+      else
+      {
+         InterpolateGeneral(field_in_h1, field_out_l2);
+      }
+
+      // Copy interpolated values for the points on element border
+      for (int j = 0; j < ncomp; j++)
+      {
+         for (int i = 0; i < indl2.Size(); i++)
+         {
+            int idx = indl2[i] + j*points_cnt;
+            field_out(idx) = field_out_l2(idx);
+         }
+      }
+   }
+}
+
+void FindPointsGSLIB::InterpolateH1(const GridFunction &field_in,
+                                    Vector &field_out)
+{
+   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
+   GridFunction field_in_scalar(&ind_fes);
+   Vector node_vals;
+
+   const int ncomp      = field_in.FESpace()->GetVDim(),
+             points_fld = field_in.Size() / ncomp,
+             points_cnt = gsl_code.Size();
+
+   field_out.SetSize(points_cnt*ncomp);
+   field_out = default_interp_value;
+
+   for (int i = 0; i < ncomp; i++)
+   {
+      const int dataptrin  = i*points_fld,
+                dataptrout = i*points_cnt;
+      field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
+      GetNodeValues(field_in_scalar, node_vals);
+
+      if (dim==2)
+      {
+         findpts_eval_2(field_out.GetData()+dataptrout, sizeof(double),
+                        gsl_code.GetData(),       sizeof(unsigned int),
+                        gsl_proc.GetData(),    sizeof(unsigned int),
+                        gsl_elem.GetData(),    sizeof(unsigned int),
+                        gsl_ref.GetData(),     sizeof(double) * dim,
+                        points_cnt, node_vals.GetData(), fdata2D);
+      }
+      else
+      {
+         findpts_eval_3(field_out.GetData()+dataptrout, sizeof(double),
+                        gsl_code.GetData(),       sizeof(unsigned int),
+                        gsl_proc.GetData(),    sizeof(unsigned int),
+                        gsl_elem.GetData(),    sizeof(unsigned int),
+                        gsl_ref.GetData(),     sizeof(double) * dim,
+                        points_cnt, node_vals.GetData(), fdata3D);
+      }
+   }
+}
+
+void FindPointsGSLIB::InterpolateGeneral(const GridFunction &field_in,
+                                         Vector &field_out)
+{
+   int ncomp   = field_in.VectorDim(),
+       nptorig = points_cnt,
+       npt     = points_cnt;
+
+   field_out.SetSize(points_cnt*ncomp);
+   field_out = default_interp_value;
+
+   if (gsl_comm->np == 1) // serial
+   {
+      for (int index = 0; index < npt; index++)
+      {
+         if (gsl_code[index] == 2) { continue; }
+         IntegrationPoint ip;
+         ip.Set2(gsl_mfem_ref.GetData()+index*dim);
+         if (dim == 3) { ip.z = gsl_mfem_ref(index*dim + 2); }
+         Vector localval(ncomp);
+         field_in.GetVectorValue(gsl_mfem_elem[index], ip, localval);
+         for (int i = 0; i < ncomp; i++)
+         {
+            field_out(index + i*npt) = localval(i);
+         }
+      }
+   }
+   else // parallel
+   {
+      // Determine number of points to be sent
+      int nptsend = 0;
+      for (int index = 0; index < npt; index++)
+      {
+         if (gsl_code[index] != 2) { nptsend +=1; }
+      }
+
+      // Pack data to send via crystal router
+      struct array *outpt = new array;
+      struct out_pt { double r[3], ival; uint index, el, proc; };
+      struct out_pt *pt;
+      array_init(struct out_pt, outpt, nptsend);
+      outpt->n=nptsend;
+      pt = (struct out_pt *)outpt->ptr;
+      for (int index = 0; index < npt; index++)
+      {
+         if (gsl_code[index] == 2) { continue; }
+         for (int d = 0; d < dim; ++d) { pt->r[d]= gsl_mfem_ref(index*dim + d); }
+         pt->index = index;
+         pt->proc  = gsl_proc[index];
+         pt->el    = gsl_mfem_elem[index];
+         ++pt;
+      }
+
+      // Transfer data to target MPI ranks
+      sarray_transfer(struct out_pt, outpt, proc, 1, cr);
+
+      if (ncomp == 1)
+      {
+         // Interpolate the grid function
+         npt = outpt->n;
+         pt = (struct out_pt *)outpt->ptr;
+         for (int index = 0; index < npt; index++)
+         {
+            IntegrationPoint ip;
+            ip.Set3(&pt->r[0]);
+            pt->ival = field_in.GetValue(pt->el, ip, 1);
+            ++pt;
+         }
+
+         // Transfer data back to source MPI rank
+         sarray_transfer(struct out_pt, outpt, proc, 1, cr);
+         npt = outpt->n;
+         pt = (struct out_pt *)outpt->ptr;
+         for (int index = 0; index < npt; index++)
+         {
+            field_out(pt->index) = pt->ival;
+            ++pt;
+         }
+         array_free(outpt);
+         delete outpt;
+      }
+      else // ncomp > 1
+      {
+         // Interpolate data and store in a Vector
+         npt = outpt->n;
+         pt = (struct out_pt *)outpt->ptr;
+         Vector vec_int_vals(npt*ncomp);
+         for (int index = 0; index < npt; index++)
+         {
+            IntegrationPoint ip;
+            ip.Set3(&pt->r[0]);
+            Vector localval(vec_int_vals.GetData()+index*ncomp, ncomp);
+            field_in.GetVectorValue(pt->el, ip, localval);
+            ++pt;
+         }
+
+         // Save index and proc data in a struct
+         struct array *savpt = new array;
+         struct sav_pt { uint index, proc; };
+         struct sav_pt *spt;
+         array_init(struct sav_pt, savpt, npt);
+         savpt->n=npt;
+         spt = (struct sav_pt *)savpt->ptr;
+         pt  = (struct out_pt *)outpt->ptr;
+         for (int index = 0; index < npt; index++)
+         {
+            spt->index = pt->index;
+            spt->proc  = pt->proc;
+            ++pt; ++spt;
+         }
+
+         array_free(outpt);
+         delete outpt;
+
+         // Copy data from save struct to send struct and send component wise
+         struct array *sendpt = new array;
+         struct send_pt { double ival; uint index, proc; };
+         struct send_pt *sdpt;
+         for (int j = 0; j < ncomp; j++)
+         {
+            array_init(struct send_pt, sendpt, npt);
+            sendpt->n=npt;
+            spt  = (struct sav_pt *)savpt->ptr;
+            sdpt = (struct send_pt *)sendpt->ptr;
+            for (int index = 0; index < npt; index++)
+            {
+               sdpt->index = spt->index;
+               sdpt->proc  = spt->proc;
+               sdpt->ival  = vec_int_vals(j + index*ncomp);
+               ++sdpt; ++spt;
+            }
+
+            sarray_transfer(struct send_pt, sendpt, proc, 1, cr);
+            sdpt = (struct send_pt *)sendpt->ptr;
+            for (int index = 0; index < nptorig; index++)
+            {
+               int idx = sdpt->index + j*nptorig;
+               field_out(idx) = sdpt->ival;
+               ++sdpt;
+            }
+            array_free(sendpt);
+         }
+         array_free(savpt);
+         delete sendpt;
+         delete savpt;
+      } // ncomp > 1
+   } // parallel
 }
 
 } // namespace mfem

fem/gslib.hpp

@@ -20,28 +20,66 @@
 struct comm;
 struct findpts_data_2;
 struct findpts_data_3;
+struct array;
+struct crystal;
 
 namespace mfem
 {
 
+/** \brief FindPointsGSLIB can robustly evaluate a GridFunction on an arbitrary
+ *  collection of points. There are three key functions in FindPointsGSLIB:
+ *
+ *  1. Setup - constructs the internal data structures of gslib.
+ *
+ *  2. FindPoints - for any given arbitrary set of points in physical space,
+ *     gslib finds the element number, MPI rank, and the reference space
+ *     coordinates inside the element that each point is located in. gslib also
+ *     returns a code that indicates whether the point was found inside an
+ *     element, on element border, or not found in the domain.
+ *
+ *  3. Interpolate - Interpolates any grid function at the points found using 2.
+ *
+ *  FindPointsGSLIB provides interface to use these functions individually or
+ *  using a single call.
+ */
 class FindPointsGSLIB
 {
+public:
+   enum AvgType {NONE, ARITHMETIC, HARMONIC}; // Average type for L2 functions
+
 protected:
-   Mesh *mesh;
-   IntegrationRule *ir_simplex;
-   struct findpts_data_2 *fdata2D;
-   struct findpts_data_3 *fdata3D;
-   int dim;
-   Array<unsigned int> gsl_code, gsl_proc, gsl_elem;
-   Vector gsl_mesh, gsl_ref, gsl_dist;
-   bool setupflag;
-
-   struct comm *gsl_comm;
+   Mesh *mesh, *meshsplit;
+   IntegrationRule *ir_simplex;    // IntegrationRule to split quads/hex -> simplex
+   struct findpts_data_2 *fdata2D; // gslib's internal data
+   struct findpts_data_3 *fdata3D; // gslib's internal data
+   struct crystal *cr;             // gslib's internal data
+   struct comm *gsl_comm;          // gslib's internal data
+   int dim, points_cnt;
+   Array<unsigned int> gsl_code, gsl_proc, gsl_elem, gsl_mfem_elem;
+   Vector gsl_mesh, gsl_ref, gsl_dist, gsl_mfem_ref;
+   bool setupflag;              // flag to indicate whether gslib data has been setup
+   double default_interp_value; // used for points that are not found in the mesh
+   AvgType avgtype;             // average type used for L2 functions
 
+   /// Get GridFunction from MFEM format to GSLIB format
    void GetNodeValues(const GridFunction &gf_in, Vector &node_vals);
+   /// Get nodal coordinates from mesh to the format expected by GSLIB for quads
+   /// and hexes
    void GetQuadHexNodalCoordinates();
+   /// Convert simplices to quad/hexes and then get nodal coordinates for each
+   /// split element into format expected by GSLIB
    void GetSimplexNodalCoordinates();
 
+   /// Use GSLIB for communication and interpolation
+   void InterpolateH1(const GridFunction &field_in, Vector &field_out);
+   /// Uses GSLIB Crystal Router for communication followed by MFEM's
+   /// interpolation functions
+   void InterpolateGeneral(const GridFunction &field_in, Vector &field_out);
+   /// Map {r,s,t} coordinates from [-1,1] to [0,1] for MFEM. For simplices mesh
+   /// find the original element number (that was split into micro quads/hexes
+   /// by GetSimplexNodalCoordinates())
+   void MapRefPosAndElemIndices();
+
 public:
    FindPointsGSLIB();
 
@@ -64,45 +102,37 @@ public:
    void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
               const int npt_max = 256);
 
-   /** Searches positions given in physical space by @a point_pos. All output
-       Arrays and Vectors are expected to have the correct size.
-
-       @param[in]  point_pos  Positions to be found. Must by ordered by nodes
-                              (XXX...,YYY...,ZZZ).
-       @param[out] codes      Return codes for each point: inside element (0),
-                              element boundary (1), not found (2).
-       @param[out] proc_ids   MPI proc ids where the points were found.
-       @param[out] elem_ids   Element ids where the points were found.
-       @param[out] ref_pos    Reference coordinates of the found point. Ordered
-                              by vdim (XYZ,XYZ,XYZ...).
-                              Note: the gslib reference frame is [-1,1].
-       @param[out] dist       Distance between the sought and the found point
-                              in physical space. */
-   void FindPoints(const Vector &point_pos, Array<unsigned int> &codes,
-                   Array<unsigned int> &proc_ids, Array<unsigned int> &elem_ids,
-                   Vector &ref_pos, Vector &dist);
+   /** Searches positions given in physical space by @a point_pos. These positions
+       must by ordered by nodes: (XXX...,YYY...,ZZZ).
+       This function populates the following member variables:
+       #gsl_code        Return codes for each point: inside element (0),
+                        element boundary (1), not found (2).
+       #gsl_proc        MPI proc ids where the points were found.
+       #gsl_elem        Element ids where the points were found.
+                        Defaults to 0 for points that were not found.
+       #gsl_mfem_elem   Element ids corresponding to MFEM-mesh where the points
+                        were found. #gsl_mfem_elem != #gsl_elem for simplices
+                        Defaults to 0 for points that were not found.
+       #gsl_ref         Reference coordinates of the found point.
+                        Ordered by vdim (XYZ,XYZ,XYZ...). Defaults to -1 for
+                        points that were not found. Note: the gslib reference
+                        frame is [-1,1].
+       #gsl_mfem_ref    Reference coordinates #gsl_ref mapped to [0,1].
+                        Defaults to 0 for points that were not found.
+       #gsl_dist        Distance between the sought and the found point
+                        in physical space. */
    void FindPoints(const Vector &point_pos);
    /// Setup FindPoints and search positions
    void FindPoints(Mesh &m, const Vector &point_pos, const double bb_t = 0.1,
                    const double newt_tol = 1.0e-12,  const int npt_max = 256);
 
    /** Interpolation of field values at prescribed reference space positions.
-
-       @param[in] codes       Return codes for each point: inside element (0),
-                              element boundary (1), not found (2).
-       @param[in] proc_ids    MPI proc ids where the points were found.
-       @param[in] elem_ids    Element ids where the points were found.
-       @param[in] ref_pos     Reference coordinates of the found point. Ordered
-                              by vdim (XYZ,XYZ,XYZ...).
-                              Note: the gslib reference frame is [-1,1].
        @param[in] field_in    Function values that will be interpolated on the
                               reference positions. Note: it is assumed that
                               @a field_in is in H1 and in the same space as the
                               mesh that was given to Setup().
-       @param[out] field_out  Interpolated values. */
-   void Interpolate(Array<unsigned int> &codes, Array<unsigned int> &proc_ids,
-                    Array<unsigned int> &elem_ids, Vector &ref_pos,
-                    const GridFunction &field_in, Vector &field_out);
+       @param[out] field_out  Interpolated values. For points that are not found
+                              the value is set to #default_interp_value. */
    void Interpolate(const GridFunction &field_in, Vector &field_out);
    /** Search positions and interpolate */
    void Interpolate(const Vector &point_pos, const GridFunction &field_in,
@@ -111,27 +141,45 @@ public:
    void Interpolate(Mesh &m, const Vector &point_pos,
                     const GridFunction &field_in, Vector &field_out);
 
+   /// Average type to be used for L2 functions in-case a point is located at
+   /// an element boundary where the function might be multi-valued.
+   void SetL2AvgType(AvgType avgtype_) { avgtype = avgtype_; }
+
+   /// Set the default interpolation value for points that are not found in the
+   /// mesh.
+   void SetDefaultInterpolationValue(double interp_value_)
+   {
+      default_interp_value = interp_value_;
+   }
+
    /** Cleans up memory allocated internally by gslib.
-       Note that in parallel, this must be called before MPI_Finalize(), as
-       it calls MPI_Comm_free() for internal gslib communicators. */
+       Note that in parallel, this must be called before MPI_Finalize(), as it
+       calls MPI_Comm_free() for internal gslib communicators. */
    void FreeData();
 
    /// Return code for each point searched by FindPoints: inside element (0), on
    /// element boundary (1), or not found (2).
    const Array<unsigned int> &GetCode() const { return gsl_code; }
    /// Return element number for each point found by FindPoints.
-   const Array<unsigned int> &GetElem() const { return gsl_elem; }
+   const Array<unsigned int> &GetElem() const { return gsl_mfem_elem; }
    /// Return MPI rank on which each point was found by FindPoints.
    const Array<unsigned int> &GetProc() const { return gsl_proc; }
    /// Return reference coordinates for each point found by FindPoints.
-   const Vector &GetReferencePosition() const { return gsl_ref;  }
+   const Vector &GetReferencePosition() const { return gsl_mfem_ref;  }
    /// Return distance Distance between the sought and the found point
    /// in physical space, for each point found by FindPoints.
    const Vector &GetDist()              const { return gsl_dist; }
+
+   /// Return element number for each point found by FindPoints corresponding to
+   /// GSLIB mesh. gsl_mfem_elem != gsl_elem for mesh with simplices.
+   const Array<unsigned int> &GetGSLIBElem() const { return gsl_elem; }
+   /// Return reference coordinates in [-1,1] (internal range in GSLIB) for each
+   /// point found by FindPoints.
+   const Vector &GetGSLIBReferencePosition() const { return gsl_ref; }
 };
 
 } // namespace mfem
 
-#endif //MFEM_USE_GSLIB
+#endif // MFEM_USE_GSLIB
 
-#endif //MFEM_GSLIB guard
+#endif // MFEM_GSLIB

fem/libceed/ceed.cpp

@@ -35,6 +35,9 @@ extern Ceed ceed;
 
 std::string ceed_path;
 
+extern CeedBasisMap ceed_basis_map;
+extern CeedRestrMap ceed_restr_map;
+
 }
 
 void InitCeedCoeff(Coefficient* Q, CeedData* ptr)
@@ -81,10 +84,9 @@ static CeedElemTopology GetCeedTopology(Geometry::Type geom)
    }
 }
 
-static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
-                                                 const IntegrationRule &ir,
-                                                 Ceed ceed, CeedBasis *basis,
-                                                 CeedElemRestriction *restr)
+static void InitCeedNonTensorBasis(const FiniteElementSpace &fes,
+                                   const IntegrationRule &ir,
+                                   Ceed ceed, CeedBasis *basis)
 {
    Mesh *mesh = fes.GetMesh();
    const FiniteElement *fe = fes.GetFE(0);
@@ -97,7 +99,73 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
    Vector qweight(Q);
    Vector shape_i(P);
    DenseMatrix grad_i(P, dim);
+   const Table &el_dof = fes.GetElementToDofTable();
+   Array<int> tp_el_dof(el_dof.Size_of_connections());
+   const TensorBasisElement * tfe =
+      dynamic_cast<const TensorBasisElement *>(fe);
+   if (tfe) // Lexicographic ordering using dof_map
+   {
+      const Array<int>& dof_map = tfe->GetDofMap();
+      for (int i = 0; i < Q; i++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(i);
+         qref(0,i) = ip.x;
+         if (dim>1) { qref(1,i) = ip.y; }
+         if (dim>2) { qref(2,i) = ip.z; }
+         qweight(i) = ip.weight;
+         fe->CalcShape(ip, shape_i);
+         fe->CalcDShape(ip, grad_i);
+         for (int j = 0; j < P; j++)
+         {
+            shape(j, i) = shape_i(dof_map[j]);
+            for (int d = 0; d < dim; ++d)
+            {
+               grad(j+i*P+d*Q*P) = grad_i(dof_map[j], d);
+            }
+         }
+      }
+   }
+   else  // Native ordering
+   {
+      for (int i = 0; i < Q; i++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(i);
+         qref(0,i) = ip.x;
+         if (dim>1) { qref(1,i) = ip.y; }
+         if (dim>2) { qref(2,i) = ip.z; }
+         qweight(i) = ip.weight;
+         fe->CalcShape(ip, shape_i);
+         fe->CalcDShape(ip, grad_i);
+         for (int j = 0; j < P; j++)
+         {
+            shape(j, i) = shape_i(j);
+            for (int d = 0; d < dim; ++d)
+            {
+               grad(j+i*P+d*Q*P) = grad_i(j, d);
+            }
+         }
+      }
+   }
+   CeedBasisCreateH1(ceed, GetCeedTopology(fe->GetGeomType()), fes.GetVDim(),
+                     fe->GetDof(), ir.GetNPoints(), shape.GetData(),
+                     grad.GetData(), qref.GetData(), qweight.GetData(), basis);
+}
 
+static void InitCeedNonTensorRestriction(const FiniteElementSpace &fes,
+                                         const IntegrationRule &ir,
+                                         Ceed ceed, CeedElemRestriction *restr)
+{
+   Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fe = fes.GetFE(0);
+   const int dim = mesh->Dimension();
+   const int P = fe->GetDof();
+   const int Q = ir.GetNPoints();
+   DenseMatrix shape(P, Q);
+   Vector grad(P*dim*Q);
+   DenseMatrix qref(dim, Q);
+   Vector qweight(Q);
+   Vector shape_i(P);
+   DenseMatrix grad_i(P, dim);
    CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
    const Table &el_dof = fes.GetElementToDofTable();
    Array<int> tp_el_dof(el_dof.Size_of_connections());
@@ -124,7 +192,6 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
             }
          }
       }
-
       for (int i = 0; i < mesh->GetNE(); i++)
       {
          const int el_offset = fe->GetDof() * i;
@@ -162,7 +229,6 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
             }
          }
       }
-
       for (int e = 0; e < mesh->GetNE(); e++)
       {
          for (int i = 0; i < P; i++)
@@ -178,19 +244,15 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
          }
       }
    }
-   CeedBasisCreateH1(ceed, GetCeedTopology(fe->GetGeomType()), fes.GetVDim(),
-                     fe->GetDof(), ir.GetNPoints(), shape.GetData(),
-                     grad.GetData(), qref.GetData(), qweight.GetData(), basis);
    CeedElemRestrictionCreate(ceed, mesh->GetNE(), fe->GetDof(), fes.GetVDim(),
                              compstride, (fes.GetVDim())*(fes.GetNDofs()),
                              CEED_MEM_HOST, CEED_COPY_VALUES,
                              tp_el_dof.GetData(), restr);
 }
 
-static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
-                                              const IntegrationRule &ir,
-                                              Ceed ceed, CeedBasis *basis,
-                                              CeedElemRestriction *restr)
+static void InitCeedTensorBasis(const FiniteElementSpace &fes,
+                                const IntegrationRule &ir,
+                                Ceed ceed, CeedBasis *basis)
 {
    Mesh *mesh = fes.GetMesh();
    const FiniteElement *fe = fes.GetFE(0);
@@ -198,7 +260,6 @@ static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
    const TensorBasisElement * tfe =
       dynamic_cast<const TensorBasisElement *>(fe);
    MFEM_VERIFY(tfe, "invalid FE");
-   const Array<int>& dof_map = tfe->GetDofMap();
    const FiniteElement *fe1d =
       fes.FEColl()->FiniteElementForGeometry(Geometry::SEGMENT);
    DenseMatrix shape1d(fe1d->GetDof(), ir.GetNPoints());
@@ -227,6 +288,28 @@ static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
                            ir.GetNPoints(), shape1d.GetData(),
                            grad1d.GetData(), qref1d.GetData(),
                            qweight1d.GetData(), basis);
+}
+
+static void InitCeedTensorRestriction(const FiniteElementSpace &fes,
+                                      const IntegrationRule &ir,
+                                      Ceed ceed, CeedElemRestriction *restr)
+{
+   Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fe = fes.GetFE(0);
+   const TensorBasisElement * tfe =
+      dynamic_cast<const TensorBasisElement *>(fe);
+   MFEM_VERIFY(tfe, "invalid FE");
+   const Array<int>& dof_map = tfe->GetDofMap();
+   const FiniteElement *fe1d =
+      fes.FEColl()->FiniteElementForGeometry(Geometry::SEGMENT);
+   DenseMatrix shape1d(fe1d->GetDof(), ir.GetNPoints());
+   DenseMatrix grad1d(fe1d->GetDof(), ir.GetNPoints());
+   Vector qref1d(ir.GetNPoints()), qweight1d(ir.GetNPoints());
+   Vector shape_i(shape1d.Height());
+   DenseMatrix grad_i(grad1d.Height(), 1);
+   const H1_SegmentElement *h1_fe1d =
+      dynamic_cast<const H1_SegmentElement *>(fe1d);
+   MFEM_VERIFY(h1_fe1d, "invalid FE");
 
    CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
    const Table &el_dof = fes.GetElementToDofTable();
@@ -258,14 +341,52 @@ void InitCeedBasisAndRestriction(const FiniteElementSpace &fes,
                                  Ceed ceed, CeedBasis *basis,
                                  CeedElemRestriction *restr)
 {
-   if (UsesTensorBasis(fes))
+   // Check for FES -> basis, restriction in hash tables
+   const Mesh *mesh = fes.GetMesh();
+   const FiniteElement *fe = fes.GetFE(0);
+   const int P = fe->GetDof();
+   const int Q = irm.GetNPoints();
+   const int nelem = mesh->GetNE();
+   const int ncomp = fes.GetVDim();
+   CeedBasisKey basis_key(&fes, &irm, ncomp, P, Q);
+   auto basis_itr = internal::ceed_basis_map.find(basis_key);
+   CeedRestrKey restr_key(&fes, nelem, P, ncomp);
+   auto restr_itr = internal::ceed_restr_map.find(restr_key);
+
+   // Init or retreive key values
+   if (basis_itr == internal::ceed_basis_map.end())
    {
-      const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, irm.GetOrder());
-      InitCeedTensorBasisAndRestriction(fes, ir, ceed, basis, restr);
+      if (UsesTensorBasis(fes))
+      {
+         const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, irm.GetOrder());
+         InitCeedTensorBasis(fes, ir, ceed, basis);
+      }
+      else
+      {
+         InitCeedNonTensorBasis(fes, irm, ceed, basis);
+      }
+      internal::ceed_basis_map[basis_key] = *basis;
    }
    else
    {
-      InitCeedNonTensorBasisAndRestriction(fes, irm, ceed, basis, restr);
+      *basis = basis_itr->second;
+   }
+   if (restr_itr == internal::ceed_restr_map.end())
+   {
+      if (UsesTensorBasis(fes))
+      {
+         const IntegrationRule &ir = IntRules.Get(Geometry::SEGMENT, irm.GetOrder());
+         InitCeedTensorRestriction(fes, ir, ceed, restr);
+      }
+      else
+      {
+         InitCeedNonTensorRestriction(fes, irm, ceed, restr);
+      }
+      internal::ceed_restr_map[restr_key] = *restr;
+   }
+   else
+   {
+      *restr = restr_itr->second;
    }
 }
 
@@ -327,8 +448,8 @@ void CeedPAAssemble(const CeedPAOperator& op,
    CeedVectorCreate(ceed, nelem * nqpts * qdatasize, &ceedData.rho);
 
    // Context data to be passed to the 'f_build_diff' Q-function.
-   ceedData.build_ctx.dim = mesh->Dimension();
-   ceedData.build_ctx.space_dim = mesh->SpaceDimension();
+   ceedData.build_ctx_data.dim = mesh->Dimension();
+   ceedData.build_ctx_data.space_dim = mesh->SpaceDimension();
 
    std::string qf_file = GetCeedPath() + op.header;
    std::string qf;
@@ -342,7 +463,7 @@ void CeedPAAssemble(const CeedPAOperator& op,
          CeedQFunctionCreateInterior(ceed, 1, op.const_qf,
                                      qf.c_str(),
                                      &ceedData.build_qfunc);
-         ceedData.build_ctx.coeff = ((CeedConstCoeff*)ceedData.coeff)->val;
+         ceedData.build_ctx_data.coeff = ((CeedConstCoeff*)ceedData.coeff)->val;
          break;
       case CeedCoeff::Grid:
          qf = qf_file + op.grid_func;
@@ -358,8 +479,12 @@ void CeedPAAssemble(const CeedPAOperator& op,
    CeedQFunctionAddInput(ceedData.build_qfunc, "weights", 1, CEED_EVAL_WEIGHT);
    CeedQFunctionAddOutput(ceedData.build_qfunc, "qdata", qdatasize,
                           CEED_EVAL_NONE);
-   CeedQFunctionSetContext(ceedData.build_qfunc, &ceedData.build_ctx,
-                           sizeof(ceedData.build_ctx));
+
+   CeedQFunctionContextCreate(ceed, &ceedData.build_ctx);
+   CeedQFunctionContextSetData(ceedData.build_ctx, CEED_MEM_HOST, CEED_USE_POINTER,
+                               sizeof(ceedData.build_ctx_data),
+                               &ceedData.build_ctx_data);
+   CeedQFunctionSetContext(ceedData.build_qfunc, ceedData.build_ctx);
 
    // Create the operator that builds the quadrature data for the operator.
    CeedOperatorCreate(ceed, ceedData.build_qfunc, NULL, NULL,
@@ -399,8 +524,7 @@ void CeedPAAssemble(const CeedPAOperator& op,
    CeedQFunctionAddInput(ceedData.apply_qfunc, "qdata", qdatasize,
                          CEED_EVAL_NONE);
    CeedQFunctionAddOutput(ceedData.apply_qfunc, "v", dimV, op.test_op);
-   CeedQFunctionSetContext(ceedData.apply_qfunc, &ceedData.build_ctx,
-                           sizeof(ceedData.build_ctx));
+   CeedQFunctionSetContext(ceedData.apply_qfunc, ceedData.build_ctx);
 
    // Create the diff operator.
    CeedOperatorCreate(ceed, ceedData.apply_qfunc, NULL, NULL, &ceedData.oper);

fem/libceed/ceed.hpp

@@ -18,6 +18,9 @@
 #include "../../general/device.hpp"
 #include "../../linalg/vector.hpp"
 #include <ceed.h>
+#include <ceed-hash.h>
+#include <tuple>
+#include <unordered_map>
 
 namespace mfem
 {
@@ -27,7 +30,47 @@ class GridFunction;
 class IntegrationRule;
 class Coefficient;
 
-namespace internal { extern Ceed ceed; } // defined in device.cpp
+// Hash table for CeedBasis
+using CeedBasisKey =
+   std::tuple<const FiniteElementSpace*, const IntegrationRule*, int, int, int>;
+struct CeedBasisHash
+{
+   std::size_t operator()(const CeedBasisKey& k) const
+   {
+      return CeedHashCombine(CeedHashCombine(CeedHashInt(
+                                                reinterpret_cast<CeedHash64_t>(std::get<0>(k))),
+                                             CeedHashInt(
+                                                reinterpret_cast<CeedHash64_t>(std::get<1>(k)))),
+                             CeedHashCombine(CeedHashCombine(CeedHashInt(std::get<2>(k)),
+                                                             CeedHashInt(std::get<3>(k))),
+                                             CeedHashInt(std::get<4>(k))));
+   }
+};
+using CeedBasisMap =
+   std::unordered_map<const CeedBasisKey, CeedBasis, CeedBasisHash>;
+
+// Hash table for CeedElemRestriction
+using CeedRestrKey = std::tuple<const FiniteElementSpace*, int, int, int>;
+struct CeedRestrHash
+{
+   std::size_t operator()(const CeedRestrKey& k) const
+   {
+      return CeedHashCombine(CeedHashCombine(CeedHashInt(
+                                                reinterpret_cast<CeedHash64_t>(std::get<0>(k))),
+                                             CeedHashInt(std::get<1>(k))),
+                             CeedHashCombine(CeedHashInt(std::get<2>(k)),
+                                             CeedHashInt(std::get<3>(k))));
+   }
+};
+using CeedRestrMap =
+   std::unordered_map<const CeedRestrKey, CeedElemRestriction, CeedRestrHash>;
+
+namespace internal
+{
+extern Ceed ceed; // defined in device.cpp
+extern CeedBasisMap basis_map;
+extern CeedRestrMap restr_map;
+}
 
 /// A structure used to pass additional data to f_build_diff and f_apply_diff
 struct BuildContext { CeedInt dim, space_dim; CeedScalar coeff; };
@@ -56,7 +99,8 @@ struct CeedData
    CeedVector node_coords, rho;
    CeedCoeff coeff_type;
    void* coeff;
-   BuildContext build_ctx;
+   CeedQFunctionContext build_ctx;
+   BuildContext build_ctx_data;
 
    CeedVector u, v;
 
@@ -64,10 +108,6 @@ struct CeedData
    {
       CeedOperatorDestroy(&build_oper);
       CeedOperatorDestroy(&oper);
-      CeedBasisDestroy(&basis);
-      CeedBasisDestroy(&mesh_basis);
-      CeedElemRestrictionDestroy(&restr);
-      CeedElemRestrictionDestroy(&mesh_restr);
       CeedElemRestrictionDestroy(&restr_i);
       CeedElemRestrictionDestroy(&mesh_restr_i);
       CeedQFunctionDestroy(&apply_qfunc);
@@ -77,8 +117,6 @@ struct CeedData
       if (coeff_type==CeedCoeff::Grid)
       {
          CeedGridCoeff* c = (CeedGridCoeff*)coeff;
-         CeedBasisDestroy(&c->basis);
-         CeedElemRestrictionDestroy(&c->restr);
          CeedVectorDestroy(&c->coeffVector);
          delete c;
       }

fem/linearform.cpp

@@ -204,6 +204,14 @@ void LinearForm::Update(FiniteElementSpace *f, Vector &v, int v_offset)
    ResetDeltaLocations();
 }
 
+void LinearForm::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
+{
+   MFEM_ASSERT(v.Size() >= v_offset + f->GetVSize(), "");
+   fes = f;
+   v.UseDevice(true);
+   this->Vector::MakeRef(v, v_offset, fes->GetVSize());
+}
+
 void LinearForm::AssembleDelta()
 {
    if (dlfi_delta.Size() == 0) { return; }

fem/linearform.hpp

@@ -26,7 +26,7 @@ protected:
    /// FE space on which the LinearForm lives. Not owned.
    FiniteElementSpace *fes;
 
-   /** @brief Indicates the LinerFormIntegrator%s stored in #dlfi, #dlfi_delta,
+   /** @brief Indicates the LinearFormIntegrator%s stored in #dlfi, #dlfi_delta,
        #blfi, and #flfi are owned by another LinearForm. */
    int extern_lfs;
 
@@ -175,6 +175,16 @@ public:
        @note This method does not perform assembly. */
    void Update(FiniteElementSpace *f, Vector &v, int v_offset);
 
+   /** @brief Make the LinearForm reference external data on a new
+       FiniteElementSpace. */
+   /** This method changes the FiniteElementSpace associated with the LinearForm
+       @a *f and sets the data of the Vector @a v (plus the @a v_offset) as
+       external data in the LinearForm.
+
+       @note This version of the method will also perform bounds checks when the
+       build option MFEM_DEBUG is enabled. */
+   virtual void MakeRef(FiniteElementSpace *f, Vector &v, int v_offset);
+
    /// Return the action of the LinearForm as a linear mapping.
    /** Linear forms are linear functionals which map GridFunctions to
        the real numbers.  This method performs this mapping which in

fem/lininteg.cpp

@@ -457,20 +457,8 @@ void VectorFEDomainLFCurlIntegrator::AssembleRHSElementVect(
 
       Tr.SetIntPoint (&ip);
       el.CalcPhysCurlShape(Tr, curlshape);
+      QF->Eval(vec, Tr, ip);
 
-      switch (spaceDim)
-      {
-         case 3:
-            MFEM_VERIFY(QF, "VectorFunctionCoefficient not provided");
-            QF->Eval(vec, Tr, ip);
-            break;
-         case 2:
-            MFEM_VERIFY(Q, "FunctionCoefficient (Scalar) not provided");
-            vec[0] = Q->Eval(Tr, ip);
-            break;
-         default:
-            break; // This should be unreachable
-      }
       vec *= ip.weight * Tr.Weight();
       curlshape.AddMult (vec, elvect);
    }
@@ -480,38 +468,17 @@ void VectorFEDomainLFCurlIntegrator::AssembleDeltaElementVect(
    const FiniteElement &fe, ElementTransformation &Trans, Vector &elvect)
 {
    int spaceDim = Trans.GetSpaceDim();
-   switch (spaceDim)
-   {
-      case 3:
-         MFEM_ASSERT(vec_delta != NULL,
-                     "coefficient must be VectorDeltaCoefficient");
-         break;
-      case 2:
-         MFEM_ASSERT(delta != NULL,
-                     "coefficient must be DeltaCoefficient");
-         break;
-      default:
-         break; // This should be unreachable
-   }
+   MFEM_ASSERT(vec_delta != NULL,
+               "coefficient must be VectorDeltaCoefficient");
    int dof = fe.GetDof();
    int n=(spaceDim == 3)? spaceDim : 1;
+   vec.SetSize(n);
    curlshape.SetSize(dof, n);
    elvect.SetSize(dof);
    fe.CalcPhysCurlShape(Trans, curlshape);
 
-   switch (spaceDim)
-   {
-      case 3:
-         vec_delta->EvalDelta(vec, Trans, Trans.GetIntPoint());
-         curlshape.Mult(vec, elvect);
-         break;
-      case 2:
-         curlshape.GetColumn(0,elvect);
-         elvect *= delta->EvalDelta(Trans, Trans.GetIntPoint());
-         break;
-      default:
-         break; // This should be unreachable
-   }
+   vec_delta->EvalDelta(vec, Trans, Trans.GetIntPoint());
+   curlshape.Mult(vec, elvect);
 }
 
 void VectorFEDomainLFDivIntegrator::AssembleRHSElementVect(

fem/lininteg.hpp

@@ -284,7 +284,6 @@ class VectorFEDomainLFCurlIntegrator : public DeltaLFIntegrator
 {
 private:
    VectorCoefficient *QF=nullptr;
-   Coefficient *Q=nullptr;
    DenseMatrix curlshape;
    Vector vec;
 
@@ -292,8 +291,6 @@ public:
    /// Constructs the domain integrator (Q, curl v)
    VectorFEDomainLFCurlIntegrator(VectorCoefficient &F)
       : DeltaLFIntegrator(F), QF(&F) { }
-   VectorFEDomainLFCurlIntegrator(Coefficient &F)
-      : DeltaLFIntegrator(F), Q(&F) { }
 
    virtual void AssembleRHSElementVect(const FiniteElement &el,
                                        ElementTransformation &Tr,

fem/nonlinearform.cpp

@@ -581,6 +581,13 @@ double BlockNonlinearForm::GetEnergyBlocked(const BlockVector &bx) const
          }
       }
 
+   // free the allocated memory
+   for (int i = 0; i < fes.Size(); ++i)
+   {
+      delete el_x[i];
+      delete vdofs[i];
+   }
+
    if (fnfi.Size())
    {
       MFEM_ABORT("TODO: add energy contribution from interior face terms");

fem/pbilinearform.cpp

@@ -565,6 +565,53 @@ HypreParMatrix* ParDiscreteLinearOperator::ParallelAssemble() const
    return RAP;
 }
 
+void ParDiscreteLinearOperator::ParallelAssemble(OperatorHandle &A)
+{
+   // construct the rectangular block-diagonal matrix dA
+   OperatorHandle dA(A.Type());
+   dA.MakeRectangularBlockDiag(domain_fes->GetComm(),
+                               range_fes->GlobalVSize(),
+                               domain_fes->GlobalVSize(),
+                               range_fes->GetDofOffsets(),
+                               domain_fes->GetDofOffsets(),
+                               mat);
+
+   OperatorHandle P_test(A.Type()), P_trial(A.Type());
+
+   // TODO - construct the Dof_TrueDof_Matrix directly in the required format.
+   P_test.ConvertFrom(range_fes->Dof_TrueDof_Matrix());
+   P_trial.ConvertFrom(domain_fes->Dof_TrueDof_Matrix());
+
+   A.MakeRAP(P_test, dA, P_trial);
+}
+
+//// @todo copied from ParMixedBilinearForm, should be some inheritance?
+void ParDiscreteLinearOperator::FormRectangularSystemMatrix(OperatorHandle &A)
+{
+   if (ext)
+   {
+      Array<int> empty;
+      ext->FormRectangularSystemOperator(empty, empty, A);
+      return;
+   }
+
+   /*
+   if (mat)
+   {
+      Finalize();
+      ParallelAssemble(p_mat);
+      delete mat;
+      mat = NULL;
+      delete mat_e;
+      mat_e = NULL;
+      p_mat_e = NULL;
+   }
+   A = p_mat;
+   */
+
+   mfem_error("not implemented!");
+}
+
 void ParDiscreteLinearOperator::GetParBlocks(Array2D<HypreParMatrix *> &blocks)
 const
 {

fem/pbilinearform.hpp

@@ -160,6 +160,9 @@ public:
    /// Get the parallel finite element space prolongation matrix
    virtual const Operator *GetProlongation() const
    { return pfes->GetProlongationMatrix(); }
+   /// Get the diagonal part of the parallel finite element space prolongation matrix
+   virtual const Operator *GetLocalProlongation() const
+   { return pfes->GetLocalProlongationMatrix(); }
    /// Get the parallel finite element space restriction matrix
    virtual const Operator *GetRestriction() const
    { return pfes->GetRestrictionMatrix(); }
@@ -301,10 +304,18 @@ public:
    /// Returns the matrix "assembled" on the true dofs
    HypreParMatrix *ParallelAssemble() const;
 
+   /** @brief Returns the matrix assembled on the true dofs, i.e.
+       @a A = P_test^t A_local P_trial, in the format (type id) specified by
+       @a A. */
+   void ParallelAssemble(OperatorHandle &A);
+
    /** Extract the parallel blocks corresponding to the vector dimensions of the
        domain and range parallel finite element spaces */
    void GetParBlocks(Array2D<HypreParMatrix *> &blocks) const;
 
+   /** @brief Return in @a A a parallel (on truedofs) version of this operator. */
+   virtual void FormRectangularSystemMatrix(OperatorHandle &A);
+
    virtual ~ParDiscreteLinearOperator() { }
 };
 

fem/pfespace.cpp

@@ -101,6 +101,7 @@ void ParFiniteElementSpace::ParInit(ParMesh *pm)
 
    P = NULL;
    Pconf = NULL;
+   Pconf_local = NULL;
    R = NULL;
 
    num_face_nbr_dofs = -1;
@@ -921,6 +922,39 @@ const Operator *ParFiniteElementSpace::GetProlongationMatrix() const
    }
 }
 
+const Operator *ParFiniteElementSpace::GetLocalProlongationMatrix() const
+{
+   if (Conforming())
+   {
+      if (Pconf_local) { return Pconf_local; }
+
+      if (NRanks == 1)
+      {
+         Pconf_local = new IdentityOperator(GetTrueVSize());
+      }
+      else
+      {
+         if (!Device::Allows(Backend::DEVICE_MASK))
+         {
+            Pconf_local = new ConformingProlongationOperator(*this, true);
+         }
+         else
+         {
+            // Pconf = new DeviceConformingProlongationOperator(*this);
+            mfem_error("Not implemented!");
+         }
+      }
+      return Pconf_local;
+   }
+   else
+   {
+      // return Dof_TrueDof_Matrix();
+      // just need diagonal portion, not too hard
+      mfem_error("Not implemented!");
+      return NULL;
+   }
+}
+
 void ParFiniteElementSpace::ExchangeFaceNbrData()
 {
    if (num_face_nbr_dofs >= 0) { return; }
@@ -2834,6 +2868,7 @@ void ParFiniteElementSpace::Destroy()
 
    delete P; P = NULL;
    delete Pconf; Pconf = NULL;
+   delete Pconf_local; Pconf_local = NULL;
    delete R; R = NULL;
 
    delete gcomm; gcomm = NULL;
@@ -2959,12 +2994,12 @@ void ParFiniteElementSpace::Update(bool want_transform)
    }
 }
 
-
 ConformingProlongationOperator::ConformingProlongationOperator(
-   const ParFiniteElementSpace &pfes)
+   const ParFiniteElementSpace &pfes, bool local_)
    : Operator(pfes.GetVSize(), pfes.GetTrueVSize()),
      external_ldofs(),
-     gc(pfes.GroupComm())
+     gc(pfes.GroupComm()),
+     local(local_)
 {
    MFEM_VERIFY(pfes.Conforming(), "");
    const Table &group_ldof = gc.GroupLDofTable();
@@ -3013,7 +3048,14 @@ void ConformingProlongationOperator::Mult(const Vector &x, Vector &y) const
    const int m = external_ldofs.Size();
 
    const int in_layout = 2; // 2 - input is ltdofs array
-   gc.BcastBegin(const_cast<double*>(xdata), in_layout);
+   if (local)
+   {
+      y = 0.0;
+   }
+   else
+   {
+      gc.BcastBegin(const_cast<double*>(xdata), in_layout);
+   }
 
    int j = 0;
    for (int i = 0; i < m; i++)
@@ -3025,7 +3067,10 @@ void ConformingProlongationOperator::Mult(const Vector &x, Vector &y) const
    std::copy(xdata+j-m, xdata+Width(), ydata+j);
 
    const int out_layout = 0; // 0 - output is ldofs array
-   gc.BcastEnd(ydata, out_layout);
+   if (!local)
+   {
+      gc.BcastEnd(ydata, out_layout);
+   }
 }
 
 void ConformingProlongationOperator::MultTranspose(
@@ -3038,7 +3083,10 @@ void ConformingProlongationOperator::MultTranspose(
    double *ydata = y.HostWrite();
    const int m = external_ldofs.Size();
 
-   gc.ReduceBegin(xdata);
+   if (!local)
+   {
+      gc.ReduceBegin(xdata);
+   }
 
    int j = 0;
    for (int i = 0; i < m; i++)
@@ -3050,7 +3098,10 @@ void ConformingProlongationOperator::MultTranspose(
    std::copy(xdata+j, xdata+Height(), ydata+j-m);
 
    const int out_layout = 2; // 2 - output is an array on all ltdofs
-   gc.ReduceEnd<double>(ydata, out_layout, GroupCommunicator::Sum);
+   if (!local)
+   {
+      gc.ReduceEnd<double>(ydata, out_layout, GroupCommunicator::Sum);
+   }
 }
 
 DeviceConformingProlongationOperator::DeviceConformingProlongationOperator(