Cleaned up unordered_map implementation and added safer float comparison as a fallback for out_of_range errors thrown by the map.

Merging sbp-dev into hashtable-sbp-dev to test hashtable implementation with more recent sbp-dev branch before merging back to sbp-dev

.appveyor.yml

@@ -43,7 +43,9 @@ before_build:
 build_script:
 - cmake --build build_parallel
 - cmake --build build_serial
+- cmake --build build_serial --target exec
 
 after_build:
 # - cmake --build build_parallel --target check
-- cmake --build build_serial --target check
+- cmake --build build_serial --target RUN_TESTS
+

.gitignore

@@ -39,6 +39,9 @@ doc/CodeDocumentation
 *.dSYM
 .DS_Store
 
+# Editor files
+.vscode
+
 # Example and miniapp binaries and outputs
 
 examples/ex[1-9]
@@ -85,6 +88,7 @@ examples/gnuplot_ex20p.inp
 examples/ex22*.mesh
 examples/ex22*.sol
 examples/ex22p_*.*
+examples/exSBP*
 
 examples/sundials/ex9
 examples/sundials/ex1[06]

.travis.yml

@@ -205,6 +205,7 @@ install:
         else
             echo "Reusing cached hypre-2.10.0b/";
         fi;
+        ln -s hypre-2.10.0b hypre;
      else
         echo "Serial build, not using hypre";
      fi

CHANGELOG

@@ -8,22 +8,21 @@
                                http://mfem.org
 
 
-Version 4.0-RC1, Apr 11, 2019
+Version 4.0-RC2, Apr 24, 2019
 =============================
 
 Requirements and Limitations
 ----------------------------
 - This is a release candidate for mfem-4.0.
-- Use at your own risk -- not everything will work, the API may change.
+- Use at your own risk -- not everything will work and the API may change.
 - We are looking for feedback from friendly users.
 - Unlike previous MFEM releases, this version requires a C++11 compiler.
 
 - GPU-related limitations:
-  * NVCC is not supported in the CMake build system yet.
-  * Element batching is currently ignored.
+  * Hypre preconditioners are not yet available in GPU mode.
+  * Only constant coefficients are currently supported on GPUs.
   * Full-assembly (on device), element assembly, and matrix-free bilinear forms
-    are not supported yet.
-  * FunctionCoefficients do not currently work on GPUs.
+    are not supported yet. Element batching is currently ignored.
   * Partial assembly kernels are not implemented yet for simplices.
 
 GPU support
@@ -145,6 +144,10 @@ New and improved solvers and preconditioners
 
 Miscellaneous
 -------------
+- In SparseMatrix added the option to perform MultTranspose() by matvec with
+  computed and stored transpose matrix. This is required for deterministic
+  results when using devices such as CUDA and OpenMP.
+
 - Added unit tests based on the Catch++ library.
 
 - Renamed the option MFEM_USE_OPENMP to MFEM_USE_LEGACY_OPENMP. This legacy

CMakeLists.txt

@@ -86,6 +86,13 @@ include("${CMAKE_CURRENT_SOURCE_DIR}/config/XSDKDefaults.cmake")
 
 # Enable languages.
 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)
+   enable_language(CUDA)
+   message(STATUS "Using CUDA architecture: ${CUDA_ARCH}")
+endif()
+
 if (XSDK_ENABLE_C)
    enable_language(C)
 endif()
@@ -266,6 +273,32 @@ if (MFEM_USE_PUMI)
   endif()
 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 ${CUDA_CCBIN_COMPILER}")
+   set(MFEM_USE_MM YES CACHE BOOL "Enable MFEM's memory manager" FORCE)
+endif()
+
+# OCCA
+if (MFEM_USE_OCCA)
+   find_package(OCCA REQUIRED)
+endif()
+
+# RAJA
+if (MFEM_USE_RAJA)
+   find_package(RAJA REQUIRED)
+endif()
+
 # MFEM_TIMER_TYPE
 if (NOT DEFINED MFEM_TIMER_TYPE)
   if (APPLE)
@@ -291,7 +324,7 @@ endif()
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP BLAS LAPACK METIS HYPRE SuiteSparse SUNDIALS PETSC
     MESQUITE SuperLUDist STRUMPACK AXOM CONDUIT GECKO GNUTLS NETCDF MPFR PUMI
-    POSIXCLOCKS MFEMBacktrace ZLIB)
+    POSIXCLOCKS MFEMBacktrace ZLIB OCCA RAJA)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")
@@ -327,6 +360,13 @@ set(MFEM_SOURCE_DIRS general linalg mesh fem)
 foreach(DIR IN LISTS MFEM_SOURCE_DIRS)
   add_subdirectory(${DIR})
 endforeach()
+
+if (MFEM_USE_CUDA)
+   foreach(file IN LISTS SOURCES)
+      set_property(SOURCE ${file} PROPERTY LANGUAGE CUDA)
+   endforeach()
+endif()
+
 add_subdirectory(config)
 set(MASTER_HEADERS
   ${PROJECT_SOURCE_DIR}/mfem.hpp
@@ -337,6 +377,11 @@ set(CMAKE_INSTALL_RPATH_USE_LINK_PATH ON CACHE BOOL "")
 set(CMAKE_INSTALL_RPATH "${_lib_path}" CACHE PATH "")
 set(CMAKE_INSTALL_NAME_DIR "${_lib_path}" CACHE PATH "")
 
+set(MFEM_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR} CACHE PATH
+    "The MFEM source directory" FORCE)
+set(MFEM_INSTALL_DIR ${CMAKE_INSTALL_PREFIX} CACHE PATH
+    "The MFEM install directory" FORCE)
+
 # Declaring the library
 add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
@@ -434,12 +479,12 @@ endif()
 # Add 'check' target - quick test
 if (NOT MFEM_USE_MPI)
   add_custom_target(check
-    ${CMAKE_CTEST_COMMAND} -R '^ex1_ser' -C ${CMAKE_CFG_INTDIR}
+    ${CMAKE_CTEST_COMMAND} -R \"^ex1_ser\" -C ${CMAKE_CFG_INTDIR}
     USES_TERMINAL)
   add_dependencies(check ex1)
 else()
   add_custom_target(check
-    ${CMAKE_CTEST_COMMAND} -R '^ex1p' -C ${CMAKE_CFG_INTDIR}
+    ${CMAKE_CTEST_COMMAND} -R \"^ex1p\" -C ${CMAKE_CFG_INTDIR}
     USES_TERMINAL)
   add_dependencies(check ex1p)
 endif()
@@ -484,6 +529,13 @@ install(DIRECTORY ${MFEM_SOURCE_DIRS}
   DESTINATION ${INSTALL_INCLUDE_DIR}/mfem
   FILES_MATCHING PATTERN "*.hpp")
 
+# Install the okl files
+if (MFEM_USE_OCCA)
+  install(DIRECTORY ${MFEM_SOURCE_DIRS}
+    DESTINATION ${INSTALL_INCLUDE_DIR}/mfem
+    FILES_MATCHING PATTERN "*.okl")
+endif()
+
 # Install ${HEADERS}
 # ---
 # foreach (HDR ${HEADERS})

CONTRIBUTING.md

@@ -142,6 +142,16 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
   + [`HypreParMatrix`](http://mfem.github.io/doxygen/html/classmfem_1_1HypreParMatrix.html) and [`HypreParVector`](http://mfem.github.io/doxygen/html/classmfem_1_1HypreParVector.html)
   + [`HypreSolver`](http://mfem.github.io/doxygen/html/classmfem_1_1HypreSolver.html) and other [hypre classes](http://mfem.github.io/doxygen/html/hypre_8hpp.html)
 
+- GPU and multi-core CPU support is based on device kernels supporting different
+  backends (CUDA, OCCA, RAJA, OpenMP, etc.) and an internal lightweight
+  device/host memory manager.
+
+- The main device-relevant classes and sources are:
+  + [`Device`](http://mfem.github.io/doxygen/html/device_8hpp.html)
+  + [`MemoryManager`](http://mfem.github.io/doxygen/html/mem_manager_8hpp.html)
+  + the [`MFEM_FORALL`](http://mfem.github.io/doxygen/html/forall_8hpp.html) macro
+  + the [`cuda.hpp`](http://mfem.github.io/doxygen/html/cuda_8hpp.html) and [`occa.hpp`](http://mfem.github.io/doxygen/html/occa_8hpp.html) files
+
 - The `general/` directory contains C++ classes that serve as utilities for
   communication, error handling, arrays, (Boolean) tables, timing, etc.
 

INSTALL

@@ -13,11 +13,17 @@ of MFEM is a (modern) C++ compiler, such as g++. The parallel version of MFEM
 requires an MPI C++ compiler, as well as the following external libraries:
 
 - hypre (a library of high-performance preconditioners)
-  http://www.llnl.gov/CASC/hypre
+  https://github.com/hypre-space/hypre
 
 - METIS (a family of multilevel partitioning algorithms)
   http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
 
+The hypre dependency can be downloaded as a tarball from GitHub or from the
+project webpage https://www.llnl.gov/casc/hypre. For example, the 2.16.0 release
+of hypre is available at
+
+   https://github.com/hypre-space/hypre/archive/v2.16.0.tar.gz
+
 The METIS dependency can be disabled but that is not generally recommended, see
 the option MFEM_USE_METIS.
 
@@ -48,7 +54,7 @@ following package managers:
 
 - Spack, https://github.com/spack/spack
 - OpenHPC, http://openhpc.community
-- Homebrew/Science, https://github.com/Homebrew/homebrew-science
+- Homebrew/Science, https://github.com/Homebrew/homebrew-science (deprecated)
 
 We also recommend downloading and building the MFEM-based GLVis visualization
 tool which can be used to visualize the meshes and solution in MFEM's examples
@@ -60,9 +66,9 @@ Serial build:
    make serial -j 4
 
 Parallel build:
-   (download hypre 2.10.0b and METIS 4 from above URLs)
+   (download hypre and METIS 4 from above URLs)
    (build METIS 4 in ../metis-4.0 relative to mfem/)
-   (build hypre 2.10.0b in ../hypre-2.10.0b relative to mfem/)
+   (build hypre in ../hypre relative to mfem/)
    make parallel -j 4
 
 CUDA build:
@@ -87,13 +93,19 @@ Serial build:
    make -j 4   (assuming "UNIX Makefiles" generator)
 
 Parallel build:
-   (download hypre 2.10.0b and METIS 4 from above URLs)
+   (download hypre and METIS 4 from above URLs)
    (build METIS 4 in ../metis-4.0 relative to mfem/)
-   (build hypre 2.10.0b in ../hypre-2.10.0b relative to mfem/)
+   (build hypre in ../hypre relative to mfem/)
    mkdir <mfem-build-dir> ; cd <mfem-build-dir>
    cmake <mfem-source-dir> -DMFEM_USE_MPI=YES
    make -j 4
 
+CUDA build:
+   (this build requires CMake 3.8 or newer)
+   mkdir <mfem-build-dir> ; cd <mfem-build-dir>
+   cmake <mfem-source-dir> -DMFEM_USE_CUDA=YES
+   make -j 4
+
 Example codes (serial/parallel, depending on the build):
    make examples -j 4
 
@@ -278,6 +290,7 @@ MFEM_THREAD_SAFE = YES/NO
 
 MFEM_USE_LEGACY_OPENMP = YES/NO
    Enable (basic) experimental OpenMP support. Requires MFEM_THREAD_SAFE.
+   This option is deprecated.
 
 MFEM_USE_OPENMP = YES/NO
    Enable the OpenMP backend.
@@ -393,7 +406,8 @@ MFEM_USE_PUMI = YES/NO
 
 MFEM_USE_MM = YES/NO
    Enables support for the MFEM's memory manager (MM), which is required to
-   support devices with different memory spaces.
+   support devices with different memory spaces. This option is required when
+   CUDA support is enabled, i.e. when MFEM_USE_CUDA=YES.
 
 MFEM_USE_CUDA = YES/NO
    Enables support for CUDA devices in MFEM. CUDA is a parallel computing
@@ -406,13 +420,15 @@ MFEM_USE_CUDA = YES/NO
 MFEM_USE_RAJA = YES/NO
    Enable support for the RAJA performance portability layer in MFEM. RAJA
    provides a portable abstraction for loops, supporting different programming
-   model backends. When using the RAJA CUDA backend, MFEM_USE_MM is required.
+   model backends. When using RAJA built with CUDA support, CUDA support must be
+   also enabled in MFEM, i.e. MFEM_USE_CUDA=YES must be set.
 
 MFEM_USE_OCCA = YES/NO
    Enables support for the OCCA library in MFEM. OCCA is an open-source library
    which aims to make it easy to program different types of devices (e.g. CPU,
    GPU, FPGA) by providing an unified API for interacting with JIT-compiled
-   backends. When using the OCCA CUDA backend, MFEM_USE_MM is required.
+   backends. In order to use the OCCA CUDA backend, CUDA support must be enabled
+   in MFEM as well, i.e. MFEM_USE_CUDA=YES must be set.
 
 MFEM_BUILD_TAG = (any value)
    An optional tag to characterize the build. Exported to config/config.mk.
@@ -435,7 +451,7 @@ directory and use the string @MFEM_DIR@, e.g. HYPRE_OPT = -I@MFEM_DIR@/../hypre.
 The specific libraries and their options are:
 
 - HYPRE, required for the parallel build, i.e. when MFEM_USE_MPI = YES.
-  URL: http://www.llnl.gov/CASC/hypre
+  URL: https://github.com/hypre-space/hypre and https://www.llnl.gov/casc/hypre
   Options: HYPRE_OPT, HYPRE_LIB.
 
 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
@@ -645,6 +661,8 @@ Configuration variables (CMake)
 ===============================
 See the configuration file config/defaults.cmake for the default settings.
 
+Note: the option MFEM_USE_CUDA requires CMake version 3.8 or newer!
+
 Non-standard CMake variables for compilers:
    CXX    - If set, overwrite the auto-detected C++ compiler, serial build
    MPICXX - If set, overwrite the auto-detected MPI C++ compiler, parallel build
@@ -675,9 +693,6 @@ MFEM_USE_NETCDF
 MFEM_USE_MPFR
 MFEM_USE_GZSTREAM
 MFEM_USE_PUMI
-
-The following GNU make options are not supported with CMake yet:
-
 MFEM_USE_CUDA
 MFEM_USE_OCCA
 MFEM_USE_RAJA
@@ -728,6 +743,8 @@ The CMake build system adds auto-detection for the following packages/libraries:
  - LIBUNWIND
  - POSIXCLOCKS
  - PUMI
+ - OCCA
+ - RAJA
 
 The following built-in CMake packages are also used:
 

README

@@ -8,9 +8,9 @@
                                http://mfem.org
 
 MFEM is a modular parallel C++ library for finite element methods. Its goal is
-to enable the research and development of scalable finite element discretization
-and solver algorithms through general finite element abstractions, accurate and
-flexible visualization, and tight integration with the hypre library.
+to enable high-performance scalable finite element discretization research and
+application development on a wide variety of platforms, ranging from laptops to
+supercomputers.
 
 * For building instructions, see the file INSTALL, or type "make help".
 
@@ -39,23 +39,24 @@ conforming and non-conforming (AMR) adaptive refinement. Arbitrary element
 transformations, allowing for high-order mesh elements with curved boundaries,
 are also supported.
 
-MFEM is commonly used as a "finite element to linear algebra translator", since
-it can take a problem described in terms of finite element-type objects, and
-produce the corresponding linear algebra vectors and sparse matrices. In order
-to facilitate this, MFEM uses compressed sparse row (CSR) sparse matrix storage
-and includes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES,
-as well as support for sequential sparse direct solvers from the SuiteSparse
+When used as a "finite element to linear algebra translator", MFEM can take a
+problem described in terms of finite element-type objects, and produce the
+corresponding linear algebra vectors and fully or partially assembled operators,
+e.g. in the form of global sparse matrices or matrix-free operators. The library
+includes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES, as
+well as support for sequential sparse direct solvers from the SuiteSparse
 library. Nonlinear solvers (the Newton method), eigensolvers (LOBPCG), and
 several explicit and implicit Runge-Kutta time integrators are also available.
 
 MFEM supports MPI-based parallelism throughout the library, and can readily be
-used as a scalable unstructured finite element problem generator. MFEM-based
-applications require minimal changes to transition from a serial to a
-high-performing parallel version of the code, where they can take advantage of
-the integrated scalable linear solvers from the hypre library. Comprehensive
-support for other external packages, e.g. PETSc and SUNDIALS is also included,
-giving access to many additional linear and nonlinear solvers, preconditioners,
-time integrators, etc.
+used as a scalable unstructured finite element problem generator. As of version
+4.0, MFEM offers initial support for GPU acceleration, and programming models,
+such as CUDA, OCCA, RAJA and OpenMP. MFEM-based applications require minimal
+changes to switch from a serial to a high-performing MPI-parallel version of the
+code, where they can take advantage of the integrated linear solvers from the
+hypre library.  Comprehensive support for other external packages, e.g. PETSc
+and SUNDIALS is also included, giving access to many additional linear and
+nonlinear solvers, preconditioners, time integrators, etc.
 
 For examples of using MFEM, see the examples/ and miniapps/ directories, as well
 as the OpenGL visualization tool GLVis which is available at http://glvis.org.

config/XSDKDefaults.cmake

@@ -74,7 +74,7 @@
 
 IF (NOT COMMAND PRINT_VAR)
   FUNCTION(PRINT_VAR  VAR_NAME)
-    MESSAGE("-- " "${VAR_NAME} = '${${VAR_NAME}}'")
+    MESSAGE(STATUS "${VAR_NAME} = '${${VAR_NAME}}'")
   ENDFUNCTION()
 ENDIF()
 
@@ -166,14 +166,14 @@ IF (USE_XSDK_DEFAULTS)
     ENDIF()
     XSDK_HANDLE_LANG_DEFAULTS(Fortran  FC  "FFLAGS;FCFLAGS")
   ENDIF()
-  
+
   # Set XSDK defaults for other CMake variables
-  
+
   IF ("${BUILD_SHARED_LIBS}"  STREQUAL  "")
     MESSAGE("-- " "XSDK: Setting default BUILD_SHARED_LIBS=TRUE")
     SET(BUILD_SHARED_LIBS  TRUE  CACHE  BOOL  "Set by default in XSDK mode")
   ENDIF()
-  
+
   IF ("${CMAKE_BUILD_TYPE}"  STREQUAL  "")
     MESSAGE("-- " "XSDK: Setting default CMAKE_BUILD_TYPE=DEBUG")
     SET(CMAKE_BUILD_TYPE  DEBUG  CACHE  STRING  "Set by default in XSDK mode")
@@ -181,6 +181,13 @@ IF (USE_XSDK_DEFAULTS)
 
 ENDIF()
 
+
+##################################################################################
+#
+#               MFEM-specific additions: set TPL MFEM_USE_* defaults
+#
+##################################################################################
+
 IF (DEFINED TPL_ENABLE_MPI)
   SET(MFEM_USE_MPI ${TPL_ENABLE_MPI} CACHE BOOL "Enable MPI parallel build" FORCE)
 ENDIF()
@@ -252,3 +259,15 @@ ENDIF()
 IF (DEFINED TPL_ENABLE_PUMI)
   SET(MFEM_USE_PUMI ${TPL_ENABLE_PUMI} CACHE BOOL "Enable PUMI" FORCE)
 ENDIF()
+
+IF (DEFINED TPL_ENABLE_CUDA)
+  SET(MFEM_USE_CUDA ${TPL_ENABLE_CUDA} CACHE BOOL "Enable CUDA" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_OCCA)
+  SET(MFEM_USE_OCCA ${TPL_ENABLE_OCCA} CACHE BOOL "Enable OCCA" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_RAJA)
+  SET(MFEM_USE_RAJA ${TPL_ENABLE_RAJA} CACHE BOOL "Enable RAJA" FORCE)
+ENDIF()

config/cmake/MFEMConfig.cmake.in

@@ -41,6 +41,10 @@ set(MFEM_USE_MPFR @MFEM_USE_MPFR@)
 set(MFEM_USE_SIDRE @MFEM_USE_SIDRE@)
 set(MFEM_USE_CONDUIT @MFEM_USE_CONDUIT@)
 set(MFEM_USE_PUMI @MFEM_USE_PUMI@)
+set(MFEM_USE_MM @MFEM_USE_MM@)
+set(MFEM_USE_CUDA @MFEM_USE_CUDA@)
+set(MFEM_USE_OCCA @MFEM_USE_OCCA@)
+set(MFEM_USE_RAJA @MFEM_USE_RAJA@)
 
 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")
 set(MFEM_CXX_FLAGS "@CMAKE_CXX_FLAGS@")

config/cmake/config.hpp.in

@@ -30,6 +30,12 @@
 #define MFEM_VERSION_MINOR (((MFEM_VERSION)/100)%100)
 #define MFEM_VERSION_PATCH ((MFEM_VERSION)%100)
 
+// MFEM source directory.
+#define MFEM_SOURCE_DIR "@MFEM_SOURCE_DIR@"
+
+// MFEM install directory.
+#define MFEM_INSTALL_DIR "@MFEM_INSTALL_DIR@"
+
 // Description of the git commit used to build MFEM.
 #cmakedefine MFEM_GIT_STRING "@MFEM_GIT_STRING@"
 
@@ -104,6 +110,19 @@
 // Enable MFEM functionality based on the PUMI library
 #cmakedefine MFEM_USE_PUMI
 
+// Build the GPU/CUDA-enabled version of the MFEM library.
+// Requires a CUDA compiler (nvcc).
+#cmakedefine MFEM_USE_CUDA
+
+// Enable MFEM functionality based on the RAJA library
+#cmakedefine MFEM_USE_RAJA
+
+// Enable MFEM functionality based on the OCCA library
+#cmakedefine MFEM_USE_OCCA
+
+// Enable MFEM's internal Memory Manager (needed e.g. for MFEM_USE_CUDA)
+#cmakedefine MFEM_USE_MM
+
 // Which library functions to use in class StopWatch for measuring time.
 // For a list of the available options, see INSTALL.
 // If not defined, an option is selected automatically.

config/cmake/modules/FindOCCA.cmake

@@ -0,0 +1,19 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Defines the following variables:
+#   - OCCA_FOUND
+#   - OCCA_LIBRARIES
+#   - OCCA_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(OCCA OCCA OCCA_DIR "include" "occa.hpp" "lib" "occa"
+  "Paths to headers required by OCCA." "Libraries required by OCCA.")

config/cmake/modules/FindRAJA.cmake

@@ -0,0 +1,30 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Defines the following variables:
+#   - RAJA_FOUND
+#   - RAJA_LIBRARIES
+#   - RAJA_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(RAJA RAJA RAJA_DIR "include" "RAJA/RAJA.hpp" "lib" "RAJA"
+  "Paths to headers required by RAJA." "Libraries required by RAJA.")
+
+if (NOT RAJA_CONFIG_CMAKE)
+   set(RAJA_CONFIG_CMAKE "${RAJA_DIR}/share/raja/cmake/raja-config.cmake")
+endif()
+if (EXISTS "${RAJA_CONFIG_CMAKE}")
+   include("${RAJA_CONFIG_CMAKE}")
+   if (ENABLE_CUDA AND NOT MFEM_USE_CUDA)
+      message(FATAL_ERROR
+         "RAJA is built with CUDA: MFEM_USE_CUDA=YES is required")
+   endif()
+endif()

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -232,10 +232,12 @@ function(mfem_find_package Name Prefix DirVar IncSuffixes Header LibSuffixes
   # If we have the TPL_ versions of _INCLUDE_DIRS and _LIBRARIES then set the
   # standard ${Prefix} versions
   if (TPL_${Prefix}_INCLUDE_DIRS)
-    set(${Prefix}_INCLUDE_DIRS ${TPL_${Prefix}_INCLUDE_DIRS} CACHE STRING "TPL_${Prefix}_INCLUDE_DIRS was found." FORCE)
+    set(${Prefix}_INCLUDE_DIRS ${TPL_${Prefix}_INCLUDE_DIRS} CACHE STRING
+      "TPL_${Prefix}_INCLUDE_DIRS was found." FORCE)
   endif()
   if (TPL_${Prefix}_LIBRARIES)
-    set(${Prefix}_LIBRARIES ${TPL_${Prefix}_LIBRARIES} CACHE STRING "TPL_${Prefix}_LIBRARIES was found." FORCE)
+    set(${Prefix}_LIBRARIES ${TPL_${Prefix}_LIBRARIES} CACHE STRING
+      "TPL_${Prefix}_LIBRARIES was found." FORCE)
   endif()
 
   # Quick return
@@ -718,7 +720,8 @@ function(mfem_export_mk_files)
       MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE
       MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GECKO MFEM_USE_GNUTLS
       MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_MPFR MFEM_USE_SIDRE
-      MFEM_USE_CONDUIT MFEM_USE_PUMI)
+      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_MM MFEM_USE_CUDA MFEM_USE_OCCA
+      MFEM_USE_RAJA)
   foreach(var ${CONFIG_MK_BOOL_VARS})
     if (${var})
       set(${var} YES)
@@ -726,6 +729,7 @@ function(mfem_export_mk_files)
       set(${var} NO)
     endif()
   endforeach()
+  # TODO: Add support for MFEM_USE_CUDA=YES
   set(MFEM_CXX ${CMAKE_CXX_COMPILER})
   set(MFEM_CPPFLAGS "")
   string(STRIP "${CMAKE_CXX_FLAGS_${BUILD_TYPE}} ${CMAKE_CXX_FLAGS}"

config/config.hpp

@@ -56,4 +56,9 @@
 #endif
 #endif // MFEM_USE_MPI not defined
 
+// CUDA requires the memory manager
+#if defined(MFEM_USE_CUDA) && !defined(MFEM_USE_MM)
+#error Building with CUDA (MFEM_USE_CUDA=YES) requires MFEM_USE_MM=YES
+#endif
+
 #endif // MFEM_CONFIG_HPP

config/defaults.cmake

@@ -42,6 +42,10 @@ option(MFEM_USE_MPFR "Enable MPFR usage." OFF)
 option(MFEM_USE_SIDRE "Enable Axom/Sidre usage" OFF)
 option(MFEM_USE_CONDUIT "Enable Conduit usage" OFF)
 option(MFEM_USE_PUMI "Enable PUMI" OFF)
+option(MFEM_USE_MM "Enable MFEM's memory manager" OFF)
+option(MFEM_USE_CUDA "Enable CUDA" OFF)
+option(MFEM_USE_OCCA "Enable OCCA" OFF)
+option(MFEM_USE_RAJA "Enable RAJA" OFF)
 
 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")
 
@@ -59,13 +63,16 @@ option(MFEM_ENABLE_MINIAPPS "Build all of the miniapps" OFF)
 # set(CXX g++)
 # set(MPICXX mpicxx)
 
+# Set the target CUDA architecture
+set(CUDA_ARCH "sm_60" CACHE STRING "Target CUDA architecture.")
+
 set(MFEM_DIR ${CMAKE_CURRENT_SOURCE_DIR})
 
 # The *_DIR paths below will be the first place searched for the corresponding
 # headers and library. If these fail, then standard cmake search is performed.
 # Note: if the variables are already in the cache, they are not overwritten.
 
-set(HYPRE_DIR "${MFEM_DIR}/../hypre-2.10.0b/src/hypre" CACHE PATH
+set(HYPRE_DIR "${MFEM_DIR}/../hypre/src/hypre" CACHE PATH
     "Path to the hypre library.")
 # If hypre was compiled to depend on BLAS and LAPACK:
 # set(HYPRE_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
@@ -154,6 +161,9 @@ set(Axom_REQUIRED_PACKAGES "Conduit/relay" CACHE STRING
 set(PUMI_DIR "${MFEM_DIR}/../pumi-2.1.0" CACHE STRING
     "Directory where PUMI is installed")
 
+set(OCCA_DIR "${MFEM_DIR}/../occa" CACHE PATH "Path to OCCA")
+set(RAJA_DIR "${MFEM_DIR}/../raja" CACHE PATH "Path to RAJA")
+
 set(BLAS_INCLUDE_DIRS "" CACHE STRING "Path to BLAS headers.")
 set(BLAS_LIBRARIES "" CACHE STRING "The BLAS library.")
 set(LAPACK_INCLUDE_DIRS "" CACHE STRING "Path to LAPACK headers.")

config/defaults.mk

@@ -136,7 +136,7 @@ LIBUNWIND_OPT = -g
 LIBUNWIND_LIB = $(if $(NOTMAC),-lunwind -ldl,)
 
 # HYPRE library configuration (needed to build the parallel version)
-HYPRE_DIR = @MFEM_DIR@/../hypre-2.10.0b/src/hypre
+HYPRE_DIR = @MFEM_DIR@/../hypre/src/hypre
 HYPRE_OPT = -I$(HYPRE_DIR)/include
 HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
 
@@ -300,19 +300,17 @@ PUMI_OPT = -I$(PUMI_DIR)/include
 PUMI_LIB = -L$(PUMI_DIR)/lib -lpumi -lcrv -lma -lmds -lapf -lpcu -lgmi -lparma\
    -llion -lmth -lapf_zoltan -lspr
 
-# CUDA library configuration. Since we compile and link with nvcc (when CUDA is
-# enabled) we only need to explicitly link with the CUDA driver, libcuda.*,
-# which is usually in a system path.
+# CUDA library configuration (currently not needed)
 CUDA_OPT =
-CUDA_LIB = $(if $(NOTMAC),,-L/usr/local/cuda/lib) -lcuda
+CUDA_LIB =
 
 # OCCA library configuration
-OCCA_DIR ?= @MFEM_DIR@/../occa
+OCCA_DIR = @MFEM_DIR@/../occa
 OCCA_OPT = -I$(OCCA_DIR)/include
 OCCA_LIB = $(XLINKER)-rpath,$(OCCA_DIR)/lib -L$(OCCA_DIR)/lib -locca
 
 # RAJA library configuration
-RAJA_DIR ?= @MFEM_DIR@/../raja
+RAJA_DIR = @MFEM_DIR@/../raja
 RAJA_OPT = -I$(RAJA_DIR)/include
 ifdef CUB_DIR
    RAJA_OPT += -I$(CUB_DIR)

config/sample-runs.sh

@@ -18,6 +18,8 @@ run_prefix=""
 run_vg="valgrind --leak-check=full --show-reachable=yes --track-origins=yes"
 run_suffix="-no-vis"
 skip_gen_meshes="yes"
+# filter-out device runs ("no") or non-device runs ("yes"):
+device_runs="no"
 cur_dir="${PWD}"
 mfem_dir="$(cd "$(dirname "$0")"/.. && pwd)"
 mfem_build_dir=""
@@ -148,6 +150,11 @@ function extract_sample_runs()
    if [ "$skip_gen_meshes" == "yes" ]; then
       runs=`printf "%s" "$runs" | grep -v ".* -m .*\.gen"`
    fi
+   if [ "$device_runs" == "yes" ]; then
+      runs=`printf "%s" "$runs" | grep ".* -d .*"`
+   else
+      runs=`printf "%s" "$runs" | grep -v ".* -d .*"`
+   fi
    IFS=$'\n'
    runs=(${runs})
    IFS="${old_IFS}"
@@ -169,6 +176,9 @@ function help_message()
       -g <dir> <pattern>
                   Specify explicitly a group (dir + file pattern) to run; This
                   option can be used multiple times to define multiple groups
+      -dev        configure only sample runs using devices.
+                  To test with a parallel build, the parallel (-p|-par) option
+                  should be set first on the command line.
       -v          Enable valgrind
       -o <dir>    [${output_dir:-"<empty>: output goes to stdout"}]
                   If not empty, save output to files inside <dir>
@@ -253,7 +263,7 @@ case "$1" in
    -h|-help)
       opt_help="yes"
       ;;
-   -p|-parallel)
+   -p|-par)
       mfem_config="MFEM_USE_MPI=YES MFEM_DEBUG=NO"
       ;;
    -g)
@@ -264,6 +274,11 @@ case "$1" in
       groups=("${groups[@]}" "${test_group}")
       shift 2
       ;;
+   -dev)
+       device_runs="yes"
+       mfem_config+=" MFEM_USE_CUDA=YES MFEM_USE_MM=YES \
+MFEM_USE_OCCA=YES MFEM_USE_RAJA=YES MFEM_USE_OPENMP=YES"
+      ;;
    -v)
       valgrind="yes"
       ;;
@@ -294,6 +309,10 @@ case "$1" in
    -n)
       run_prefix="echo"
       ;;
+   -*)
+      echo "unknown option: '$1'"
+      exit 1
+      ;;
    *=*)
       eval $1
       ;;

doc/CodeDocumentation.dox

@@ -35,6 +35,10 @@ namespace mfem {
  * - HypreParMatrix and HypreParVector
  * - HypreSolver and other \link hypre.hpp hypre classes\endlink
  *
+ * <H3>Main GPU classes</H3>
+ * - Device
+ * - MemoryManager
+ *
  * <H3>Example codes</H3>
  * - <a class="el" href="examples_2ex1_8cpp_source.html">Example 1</a>: nodal H1 FEM for the Laplace problem
  * - <a class="el" href="examples_2ex1p_8cpp_source.html">Example 1p</a>: parallel nodal H1 FEM for the Laplace problem

examples/CMakeLists.txt

@@ -27,7 +27,6 @@ list(APPEND ALL_EXE_SRCS
   ex18.cpp
   ex19.cpp
   ex20.cpp
-  ex21.cpp
   ex22.cpp
   )
 
@@ -53,7 +52,6 @@ if (MFEM_USE_MPI)
     ex18p.cpp
     ex19p.cpp
     ex20p.cpp
-    ex21p.cpp
     ex22p.cpp
     )
 endif()

examples/ex1.cpp

@@ -26,12 +26,12 @@
 //               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 -m ../data/beam-hex.mesh -pa -d cuda
+//               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 -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Laplace problem

examples/ex1p.cpp

@@ -26,9 +26,9 @@
 //               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 cuda
+//               mpirun -np 4 ex1p -pa -d occa-cuda
+//               mpirun -np 4 ex1p -pa -d raja-omp
 //
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Laplace problem

examples/ex21.cpp

@@ -1,477 +0,0 @@
-//                               MFEM Example 21
-//
-// Compile with: make ex21
-//
-// Sample runs:  ex21 -m ../data/inline-segment.mesh -o 3
-//               ex21 -m ../data/inline-tri.mesh -o 3
-//               ex21 -m ../data/inline-quad.mesh -o 3
-//               ex21 -m ../data/inline-quad.mesh -o 3 -p 1
-//               ex21 -m ../data/inline-quad.mesh -o 3 -p 2
-//               ex21 -m ../data/inline-tet.mesh -o 2
-//               ex21 -m ../data/inline-hex.mesh -o 2
-//               ex21 -m ../data/inline-hex.mesh -o 2 -p 1
-//               ex21 -m ../data/inline-hex.mesh -o 2 -p 2
-//               ex21 -m ../data/star.mesh -o 2 -sigma 10.0
-//
-// Description:  This example code demonstrates the use of MFEM to define and
-//               solve simple complex-valued linear systems.  We implement three
-//               variants of a damped harmonic oscillator:
-//
-//               1) A scalar H1 field
-//                  -Div(a Grad u) - omega^2 b u + i omega c u = 0
-//
-//               2) A vector H(Curl) field
-//                  Curl(a Curl u) - omega^2 b u + i omega c u = 0
-//
-//               3) A vector H(Div) field
-//                  -Grad(a Div u) - omega^2 b u + i omega c u = 0
-//
-//               In each case the field is driven by a forced oscillation, with
-//               angular frequency omega, imposed at the boundary or a portion
-//               of the boundary.
-//
-//               In electromagnetics the coefficients are typically named the
-//               permeability, mu = 1/a, permittivity, epsilon = b, and
-//               conductivity, sigma = c.  The user can specify these constants
-//               using either set of names.
-//
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-
-using namespace std;
-using namespace mfem;
-
-static double mu_ = 1.0;
-static double epsilon_ = 1.0;
-static double sigma_ = 20.0;
-static double omega_ = 10.0;
-
-double u0_real_exact(const Vector &);
-double u0_imag_exact(const Vector &);
-
-void u1_real_exact(const Vector &, Vector &);
-void u1_imag_exact(const Vector &, Vector &);
-
-void u2_real_exact(const Vector &, Vector &);
-void u2_imag_exact(const Vector &, Vector &);
-
-bool check_for_inline_mesh(const char * mesh_file);
-
-int main(int argc, char *argv[])
-{
-   // 1. Parse command-line options.
-   const char *mesh_file = "../data/inline-quad.mesh";
-   int ref_levels = 0;
-   int order = 1;
-   int prob = 0;
-   double freq = -1.0;
-   double a_coef = 0.0;
-   bool visualization = 1;
-   bool herm_conv = true;
-   bool exact_sol = true;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&ref_levels, "-r", "--refine",
-                  "Number of times to refine the mesh uniformly.");
-   args.AddOption(&order, "-o", "--order",
-                  "Finite element order (polynomial degree).");
-   args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose from 0: H_1, 1: H(Curl), or 2: H(Div) "
-                  "damped harmonic oscillator.");
-   args.AddOption(&a_coef, "-a", "--stiffness-coef",
-                  "Stiffness coefficient (spring constant or 1/mu).");
-   args.AddOption(&epsilon_, "-b", "--mass-coef",
-                  "Mass coefficient (or epsilon).");
-   args.AddOption(&sigma_, "-c", "--damping-coef",
-                  "Damping coefficient (or sigma).");
-   args.AddOption(&mu_, "-mu", "--permeability",
-                  "Permeability of free space (or 1/(spring constant)).");
-   args.AddOption(&epsilon_, "-eps", "--permittivity",
-                  "Permittivity of free space (or mass constant).");
-   args.AddOption(&sigma_, "-sigma", "--conductivity",
-                  "Conductivity (or damping constant).");
-   args.AddOption(&freq, "-f", "--frequency",
-                  "Frequency (in Hz).");
-   args.AddOption(&herm_conv, "-herm", "--hermitian", "-no-herm",
-                  "--no-hermitian", "Use convention for Hermitian operators.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   args.PrintOptions(cout);
-
-   if ( a_coef != 0.0 )
-   {
-      mu_ = 1.0 / a_coef;
-   }
-   if ( freq > 0.0 )
-   {
-      omega_ = 2.0 * M_PI * freq;
-   }
-
-   exact_sol = check_for_inline_mesh(mesh_file);
-   if (exact_sol)
-   {
-      cout << "Identified an 'inline' mesh" << endl;
-   }
-
-   ComplexOperator::Convention conv =
-      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;
-
-   // 2. 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
-   //    '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++)
-   {
-      mesh->UniformRefinement();
-   }
-
-   // 4. 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 )
-   {
-      cout << "Switching to problem type 0, H1 basis functions, "
-           << "for 1 dimensional mesh." << endl;
-      prob = 0;
-   }
-
-   FiniteElementCollection *fec;
-   switch (prob)
-   {
-      case 0:  fec = new H1_FECollection(order, dim);      break;
-      case 1:  fec = new ND_FECollection(order, dim);      break;
-      case 2:  fec = new RT_FECollection(order - 1, dim);  break;
-   }
-   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
-   cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
-        << endl;
-
-   // 5. 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;
-   Array<int> ess_bdr;
-   if (mesh->bdr_attributes.Size())
-   {
-      ess_bdr.SetSize(mesh->bdr_attributes.Max());
-      ess_bdr = 1;
-      if (exact_sol)
-      {
-         switch (prob)
-         {
-            case 0:   ess_bdr = 0; ess_bdr[0] = 1;  break;
-            default:  ess_bdr = 1; ess_bdr[2] = 0;  break;
-         }
-      }
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-   }
-
-   // 6. 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 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);
-   ComplexGridFunction * u_exact = NULL;
-   if (exact_sol) { u_exact = new ComplexGridFunction(fespace); }
-
-   FunctionCoefficient u0_r(u0_real_exact);
-   FunctionCoefficient u0_i(u0_imag_exact);
-   VectorFunctionCoefficient u1_r(dim, u1_real_exact);
-   VectorFunctionCoefficient u1_i(dim, u1_imag_exact);
-   VectorFunctionCoefficient u2_r(dim, u2_real_exact);
-   VectorFunctionCoefficient u2_i(dim, u2_imag_exact);
-
-   ConstantCoefficient zeroCoef(0.0);
-   ConstantCoefficient oneCoef(1.0);
-
-   Vector zeroVec(dim); zeroVec = 0.0;
-   Vector  oneVec(dim);  oneVec = 0.0; oneVec[(prob==2)?(dim-1):0] = 1.0;
-   VectorConstantCoefficient zeroVecCoef(zeroVec);
-   VectorConstantCoefficient oneVecCoef(oneVec);
-
-   switch (prob)
-   {
-      case 0:
-         u.ProjectBdrCoefficient(oneCoef, zeroCoef, ess_bdr);
-         if (exact_sol) { u_exact->ProjectCoefficient(u0_r, u0_i); }
-         break;
-      case 1:
-         u.ProjectBdrCoefficientTangent(oneVecCoef, zeroVecCoef, ess_bdr);
-         if (exact_sol) { u_exact->ProjectCoefficient(u1_r, u1_i); }
-         break;
-      case 2:
-         u.ProjectBdrCoefficientNormal(oneVecCoef, zeroVecCoef, ess_bdr);
-         if (exact_sol) { u_exact->ProjectCoefficient(u2_r, u2_i); }
-         break;
-   }
-
-   if (visualization && exact_sol)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
-      sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
-      sol_sock_r << "solution\n" << *mesh << u_exact->real()
-                 << "window_title 'Exact Real Part'" << flush;
-      sol_sock_i << "solution\n" << *mesh << u_exact->imag()
-                 << "window_title 'Exact Imaginary Part'" << flush;
-   }
-
-   // 8. Set up the sesquilinear form a(.,.) on the finite element
-   //    space corresponding to the damped harmonic oscillator operator
-   //    of the appropriate type:
-   //
-   //    0) A scalar H1 field
-   //       -Div(a Grad) - omega^2 b + i omega c
-   //
-   //    1) A vector H(Curl) field
-   //       Curl(a Curl) - omega^2 b + i omega c
-   //
-   //    2) A vector H(Div) field
-   //       -Grad(a Div) - omega^2 b + i omega c
-   //
-   ConstantCoefficient stiffnessCoef(1.0/mu_);
-   ConstantCoefficient massCoef(-omega_ * omega_ * epsilon_);
-   ConstantCoefficient lossCoef(omega_ * sigma_);
-   ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);
-
-   SesquilinearForm *a = new SesquilinearForm(fespace, conv);
-   switch (prob)
-   {
-      case 0:
-         a->AddDomainIntegrator(new DiffusionIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new MassIntegrator(massCoef),
-                                new MassIntegrator(lossCoef));
-         break;
-      case 1:
-         a->AddDomainIntegrator(new CurlCurlIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
-         break;
-      case 2:
-         a->AddDomainIntegrator(new DivDivIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
-         break;
-   }
-
-   // 9. Assemble the bilinear form and the corresponding linear
-   //    system, applying any necessary transformations such as:
-   //    assembly, eliminating boundary conditions, applying conforming
-   //    constraints for non-conforming AMR, etc.
-   a->Assemble();
-
-   OperatorHandle A;
-   Vector B, U;
-
-   a->FormLinearSystem(ess_tdof_list, u, b, A, U, B);
-   u = 0.0;
-   U = 0.0;
-
-   {
-      ComplexSparseMatrix * Asp =
-         dynamic_cast<ComplexSparseMatrix*>(A.Ptr());
-
-      cout << "Size of linear system: "
-           << 2 * Asp->real().Width() << endl << endl;
-   }
-
-   // 10. Define and apply a GMRES solver for AU=B.
-   {
-      GMRESSolver gmres;
-      gmres.SetOperator(*A.Ptr());
-      gmres.SetRelTol(1e-12);
-      gmres.SetMaxIter(1000);
-      gmres.SetPrintLevel(1);
-      gmres.Mult(B, U);
-   }
-
-   // 11. Recover the solution as a finite element grid function and
-   //     compute the errors if the exact solution is known.
-   a->RecoverFEMSolution(U, b, u);
-
-   if (exact_sol)
-   {
-      double err_r = -1.0;
-      double err_i = -1.0;
-
-      switch (prob)
-      {
-         case 0:
-            err_r = u.real().ComputeL2Error(u0_r);
-            err_i = u.imag().ComputeL2Error(u0_i);
-            break;
-         case 1:
-            err_r = u.real().ComputeL2Error(u1_r);
-            err_i = u.imag().ComputeL2Error(u1_i);
-            break;
-         case 2:
-            err_r = u.real().ComputeL2Error(u2_r);
-            err_i = u.imag().ComputeL2Error(u2_i);
-            break;
-      }
-
-      cout << endl;
-      cout << "|| Re (u_h - u) ||_{L^2} = " << err_r << endl;
-      cout << "|| Im (u_h - u) ||_{L^2} = " << err_i << endl;
-      cout << endl;
-   }
-
-   // 12. 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");
-      mesh_ofs.precision(8);
-      mesh->Print(mesh_ofs);
-
-      ofstream sol_r_ofs("sol_r.gf");
-      ofstream sol_i_ofs("sol_i.gf");
-      sol_r_ofs.precision(8);
-      sol_i_ofs.precision(8);
-      u.real().Save(sol_r_ofs);
-      u.imag().Save(sol_i_ofs);
-   }
-
-   // 13. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
-      sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
-      sol_sock_r << "solution\n" << *mesh << u.real()
-                 << "window_title 'Comp Real Part'" << flush;
-      sol_sock_i << "solution\n" << *mesh << u.imag()
-                 << "window_title 'Comp Imaginary Part'" << flush;
-   }
-   if (visualization && exact_sol)
-   {
-      *u_exact -= u;
-
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
-      sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
-      sol_sock_r << "solution\n" << *mesh << u_exact->real()
-                 << "window_title 'Exact-Comp Real Part'" << flush;
-      sol_sock_i << "solution\n" << *mesh << u_exact->imag()
-                 << "window_title 'Exact-Comp Imaginary Part'" << flush;
-   }
-   if (visualization)
-   {
-      GridFunction u_t(fespace);
-      u_t = u.real();
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock(vishost, visport);
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << *mesh << u_t
-               << "window_title 'Harmonic Solution (t = 0.0 T)'"
-               << "pause\n" << flush;
-
-      cout << "GLVis visualization paused."
-           << " Press space (in the GLVis window) to resume it.\n";
-      int num_frames = 32;
-      int i = 0;
-      while (sol_sock)
-      {
-         double t = (double)(i % num_frames) / num_frames;
-         ostringstream oss;
-         oss << "Harmonic Solution (t = " << t << " T)";
-
-         add(cos( 2.0 * M_PI * t), u.real(),
-             sin(-2.0 * M_PI * t), u.imag(), u_t);
-         sol_sock << "solution\n" << *mesh << u_t
-                  << "window_title '" << oss.str() << "'" << flush;
-         i++;
-      }
-   }
-
-   // 14. Free the used memory.
-   delete a;
-   delete u_exact;
-   delete fespace;
-   delete fec;
-   delete mesh;
-
-   return 0;
-}
-
-bool check_for_inline_mesh(const char * mesh_file)
-{
-   string file(mesh_file);
-   size_t p0 = file.find_last_of("/");
-   string s0 = file.substr((p0==string::npos)?0:(p0+1),7);
-   return s0 == "inline-";
-}
-
-complex<double> u0_exact(const Vector &x)
-{
-   int dim = x.Size();
-   complex<double> i(0.0, 1.0);
-   complex<double> alpha = (epsilon_ * omega_ - i * sigma_);
-   complex<double> kappa = std::sqrt(mu_ * omega_* alpha);
-   return std::exp(-i * kappa * x[dim - 1]);
-}
-
-double u0_real_exact(const Vector &x)
-{
-   return u0_exact(x).real();
-}
-
-double u0_imag_exact(const Vector &x)
-{
-   return u0_exact(x).imag();
-}
-
-void u1_real_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[0] = u0_real_exact(x);
-}
-
-void u1_imag_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[0] = u0_imag_exact(x);
-}
-
-void u2_real_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[dim-1] = u0_real_exact(x);
-}
-
-void u2_imag_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[dim-1] = u0_imag_exact(x);
-}

examples/ex21p.cpp

@@ -1,658 +0,0 @@
-//                       MFEM Example 21 - Parallel Version
-//
-// Compile with: make ex21p
-//
-// Sample runs:  mpirun -np 4 ex21p -m ../data/inline-segment.mesh -o 3
-//               mpirun -np 4 ex21p -m ../data/inline-tri.mesh -o 3
-//               mpirun -np 4 ex21p -m ../data/inline-quad.mesh -o 3
-//               mpirun -np 4 ex21p -m ../data/inline-quad.mesh -o 3 -p 1
-//               mpirun -np 4 ex21p -m ../data/inline-quad.mesh -o 3 -p 2
-//               mpirun -np 4 ex21p -m ../data/inline-tet.mesh -o 2
-//               mpirun -np 4 ex21p -m ../data/inline-hex.mesh -o 2
-//               mpirun -np 4 ex21p -m ../data/inline-hex.mesh -o 2 -p 1
-//               mpirun -np 4 ex21p -m ../data/inline-hex.mesh -o 2 -p 2
-//               mpirun -np 4 ex21p -m ../data/star.mesh -o 2 -sigma 10.0
-//
-// Description:  This example code demonstrates the use of MFEM to define and
-//               solve simple complex-valued linear systems.  We implement three
-//               variants of a damped harmonic oscillator:
-//
-//               1) A scalar H1 field
-//                  -Div(a Grad u) - omega^2 b u + i omega c u = 0
-//
-//               2) A vector H(Curl) field
-//                  Curl(a Curl u) - omega^2 b u + i omega c u = 0
-//
-//               3) A vector H(Div) field
-//                  -Grad(a Div u) - omega^2 b u + i omega c u = 0
-//
-//               In each case the field is driven by a forced oscillation, with
-//               angular frequency omega, imposed at the boundary or a portion
-//               of the boundary.
-//
-//               In electromagnetics the coefficients are typically named the
-//               permeability, mu = 1/a, permittivity, epsilon = b, and
-//               conductivity, sigma = c.  The user can specify these constants
-//               using either set of names.
-//
-//#define MFEM_STRUMPACK_SRC
-
-#include <fstream>
-#include <iostream>
-#include "mfem.hpp"
-
-using namespace std;
-using namespace mfem;
-
-static double mu_ = 1.0;
-static double epsilon_ = 1.0;
-static double sigma_ = 20.0;
-static double omega_ = 10.0;
-
-double u0_real_exact(const Vector &);
-double u0_imag_exact(const Vector &);
-
-void u1_real_exact(const Vector &, Vector &);
-void u1_imag_exact(const Vector &, Vector &);
-
-void u2_real_exact(const Vector &, Vector &);
-void u2_imag_exact(const Vector &, Vector &);
-
-bool check_for_inline_mesh(const char * mesh_file);
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI.
-   int num_procs, myid;
-   MPI_Init(&argc, &argv);
-   MPI_Comm comm = MPI_COMM_WORLD;
-   MPI_Comm_size(comm, &num_procs);
-   MPI_Comm_rank(comm, &myid);
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../data/inline-quad.mesh";
-   int ser_ref_levels = 1;
-   int par_ref_levels = 1;
-   int order = 1;
-   int prob = 0;
-   double freq = -1.0;
-   double a_coef = 0.0;
-   bool visualization = 1;
-   bool herm_conv = true;
-   bool exact_sol = true;
-#ifdef MFEM_USE_STRUMPACK
-   bool strumpack = false;
-#endif
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
-                  "Number of times to refine the mesh uniformly in serial.");
-   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
-                  "Number of times to refine the mesh uniformly in parallel.");
-   args.AddOption(&order, "-o", "--order",
-                  "Finite element order (polynomial degree).");
-   args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose from 0: H_1, 1: H(Curl), or 2: H(Div) "
-                  "damped harmonic oscillator.");
-   args.AddOption(&a_coef, "-a", "--stiffness-coef",
-                  "Stiffness coefficient (spring constant or 1/mu).");
-   args.AddOption(&epsilon_, "-b", "--mass-coef",
-                  "Mass coefficient (or epsilon).");
-   args.AddOption(&sigma_, "-c", "--damping-coef",
-                  "Damping coefficient (or sigma).");
-   args.AddOption(&mu_, "-mu", "--permeability",
-                  "Permeability of free space (or 1/(spring constant)).");
-   args.AddOption(&epsilon_, "-eps", "--permittivity",
-                  "Permittivity of free space (or mass constant).");
-   args.AddOption(&sigma_, "-sigma", "--conductivity",
-                  "Conductivity (or damping constant).");
-   args.AddOption(&freq, "-f", "--frequency",
-                  "Frequency (in Hz).");
-#ifdef MFEM_USE_STRUMPACK
-   args.AddOption(&strumpack, "-strumpack", "--strumpack-solver",
-                  "-no-strumpack", "--no-strumpack-solver",
-                  "Use STRUMPACK's double complex linear solver.");
-#endif
-   args.AddOption(&herm_conv, "-herm", "--hermitian", "-no-herm",
-                  "--no-hermitian", "Use convention for Hermitian operators.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.Parse();
-   if (!args.Good())
-   {
-      if (myid == 0)
-      {
-         args.PrintUsage(cout);
-      }
-      MPI_Finalize();
-      return 1;
-   }
-   if (myid == 0)
-   {
-      args.PrintOptions(cout);
-   }
-
-   if ( a_coef != 0.0 )
-   {
-      mu_ = 1.0 / a_coef;
-   }
-   if ( freq > 0.0 )
-   {
-      omega_ = 2.0 * M_PI * freq;
-   }
-
-   exact_sol = check_for_inline_mesh(mesh_file);
-   if (myid == 0 && exact_sol)
-   {
-      cout << "Identified an 'inline' mesh" << endl;
-   }
-
-   ComplexOperator::Convention conv =
-      herm_conv ? ComplexOperator::HERMITIAN : ComplexOperator::BLOCK_SYMMETRIC;
-
-   // 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);
-   int dim = mesh->Dimension();
-
-   // 4. 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
-   //    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;
-   for (int l = 0; l < par_ref_levels; l++)
-   {
-      pmesh->UniformRefinement();
-   }
-
-   // 6. 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 )
-   {
-      if (myid == 0)
-      {
-         cout << "Switching to problem type 0, H1 basis functions, "
-              << "for 1 dimensional mesh." << endl;
-      }
-      prob = 0;
-   }
-
-   FiniteElementCollection *fec;
-   switch (prob)
-   {
-      case 0:  fec = new H1_FECollection(order, dim);      break;
-      case 1:  fec = new ND_FECollection(order, dim);      break;
-      case 2:  fec = new RT_FECollection(order - 1, dim);  break;
-   }
-   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
-   //    based on the type of mesh and the problem type.
-   Array<int> ess_tdof_list;
-   Array<int> ess_bdr;
-   if (pmesh->bdr_attributes.Size())
-   {
-      ess_bdr.SetSize(pmesh->bdr_attributes.Max());
-      ess_bdr = 1;
-      if (exact_sol)
-      {
-         switch (prob)
-         {
-            case 0:   ess_bdr = 0; ess_bdr[0] = 1;  break;
-            default:  ess_bdr = 1; ess_bdr[2] = 0;  break;
-         }
-      }
-      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.
-   ParComplexLinearForm b(fespace, conv);
-   b.Vector::operator=(0.0);
-
-   // 9. Define the solution vector u as a parallel 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); }
-
-   FunctionCoefficient u0_r(u0_real_exact);
-   FunctionCoefficient u0_i(u0_imag_exact);
-   VectorFunctionCoefficient u1_r(dim, u1_real_exact);
-   VectorFunctionCoefficient u1_i(dim, u1_imag_exact);
-   VectorFunctionCoefficient u2_r(dim, u2_real_exact);
-   VectorFunctionCoefficient u2_i(dim, u2_imag_exact);
-
-   ConstantCoefficient zeroCoef(0.0);
-   ConstantCoefficient oneCoef(1.0);
-
-   Vector zeroVec(dim); zeroVec = 0.0;
-   Vector  oneVec(dim);  oneVec = 0.0; oneVec[(prob==2)?(dim-1):0] = 1.0;
-   VectorConstantCoefficient zeroVecCoef(zeroVec);
-   VectorConstantCoefficient oneVecCoef(oneVec);
-
-   switch (prob)
-   {
-      case 0:
-         u.ProjectBdrCoefficient(oneCoef, zeroCoef, ess_bdr);
-         if (exact_sol) { u_exact->ProjectCoefficient(u0_r, u0_i); }
-         break;
-      case 1:
-         u.ProjectBdrCoefficientTangent(oneVecCoef, zeroVecCoef, ess_bdr);
-         if (exact_sol) { u_exact->ProjectCoefficient(u1_r, u1_i); }
-         break;
-      case 2:
-         u.ProjectBdrCoefficientNormal(oneVecCoef, zeroVecCoef, ess_bdr);
-         if (exact_sol) { u_exact->ProjectCoefficient(u2_r, u2_i); }
-         break;
-   }
-
-   if (visualization && exact_sol)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
-      sol_sock_r << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
-      sol_sock_r << "solution\n" << *pmesh << u_exact->real()
-                 << "window_title 'Exact Real Part'" << flush;
-      sol_sock_i << "solution\n" << *pmesh << u_exact->imag()
-                 << "window_title 'Exact Imaginary Part'" << flush;
-   }
-
-   // 10. Set up the parallel sesquilinear form a(.,.) on the finite element
-   //     space corresponding to the damped harmonic oscillator operator
-   //     of the appropriate type:
-   //
-   //     0) A scalar H1 field
-   //        -Div(a Grad) - omega^2 b + i omega c
-   //
-   //     1) A vector H(Curl) field
-   //        Curl(a Curl) - omega^2 b + i omega c
-   //
-   //     2) A vector H(Div) field
-   //        -Grad(a Div) - omega^2 b + i omega c
-   //
-   ConstantCoefficient stiffnessCoef(1.0/mu_);
-   ConstantCoefficient massCoef(-omega_ * omega_ * epsilon_);
-   ConstantCoefficient lossCoef(omega_ * sigma_);
-   ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);
-
-   ParSesquilinearForm *a = new ParSesquilinearForm(fespace, conv);
-   switch (prob)
-   {
-      case 0:
-         a->AddDomainIntegrator(new DiffusionIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new MassIntegrator(massCoef),
-                                new MassIntegrator(lossCoef));
-         break;
-      case 1:
-         a->AddDomainIntegrator(new CurlCurlIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
-         break;
-      case 2:
-         a->AddDomainIntegrator(new DivDivIntegrator(stiffnessCoef),
-                                NULL);
-         a->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef),
-                                new VectorFEMassIntegrator(lossCoef));
-         break;
-   }
-
-   // 10a. Set up the parallel bilinear form for the preconditioner
-   //      corresponding to the appropriate operator if the STRUMPACK solver
-   //      has not been selected.
-   //
-   //      0) A scalar H1 field
-   //         -Div(a Grad) - omega^2 b + omega c
-   //
-   //      1) A vector H(Curl) field
-   //         Curl(a Curl) + omega^2 b + omega c
-   //
-   //      2) A vector H(Div) field
-   //         -Grad(a Div) - omega^2 b + omega c
-   //
-   ParBilinearForm *pcOp = NULL;
-#ifdef MFEM_USE_STRUMPACK
-   if (!strumpack)
-#endif
-   {
-      pcOp = new ParBilinearForm(fespace);
-      switch (prob)
-      {
-         case 0:
-            pcOp->AddDomainIntegrator(new DiffusionIntegrator(stiffnessCoef));
-            pcOp->AddDomainIntegrator(new MassIntegrator(massCoef));
-            pcOp->AddDomainIntegrator(new MassIntegrator(lossCoef));
-            break;
-         case 1:
-            pcOp->AddDomainIntegrator(new CurlCurlIntegrator(stiffnessCoef));
-            pcOp->AddDomainIntegrator(new VectorFEMassIntegrator(negMassCoef));
-            pcOp->AddDomainIntegrator(new VectorFEMassIntegrator(lossCoef));
-            break;
-         case 2:
-            pcOp->AddDomainIntegrator(new DivDivIntegrator(stiffnessCoef));
-            pcOp->AddDomainIntegrator(new VectorFEMassIntegrator(massCoef));
-            pcOp->AddDomainIntegrator(new VectorFEMassIntegrator(lossCoef));
-            break;
-      }
-   }
-
-   // 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, etc.
-   a->Assemble();
-   if (pcOp) { pcOp->Assemble(); }
-
-   OperatorHandle A;
-   Vector B, U;
-
-   a->FormLinearSystem(ess_tdof_list, u, b, A, U, B);
-   u = 0.0;
-   U = 0.0;
-
-   OperatorHandle PCOp;
-   if (pcOp) { pcOp->FormSystemMatrix(ess_tdof_list, PCOp); }
-
-   if (myid == 0)
-   {
-      ComplexHypreParMatrix * Ahyp =
-         dynamic_cast<ComplexHypreParMatrix*>(A.Ptr());
-
-      cout << "Size of linear system: "
-           << 2 * Ahyp->real().GetGlobalNumRows() << endl << endl;
-   }
-
-   // 12. Define and apply a parallel FGMRES solver for AU=B with a
-   //     block diagonal preconditioner based on the appropriate multigrid
-   //     preconditioner from hypre or simply use STRUMPACK.
-#ifdef MFEM_USE_STRUMPACK
-   if (!strumpack)
-#endif
-   {
-      Array<HYPRE_Int> blockTrueOffsets;
-      blockTrueOffsets.SetSize(3);
-      blockTrueOffsets[0] = 0;
-      blockTrueOffsets[1] = PCOp.Ptr()->Height();
-      blockTrueOffsets[2] = PCOp.Ptr()->Height();
-      blockTrueOffsets.PartialSum();
-
-      BlockDiagonalPreconditioner BDP(blockTrueOffsets);
-
-      Operator * pc_r = NULL;
-      Operator * pc_i = NULL;
-
-      switch (prob)
-      {
-         case 0:
-            pc_r =
-               new HypreBoomerAMG(dynamic_cast<HypreParMatrix&>(*PCOp.Ptr()));
-            pc_i = new ScaledOperator(pc_r,
-                                      (conv == ComplexOperator::HERMITIAN) ?
-                                      1.0:-1.0);
-            break;
-         case 1:
-            pc_r = new HypreAMS(dynamic_cast<HypreParMatrix&>(*PCOp.Ptr()),
-                                fespace);
-            pc_i = new ScaledOperator(pc_r,
-                                      (conv == ComplexOperator::HERMITIAN) ?
-                                      1.0:-1.0);
-            break;
-         case 2:
-            if (dim == 2 )
-            {
-               pc_r = new HypreAMS(dynamic_cast<HypreParMatrix&>(*PCOp.Ptr()),
-                                   fespace);
-            }
-            else
-            {
-               pc_r = new HypreADS(dynamic_cast<HypreParMatrix&>(*PCOp.Ptr()),
-                                   fespace);
-            }
-            pc_i = new ScaledOperator(pc_r,
-                                      (conv == ComplexOperator::HERMITIAN) ?
-                                      1.0:-1.0);
-            break;
-      }
-      BDP.SetDiagonalBlock(0, pc_r);
-      BDP.SetDiagonalBlock(1, pc_i);
-      BDP.owns_blocks = 0;
-
-      FGMRESSolver fgmres(MPI_COMM_WORLD);
-      fgmres.SetPreconditioner(BDP);
-      fgmres.SetOperator(*A.Ptr());
-      fgmres.SetRelTol(1e-12);
-      fgmres.SetMaxIter(1000);
-      fgmres.SetPrintLevel(1);
-      fgmres.Mult(B, U);
-   }
-#ifdef MFEM_USE_STRUMPACK
-   else
-   {
-      ComplexHypreParMatrix * Ahyp =
-         dynamic_cast<ComplexHypreParMatrix*>(A.Ptr());
-
-      STRUMPACKRowLocCmplxMatrix A_strmp(Ahyp->real(), Ahyp->imag());
-
-      STRUMPACKCmplxSolver strmp(argc, argv, comm);
-
-      strmp.SetPrintFactorStatistics(true);
-      strmp.SetPrintSolveStatistics(true);
-      // strmp.SetKrylovSolver(strumpack::KrylovSolver::AUTO); // core dump
-      strmp.SetKrylovSolver(strumpack::KrylovSolver::DIRECT); // core dump
-      // strmp.SetKrylovSolver(strumpack::KrylovSolver::REFINE); // core dump
-      // strmp.SetKrylovSolver(strumpack::KrylovSolver::PREC_GMRES); // index out of range asserts from strumpack::DenseMatrix
-      // strmp.SetKrylovSolver(strumpack::KrylovSolver::GMRES); // WORKS
-      strmp.SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
-      strmp.SetOperator(A_strmp);
-      strmp.SetFromCommandLine();
-      strmp.Mult(B, U);
-   }
-#endif
-
-   // 13. Recover the parallel grid function corresponding to U. This is the
-   //     local finite element solution on each processor.
-   a->RecoverFEMSolution(U, b, u);
-
-   if (exact_sol)
-   {
-      double err_r = -1.0;
-      double err_i = -1.0;
-
-      switch (prob)
-      {
-         case 0:
-            err_r = u.real().ComputeL2Error(u0_r);
-            err_i = u.imag().ComputeL2Error(u0_i);
-            break;
-         case 1:
-            err_r = u.real().ComputeL2Error(u1_r);
-            err_i = u.imag().ComputeL2Error(u1_i);
-            break;
-         case 2:
-            err_r = u.real().ComputeL2Error(u2_r);
-            err_i = u.imag().ComputeL2Error(u2_i);
-            break;
-      }
-
-      if ( myid == 0 )
-      {
-         cout << endl;
-         cout << "|| Re (u_h - u) ||_{L^2} = " << err_r << endl;
-         cout << "|| Im (u_h - u) ||_{L^2} = " << err_i << endl;
-         cout << 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_r_name, sol_i_name;
-      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
-      sol_r_name << "sol_r." << setfill('0') << setw(6) << myid;
-      sol_i_name << "sol_i." << setfill('0') << setw(6) << myid;
-
-      ofstream mesh_ofs(mesh_name.str().c_str());
-      mesh_ofs.precision(8);
-      pmesh->Print(mesh_ofs);
-
-      ofstream sol_r_ofs(sol_r_name.str().c_str());
-      ofstream sol_i_ofs(sol_i_name.str().c_str());
-      sol_r_ofs.precision(8);
-      sol_i_ofs.precision(8);
-      u.real().Save(sol_r_ofs);
-      u.imag().Save(sol_i_ofs);
-   }
-
-   // 15. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
-      sol_sock_r << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
-      sol_sock_r << "solution\n" << *pmesh << u.real()
-                 << "window_title 'Comp Real Part'" << flush;
-      sol_sock_i << "solution\n" << *pmesh << u.imag()
-                 << "window_title 'Comp Imaginary Part'" << flush;
-   }
-   if (visualization && exact_sol)
-   {
-      *u_exact -= u;
-
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock_r(vishost, visport);
-      socketstream sol_sock_i(vishost, visport);
-      sol_sock_r << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_i << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock_r.precision(8);
-      sol_sock_i.precision(8);
-      sol_sock_r << "solution\n" << *pmesh << u_exact->real()
-                 << "window_title 'Exact-Comp Real Part'" << flush;
-      sol_sock_i << "solution\n" << *pmesh << u_exact->imag()
-                 << "window_title 'Exact-Comp Imaginary Part'" << flush;
-   }
-   if (visualization)
-   {
-      ParGridFunction u_t(fespace);
-      u_t = u.real();
-      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 << u_t
-               << "window_title 'Harmonic Solution (t = 0.0 T)'"
-               << "pause\n" << flush;
-      if (myid == 0)
-         cout << "GLVis visualization paused."
-              << " Press space (in the GLVis window) to resume it.\n";
-      int num_frames = 32;
-      int i = 0;
-      while (sol_sock)
-      {
-         double t = (double)(i % num_frames) / num_frames;
-         ostringstream oss;
-         oss << "Harmonic Solution (t = " << t << " T)";
-
-         add(cos( 2.0 * M_PI * t), u.real(),
-             sin(-2.0 * M_PI * t), u.imag(), u_t);
-         sol_sock << "parallel " << num_procs << " " << myid << "\n";
-         sol_sock << "solution\n" << *pmesh << u_t
-                  << "window_title '" << oss.str() << "'" << flush;
-         i++;
-      }
-   }
-
-   // 16. Free the used memory.
-   delete a;
-   delete u_exact;
-   delete pcOp;
-   delete fespace;
-   delete fec;
-   delete pmesh;
-
-   MPI_Finalize();
-
-   return 0;
-}
-
-bool check_for_inline_mesh(const char * mesh_file)
-{
-   string file(mesh_file);
-   size_t p0 = file.find_last_of("/");
-   string s0 = file.substr((p0==string::npos)?0:(p0+1),7);
-   return s0 == "inline-";
-}
-
-complex<double> u0_exact(const Vector &x)
-{
-   int dim = x.Size();
-   complex<double> i(0.0, 1.0);
-   complex<double> alpha = (epsilon_ * omega_ - i * sigma_);
-   complex<double> kappa = std::sqrt(mu_ * omega_* alpha);
-   return std::exp(-i * kappa * x[dim - 1]);
-}
-
-double u0_real_exact(const Vector &x)
-{
-   return u0_exact(x).real();
-}
-
-double u0_imag_exact(const Vector &x)
-{
-   return u0_exact(x).imag();
-}
-
-void u1_real_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[0] = u0_real_exact(x);
-}
-
-void u1_imag_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[0] = u0_imag_exact(x);
-}
-
-void u2_real_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[dim-1] = u0_real_exact(x);
-}
-
-void u2_imag_exact(const Vector &x, Vector &v)
-{
-   int dim = x.Size();
-   v.SetSize(dim); v = 0.0; v[dim-1] = u0_imag_exact(x);
-}

examples/ex3p_sp.cpp

@@ -1,334 +0,0 @@
-//                       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;
-
-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;
-#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(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();
-
-   // 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();
-   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
-   //    (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(-1.0);
-   ParBilinearForm *a = new ParBilinearForm(fespace);
-   a->AddDomainIntegrator(new CurlCurlIntegrator(*muinv));
-   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
-
-   // 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);
-
-      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();
-   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);
-      if (myid == 0)
-      {
-         cout << "\n|| E_h - E ||_{L^2} = " << err << '\n' << 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) = (1. + kappa * kappa) * sin(kappa * x(1));
-      f(1) = (1. + kappa * kappa) * sin(kappa * x(2));
-      f(2) = (1. + 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

@@ -16,9 +16,9 @@
 //               ex6 -m ../data/amr-quad.mesh
 //
 // Device sample runs:
-//             > ex6 -pa -d cuda
-//             > ex6 -pa -d occa-cuda
-//             > ex6 -pa -d raja-omp
+//               ex6 -pa -d cuda
+//               ex6 -pa -d occa-cuda
+//               ex6 -pa -d raja-omp
 //
 // Description:  This is a version of Example 1 with a simple adaptive mesh
 //               refinement loop. The problem being solved is again the Laplace

examples/ex6p.cpp

@@ -16,9 +16,9 @@
 //               mpirun -np 4 ex6p -m ../data/amr-quad.mesh
 //
 // Device sample runs:
-//             > mpirun -np 4 ex6p -pa -d cuda
-//             > mpirun -np 4 ex6p -pa -d occa-cuda
-//             > mpirun -np 4 ex6p -pa -d raja-omp
+//               mpirun -np 4 ex6p -pa -d cuda
+//               mpirun -np 4 ex6p -pa -d occa-cuda
+//               mpirun -np 4 ex6p -pa -d raja-omp
 //
 // Description:  This is a version of Example 1 with a simple adaptive mesh
 //               refinement loop. The problem being solved is again the Laplace

examples/exSBP.cpp

@@ -0,0 +1,359 @@
+//                                MFEM Example 1
+//
+// Compile with: make exSBP
+//
+// Sample runs:  exSBP -sbp -o 0 -p 0 -r 1
+//               exSBP -sbp -o 4 -p 3
+//               
+//
+// Description:  This example code builds on Example 1 but adds SBP operators.
+//               It 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 or SBP 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>
+#include <chrono>
+
+using namespace std;
+using namespace mfem;
+
+int problem;
+
+// Prescribed time-independent boundary and right-hand side functions.
+double bdr_func(const Vector &pt);
+double rhs_func(const Vector &pt);
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../data/unitGridTestMesh.msh";
+   int order = 1;
+   bool static_cond = false;
+	bool visualization = 1;
+	bool sbp = 1;
+	problem = 1;
+	int ref_levels = 0;
+	bool convOut = false;
+
+   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.AddOption(&sbp, "-sbp", "--summationbyparts", "-no-sbp",
+                  "--no-summationbyparts",
+                  "Enable or disable use of SBP operators.");
+	args.AddOption(&problem, "-p", "--problem",
+                  "Problem setup to use: 0 = transcendental manufactured solution, "
+						"1 = linear displacement, "
+						"2 = quadratic displacement, "
+						"3 = cubic displacement, "
+						"4 = quartic displacement.");
+	args.AddOption(&ref_levels, "-r", "--ref-levels",
+                  "Number of initial uniform refinement levels.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. 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 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.
+   {
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 4. 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;
+   if (sbp)
+   {
+      fec = new C_SBPCollection(order, dim);
+   }
+   else if (order > 0)
+   {
+      fec = new H1_FECollection(order, dim);
+   }
+   else if (mesh->GetNodes())
+   {
+      fec = mesh->GetNodes()->OwnFEC();
+      cout << "Using isoparametric FEs: " << fec->Name() << endl;
+   }
+   else
+   {
+      fec = new H1_FECollection(order = 1, dim);
+   }
+   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
+   cout << "Number of finite element unknowns: "
+        << fespace->GetTrueVSize() << endl;
+
+   // 7. 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;
+
+	// Create function coefficient bdr which holds the exact solution and is
+	// used to strongly impose boundary conditions.
+	FunctionCoefficient bdr(bdr_func);
+
+   // 5. 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;
+
+		// Project boundary conditions onto grid function to strongly impose
+		// boundary conditions. BC's are defined in the function `bdr_func`.
+		x.ProjectBdrCoefficient(bdr, ess_bdr);
+
+      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   }
+
+   // 6. 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 = new LinearForm(fespace);
+	
+	FunctionCoefficient rhs(rhs_func);
+	b->AddDomainIntegrator(new DomainLFIntegrator(rhs));
+
+	if (problem < 0 || problem > 4)
+	{
+		mfem::out << "Invalid problem type: " << problem << "\n";
+		delete mesh;
+      return 3;
+	}
+	
+   // // Start timing
+   // std::chrono::time_point<std::chrono::high_resolution_clock> start = std::chrono::high_resolution_clock::now();
+
+   b->Assemble();
+
+   // // End timing and compute interval
+   // std::chrono::time_point<std::chrono::high_resolution_clock> finish = std::chrono::high_resolution_clock::now();
+   // std::chrono::duration<double> elapsed = finish - start;
+   // std::cout << "\nb->Assemble() elapsed time: " << elapsed.count() << " s\n";
+
+   // 8. 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 = new BilinearForm(fespace);
+	ConstantCoefficient one(1.0);
+   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+
+   // 9. 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(); }
+
+   // // Start timing
+   // start = std::chrono::high_resolution_clock::now();
+
+   a->Assemble();
+
+   // // End timing and compute interval
+   // finish = std::chrono::high_resolution_clock::now();
+   // elapsed = finish - start;
+   // std::cout << "\na->Assemble() elapsed time: " << elapsed.count() << " s\n";
+
+   SparseMatrix A;
+   Vector B, X;
+   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+
+   mfem::out << "Size of linear system: " << A.Height() << endl;
+
+#ifndef MFEM_USE_SUITESPARSE
+   // 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
+   //     solve the system A X = B with PCG.
+   GSSmoother M(A);
+   PCG(A, M, B, X, 1, 1000, 1e-12, 0.0);
+#else
+   // 10. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
+   UMFPackSolver umf_solver;
+   umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+   umf_solver.SetOperator(A);
+   umf_solver.Mult(B, X);
+#endif
+
+   // 11. Recover the solution as a finite element grid function.
+   a->RecoverFEMSolution(X, *b, x);
+
+	// 12. Compute and print the L^2 norm of the error.
+   mfem::out << "\n|| u_h - u ||_{L^2} = " << x.ComputeL2Error(bdr) << '\n' << endl;
+	// mfem::out << "h: " << 0.1 / pow(2, ref_levels) << "\n";
+
+   // 12. 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);
+   // mesh->PrintVTK(mesh_ofs); 
+   ofstream sol_ofs("sol.gf");
+   sol_ofs.precision(8);
+   x.Save(sol_ofs);
+
+   // Save solution mesh in vtk file
+   char solFileName[32];
+   if (sbp)
+   {
+      snprintf(solFileName, 32, "exSBP_SBP_O%d_P%d.vtk", order, problem);
+   }
+   else
+   {
+      snprintf(solFileName, 32, "exSBP_FE_O%d_P%d.vtk", order, problem);
+   }
+
+	if (convOut)
+	{
+		// Save convergence study information in output file
+		char outfileName[32];
+		if (problem == 0)
+		{
+			snprintf(outfileName, 32, "convOutputP%d_manufactured.txt", order);
+		}
+		else if (problem == 1)
+		{
+			snprintf(outfileName, 32, "convOutputP%d_lin.txt", order);
+		}
+		else if (problem == 2)
+		{
+			snprintf(outfileName, 32, "convOutputP%d_quad.txt", order);
+		}
+		else if (problem == 3)
+		{
+			snprintf(outfileName, 32, "convOutputP%d_cubic.txt", order);
+		}
+		else if (problem == 4)
+		{
+			snprintf(outfileName, 32, "convOutputP%d_quartic.txt", order);
+		}
+		
+
+		ofstream outputFile;
+		outputFile.open(outfileName, ios::out | ios::app); 
+
+		if (outputFile.is_open())
+		{
+			outputFile << x.ComputeL2Error(bdr) << ", " << 0.1 / pow(2, ref_levels) << "\n";
+		}
+		outputFile.close();
+	}
+
+   ofstream omesh(solFileName);
+   omesh.precision(14); 
+   mesh->PrintVTK(omesh, 1); 
+   x.SaveVTK(omesh, "sol", 1);
+
+   // 13. 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;
+   }
+
+   // 14. Free the used memory.
+   delete a;
+   delete b;
+   delete fespace;
+   if (order > 0) { delete fec; }
+   delete mesh;
+
+   return 0;
+}
+
+// Exact solution, used for the Dirichlet BC.
+double bdr_func(const Vector &pt)
+{
+	double x = pt(0), y = pt(1), z = 0.0;
+
+	if (problem == 0) // manufactured solution
+	{
+		z = sin(M_PI*x)*sin(M_PI*y);
+	}
+	else if (problem == 1) // linear displacement
+	{
+		z = 0.5*x + 0.5*y;
+	}
+	else if (problem == 2) // quadratic displacement
+	{
+		z = 0.5*x*x + 0.5*y*y;
+	}
+	else if (problem == 3) // manufactured solution
+	{
+		z = 0.5*x*x*x + 0.5*y*y*y;
+	}
+	else if (problem == 4) // manufactured solution
+	{
+		z = 0.5*x*x*x*x + 0.5*y*y*y*y;
+	}
+	return z;
+}
+
+// right hand side function for manufactured solution
+double rhs_func(const Vector &pt)
+{
+	double x = pt(0), y = pt(1), z = 0.0;
+	if (problem == 0)
+	{
+		z = 2*M_PI*M_PI*sin(M_PI*x)*sin(M_PI*y);
+	}
+	else if (problem == 1)
+	{
+		z = 0;
+	}
+	else if (problem == 2)
+	{
+		z = -2;
+	}
+	else if (problem == 3)
+	{
+		z = -3*(x+y);
+	}
+	else if (problem == 4)
+	{
+		z = -6*(x*x + y*y);
+	}
+	return z;
+}

examples/makefile

@@ -22,9 +22,9 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 SEQ_EXAMPLES = ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 ex17\
-  ex18 ex19 ex20 ex21 ex22
+  ex18 ex19 ex20 ex22 exSBP
 PAR_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p ex12p\
- ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p
+ ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex22p
 
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)
@@ -118,7 +118,7 @@ clean-build:
 clean-exec:
 	@rm -f refined.mesh displaced.mesh mesh.* ex5.mesh
 	@rm -rf Example5* Example9* Example15* Example16*
-	@rm -f sphere_refined.* sol.* sol_u.* sol_p.* sol_r.* sol_i.*
+	@rm -f sphere_refined.* sol.* sol_u.* sol_p.*
 	@rm -f ex9.mesh ex9-mesh.* ex9-init.* ex9-final.*
 	@rm -f deformed.* velocity.* elastic_energy.* mode_*
 	@rm -f ex16.mesh ex16-mesh.* ex16-init.* ex16-final.*

fem/bilinearform.cpp

@@ -588,14 +588,18 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
                                     Vector &b, OperatorHandle &A, Vector &X,
                                     Vector &B, int copy_interior)
 {
+   const SparseMatrix *P = fes->GetConformingProlongation();
+
    if (ext)
    {
+      if (P != NULL && assembly != AssemblyLevel::FULL && Device::IsEnabled())
+      {
+         P->BuildTranspose();
+      }
       ext->FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
       return;
    }
 
-   const SparseMatrix *P = fes->GetConformingProlongation();
-
    FormSystemMatrix(ess_tdof_list, A);
 
    // Transform the system and perform the elimination in B, based on the

fem/bilininteg.cpp

@@ -415,6 +415,13 @@ void DiffusionIntegrator::AssembleElementMatrix
       {
          ir = &RefinedIntRules.Get(el.GetGeomType(), order);
       }
+      else if (el.Space() == FunctionSpace::SBPk)
+      {
+         ir = &el.GetNodes(); // SBP elements have collocated quadrature nodes
+                              // and DOFs, weights are included in element
+                              // construction so complete integration rule is
+                              // defined by the element's `Nodes`
+      }
       else
       {
          ir = &IntRules.Get(el.GetGeomType(), order);

fem/complex_fem.cpp

@@ -1,784 +0,0 @@
-// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
-// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
-// reserved. See file COPYRIGHT for details.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability see http://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the GNU Lesser General Public License (as published by the Free
-// Software Foundation) version 2.1 dated February 1999.
-
-#include "complex_fem.hpp"
-
-using namespace std;
-
-namespace mfem
-{
-
-ComplexGridFunction::ComplexGridFunction(FiniteElementSpace *fes)
-   : Vector(2*(fes->GetVSize()))
-{
-   gfr_ = new GridFunction(fes, &data[0]);
-   gfi_ = new GridFunction(fes, &data[fes->GetVSize()]);
-}
-
-void
-ComplexGridFunction::Update()
-{
-   FiniteElementSpace * fes = gfr_->FESpace();
-
-   int vsize = fes->GetVSize();
-
-   const Operator *T = fes->GetUpdateOperator();
-   if (T)
-   {
-      // Update the individual GridFunction objects.  This will allocate
-      // new data arrays for each GridFunction.
-      gfr_->Update();
-      gfi_->Update();
-
-      // Our data array now contains old data as well as being the wrong size
-      // so reallocate it.
-      this->SetSize(2 * vsize);
-
-      // Create temporary vectors which point to the new data array
-      Vector gf_r(&data[0], vsize);
-      Vector gf_i(&data[vsize], vsize);
-
-      // Copy the updated GridFunctions into the new data array
-      gf_r = *gfr_;
-      gf_i = *gfi_;
-
-      // Replace the individual data arrays with pointers into the new data array
-      gfr_->NewDataAndSize(&data[0], vsize);
-      gfi_->NewDataAndSize(&data[vsize], vsize);
-   }
-   else
-   {
-      // The existing data will not be transferred to the new GridFunctions
-      // so delete it a allocate a new array
-      this->SetSize(2 * vsize);
-
-      // Point the individual GridFunctions to the new data array
-      gfr_->NewDataAndSize(&data[0], vsize);
-      gfi_->NewDataAndSize(&data[vsize], vsize);
-
-      // These updates will only set the proper 'sequence' value within
-      // the individual GridFunction objects because their sizes are
-      // already correct
-      gfr_->Update();
-      gfi_->Update();
-   }
-}
-
-void
-ComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff,
-                                        Coefficient &imag_coeff)
-{
-   gfr_->ProjectCoefficient(real_coeff);
-   gfi_->ProjectCoefficient(imag_coeff);
-}
-
-void
-ComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
-                                        VectorCoefficient &imag_vcoeff)
-{
-   gfr_->ProjectCoefficient(real_vcoeff);
-   gfi_->ProjectCoefficient(imag_vcoeff);
-}
-
-void
-ComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
-                                           Coefficient &imag_coeff,
-                                           Array<int> &attr)
-{
-   gfr_->ProjectBdrCoefficient(real_coeff, attr);
-   gfi_->ProjectBdrCoefficient(imag_coeff, attr);
-}
-
-void
-ComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient &real_vcoeff,
-                                                 VectorCoefficient &imag_vcoeff,
-                                                 Array<int> &attr)
-{
-   gfr_->ProjectBdrCoefficientNormal(real_vcoeff, attr);
-   gfi_->ProjectBdrCoefficientNormal(imag_vcoeff, attr);
-}
-
-void
-ComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
-                                                  &real_vcoeff,
-                                                  VectorCoefficient
-                                                  &imag_vcoeff,
-                                                  Array<int> &attr)
-{
-   gfr_->ProjectBdrCoefficientTangent(real_vcoeff, attr);
-   gfi_->ProjectBdrCoefficientTangent(imag_vcoeff, attr);
-}
-
-
-ComplexLinearForm::ComplexLinearForm(FiniteElementSpace *f,
-                                     ComplexOperator::Convention convention)
-   : Vector(2*(f->GetVSize())),
-     conv_(convention)
-{
-   lfr_ = new LinearForm(f, &data[0]);
-   lfi_ = new LinearForm(f, &data[f->GetVSize()]);
-}
-
-ComplexLinearForm::~ComplexLinearForm()
-{
-   delete lfr_;
-   delete lfi_;
-}
-
-void
-ComplexLinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi_real,
-                                       LinearFormIntegrator *lfi_imag)
-{
-   if ( lfi_real ) { lfr_->AddDomainIntegrator(lfi_real); }
-   if ( lfi_imag ) { lfi_->AddDomainIntegrator(lfi_imag); }
-}
-
-void
-ComplexLinearForm::Update()
-{
-   FiniteElementSpace *fes = lfr_->FESpace();
-
-   this->Update(fes);
-}
-
-void
-ComplexLinearForm::Update(FiniteElementSpace *fes)
-{
-   int vsize = fes->GetVSize();
-   SetSize(2 * vsize);
-
-   Vector lfr(&data[0], vsize);
-   Vector lfi(&data[vsize], vsize);
-
-   lfr_->Update(fes, lfr, 0);
-   lfi_->Update(fes, lfi, 0);
-}
-
-void
-ComplexLinearForm::Assemble()
-{
-   lfr_->Assemble();
-   lfi_->Assemble();
-   if (conv_ == ComplexOperator::BLOCK_SYMMETRIC)
-   {
-      *lfi_ *= -1.0;
-   }
-}
-
-complex<double>
-ComplexLinearForm::operator()(const ComplexGridFunction &gf) const
-{
-   double s = (conv_ == ComplexOperator::HERMITIAN)?1.0:-1.0;
-   return complex<double>((*lfr_)(gf.real()) - s * (*lfi_)(gf.imag()),
-                          (*lfr_)(gf.imag()) + s * (*lfi_)(gf.real()));
-}
-
-
-SesquilinearForm::SesquilinearForm(FiniteElementSpace *f,
-                                   ComplexOperator::Convention convention)
-   : conv_(convention),
-     blfr_(new BilinearForm(f)),
-     blfi_(new BilinearForm(f))
-{}
-
-SesquilinearForm::~SesquilinearForm()
-{
-   delete blfr_;
-   delete blfi_;
-}
-
-void SesquilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi_real,
-                                           BilinearFormIntegrator *bfi_imag)
-{
-   if (bfi_real) { blfr_->AddDomainIntegrator(bfi_real); }
-   if (bfi_imag) { blfi_->AddDomainIntegrator(bfi_imag); }
-}
-
-void
-SesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                                        BilinearFormIntegrator *bfi_imag)
-{
-   if (bfi_real) { blfr_->AddBoundaryIntegrator(bfi_real); }
-   if (bfi_imag) { blfi_->AddBoundaryIntegrator(bfi_imag); }
-}
-
-void
-SesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                                        BilinearFormIntegrator *bfi_imag,
-                                        Array<int> & bdr_marker)
-{
-   if (bfi_real) { blfr_->AddBoundaryIntegrator(bfi_real, bdr_marker); }
-   if (bfi_imag) { blfi_->AddBoundaryIntegrator(bfi_imag, bdr_marker); }
-}
-
-void
-SesquilinearForm::Assemble(int skip_zeros)
-{
-   blfr_->Assemble(skip_zeros);
-   blfi_->Assemble(skip_zeros);
-}
-
-void
-SesquilinearForm::Finalize(int skip_zeros)
-{
-   blfr_->Finalize(skip_zeros);
-   blfi_->Finalize(skip_zeros);
-}
-
-ComplexSparseMatrix *
-SesquilinearForm::AssembleCompSpMat()
-{
-   return new ComplexSparseMatrix(&blfr_->SpMat(),
-                                  &blfi_->SpMat(),
-                                  false, false, conv_);
-
-}
-
-void
-SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
-                                   Vector &x, Vector &b,
-                                   OperatorHandle &A,
-                                   Vector &X, Vector &B,
-                                   int ci)
-{
-   FiniteElementSpace * fes = blfr_->FESpace();
-
-   int vsize  = fes->GetVSize();
-   // int tvsize = pfes->GetTrueVSize();
-
-   double s = (conv_ == ComplexOperator::HERMITIAN)?1.0:-1.0;
-
-   // Allocate temporary vectors
-   Vector b_0(vsize);  b_0 = 0.0;
-   // Vector B_0(tvsize); 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);
-
-   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_i *= s;
-   /*
-   X.SetSize(2 * tvsize);
-   Vector X_r(X.GetData(), tvsize);
-   Vector X_i(&(X.GetData())[tvsize], tvsize);
-
-   B.SetSize(2 * tvsize);
-   Vector B_r(B.GetData(), tvsize);
-   Vector B_i(&(B.GetData())[tvsize], tvsize);
-   */
-   SparseMatrix * A_r = new SparseMatrix;
-   SparseMatrix * A_i = new SparseMatrix;
-   Vector X_0, B_0;
-
-   b_0 = b_r;
-   blfr_->FormLinearSystem(ess_tdof_list, x_r, b_r, *A_r, X_0, B_0, ci);
-
-   int tvsize = B_0.Size();
-   X.SetSize(2 * tvsize);
-   B.SetSize(2 * 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);
-   X_r = X_0; B_r = B_0;
-
-   b_0 = 0.0;
-   blfi_->FormLinearSystem(ess_tdof_list, x_i, b_0, *A_i, X_0, B_0, false);
-   B_r -= B_0;
-
-   b_0 = b_i;
-   blfr_->FormLinearSystem(ess_tdof_list, x_i, b_0, *A_r, X_0, B_0, ci);
-   X_i = X_0; B_i = B_0;
-
-   b_0 = 0.0;
-   blfi_->FormLinearSystem(ess_tdof_list, x_r, b_0, *A_i, X_0, B_0, false);
-   B_i += B_0;
-
-   B_i *= s;
-   b_i *= s;
-
-   // A = A_r + i A_i
-   A.Clear();
-   ComplexSparseMatrix * A_sp =
-      new ComplexSparseMatrix(A_r, A_i, true, true, conv_);
-   A.Reset<ComplexSparseMatrix>(A_sp, true);
-}
-
-void
-SesquilinearForm::RecoverFEMSolution(const Vector &X, const Vector &b,
-                                     Vector &x)
-{
-   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;
-   }
-   else
-   {
-      // Apply conforming prolongation
-      P->Mult(X_r, x_r);
-      P->Mult(X_i, x_i);
-   }
-}
-
-void
-SesquilinearForm::Update(FiniteElementSpace *nfes)
-{
-   if ( blfr_ ) { blfr_->Update(nfes); }
-   if ( blfi_ ) { blfi_->Update(nfes); }
-}
-
-
-#ifdef MFEM_USE_MPI
-
-ParComplexGridFunction::ParComplexGridFunction(ParFiniteElementSpace *pfes)
-   : Vector(2*(pfes->GetVSize()))
-{
-   pgfr_ = new ParGridFunction(pfes, &data[0]);
-   pgfi_ = new ParGridFunction(pfes, &data[pfes->GetVSize()]);
-}
-
-void
-ParComplexGridFunction::Update()
-{
-   ParFiniteElementSpace * pfes = pgfr_->ParFESpace();
-
-   int vsize = pfes->GetVSize();
-
-   const Operator *T = pfes->GetUpdateOperator();
-   if (T)
-   {
-      // Update the individual GridFunction objects.  This will allocate
-      // new data arrays for each GridFunction.
-      pgfr_->Update();
-      pgfi_->Update();
-
-      // Our data array now contains old data as well as being the wrong size
-      // so reallocate it.
-      this->SetSize(2 * vsize);
-
-      // Create temporary vectors which point to the new data array
-      Vector gf_r(&data[0], vsize);
-      Vector gf_i(&data[vsize], vsize);
-
-      // Copy the updated GridFunctions into the new data array
-      gf_r = *pgfr_;
-      gf_i = *pgfi_;
-
-      // Replace the individual data arrays with pointers into the new data array
-      pgfr_->NewDataAndSize(&data[0], vsize);
-      pgfi_->NewDataAndSize(&data[vsize], vsize);
-   }
-   else
-   {
-      // The existing data will not be transferred to the new GridFunctions
-      // so delete it a allocate a new array
-      this->SetSize(2 * vsize);
-
-      // Point the individual GridFunctions to the new data array
-      pgfr_->NewDataAndSize(&data[0], vsize);
-      pgfi_->NewDataAndSize(&data[vsize], vsize);
-
-      // These updates will only set the proper 'sequence' value within
-      // the individual GridFunction objects because their sizes are
-      // already correct
-      pgfr_->Update();
-      pgfi_->Update();
-   }
-}
-
-void
-ParComplexGridFunction::ProjectCoefficient(Coefficient &real_coeff,
-                                           Coefficient &imag_coeff)
-{
-   pgfr_->ProjectCoefficient(real_coeff);
-   pgfi_->ProjectCoefficient(imag_coeff);
-}
-
-void
-ParComplexGridFunction::ProjectCoefficient(VectorCoefficient &real_vcoeff,
-                                           VectorCoefficient &imag_vcoeff)
-{
-   pgfr_->ProjectCoefficient(real_vcoeff);
-   pgfi_->ProjectCoefficient(imag_vcoeff);
-}
-
-void
-ParComplexGridFunction::ProjectBdrCoefficient(Coefficient &real_coeff,
-                                              Coefficient &imag_coeff,
-                                              Array<int> &attr)
-{
-   pgfr_->ProjectBdrCoefficient(real_coeff, attr);
-   pgfi_->ProjectBdrCoefficient(imag_coeff, attr);
-}
-
-void
-ParComplexGridFunction::ProjectBdrCoefficientNormal(VectorCoefficient
-                                                    &real_vcoeff,
-                                                    VectorCoefficient
-                                                    &imag_vcoeff,
-                                                    Array<int> &attr)
-{
-   pgfr_->ProjectBdrCoefficientNormal(real_vcoeff, attr);
-   pgfi_->ProjectBdrCoefficientNormal(imag_vcoeff, attr);
-}
-
-void
-ParComplexGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient
-                                                     &real_vcoeff,
-                                                     VectorCoefficient
-                                                     &imag_vcoeff,
-                                                     Array<int> &attr)
-{
-   pgfr_->ProjectBdrCoefficientTangent(real_vcoeff, attr);
-   pgfi_->ProjectBdrCoefficientTangent(imag_vcoeff, attr);
-}
-
-void
-ParComplexGridFunction::Distribute(const Vector *tv)
-{
-   ParFiniteElementSpace * pfes = pgfr_->ParFESpace();
-   HYPRE_Int size = pfes->GetTrueVSize();
-
-   double * tvd = tv->GetData();
-   Vector tvr(tvd, size);
-   Vector tvi(&tvd[size], size);
-
-   pgfr_->Distribute(tvr);
-   pgfi_->Distribute(tvi);
-}
-
-void
-ParComplexGridFunction::ParallelProject(Vector &tv) const
-{
-   ParFiniteElementSpace * pfes = pgfr_->ParFESpace();
-   HYPRE_Int size = pfes->GetTrueVSize();
-
-   double * tvd = tv.GetData();
-   Vector tvr(tvd, size);
-   Vector tvi(&tvd[size], size);
-
-   pgfr_->ParallelProject(tvr);
-   pgfi_->ParallelProject(tvi);
-}
-
-
-ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
-                                           ComplexOperator::Convention
-                                           convention)
-   : Vector(2*(pfes->GetVSize())),
-     conv_(convention)
-{
-   plfr_ = new ParLinearForm(pfes, &data[0]);
-   plfi_ = new ParLinearForm(pfes, &data[pfes->GetVSize()]);
-
-   HYPRE_Int * tdof_offsets = pfes->GetTrueDofOffsets();
-
-   int n = (HYPRE_AssumedPartitionCheck()) ? 2 : pfes->GetNRanks();
-   tdof_offsets_ = new HYPRE_Int[n+1];
-
-   for (int i=0; i<=n; i++)
-   {
-      tdof_offsets_[i] = 2 * tdof_offsets[i];
-   }
-}
-
-ParComplexLinearForm::~ParComplexLinearForm()
-{
-   delete plfr_;
-   delete plfi_;
-   delete [] tdof_offsets_;
-}
-
-void
-ParComplexLinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi_real,
-                                          LinearFormIntegrator *lfi_imag)
-{
-   if ( lfi_real ) { plfr_->AddDomainIntegrator(lfi_real); }
-   if ( lfi_imag ) { plfi_->AddDomainIntegrator(lfi_imag); }
-}
-
-void
-ParComplexLinearForm::Update(ParFiniteElementSpace *pf)
-{
-   ParFiniteElementSpace *pfes = (pf!=NULL)?pf:plfr_->ParFESpace();
-   int vsize = pfes->GetVSize();
-   SetSize(2 * vsize);
-
-   Vector plfr(&data[0], vsize);
-   Vector plfi(&data[vsize], vsize);
-
-   plfr_->Update(pfes, plfr, 0);
-   plfi_->Update(pfes, plfi, 0);
-}
-
-void
-ParComplexLinearForm::Assemble()
-{
-   plfr_->Assemble();
-   plfi_->Assemble();
-   if (conv_ == ComplexOperator::BLOCK_SYMMETRIC)
-   {
-      *plfi_ *= -1.0;
-   }
-}
-
-void
-ParComplexLinearForm::ParallelAssemble(Vector &tv)
-{
-   HYPRE_Int size = plfr_->ParFESpace()->GetTrueVSize();
-
-   double * tvd = tv.GetData();
-   Vector tvr(tvd, size);
-   Vector tvi(&tvd[size], size);
-
-   plfr_->ParallelAssemble(tvr);
-   plfi_->ParallelAssemble(tvi);
-}
-
-HypreParVector *
-ParComplexLinearForm::ParallelAssemble()
-{
-   const ParFiniteElementSpace * pfes = plfr_->ParFESpace();
-
-   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[size], size);
-
-   plfr_->ParallelAssemble(tvr);
-   plfi_->ParallelAssemble(tvi);
-
-   return tv;
-}
-
-complex<double>
-ParComplexLinearForm::operator()(const ParComplexGridFunction &gf) const
-{
-   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()));
-}
-
-
-ParSesquilinearForm::ParSesquilinearForm(ParFiniteElementSpace *pf,
-                                         ComplexOperator::Convention
-                                         convention)
-   : conv_(convention),
-     pblfr_(new ParBilinearForm(pf)),
-     pblfi_(new ParBilinearForm(pf))
-{}
-
-ParSesquilinearForm::~ParSesquilinearForm()
-{
-   delete pblfr_;
-   delete pblfi_;
-}
-
-void ParSesquilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi_real,
-                                              BilinearFormIntegrator *bfi_imag)
-{
-   if (bfi_real) { pblfr_->AddDomainIntegrator(bfi_real); }
-   if (bfi_imag) { pblfi_->AddDomainIntegrator(bfi_imag); }
-}
-
-void
-ParSesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                                           BilinearFormIntegrator *bfi_imag)
-{
-   if (bfi_real) { pblfr_->AddBoundaryIntegrator(bfi_real); }
-   if (bfi_imag) { pblfi_->AddBoundaryIntegrator(bfi_imag); }
-}
-
-void
-ParSesquilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                                           BilinearFormIntegrator *bfi_imag,
-                                           Array<int> & bdr_marker)
-{
-   if (bfi_real) { pblfr_->AddBoundaryIntegrator(bfi_real, bdr_marker); }
-   if (bfi_imag) { pblfi_->AddBoundaryIntegrator(bfi_imag, bdr_marker); }
-}
-
-void
-ParSesquilinearForm::Assemble(int skip_zeros)
-{
-   pblfr_->Assemble(skip_zeros);
-   pblfi_->Assemble(skip_zeros);
-}
-
-void
-ParSesquilinearForm::Finalize(int skip_zeros)
-{
-   pblfr_->Finalize(skip_zeros);
-   pblfi_->Finalize(skip_zeros);
-}
-
-ComplexHypreParMatrix *
-ParSesquilinearForm::ParallelAssemble()
-{
-   return new ComplexHypreParMatrix(pblfr_->ParallelAssemble(),
-                                    pblfi_->ParallelAssemble(),
-                                    true, true, conv_);
-
-}
-
-void
-ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
-                                      Vector &x, Vector &b,
-                                      OperatorHandle &A,
-                                      Vector &X, Vector &B,
-                                      int ci)
-{
-   ParFiniteElementSpace * pfes = pblfr_->ParFESpace();
-
-   int tvs = pfes->TrueVSize();
-   cout << "TrueVSize returns " << tvs << endl;
-   cout << "GetVSize returns " << pfes->GetVSize() << endl;
-
-   int vsize = x.Size() / 2;
-   // int vsize  = pfes->GetVSize();
-   // int tvsize = pfes->GetTrueVSize();
-
-   cout << "x.Size/2 returns " << vsize << endl;
-
-   double s = (conv_ == ComplexOperator::HERMITIAN)?1.0:-1.0;
-
-   // Allocate temporary vectors
-   Vector b_0(vsize);  b_0 = 0.0;
-   // Vector B_0(tvsize); 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);
-
-   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_i *= s;
-   /*
-   X.SetSize(2 * tvsize);
-   Vector X_r(X.GetData(), tvsize);
-   Vector X_i(&(X.GetData())[tvsize], tvsize);
-
-   B.SetSize(2 * tvsize);
-   Vector B_r(B.GetData(), tvsize);
-   Vector B_i(&(B.GetData())[tvsize], tvsize);
-   */
-   OperatorHandle A_r, A_i;
-   Vector X_0, B_0;
-   cout << "pblfr fls 1" << endl << flush;
-   b_0 = b_r;
-   pblfr_->FormLinearSystem(ess_tdof_list, x_r, b_0, A_r, X_0, B_0, ci);
-
-   int tvsize = B_0.Size();
-   X.SetSize(2 * tvsize);
-   B.SetSize(2 * 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);
-   X_r = X_0; B_r = B_0;
-   cout << "pblfi fls 1" << endl << flush;
-   b_0 = 0.0;
-   pblfi_->FormLinearSystem(ess_tdof_list, x_i, b_0, A_i, X_0, B_0, false);
-   B_r -= B_0;
-   cout << "pblfr fls 2" << endl << flush;
-   b_0 = b_i;
-   pblfr_->FormLinearSystem(ess_tdof_list, x_i, b_0, A_r, X_0, B_0, ci);
-   X_i = X_0; B_i = B_0;
-   cout << "pblfi fls 2" << endl << flush;
-   b_0 = 0.0;
-   pblfi_->FormLinearSystem(ess_tdof_list, x_r, b_0, A_i, X_0, B_0, false);
-   B_i += B_0;
-
-   B_i *= s;
-   b_i *= s;
-
-   // A = A_r + i A_i
-   A.Clear();
-   if ( A_r.Type() == Operator::Hypre_ParCSR &&
-        A_i.Type() == Operator::Hypre_ParCSR )
-   {
-      ComplexHypreParMatrix * A_hyp =
-         new ComplexHypreParMatrix(A_r.As<HypreParMatrix>(),
-                                   A_i.As<HypreParMatrix>(),
-                                   A_r.OwnsOperator(),
-                                   A_i.OwnsOperator(),
-                                   conv_);
-      A.Reset<ComplexHypreParMatrix>(A_hyp, true);
-   }
-   else
-   {
-      ComplexOperator * A_op =
-         new ComplexOperator(A_r.As<Operator>(),
-                             A_i.As<Operator>(),
-                             A_r.OwnsOperator(),
-                             A_i.OwnsOperator(),
-                             conv_);
-      A.Reset<ComplexOperator>(A_op, true);
-   }
-}
-
-void
-ParSesquilinearForm::RecoverFEMSolution(const Vector &X, const Vector &b,
-                                        Vector &x)
-{
-   ParFiniteElementSpace * pfes = pblfr_->ParFESpace();
-
-   const Operator &P = *pfes->GetProlongationMatrix();
-
-   int vsize  = pfes->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);
-
-   // Apply conforming prolongation
-   P.Mult(X_r, x_r);
-   P.Mult(X_i, x_i);
-}
-
-void
-ParSesquilinearForm::Update(FiniteElementSpace *nfes)
-{
-   if ( pblfr_ ) { pblfr_->Update(nfes); }
-   if ( pblfi_ ) { pblfi_->Update(nfes); }
-}
-
-
-#endif // MFEM_USE_MPI
-
-}

fem/complex_fem.hpp

@@ -1,356 +0,0 @@
-// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
-// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
-// reserved. See file COPYRIGHT for details.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability see http://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the GNU Lesser General Public License (as published by the Free
-// Software Foundation) version 2.1 dated February 1999.
-
-#ifndef MFEM_COMPLEX_FEM
-#define MFEM_COMPLEX_FEM
-
-#include "../linalg/complex_operator.hpp"
-#include "gridfunc.hpp"
-#include "linearform.hpp"
-#include "bilinearform.hpp"
-#ifdef MFEM_USE_MPI
-#include "pgridfunc.hpp"
-#include "plinearform.hpp"
-#include "pbilinearform.hpp"
-#endif
-#include <complex>
-
-namespace mfem
-{
-
-/// Class for complex-valued grid function - Vector with associated FE space.
-class ComplexGridFunction : public Vector
-{
-private:
-
-   GridFunction * gfr_;
-   GridFunction * gfi_;
-
-protected:
-   void Destroy() { delete gfr_; delete gfi_; }
-
-public:
-
-   /* @brief Construct a ComplexGridFunction associated with the
-      FiniteElementSpace @a *f. */
-   ComplexGridFunction(FiniteElementSpace *f);
-
-   void Update();
-
-   /// Assign constant values to the ComplexGridFunction data.
-   ComplexGridFunction &operator=(const std::complex<double> & value)
-   { *gfr_ = value.real(); *gfi_ = value.imag(); return *this; }
-
-   virtual void ProjectCoefficient(Coefficient &real_coeff,
-                                   Coefficient &imag_coeff);
-   virtual void ProjectCoefficient(VectorCoefficient &real_vcoeff,
-                                   VectorCoefficient &imag_vcoeff);
-
-   virtual void ProjectBdrCoefficient(Coefficient &real_coeff,
-                                      Coefficient &imag_coeff,
-                                      Array<int> &attr);
-   virtual void ProjectBdrCoefficientNormal(VectorCoefficient &real_coeff,
-                                            VectorCoefficient &imag_coeff,
-                                            Array<int> &attr);
-   virtual void ProjectBdrCoefficientTangent(VectorCoefficient &real_coeff,
-                                             VectorCoefficient &imag_coeff,
-                                             Array<int> &attr);
-
-   FiniteElementSpace *FESpace() { return gfr_->FESpace(); }
-   const FiniteElementSpace *FESpace() const { return gfr_->FESpace(); }
-
-   GridFunction & real() { return *gfr_; }
-   GridFunction & imag() { return *gfi_; }
-   const GridFunction & real() const { return *gfr_; }
-   const GridFunction & imag() const { return *gfi_; }
-
-   /// Destroys grid function.
-   virtual ~ComplexGridFunction() { Destroy(); }
-
-};
-
-class ComplexLinearForm : public Vector
-{
-private:
-   ComplexOperator::Convention conv_;
-
-protected:
-   LinearForm * lfr_;
-   LinearForm * lfi_;
-
-   // HYPRE_Int * tdof_offsets_;
-
-public:
-
-   ComplexLinearForm(FiniteElementSpace *fes,
-                     ComplexOperator::Convention
-                     convention = ComplexOperator::HERMITIAN);
-
-   virtual ~ComplexLinearForm();
-
-   /// Adds new Domain Integrator.
-   void AddDomainIntegrator(LinearFormIntegrator *lfi_real,
-                            LinearFormIntegrator *lfi_imag);
-
-   FiniteElementSpace *FESpace() const { return lfr_->FESpace(); }
-
-   LinearForm & real() { return *lfr_; }
-   LinearForm & imag() { return *lfi_; }
-   const LinearForm & real() const { return *lfr_; }
-   const LinearForm & imag() const { return *lfi_; }
-
-   void Update();
-   void Update(FiniteElementSpace *f);
-
-   /// Assembles the linear form i.e. sums over all domain/bdr integrators.
-   void Assemble();
-
-   std::complex<double> operator()(const ComplexGridFunction &gf) const;
-
-};
-
-// Class for sesquilinear form
-class SesquilinearForm
-{
-private:
-   ComplexOperator::Convention conv_;
-
-   //protected:
-   BilinearForm *blfr_;
-   BilinearForm *blfi_;
-
-public:
-   SesquilinearForm(FiniteElementSpace *fes,
-                    ComplexOperator::Convention
-                    convention = ComplexOperator::HERMITIAN);
-
-   ComplexOperator::Convention GetConvention() const { return conv_; }
-   void SetConvention(const ComplexOperator::Convention &
-                      convention) { conv_  = convention; }
-
-   BilinearForm & real() { return *blfr_; }
-   BilinearForm & imag() { return *blfi_; }
-   const BilinearForm & real() const { return *blfr_; }
-   const BilinearForm & imag() const { return *blfi_; }
-
-   /// Adds new Domain Integrator.
-   void AddDomainIntegrator(BilinearFormIntegrator *bfi_real,
-                            BilinearFormIntegrator *bfi_imag);
-
-   /// Adds new Boundary Integrator.
-   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                              BilinearFormIntegrator *bfi_imag);
-
-   /// Adds new Boundary Integrator, restricted to specific boundary attributes.
-   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                              BilinearFormIntegrator *bfi_imag,
-                              Array<int> &bdr_marker);
-
-   /// Assemble the local matrix
-   void Assemble(int skip_zeros = 1);
-
-   /// Finalizes the matrix initialization.
-   void Finalize(int skip_zeros = 1);
-
-   /// Returns the matrix assembled on the true dofs, i.e. P^t A P.
-   /** The returned matrix has to be deleted by the caller. */
-   ComplexSparseMatrix *AssembleCompSpMat();
-
-   /// Return the parallel FE space associated with the ParBilinearForm.
-   FiniteElementSpace *FESpace() const { return blfr_->FESpace(); }
-
-   void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x, Vector &b,
-                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
-
-   /** Call this method after solving a linear system constructed using the
-       FormLinearSystem method to recover the solution as a ParGridFunction-size
-       vector in x. Use the same arguments as in the FormLinearSystem call. */
-   virtual void RecoverFEMSolution(const Vector &X, const Vector &b, Vector &x);
-
-   virtual void Update(FiniteElementSpace *nfes = NULL);
-
-   virtual ~SesquilinearForm();
-};
-
-#ifdef MFEM_USE_MPI
-
-/// Class for complex-valued grid function - Vector with associated FE space.
-class ParComplexGridFunction : public Vector
-{
-private:
-
-   ParGridFunction * pgfr_;
-   ParGridFunction * pgfi_;
-
-protected:
-   void Destroy() { delete pgfr_; delete pgfi_; }
-
-public:
-
-   /* @brief Construct a ParComplexGridFunction associated with the
-      ParFiniteElementSpace @a *f. */
-   ParComplexGridFunction(ParFiniteElementSpace *pf);
-
-   void Update();
-
-   /// Assign constant values to the ParComplexGridFunction data.
-   ParComplexGridFunction &operator=(const std::complex<double> & value)
-   { *pgfr_ = value.real(); *pgfi_ = value.imag(); return *this; }
-
-   virtual void ProjectCoefficient(Coefficient &real_coeff,
-                                   Coefficient &imag_coeff);
-   virtual void ProjectCoefficient(VectorCoefficient &real_vcoeff,
-                                   VectorCoefficient &imag_vcoeff);
-
-   virtual void ProjectBdrCoefficient(Coefficient &real_coeff,
-                                      Coefficient &imag_coeff,
-                                      Array<int> &attr);
-   virtual void ProjectBdrCoefficientNormal(VectorCoefficient &real_coeff,
-                                            VectorCoefficient &imag_coeff,
-                                            Array<int> &attr);
-   virtual void ProjectBdrCoefficientTangent(VectorCoefficient &real_coeff,
-                                             VectorCoefficient &imag_coeff,
-                                             Array<int> &attr);
-
-   void Distribute(const Vector *tv);
-   void Distribute(const Vector &tv) { Distribute(&tv); }
-
-   /// Returns the vector restricted to the true dofs.
-   void ParallelProject(Vector &tv) const;
-
-   FiniteElementSpace *FESpace() { return pgfr_->FESpace(); }
-   const FiniteElementSpace *FESpace() const { return pgfr_->FESpace(); }
-
-   ParGridFunction & real() { return *pgfr_; }
-   ParGridFunction & imag() { return *pgfi_; }
-   const ParGridFunction & real() const { return *pgfr_; }
-   const ParGridFunction & imag() const { return *pgfi_; }
-
-   /// Destroys grid function.
-   virtual ~ParComplexGridFunction() { Destroy(); }
-
-};
-
-class ParComplexLinearForm : public Vector
-{
-private:
-   ComplexOperator::Convention conv_;
-
-protected:
-   ParLinearForm * plfr_;
-   ParLinearForm * plfi_;
-
-   HYPRE_Int * tdof_offsets_;
-
-public:
-
-   ParComplexLinearForm(ParFiniteElementSpace *pf,
-                        ComplexOperator::Convention
-                        convention = ComplexOperator::HERMITIAN);
-
-   virtual ~ParComplexLinearForm();
-
-   /// Adds new Domain Integrator.
-   void AddDomainIntegrator(LinearFormIntegrator *lfi_real,
-                            LinearFormIntegrator *lfi_imag);
-
-   ParFiniteElementSpace *ParFESpace() const { return plfr_->ParFESpace(); }
-
-   ParLinearForm & real() { return *plfr_; }
-   ParLinearForm & imag() { return *plfi_; }
-   const ParLinearForm & real() const { return *plfr_; }
-   const ParLinearForm & imag() const { return *plfi_; }
-
-   void Update(ParFiniteElementSpace *pf = NULL);
-
-   /// Assembles the linear form i.e. sums over all domain/bdr integrators.
-   void Assemble();
-
-   /// Assemble the vector on the true dofs, i.e. P^t v.
-   void ParallelAssemble(Vector &tv);
-
-   /// Returns the vector assembled on the true dofs, i.e. P^t v.
-   HypreParVector *ParallelAssemble();
-
-   std::complex<double> operator()(const ParComplexGridFunction &gf) const;
-
-};
-
-// Class for parallel sesquilinear form
-class ParSesquilinearForm
-{
-private:
-   ComplexOperator::Convention conv_;
-
-   //protected:
-   ParBilinearForm *pblfr_;
-   ParBilinearForm *pblfi_;
-
-public:
-   ParSesquilinearForm(ParFiniteElementSpace *pf,
-                       ComplexOperator::Convention
-                       convention = ComplexOperator::HERMITIAN);
-
-   ComplexOperator::Convention GetConvention() const { return conv_; }
-   void SetConvention(const ComplexOperator::Convention &
-                      convention) { conv_  = convention; }
-
-   ParBilinearForm & real() { return *pblfr_; }
-   ParBilinearForm & imag() { return *pblfi_; }
-   const ParBilinearForm & real() const { return *pblfr_; }
-   const ParBilinearForm & imag() const { return *pblfi_; }
-
-   /// Adds new Domain Integrator.
-   void AddDomainIntegrator(BilinearFormIntegrator *bfi_real,
-                            BilinearFormIntegrator *bfi_imag);
-
-   /// Adds new Boundary Integrator.
-   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                              BilinearFormIntegrator *bfi_imag);
-
-   /// Adds new Boundary Integrator, restricted to specific boundary attributes.
-   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi_real,
-                              BilinearFormIntegrator *bfi_imag,
-                              Array<int> &bdr_marker);
-
-   /// Assemble the local matrix
-   void Assemble(int skip_zeros = 1);
-
-   /// Finalizes the matrix initialization.
-   void Finalize(int skip_zeros = 1);
-
-   /// Returns the matrix assembled on the true dofs, i.e. P^t A P.
-   /** The returned matrix has to be deleted by the caller. */
-   ComplexHypreParMatrix *ParallelAssemble();
-
-   /// Return the parallel FE space associated with the ParBilinearForm.
-   ParFiniteElementSpace *ParFESpace() const { return pblfr_->ParFESpace(); }
-
-   void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x, Vector &b,
-                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
-
-   /** Call this method after solving a linear system constructed using the
-       FormLinearSystem method to recover the solution as a ParGridFunction-size
-       vector in x. Use the same arguments as in the FormLinearSystem call. */
-   virtual void RecoverFEMSolution(const Vector &X, const Vector &b, Vector &x);
-
-   virtual void Update(FiniteElementSpace *nfes = NULL);
-
-   virtual ~ParSesquilinearForm();
-};
-
-#endif // MFEM_USE_MPI
-
-}
-
-#endif // MFEM_COMPLEX_FEM

fem/fe.cpp

@@ -11845,6 +11845,376 @@ void NURBS3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
    }
 }
 
+/// SBP_SegmentElement is a segment element with nodes at Gauss Lobatto
+/// points with ordering consistent with SBP_TriangleElement's edges.
+
+//////////////////////////////////////////////////////////////////////////
+/// Not currently implemented as collocated SBP type element
+//////////////////////////////////////////////////////////////////////////
+SBP_SegmentElement::SBP_SegmentElement(const int p)
+   : NodalTensorFiniteElement(1, p+1, BasisType::GaussLobatto, H1_DOF_MAP)
+{
+   const double *cp = poly1d.ClosedPoints(p+1, b_type);
+
+#ifndef MFEM_THREAD_SAFE
+   shape_x.SetSize(p+2);
+   dshape_x.SetSize(p+2);
+#endif
+
+   Nodes.IntPoint(0).x = cp[0];
+   Nodes.IntPoint(1).x = cp[p+1];
+
+   switch (p)
+   {
+      case 1:
+         Nodes.IntPoint(2).x = cp[1];
+         break;
+      case 2:
+         Nodes.IntPoint(2).x = cp[1];
+         Nodes.IntPoint(3).x = cp[2];
+         break;
+      case 3:
+         Nodes.IntPoint(2).x = cp[2];
+         Nodes.IntPoint(3).x = cp[1];
+         Nodes.IntPoint(4).x = cp[3];
+         break;
+      case 4:
+         Nodes.IntPoint(2).x = cp[2];
+         Nodes.IntPoint(3).x = cp[3];
+         Nodes.IntPoint(4).x = cp[1];
+         Nodes.IntPoint(5).x = cp[4];
+         break;
+   }
+}
+
+void SBP_SegmentElement::CalcShape(const IntegrationPoint &ip,
+                                  Vector &shape) const
+{
+   const int p = Order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+2);
+#endif
+
+   basis1d.Eval(ip.x, shape_x);
+
+   shape(0) = shape_x(0);
+   shape(1) = shape_x(p+1);
+
+   switch (p)
+   {
+      case 1:
+         shape(2) = shape_x(1);
+         break;
+      case 2:
+         shape(2) = shape_x(1);
+         shape(3) = shape_x(2);
+         break;
+      case 3:
+         shape(2) = shape_x(2);
+         shape(3) = shape_x(1);
+         shape(4) = shape_x(3);
+         break;
+      case 4:
+         shape(2) = shape_x(2);
+         shape(3) = shape_x(3);
+         shape(4) = shape_x(1);
+         shape(5) = shape_x(4);
+         break;
+   }
+}
+
+void SBP_SegmentElement::CalcDShape(const IntegrationPoint &ip,
+                                   DenseMatrix &dshape) const
+{
+   const int p = Order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+2), dshape_x(p+2);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x);
+
+   dshape(0,0) = dshape_x(0);
+   dshape(1,0) = dshape_x(p+1);
+
+   switch (p)
+   {
+      case 1:
+         dshape(2,0) = dshape_x(1);
+         break;
+      case 2:
+         dshape(2,0) = dshape_x(1);
+         dshape(3,0) = dshape_x(2);
+         break;
+      case 3:
+         dshape(2,0) = dshape_x(2);
+         dshape(3,0) = dshape_x(1);
+         dshape(4,0) = dshape_x(3);
+         break;
+      case 4:
+         dshape(2,0) = dshape_x(2);
+         dshape(3,0) = dshape_x(3);
+         dshape(4,0) = dshape_x(1);
+         dshape(5,0) = dshape_x(4);
+         break;
+   }
+}
+
+// Leftover function from H1_Segment element
+// void SBP_SegmentElement::ProjectDelta(int vertex, Vector &dofs) const
+// {
+//    const int p = Order;
+//    const double *cp = poly1d.ClosedPoints(p, b_type);
+
+//    switch (vertex)
+//    {
+//       case 0:
+//          dofs(0) = poly1d.CalcDelta(p, (1.0 - cp[0]));
+//          dofs(1) = poly1d.CalcDelta(p, (1.0 - cp[p]));
+//          for (int i = 1; i < p; i++)
+//          {
+//             dofs(i+1) = poly1d.CalcDelta(p, (1.0 - cp[i]));
+//          }
+//          break;
+
+//       case 1:
+//          dofs(0) = poly1d.CalcDelta(p, cp[0]);
+//          dofs(1) = poly1d.CalcDelta(p, cp[p]);
+//          for (int i = 1; i < p; i++)
+//          {
+//             dofs(i+1) = poly1d.CalcDelta(p, cp[i]);
+//          }
+//          break;
+//    }
+// }
+
+SBP_TriangleElement::SBP_TriangleElement(const int p, const int Do)
+   : NodalFiniteElement(2, Geometry::TRIANGLE, Do, p,
+                        FunctionSpace::SBPk)
+{
+   /// Header file including SBP Dx and Dy matrix data
+   #include "fe_sbp.hpp"
+
+   // Create Dx and Dy matrixes
+   Dx = new DenseMatrix(Dof);
+   Dy = new DenseMatrix(Dof);
+   
+   // Populate the Dx and Dy matrices and create the element's Nodes
+   switch (p)
+   {
+      case 0:
+         *Dx=p0Dx;
+         *Dy=p0Dy;
+
+         Nodes.IntPoint(0).Set2w(0.0, 0.0, 0.16666666666666666);
+         Nodes.IntPoint(1).Set2w(1.0, 0.0, 0.16666666666666666);
+         Nodes.IntPoint(2).Set2w(0.0, 1.0, 0.16666666666666666);
+         break;
+      case 1:
+         *Dx=p1Dx;
+         *Dy=p1Dy;
+
+         Nodes.IntPoint(0).Set2w(0.0, 0.0, 0.024999999999999998);
+         Nodes.IntPoint(1).Set2w(1.0, 0.0, 0.024999999999999998);
+         Nodes.IntPoint(2).Set2w(0.0, 1.0, 0.024999999999999998);
+         Nodes.IntPoint(3).Set2w(0.5, 0.0, 0.06666666666666667);
+         Nodes.IntPoint(4).Set2w(0.5, 0.5, 0.06666666666666667);
+         Nodes.IntPoint(5).Set2w(0.0, 0.5, 0.06666666666666667);
+         Nodes.IntPoint(6).Set2w(0.3333333333333333, 0.3333333333333333, 0.22500000000000006);
+         break;
+      case 2:
+         *Dx=p2Dx;
+         *Dy=p2Dy;
+  
+         // vertices
+         Nodes.IntPoint(0).Set2w(0.0, 0.0, 0.006261126504899741);
+         Nodes.IntPoint(1).Set2w(1.0, 0.0, 0.006261126504899741);
+         Nodes.IntPoint(2).Set2w(0.0, 1.0, 0.006261126504899741);
+
+         // edges
+         Nodes.IntPoint(3).Set2w(0.27639320225002106, 0.0, 0.026823800250389242);
+         Nodes.IntPoint(4).Set2w(0.7236067977499789, 0.0, 0.026823800250389242);
+         Nodes.IntPoint(5).Set2w(0.7236067977499789, 0.27639320225002106, 0.026823800250389242);
+         Nodes.IntPoint(6).Set2w(0.27639320225002106, 0.7236067977499789, 0.026823800250389242);
+         Nodes.IntPoint(7).Set2w(0.0, 0.7236067977499789, 0.026823800250389242);
+         Nodes.IntPoint(8).Set2w(0.0, 0.27639320225002106, 0.026823800250389242);
+
+         // interior
+         Nodes.IntPoint(9).Set2w(0.21285435711180825, 0.5742912857763836, 0.10675793966098839);
+         Nodes.IntPoint(10).Set2w(0.21285435711180825, 0.21285435711180825, 0.10675793966098839);
+         Nodes.IntPoint(11).Set2w(0.5742912857763836, 0.21285435711180825, 0.10675793966098839);
+         break;
+      case 3:
+         *Dx=p3Dx;
+         *Dy=p3Dy;
+   
+         // vertices
+         Nodes.IntPoint(0).Set2w(0.0, 0.0, 0.0022825661430496253);
+         Nodes.IntPoint(1).Set2w(1.0, 0.0, 0.0022825661430496253);
+         Nodes.IntPoint(2).Set2w(0.0, 1.0, 0.0022825661430496253);
+
+         // edges
+         Nodes.IntPoint(3).Set2w(0.5, 0.0, 0.015504052643022513);
+         Nodes.IntPoint(4).Set2w(0.17267316464601146, 0.0, 0.011342592592592586);
+         Nodes.IntPoint(5).Set2w(0.8273268353539885, 0.0, 0.011342592592592586);
+
+         Nodes.IntPoint(6).Set2w(0.5, 0.5, 0.015504052643022513);
+         Nodes.IntPoint(7).Set2w(0.8273268353539885, 0.17267316464601146, 0.011342592592592586);
+         Nodes.IntPoint(8).Set2w(0.17267316464601146, 0.8273268353539885, 0.011342592592592586);
+
+         Nodes.IntPoint(9).Set2w(0.0, 0.5, 0.015504052643022513);
+         Nodes.IntPoint(10).Set2w(0.0, 0.8273268353539885, 0.011342592592592586);
+         Nodes.IntPoint(11).Set2w(0.0, 0.17267316464601146, 0.011342592592592586);
+
+         // interior
+         Nodes.IntPoint(12).Set2w(0.4243860251718814, 0.1512279496562372, 0.07467669469983994);
+         Nodes.IntPoint(13).Set2w(0.4243860251718814, 0.4243860251718814, 0.07467669469983994);
+         Nodes.IntPoint(14).Set2w(0.1512279496562372, 0.4243860251718814, 0.07467669469983994);
+
+         Nodes.IntPoint(15).Set2w(0.14200508409677795, 0.7159898318064442, 0.051518167995569394);
+         Nodes.IntPoint(16).Set2w(0.14200508409677795, 0.14200508409677795, 0.051518167995569394);
+         Nodes.IntPoint(17).Set2w(0.7159898318064442, 0.14200508409677795, 0.051518167995569394);
+
+         break;
+      case 4:
+         *Dx=p4Dx;
+         *Dy=p4Dy; 
+
+         // vertices
+         Nodes.IntPoint(0).Set2w(0.000000000000000000,0.000000000000000000,0.001090393904993471);
+         Nodes.IntPoint(1).Set2w(1.000000000000000000,0.000000000000000000,0.001090393904993471);
+         Nodes.IntPoint(2).Set2w(0.000000000000000000,1.000000000000000000,0.001090393904993471);
+
+         // edges
+         Nodes.IntPoint(3).Set2w(0.357384241759677534,0.000000000000000000,0.006966942871463700);
+         Nodes.IntPoint(4).Set2w(0.642615758240322466,0.000000000000000000,0.006966942871463700);
+         Nodes.IntPoint(5).Set2w(0.117472338035267576,0.000000000000000000,0.005519747637357106);
+         Nodes.IntPoint(6).Set2w(0.882527661964732424,0.000000000000000000,0.005519747637357106);
+
+         Nodes.IntPoint(7).Set2w(0.642615758240322466,0.357384241759677534,0.006966942871463700);
+         Nodes.IntPoint(8).Set2w(0.357384241759677534,0.642615758240322466,0.006966942871463700);
+         Nodes.IntPoint(9).Set2w(0.882527661964732424,0.117472338035267576,0.005519747637357106);
+         Nodes.IntPoint(10).Set2w(0.117472338035267576,0.882527661964732424,0.005519747637357106);
+
+         Nodes.IntPoint(11).Set2w(0.000000000000000000,0.642615758240322466,0.006966942871463700);
+         Nodes.IntPoint(12).Set2w(0.000000000000000000,0.357384241759677534,0.006966942871463700);
+         Nodes.IntPoint(13).Set2w(0.000000000000000000,0.882527661964732424,0.005519747637357106);
+         Nodes.IntPoint(14).Set2w(0.000000000000000000,0.117472338035267576,0.005519747637357106);
+
+         // interior
+         Nodes.IntPoint(15).Set2w(0.103677508142805172,0.792644983714389628,0.028397190663911491);
+         Nodes.IntPoint(16).Set2w(0.103677508142805172,0.103677508142805172,0.028397190663911491);
+         Nodes.IntPoint(17).Set2w(0.792644983714389628,0.103677508142805172,0.028397190663911491);
+         Nodes.IntPoint(18).Set2w(0.265331380484209678,0.469337239031580644,0.039960048027851809);
+         Nodes.IntPoint(19).Set2w(0.265331380484209678,0.265331380484209678,0.039960048027851809);
+         Nodes.IntPoint(20).Set2w(0.469337239031580644,0.265331380484209678,0.039960048027851809);
+         Nodes.IntPoint(21).Set2w(0.587085567133367348,0.088273960601581103,0.036122826526134168);
+         Nodes.IntPoint(22).Set2w(0.324640472265051494,0.088273960601581103,0.036122826526134168);
+         Nodes.IntPoint(23).Set2w(0.324640472265051494,0.587085567133367348,0.036122826526134168);
+         Nodes.IntPoint(24).Set2w(0.587085567133367348,0.324640472265051494,0.036122826526134168);
+         Nodes.IntPoint(25).Set2w(0.088273960601581103,0.324640472265051494,0.036122826526134168);
+         Nodes.IntPoint(26).Set2w(0.088273960601581103,0.587085567133367348,0.036122826526134168);
+
+         break;
+      default:
+         mfem_error("SBP elements are currently only supported for 0 <= order <= 4");
+         break;
+   }
+
+   // populate unordered_map with mapping from IntPoint address to index
+   for (int i = 0; i < Dof; i++)
+   {
+      ipIdxMap[&(Nodes.IntPoint(i))] = i;
+   }
+}
+
+/// CalcShape outputs ndofx1 vector shape based on Kronecker \delta_{i, ip}
+/// where ip is the integration point CalcShape is evaluated at. 
+void SBP_TriangleElement::CalcShape(const IntegrationPoint &ip,
+                                   Vector &shape) const
+{
+   int ipIdx;
+   try
+   {
+      ipIdx = ipIdxMap.at(&ip);
+   }
+   catch (const std::out_of_range& oor)
+   // error handling code to handle cases where the pointer to ip is not
+   // in the map. Problems arise in GridFunction::SaveVTK() ->  GridFunction::GetValues()
+   // which calls CalcShape() with an `IntegrationPoint` defined by a refined
+   // geometry type. Since the IntegrationPoint is not in Nodes, its address is
+   // not in the ipIdxMap, and an out_of_range error is thrown. This code catches
+   // the error and uses float comparisons to determine the IntegrationPoint
+   // index.
+   {
+      double tol = 1e-12;
+      for (int i = 0; i < Dof; i++)
+      {
+         double delta_x = ip.x - Nodes.IntPoint(i).x;
+         double delta_y = ip.y - Nodes.IntPoint(i).y;
+         if (delta_x*delta_x + delta_y*delta_y < tol)
+         {
+            ipIdx = i;
+            break;
+         }
+      }
+   }
+   shape = 0.0;
+   shape(ipIdx) = 1.0;
+}
+
+/// CalcDShape outputs ndof x ndim DenseMatrix dshape, where the first column
+/// is the ith row of Dx, and the second column is the ith row of Dy, where i
+/// is the integration point CalcDShape is evaluated at. Since DenseMatrices 
+/// are stored a column major we should store the transpose so accessing a row
+/// is faster, but this is not done here.
+void SBP_TriangleElement::CalcDShape(const IntegrationPoint &ip,
+                                    DenseMatrix &dshape) const
+{
+   int ipIdx;
+   try
+   {
+      ipIdx = ipIdxMap.at(&ip);
+   }
+   catch (const std::out_of_range& oor)
+   // error handling code to handle cases where the pointer to ip is not
+   // in the map. Problems arise in GridFunction::SaveVTK() ->  GridFunction::GetValues()
+   // which calls CalcShape() with an `IntegrationPoint` defined by a refined
+   // geometry type. Since the IntegrationPoint is not in Nodes, its address is
+   // not in the ipIdxMap, and an out_of_range error is thrown. This code catches 
+   // the error and uses float comparisons to determine the IntegrationPoint
+   // index.
+   {
+      double tol = 1e-12;
+      for (int i = 0; i < Dof; i++)
+      {
+         double delta_x = ip.x - Nodes.IntPoint(i).x;
+         double delta_y = ip.y - Nodes.IntPoint(i).y;
+         if (delta_x*delta_x + delta_y*delta_y < tol)
+         {
+            ipIdx = i;
+            break;
+         }
+      }
+   }
+   dshape = 0.0;
+
+   Vector tempVec(Dof);
+
+   // when we switch to storing Dx and Dy transpose so that access to the row we want
+   // is faster Dx->GetRow() will be replaced with Dx->GetColumnReference()
+   Dx->GetRow(ipIdx, tempVec);
+   dshape.SetCol(0, tempVec);
+   Dy->GetRow(ipIdx, tempVec);
+   dshape.SetCol(1, tempVec);
+}
+
+SBP_TriangleElement::~SBP_TriangleElement()
+{
+   delete Dx;
+   delete Dy;
+}
 
 // Global object definitions
 

fem/fe.hpp

@@ -19,6 +19,7 @@
 #include "geom.hpp"
 
 #include <map>
+#include <unordered_map>
 
 namespace mfem
 {
@@ -126,7 +127,8 @@ public:
    {
       Pk, ///< Polynomials of order k
       Qk, ///< Tensor products of polynomials of order k
-      rQk ///< Refined tensor products of polynomials of order k
+      rQk,///< Refined tensor products of polynomials of order k
+      SBPk///< Summation-by-parts operator of order k with no explicit basis
    };
 };
 
@@ -2819,6 +2821,44 @@ public:
                            DenseMatrix &dshape) const;
 };
 
+/// Class for summation-by-parts operator on interval
+class SBP_SegmentElement : public NodalTensorFiniteElement
+{
+private:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector shape_x, dshape_x;
+#endif
+
+public:
+   SBP_SegmentElement(const int p);
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+   
+   // ProjectDelta is leftover function from H1_SegmentElement
+   // virtual void ProjectDelta(int vertex, Vector &dofs) const;
+};
+
+/// Class for (diagonal-norm) summation-by-parts operator on triangles
+class SBP_TriangleElement : public NodalFiniteElement
+{
+private:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector shape_x, shape_y, shape_l, dshape_x, dshape_y, dshape_l, u;
+   mutable Vector ddshape_x, ddshape_y, ddshape_l;
+   mutable DenseMatrix du, ddu;
+#endif
+   DenseMatrix *Dx, *Dy;
+   std::unordered_map<const IntegrationPoint*, int> ipIdxMap;
+
+public:
+   SBP_TriangleElement(const int p, const int Do);
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+   virtual ~SBP_TriangleElement();
+};
+
 } // namespace mfem
 
 #endif

fem/fe_coll.cpp

@@ -274,6 +274,10 @@ FiniteElementCollection *FiniteElementCollection::New(const char *name)
          fec = new NURBSFECollection();
       }
    }
+   else if (!strncmp(name, "SBP_", 4))
+   {
+      fec = new C_SBPCollection(atoi(name+8), atoi(name+4));
+   }
    else
    {
       MFEM_ABORT("unknown FiniteElementCollection: " << name);
@@ -2542,4 +2546,159 @@ FiniteElementCollection *NURBSFECollection::GetTraceCollection() const
    return NULL;
 }
 
+C_SBPCollection::C_SBPCollection(const int p, const int dim)
+{
+   MFEM_VERIFY(p >= 0 && p <= 4, "C_SBPCollection requires 0 <= order <= 4.");
+   MFEM_VERIFY(dim == 2, "C_SBPCollection requires dim == 2.");
+
+   snprintf(c_SBPname, 32, "SBP_%dD_P%d", dim, p);
+
+   for (int g = 0; g < Geometry::NumGeom; g++)
+   {
+      C_SBPdof[g] = 0;
+      C_SBPElements[g] = NULL;
+   }
+   for (int i = 0; i < 2; i++)
+   {
+      SegDofOrd[i] = NULL;
+   }
+
+   C_SBPdof[Geometry::POINT] = 1;
+   C_SBPElements[Geometry::POINT] = new PointFiniteElement;
+
+   if (dim >= 1)
+   {
+      C_SBPdof[Geometry::SEGMENT] = p;
+
+      C_SBPElements[Geometry::SEGMENT] = new SBP_SegmentElement(p);
+
+      int nodeOrder0[] = {};
+      int nodeOrder1[1] = {0};
+      int nodeOrder2[2] = {0, 1};
+      int nodeOrder3[3] = {0, 1, 2};
+      int nodeOrder4[4] = {0, 1, 2, 3};
+
+      int revNodeOrder0[] = {};
+      int revNodeOrder1[1] = {0};
+      int revNodeOrder2[2] = {1, 0};
+      int revNodeOrder3[3] = {0, 2, 1};
+      int revNodeOrder4[4] = {1, 0, 3, 2};
+
+      switch (p)
+      {
+         case 0:
+            SegDofOrd[0] = new int[p];
+            SegDofOrd[1] = new int[p];
+            for (int i = 0; i < p; i++)
+            {
+               SegDofOrd[0][i] = nodeOrder0[i];
+               SegDofOrd[1][i] = revNodeOrder0[i];
+            }
+            break;
+         case 1:
+            SegDofOrd[0] = new int[p];
+            SegDofOrd[1] = new int[p];
+            for (int i = 0; i < p; i++)
+            {
+               SegDofOrd[0][i] = nodeOrder1[i];
+               SegDofOrd[1][i] = revNodeOrder1[i];
+            }
+            break;
+         case 2:
+            SegDofOrd[0] = new int[p];
+            SegDofOrd[1] = new int[p];
+            for (int i = 0; i < p; i++)
+            {
+               SegDofOrd[0][i] = nodeOrder2[i];
+               SegDofOrd[1][i] = revNodeOrder2[i];
+            }
+            break;
+         case 3:
+            SegDofOrd[0] = new int[p];
+            SegDofOrd[1] = new int[p];
+            for (int i = 0; i < p; i++)
+            {
+               SegDofOrd[0][i] = nodeOrder3[i];
+               SegDofOrd[1][i] = revNodeOrder3[i];
+            }
+            break;
+         case 4:
+            SegDofOrd[0] = new int[p];
+            SegDofOrd[1] = new int[p];
+            for (int i = 0; i < p; i++)
+            {
+               SegDofOrd[0][i] = nodeOrder4[i];
+               SegDofOrd[1][i] = revNodeOrder4[i];
+            }
+            break;
+         default:
+            mfem_error("SBP elements are currently only supported for 0 <= order <= 4");
+            break;
+
+      }
+   }
+
+   if (dim >= 2)
+   {
+      switch (p)
+      {
+         case 0:
+            C_SBPdof[Geometry::TRIANGLE] = 3 - 3 - 3*p;
+            break;
+         case 1:
+            C_SBPdof[Geometry::TRIANGLE] = 7 - 3 - 3*p;
+            break;
+         case 2:
+            C_SBPdof[Geometry::TRIANGLE] = 12 - 3 - 3*p;
+            break;
+         case 3:
+            C_SBPdof[Geometry::TRIANGLE] = 18 - 3 - 3*p;
+            break;
+         case 4:
+            C_SBPdof[Geometry::TRIANGLE] = 27 - 3 - 3*p;
+            break;
+         default:
+            mfem_error("SBP elements are currently only supported for 0 <= order <= 4");
+            break;
+      }
+
+      const int &TriDof = C_SBPdof[Geometry::TRIANGLE] + 3*C_SBPdof[Geometry::POINT] + 3*C_SBPdof[Geometry::SEGMENT];
+
+      C_SBPElements[Geometry::TRIANGLE] = new SBP_TriangleElement(p, TriDof);
+   }
+}
+
+const FiniteElement *C_SBPCollection::FiniteElementForGeometry(
+      Geometry::Type GeomType) const
+{
+   if (GeomType == Geometry::TRIANGLE || GeomType == Geometry::SEGMENT || GeomType == Geometry::POINT)
+   {
+
+   }
+   else
+   {
+      MFEM_ABORT("Unsupported geometry type " << GeomType);
+   }
+   return C_SBPElements[GeomType]; 
+}
+
+const int *C_SBPCollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                   int Or) const
+{
+   if (GeomType == Geometry::SEGMENT)
+   {
+      return (Or > 0) ? SegDofOrd[0] : SegDofOrd[1];
+   }
+   return NULL;
+}
+
+C_SBPCollection::~C_SBPCollection()
+{
+   delete [] SegDofOrd[0];
+   for (int g = 0; g < Geometry::NumGeom; g++)
+   {
+      delete C_SBPElements[g];
+   }
+}
+
 }

fem/fe_coll.hpp

@@ -884,6 +884,30 @@ public:
    virtual ~Local_FECollection() { delete Local_Element; }
 };
 
+/// Arbitrary order H1-conforming (continuous) Summation By Parts
+/// opperators.
+class C_SBPCollection : public FiniteElementCollection
+{
+
+protected:
+   char c_SBPname[32];
+   FiniteElement *C_SBPElements[Geometry::NumGeom];
+   int  C_SBPdof[Geometry::NumGeom];
+   int *SegDofOrd[2];
+
+public:
+   explicit C_SBPCollection(const int p, const int dim = 2);
+
+   virtual const FiniteElement *FiniteElementForGeometry(
+      Geometry::Type GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const
+   { return C_SBPdof[GeomType]; }
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
+   virtual const char *Name() const { return c_SBPname; }
+   virtual ~C_SBPCollection();
+};
+
 }
 
 #endif

fem/fe_sbp.hpp

@@ -0,0 +1,141 @@
+/// SBP Triangle Dx and Dy matrix data arrays, stored column major format
+const double p0Dx[9] = {-0.9999999999999984,-1.000000000000001,-0.9999999999999988,
+         1.000000000000001,0.9999999999999974,0.9999999999999994,
+         1.3322676295501878e-15,-1.9984014443252818e-15,9.992007221626409e-16};
+const double p0Dy[9] = {-0.9999999999999974,-0.9999999999999994,-1.0000000000000009,
+		1.9984014443252818e-15,-9.992007221626409e-16,-1.7486012637846216e-15,
+		1.0000000000000009,0.9999999999999991,0.9999999999999984};
+const double p1Dx[49] = {-3.333333333333333, 0.21647921352995003, 0.10823960676497299, -0.8824293926518367, 0.7863909022744312, -0.051249687578105226, -0.362809297675581,
+-0.21647921352995003, 3.333333333333333, -0.10823960676497392, 0.8824293926518368, 0.05124968757810527, -0.7863909022744306, 0.3628092976755813,
+-0.10823960676497299, 0.10823960676497392, 0.0, 7.406681257404114e-16, -0.8311797050737315, 0.8311797050737307, -1.9769834191462048e-16,
+2.3531450470715645, -2.353145047071565, -1.9751150019744302e-15, 0.0, -0.2351412146963257, 0.23514121469632399, 3.1540140465066577e-17,
+-2.09704240606515, -0.13666583354161405, 2.2164792135299507, 0.2351412146963257, 5.0, 0.47028242939265, 1.2743814046488378,
+0.13666583354161393, 2.0970424060651482, -2.2164792135299485, -0.23514121469632399, -0.47028242939265, -5.0, -1.2743814046488378,
+3.2652836790802304, -3.2652836790802326, 1.7792850772315852e-15, -1.0644797406959973e-16, -4.301037240689829, 4.301037240689829, 0.0};
+const double p1Dy[49] = {-3.333333333333333, 0.10823960676497733, 0.21647921352994814, -0.0512496875781027, 0.7863909022744318, -0.8824293926518388, -0.3628092976755811,
+-0.10823960676497733, 0.0, 0.10823960676497837, 0.8311797050737281, -0.8311797050737287, 9.745633233426465e-17, -3.4329014409980615e-16,
+-0.21647921352994814, -0.10823960676497837, 3.333333333333333, -0.7863909022744319, 0.051249687578102346, 0.8824293926518396, 0.3628092976755813,
+0.1366658335416072, -2.216479213529942, 2.0970424060651514, -5.0, -0.4702824293926414, -0.23514121469633495, -1.274381404648838,
+-2.0970424060651514, 2.216479213529943, -0.13666583354160625, 0.4702824293926414, 5.0, 0.235141214696336, 1.2743814046488384,
+2.3531450470715702, -2.5988355289137243e-16, -2.3531450470715725, 0.23514121469633495, -0.235141214696336, 0.0, 3.7848168558079887e-16,
+3.2652836790802313, 3.0896112968982564e-15, -3.2652836790802326, 4.30103724068983, -4.301037240689832, -1.2773756888351966e-15, 0.0};
+
+const double p2Dx[144] = {-6.654819485608504, -0.2644800033235228, -0.13224000166175998, -1.4588736121976598, 0.16568196946098376, -0.18364010800322192, -0.49629408766969996, 0.18676496181247967, -0.32850861828832895, 0.17877251381228318, -0.18297783134208934, 0.16855922332582518,
+0.2644800033235228, 6.654819485608504, 0.13224000166176486, -0.1656819694609847, 1.4588736121976598, 0.3285086182883251, -0.18676496181248323, 0.4962940876696997, 0.18364010800322153, -0.1787725138122836, -0.16855922332582482, 0.18297783134208834,
+0.13224000166175998, -0.13224000166176486, 0.0, -0.31265397966647923, 0.3126539796664765, -0.021082992351498762, -1.1303649939093317, 1.1303649939093305, 0.0210829923514981, -3.1850260779507576e-16, 0.010213290486458549, -0.010213290486458991,
+6.25007885298757, 0.7098115731146227, 1.3394662911697857, 0.0, -1.0987526276656132, 0.8391459038761706, -0.7493297423228898, -1.0608454694676046, 0.7982718911706455, 0.47711018331982885, -0.20709875867432972, -0.4372738402113571,
+-0.7098115731146187, -6.25007885298757, -1.339466291169774, 1.0987526276656132, 0.0, -0.7982718911706481, 1.0608454694676077, 0.7493297423228901, -0.8391459038761684, -0.47711018331982796, 0.4372738402113582, 0.20709875867432867,
+0.7867474920341369, -1.407390435347625, 0.09032335875573284, -0.8391459038761706, 0.7982718911706481, 7.766734444360106, 0.549376313832808, -1.8999913733437686, 1.4986594846457786, 0.7173852412251129, -0.7042577654543215, 1.9425023749691277,
+2.126213783203917, 0.8001349318703544, 4.842688417639932, 0.7493297423228898, -1.0608454694676077, -0.549376313832808, 7.766734444360106, 1.5965437823412956, -1.8999913733437699, 1.7354036162948008, -0.2271475821344933, 0.2801114010137556,
+-0.8001349318703392, -2.1262137832039163, -4.842688417639927, 1.0608454694676046, -0.7493297423228901, 1.8999913733437686, -1.5965437823412956, -7.766734444360106, 0.5493763138328077, -1.7354036162947999, -0.28011140101375603, 0.22714758213449346,
+1.4073904353476412, -0.7867474920341352, -0.09032335875573, -0.7982718911706455, 0.8391459038761684, -1.4986594846457786, 1.8999913733437699, -0.5493763138328077, -7.766734444360106, -0.7173852412251128, -1.9425023749691277, 0.7042577654543228,
+-3.0482350464695736, 3.0482350464695807, 5.4307610872012924e-15, -1.8988845609884182, 1.8988845609884146, -2.8551722567827746, -6.906855584460779, 6.906855584460776, 2.855172256782774, 0.0, 1.0883892687387082, -1.088389268738702,
+3.11993956078517, 2.8740890922806273, -0.1741459541889496, 0.8242469961764219, -1.7403370817278376, 2.8029252875555524, 0.904040726567137, 1.114835175054942, 7.73110258063719, -1.0883892687387082, 0.0, -2.176778537477416,
+-2.8740890922806335, -3.119939560785153, 0.17414595418895715, 1.7403370817278334, -0.8242469961764177, -7.73110258063719, -1.1148351750549401, -0.9040407265671375, -2.8029252875555577, 1.088389268738702, 2.176778537477416, 0.0};
+
+const double p2Dy[144] = {-6.654819485608504, -0.13224000166176303, -0.26448000332352145, -0.3285086182883249, 0.1867649618124839, -0.49629408766970096, -0.18364010800322322, 0.16568196946098196, -1.4588736121976569, 0.16855922332582438, -0.1829778313420883, 0.17877251381228437,
+0.13224000166176303, 0.0, -0.13224000166176358, 0.021082992351497333, 1.1303649939093325, -1.13036499390933, -0.0210829923514987, 0.31265397966647596, -0.3126539796664774, -0.010213290486459194, 0.010213290486458717, 1.7550143694830702e-16,
+0.26448000332352145, 0.13224000166176358, 6.654819485608504, 0.18364010800321912, 0.49629408766969646, -0.18676496181248112, 0.32850861828832506, 1.4588736121976555, -0.16568196946098368, 0.18297783134208803, -0.16855922332582496, -0.17877251381228357,
+1.4073904353476239, -0.09032335875572672, -0.7867474920341248, -7.766734444360106, -0.5493763138328086, 1.8999913733437714, -1.498659484645771, 0.8391459038761694, -0.7982718911706419, 0.7042577654543205, -1.9425023749691286, -0.7173852412251152,
+-0.8001349318703573, -4.842688417639936, -2.1262137832039025, 0.5493763138328086, -7.766734444360106, -1.5965437823412931, 1.8999913733437763, -0.7493297423228881, 1.060845469467605, 0.22714758213449282, -0.28011140101375637, -1.7354036162948017,
+2.1262137832039216, 4.842688417639926, 0.8001349318703455, -1.8999913733437714, 1.5965437823412931, 7.766734444360106, -0.5493763138328039, -1.0608454694675977, 0.7493297423228871, 0.280111401013755, -0.22714758213449193, 1.7354036162947997,
+0.7867474920341424, 0.09032335875573258, -1.4073904353476248, 1.498659484645771, -1.8999913733437763, 0.5493763138328039, 7.766734444360106, 0.7982718911706495, -0.8391459038761694, 1.942502374969129, -0.7042577654543208, 0.7173852412251135,
+-0.709811573114611, -1.3394662911697717, -6.250078852987552, -0.8391459038761694, 0.7493297423228881, 1.0608454694675977, -0.7982718911706495, 0.0, 1.0987526276656179, 0.20709875867432867, 0.43727384021135907, -0.47711018331982974,
+6.250078852987558, 1.339466291169778, 0.7098115731146183, 0.7982718911706419, -1.060845469467605, -0.7493297423228871, 0.8391459038761694, -1.0987526276656179, 0.0, -0.4372738402113571, -0.20709875867432725, 0.4771101833198306,
+-2.8740890922806197, 0.17414595418896062, -3.1199395607851477, -2.8029252875555484, -0.904040726567135, -1.114835175054938, -7.731102580637195, -0.8242469961764177, 1.7403370817278334, 0.0, 2.1767785374774147, 1.0883892687387102,
+3.119939560785152, -0.17414595418895248, 2.8740890922806295, 7.731102580637194, 1.1148351750549435, 0.9040407265671315, 2.8029252875555497, -1.7403370817278412, 0.8242469961764122, -2.1767785374774147, 0.0, -1.0883892687387073,
+-3.048235046469594, -2.9924601909068347e-15, 3.04823504646958, 2.8551722567827835, 6.906855584460783, -6.906855584460775, -2.855172256782777, 1.8988845609884217, -1.8988845609884253, -1.0883892687387102, 1.0883892687387073, 0.0};
+
+const double p3Dx[324] = {-10.952585131486583, -0.1691685246371182, -0.08458426231856121, 0.2782043329268357, -2.305479077267717, -0.07465619884488185, 0.08251879096720546, 0.22849304912079002, 0.5302407771816927, 0.28327860677318784, -0.11951297527437506, -0.5003055437372067, 0.12448476066856992, -0.09239160861978224, 0.10362923976480765, -0.16947318256573993, -0.12955658105892584, -0.0720914264099959,
+0.1691685246371182, 10.952585131486583, 0.08458426231855752, -0.2782043329268405, 0.0746561988448885, 2.3054790772677194, -0.2832786067731876, 0.5003055437372037, 0.11951297527437463, -0.08251879096721035, -0.5302407771816938, -0.2284930491207896, -0.12448476066856932, -0.10362923976480676, 0.09239160861978266, 0.16947318256574107, 0.07209142640999573, 0.12955658105892595,
+0.08458426231856121, -0.08458426231855752, 0.0, 1.1683416656308464e-15, 0.3017477280608998, -0.3017477280609013, -0.005074273846349578, 0.04485677642949094, -1.8051735335305155, 0.0050742738463512614, 1.805173533530519, -0.04485677642949147, 4.205982075638532e-16, 0.020855520903763268, -0.020855520903761818, 7.395777588076851e-16, -0.0973817561557449, 0.09738175615574554,
+-1.8896690623176595, 1.8896690623176922, -7.935818527815355e-15, 0.0, 2.0050512471695137, -2.0050512471695145, -0.8926105190374908, 1.6696076717446249, 0.020736328416563414, 0.8926105190375015, -0.020736328416544252, -1.669607671744625, -4.429107086712402e-16, 0.4633133883374836, -0.46331338833748054, 1.783666940029547e-15, 0.7834980551346994, -0.783498055134701,
+11.456452196936608, -0.3709837064689789, -1.4994533917700335, -1.4668732071255282, 0.0, 0.43808614602067847, -0.03454227374421423, -0.36820417663301963, 0.6765153661826107, -1.2393619133905875, 1.2485385227460366, 1.2932580655616601, -0.24307113935772914, 0.052425055137118155, 0.44269118420721065, -0.48976278487794334, -0.3768721550070895, 0.17743932374896715,
+0.3709837064689459, -11.45645219693662, 1.4994533917700408, 1.4668732071255288, -0.43808614602067847, 0.0, 1.2393619133905824, -1.2932580655616563, -1.2485385227460208, 0.034542273744204106, -0.6765153661826184, 0.36820417663302096, 0.24307113935772948, -0.44269118420720915, -0.052425055137118384, 0.4897627848779442, -0.1774393237489731, 0.3768721550070885,
+-0.5604988416610844, 1.924135449667926, 0.03446638735025072, 0.8926105190374908, 0.04721541624352583, -1.6940688111740314, 11.466536000042892, -1.1244968786658345, 0.8805543685036823, 1.785221038074984, -3.363676482918665, 0.026479087826965113, -0.42363907421033664, 2.460011157605557, -0.8869524625478119, 1.3603474091530658, 0.13068371284607608, 0.5768493540183615,
+-1.135434157870106, -2.486132536271146, -0.22290356912810128, -1.2214664156593342, 0.36820417663301963, 1.2932580655616563, 0.8226694181207354, 12.000000000000005, -0.21904307301033732, 0.01937180635024931, 1.6167426993790468, -1.3530307323652335, -0.6132774672199158, 0.43432201350751304, -0.11093602189671813, -0.6100947628964166, 0.7813784140227625, 2.7998077074825853,
+-2.634887549640154, -0.5938872755970562, 8.97031966066547, -0.01517046739396432, -0.6765153661826107, 1.2485385227460208, -0.6442037890047951, 0.21904307301033732, 12.000000000000005, -2.460828329049918, 2.586516131123318, 1.6167426993790477, -0.0585109667596005, 0.19125087414978273, -0.17058628301270465, 2.4229355524754963, 0.29161562914482175, -0.43265543914744503,
+-1.9241354496679275, 0.5604988416611175, -0.034466387350262154, -0.8926105190375015, 1.6940688111740383, -0.047215416243512, -1.785221038074984, -0.026479087826961595, 3.3636764829186583, -11.466536000042892, -0.8805543685036843, 1.1244968786658245, 0.42363907421033115, 0.8869524625478146, -2.4600111576055554, -1.3603474091530607, -0.5768493540183651, -0.13068371284607755,
+0.5938872755970585, 2.634887549640159, -8.97031966066549, 0.0151704673939503, -1.2485385227460366, 0.6765153661826184, 2.460828329049923, -1.6167426993790468, -2.586516131123318, 0.6442037890047966, -12.000000000000005, -0.21904307301033812, 0.05851096675959981, 0.17058628301270434, -0.19125087414978267, -2.422935552475496, 0.43265543914744814, -0.29161562914482114,
+2.486132536271161, 1.1354341578701037, 0.22290356912810394, 1.2214664156593344, -1.2932580655616601, -0.36820417663302096, -0.019371806350251885, 1.3530307323652335, -1.6167426993790477, -0.822669418120728, 0.21904307301033812, -12.000000000000005, 0.613277467219916, 0.11093602189671813, -0.43432201350751237, 0.6100947628964153, -2.7998077074825867, -0.7813784140227636,
+-4.072657651361357, 4.072657651361338, -1.3760339008438063e-14, 2.133320141015979e-15, 1.6003174861462979, -1.6003174861463, 2.0404965421712293, 4.037660156795314, 0.38522106525739636, -2.0404965421712027, -0.38522106525739186, -4.037660156795315, 0.0, -1.4579314260766258, 1.4579314260766234, 2.0161871961592337e-15, 3.273923136675281, -3.2739231366752755,
+3.0226944225627097, 3.3903460469074083, -0.6823116044539523, -2.2315915230588144, -0.34515299788282433, 2.914564209151067, -11.84886986676902, -2.859463754812241, -1.2591462686659354, -4.272088065230016, -1.1230959476442317, -0.7303740631402172, 1.4579314260766258, 0.0, 2.9158628521532504, 1.6703256795818853, -0.3883097004508776, -1.603597457093401,
+-3.390346046907437, -3.022694422562723, 0.6823116044539049, 2.2315915230587997, -2.914564209151077, 0.34515299788282583, 4.272088065230004, 0.7303740631402172, 1.1230959476442337, 11.84886986676901, 1.2591462686659352, 2.8594637548122366, -1.4579314260766234, -2.9158628521532504, 0.0, -1.6703256795818826, 1.6035974570934062, 0.3883097004508795,
+3.825058001824472, -3.8250580018244977, -1.669248067139698e-14, -5.926918282616925e-15, 2.2245074239726854, -2.2245074239726894, -4.520276599333233, 2.771056460992968, -11.004997298094699, 4.520276599333215, 11.004997298094697, -2.7710564609929618, -1.3909328887646931e-15, -1.1523289737701476, 1.1523289737701459, 0.0, -0.9410755641839665, 0.9410755641839751,
+2.9241289363066816, -1.6271240279890726, 2.1979339738354153, -2.6034731278339045, 1.7117570640055604, 0.8059311674378296, -0.4342468145397358, -3.5490285023571575, -1.3245210783844836, 1.9168034714993238, -1.9651252935551593, 12.716754362100263, -2.258623293890646, 0.26788818737287284, -1.1062943201205055, 0.9410755641839665, 0.0, 1.8821511283679513,
+1.6271240279890764, -2.9241289363066834, -2.1979339738354295, 2.60347312783391, -0.8059311674378026, -1.711757064005556, -1.9168034714993114, -12.716754362100257, 1.9651252935551453, 0.4342468145397406, 1.324521078384481, 3.5490285023571624, 2.258623293890642, 1.106294320120502, -0.2678881873728741, -0.9410755641839751, -1.8821511283679513, 0.0};
+
+const double p3Dy[324] = {-10.952585131486583, -0.08458426231856092, -0.16916852463712426, 0.28327860677318756, -0.5003055437372038, -0.11951297527437327, 0.0825187909672079, 0.5302407771816892, 0.22849304912079044, 0.2782043329268377, -0.07465619884488649, -2.305479077267721, 0.1036292397648074, -0.09239160861978217, 0.12448476066856967, -0.07209142640999439, -0.12955658105892628, -0.16947318256574065,
+0.08458426231856092, 0.0, -0.08458426231857115, 0.00507427384635043, -0.044856776429489494, 1.8051735335305168, -0.005074273846348987, -1.805173533530519, 0.04485677642949065, -2.536797215167323e-16, -0.30174772806090094, 0.3017477280609018, -0.020855520903761887, 0.020855520903762893, 3.895409306444457e-16, 0.09738175615574617, -0.09738175615574511, -2.518495690291951e-17,
+0.16916852463712426, 0.08458426231857115, 10.952585131486583, -0.08251879096720664, -0.2284930491207953, -0.5302407771816934, -0.2832786067731896, 0.11951297527436967, 0.5003055437372073, -0.2782043329268386, 2.305479077267721, 0.07465619884488589, 0.09239160861978252, -0.10362923976480695, -0.12448476066856902, 0.12955658105892542, 0.07209142640999575, 0.1694731825657405,
+-1.9241354496679255, -0.034466387350256505, 0.5604988416610924, -11.466536000042892, 1.124496878665824, -0.8805543685036857, -1.7852210380749862, 3.3636764829186614, -0.026479087826939977, -0.8926105190374863, -0.04721541624350879, 1.6940688111740283, -2.4600111576055577, 0.8869524625478143, 0.42363907421033403, -0.13068371284608143, -0.5768493540183609, -1.3603474091530663,
+2.4861325362711466, 0.2229035691280941, 1.1354341578701321, -0.8226694181207276, -12.000000000000005, 0.21904307301034107, -0.01937180635025535, -1.6167426993790432, 1.3530307323652313, 1.2214664156593333, -0.3682041766330094, -1.2932580655616668, -0.4343220135075129, 0.11093602189671664, 0.6132774672199158, -0.7813784140227632, -2.799807707482588, 0.6100947628964168,
+0.5938872755970495, -8.97031966066548, 2.634887549640157, 0.6442037890047976, -0.21904307301034107, -12.000000000000005, 2.4608283290499164, -2.586516131123313, -1.6167426993790395, 0.015170467393960869, 0.6765153661826211, -1.2485385227460257, -0.19125087414978525, 0.17058628301270676, 0.058510966759598895, -0.2916156291448204, 0.43265543914744725, -2.4229355524754985,
+-0.560498841661101, 0.03446638735024671, 1.9241354496679397, 1.7852210380749862, 0.026479087826969852, -3.363676482918656, 11.466536000042892, 0.8805543685036855, -1.1244968786658387, 0.8926105190374908, -1.6940688111740407, 0.047215416243521366, -0.8869524625478177, 2.460011157605558, -0.4236390742103285, 0.5768493540183687, 0.13068371284607674, 1.360347409153062,
+-2.634887549640136, 8.97031966066549, -0.5938872755970316, -2.4608283290499204, 1.6167426993790432, 2.586516131123313, -0.6442037890047975, 12.000000000000005, 0.2190430730103402, -0.015170467393955334, 1.2485385227460235, -0.6765153661826085, -0.17058628301270545, 0.19125087414978356, -0.05851096675960009, -0.432655439147446, 0.2916156291448159, 2.4229355524755003,
+-1.135434157870108, -0.22290356912809986, -2.4861325362711635, 0.019371806350233497, -1.3530307323652313, 1.6167426993790395, 0.8226694181207385, -0.2190430730103402, 12.000000000000005, -1.221466415659336, 1.2932580655616515, 0.3682041766330148, -0.11093602189671982, 0.43432201350751376, -0.6132774672199166, 2.7998077074825862, 0.781378414022764, -0.6100947628964163,
+-1.889669062317673, 1.72308862498413e-15, 1.8896690623176793, 0.8926105190374863, -1.6696076717446235, -0.0207363284165587, -0.8926105190374908, 0.020736328416551132, 1.669607671744627, 0.0, -2.005051247169507, 2.005051247169518, -0.46331338833748403, 0.4633133883374836, -7.923728999874815e-16, -0.7834980551347012, 0.7834980551346985, 2.487535508292328e-15,
+0.37098370646896894, 1.499453391770039, -11.456452196936628, 0.03454227374420177, 0.3682041766330094, -0.6765153661826211, 1.2393619133905893, -1.2485385227460235, -1.2932580655616515, 1.4668732071255233, 0.0, -0.43808614602068285, -0.0524250551371181, -0.44269118420721065, 0.24307113935773086, 0.37687215500708976, -0.17743932374896845, 0.48976278487794267,
+11.456452196936628, -1.4994533917700434, -0.37098370646896595, -1.2393619133905802, 1.2932580655616668, 1.2485385227460257, -0.03454227374421096, 0.6765153661826085, -0.3682041766330148, -1.4668732071255315, 0.43808614602068285, 0.0, 0.44269118420721193, 0.05242505513711802, -0.24307113935772984, 0.17743932374897087, -0.37687215500708626, -0.48976278487794556,
+-3.3903460469074287, 0.682311604453907, -3.022694422562719, 11.848869866769022, 2.85946375481224, 1.2591462686659523, 4.272088065230031, 1.123095947644239, 0.7303740631402283, 2.2315915230588166, 0.34515299788282394, -2.9145642091510853, 0.0, -2.9158628521532504, -1.4579314260766258, 0.3883097004508778, 1.6035974570934002, -1.6703256795818757,
+3.0226944225627075, -0.68231160445394, 3.3903460469074145, -4.272088065230015, -0.7303740631402075, -1.1230959476442475, -11.848869866769023, -1.259146268665941, -2.859463754812246, -2.2315915230588144, 2.914564209151077, -0.3451529978828235, 2.9158628521532504, 0.0, 1.4579314260766267, -1.6035974570933964, -0.3883097004508765, 1.6703256795818802,
+-4.072657651361349, -1.2744265588712169e-14, 4.072657651361328, -2.040496542171217, -4.037660156795314, -0.3852210652573858, 2.04049654217119, 0.3852210652573937, 4.037660156795319, 3.816536908330339e-15, -1.6003174861463092, 1.6003174861463025, 1.4579314260766258, -1.4579314260766267, 0.0, -3.2739231366752795, 3.273923136675281, -1.5485517097979382e-15,
+1.6271240279890422, -2.1979339738354438, -2.924128936306672, 0.43424681453975356, 3.5490285023571606, 1.3245210783844776, -1.9168034714993356, 1.9651252935551495, -12.71675436210026, 2.6034731278339103, -1.7117570640055617, -0.8059311674378195, -0.26788818737287295, 1.1062943201204989, 2.2586232938906448, 0.0, -1.8821511283679437, -0.941075564183975,
+2.9241289363066914, 2.1979339738354198, -1.627124027989073, 1.9168034714993096, 12.71675436210027, -1.9651252935551553, -0.434246814539738, -1.324521078384457, -3.549028502357164, -2.6034731278339014, 0.8059311674378086, 1.7117570640055457, -1.1062943201205013, 0.26788818737287207, -2.258623293890646, 1.8821511283679437, 0.0, 0.9410755641839769,
+3.825058001824488, 5.68431650770163e-16, -3.825058001824485, 4.520276599333235, -2.7710564609929693, 11.00499729809471, -4.5202765993332195, -11.004997298094716, 2.7710564609929667, -8.265791864994906e-15, -2.2245074239726823, 2.2245074239726956, 1.152328973770141, -1.152328973770144, 1.0683192052870465e-15, 0.941075564183975, -0.9410755641839769, 0.0};
+
+const double p4Dx[729] = {-15.28499617463146, 0.1965429454017319, 0.09827147270087869, 0.4207579292099769, -0.03011871770800639, -3.318562255325795, -0.12660138709292057, -0.20489551789966803, -0.1525100012592784, -0.02465488205886147, -0.44232233201277743, -0.16408537644014787, 0.28709832395121765, 0.06989189152237547, -0.445234967991587, 0.1446267442307163, -0.13342014677484493, 0.04884580398085625, -0.06120785634410805, -0.0065053622920859784, -0.055536979099377465, -0.05310883929020609, 0.137613494649232, 0.09694858537476729, 0.05875484376287877, 0.11266078234486253, -0.10900916485152536,
+-0.1965429454017319, 15.28499617463146, -0.09827147270085763, 0.030118717708007003, -0.42075792920997546, 0.12660138709291616, 3.318562255325798, -0.28709832395121665, 0.16408537644014565, 0.4452349679915819, -0.06989189152237295, 0.15251000125928654, 0.20489551789967583, 0.44232233201277626, 0.024654882058862064, -0.14462674423071573, -0.048845803980857666, 0.13342014677484318, 0.06120785634410922, 0.055536979099377264, 0.006505362292085202, -0.13761349464923325, 0.0531088392902052, 0.10900916485152572, -0.11266078234486292, -0.05875484376287771, -0.09694858537476635,
+-0.09827147270087869, 0.09827147270085763, 0.0, 0.05238551664039212, -0.05238551664039154, -0.41766744995391064, 0.41766744995391425, 0.13396665873213762, 0.13365960525875686, -0.19649327861528906, -2.87332728733421, -0.1336596052587585, -0.13396665873213948, 2.873327287334207, 0.19649327861529092, 7.071416687303329e-16, 0.0957809402498582, -0.09578094024985911, 5.095198309682238e-16, -0.005670877244732207, 0.005670877244731516, -0.0381937416118884, 0.03819374161188797, 0.024952712304370763, 0.055900325561320505, -0.05590032556132075, -0.02495271230436985,
+-2.688383016538256, -0.19243998400255485, -0.3347110618046863, 0.0, -1.8584179757445634, 2.9254109394468375, 0.5544784209743959, -0.09619204170147806, 0.9621335517719756, -0.7640240022365051, -0.17045575971749122, -0.32599503457469536, 1.5819839652391803, -0.1673484738314025, -2.1466117678065375, 0.20084022575022525, 0.8121668775566188, 0.28698839120282377, 0.22242408399761535, 0.1007642564284906, 0.1396610379722831, -0.4047350379804057, -0.19103788701331148, -0.4861845324334061, 0.0708248987102739, -0.5390429074476013, 0.02706866117436579,
+0.1924399840025509, 2.688383016538247, 0.3347110618046826, 1.8584179757445634, 0.0, -0.5544784209744025, -2.9254109394468055, -1.5819839652391763, 0.32599503457469153, 2.1466117678065477, 0.1673484738314174, -0.9621335517719789, 0.09619204170146632, 0.1704557597174755, 0.7640240022365011, -0.20084022575022814, -0.28698839120282255, -0.8121668775566167, -0.22242408399761296, -0.13966103797228493, -0.10076425642849256, 0.19103788701331245, 0.40473503798040156, -0.027068661174367476, 0.5390429074475989, -0.07082489871027405, 0.48618453243340803,
+16.79909075460827, -0.6408763879659072, 2.114299162464476, -2.3177353997619106, 0.43930042352937404, 0.0, 0.23758827371798064, 0.14587872928125803, -0.026683834684955113, 0.27594927228434313, -0.8508769996321647, 1.733847812899358, -1.9338802842578322, -1.4125593711637086, 1.7702761450361215, 0.49385180688379604, -0.48895648790844665, -0.15872007418498266, -0.09920419307861998, 0.12317929238116793, 0.08585557349611746, 0.09370614907316197, -0.2607460957437406, -0.00372051314937977, -0.04020180712625255, 0.5265453421646704, -0.4929563256972127,
+0.6408763879659295, -16.79909075460828, -2.1142991624644942, -0.4393004235293688, 2.3177353997618853, -0.23758827371798064, 0.0, 1.9338802842578542, -1.733847812899381, -1.7702761450361162, 1.4125593711636986, 0.026683834684962007, -0.14587872928127077, 0.8508769996321606, -0.27594927228435256, -0.4938518068837918, 0.15872007418498413, 0.4889564879084464, 0.0992041930786239, -0.08585557349611386, -0.1231792923811642, 0.26074609574374336, -0.09370614907315725, 0.49295632569721404, -0.5265453421646692, 0.040201807126253306, 0.0037205131493783417,
+1.3091556741914314, 1.834380779552396, -0.8559641188321434, 0.09619204170147806, 1.5819839652391763, -0.1841259491984436, -2.440914756589403, 19.910396398833793, 0.9292089878722896, -0.6009288150226979, -0.17768908386483087, -0.22980299287322684, -1.9242671035439767, 2.9524607667234655, 0.2041356965652301, -1.1190995177139584, -0.24116380960165718, 0.7245564881296083, -0.49029775323051117, -0.04870816987800388, -0.7132041988172136, -0.454608663355292, 0.08758856822375095, 1.0907550537346067, 4.030854005025503, 0.7748473349352286, 0.07689148379455818,
+0.9744446123867609, -1.0484041028347049, -0.8540022369858385, -0.9621335517719756, -0.32599503457469153, 0.03367993684774262, 2.18843676448695, -0.9292089878722896, 19.910396398833793, 0.3767893371095702, 2.3244821244241383, 3.163967930478371, -0.22980299287321784, -4.587526524395932, -0.3514744230298633, 1.53672336568623, -0.04032358385143443, -0.832111126511136, -0.6124399423887177, 0.1737159141196091, -0.3506367152582221, 0.14771638250483257, 0.2886628025018225, 3.839816118012189, 0.6860200157542047, 0.11465722939811557, -0.9936515708028879,
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+1.048404102834719, -0.9744446123868129, 0.8540022369858489, 0.32599503457469536, 0.9621335517719789, -2.1884367644869207, -0.03367993684775132, 0.22980299287322684, -3.163967930478371, 0.3514744230298829, 4.587526524395912, -19.910396398833793, 0.9292089878722776, -2.324482124424116, -0.37678933710957857, -1.536723365686234, 0.8321111265111332, 0.04032358385143004, 0.612439942388719, 0.35063671525822543, -0.17371591411960696, -0.28866280250182014, -0.14771638250483188, 0.9936515708028864, -0.11465722939811639, -0.6860200157542059, -3.8398161180121906,
+-1.8343807795524023, -1.3091556741914812, 0.8559641188321553, -1.5819839652391803, -0.09619204170146632, 2.440914756589375, 0.18412594919845968, 1.9242671035439767, 0.22980299287321784, -0.2041356965652155, -2.9524607667234513, -0.9292089878722776, -19.910396398833793, 0.17768908386480717, 0.6009288150227365, 1.1190995177139624, -0.7245564881296058, 0.24116380960166542, 0.49029775323050956, 0.7132041988172101, 0.04870816987800567, -0.08758856822375086, 0.4546086633552912, -0.07689148379455372, -0.7748473349352273, -4.030854005025498, -1.0907550537346087,
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+2.2538503300374226, -0.12480694029057034, -0.994680276023551, 1.7007108357677354, -0.6053185391404025, -1.7702761450361215, 0.27594927228435256, -0.16173198913850842, 0.2784650530230271, -1.7017539992643287, 1.6885086434480694, 0.29852147371706533, -0.476101995974123, 0.11879413685897054, -17.141859608597226, -0.5994748509692417, -3.6746404245088935, 0.6941668393814934, 0.09744008746280555, 0.39630394672766056, -0.2027967172087368, -0.6600584756782925, 0.7855375215315809, -0.20287631854527904, 0.16871993636572646, -0.7038226731025339, 0.4640248521828319,
+-3.766522549523058, 3.7665225495230428, -1.8416130814168517e-14, -0.8186227860390011, 0.818622786039013, -2.5406965754889375, 2.5406965754889157, 4.561438634236725, -6.263669333621437, -3.0840905707320223, -16.389240973690264, 6.263669333621453, -4.561438634236742, 16.38924097369023, 3.0840905707320356, 0.0, 0.8064071592627126, -0.8064071592627154, -3.27587819047868e-15, -0.2376302079323201, 0.23763020793230094, -0.5181032452374912, 0.5181032452374866, -2.3969263418417017, 0.8425636809391238, -0.8425636809391335, 2.396926341841694,
+3.474668492754472, 1.2720940592425334, -2.494428490280513, -3.3103842098885403, 1.169761861647588, 2.5155118541145702, -0.8165598329744024, 0.9829813174648175, 0.1643585314258267, 3.571248068855471, 1.030551493366546, -3.3916767725891264, 2.953285123732874, 2.267530737757596, 18.904752827804817, -0.8064071592627126, 0.0, -1.6128143185254504, 0.281848015316382, -1.069973391943026, 0.5194782232486872, 1.842445782443736, -3.2355644271100483, -0.020449207033394267, -0.5385524522708879, -0.8386380852683435, 0.9998821015046064,
+-1.2720940592424965, -3.474668492754426, 2.4944284902805367, -1.169761861647593, 3.310384209888532, 0.8165598329743948, -2.515511854114569, -2.953285123732884, 3.391676772589138, -18.904752827804824, -2.2675307377576006, -0.1643585314258088, -0.9829813174648512, -1.0305514933665705, -3.571248068855467, 0.8064071592627154, 1.6128143185254504, 0.0, -0.2818480153163751, -0.5194782232487007, 1.0699733919430288, 3.235564427110037, -1.8424457824437297, -0.9998821015046048, 0.8386380852683486, 0.5385524522708905, 0.020449207033400366,
+2.2431057877263694, -2.243105787726412, -1.867255202307378e-14, -1.275749958493393, 1.2757499584933791, 0.7181857904438594, -0.7181857904438878, 2.8121834969091495, 3.512750134965057, 0.7054146005697136, 1.977277771072542, -3.5127501349650645, -2.8121834969091406, -1.9772777710725515, -0.705414600569697, 4.609760570128499e-15, -0.39661177621033, 0.3966117762103203, 0.0, 1.473286325955928, -1.4732863259559217, 0.03294149361242836, -0.0329414936124289, -3.953179136944931, -1.408551582879458, 1.4085515828794593, 3.9531791369449287,
+0.23840429448465078, -2.035283159571775, 0.20782262815464633, -0.5779499847581375, 0.8010488801122674, -0.8917528051961954, 0.6215488579847753, 0.27937372870475113, -0.996376229788628, -1.468140772361843, -0.749954981917987, -2.0111346167968778, -4.090700119723205, -0.08386574258491672, -2.869030576268716, 0.3343892230125261, 1.5056485212427524, 0.7310009992228542, -1.473286325955928, 0.0, -2.9465726519118554, -0.8795833962368981, 0.19919319766269372, 0.49291247512221925, 0.5258539687346377, 4.152372334607633, 0.5289681866425602,
+2.035283159571782, -0.23840429448462236, -0.20782262815462102, -0.801048880112257, 0.5779499847581487, -0.6215488579848013, 0.8917528051961683, 4.090700119723225, 2.0111346167968587, 2.869030576268717, 0.0838657425849028, 0.9963762297886157, -0.27937372870476146, 0.7499549819179745, 1.468140772361822, -0.3343892230124991, -0.7310009992228351, -1.5056485212427564, 1.4732863259559217, 2.9465726519118554, 0.0, -0.19919319766269705, 0.8795833962369017, -0.5289681866425588, -4.152372334607625, -0.5258539687346414, -0.49291247512221426,
+1.759402157237792, 4.558892315982919, 1.2652912826383578, 2.0985063083979236, -0.9905102682507421, -0.6132401678100317, -1.706397937502056, 2.357095527641503, -0.7658930694187117, 5.140784956908139, -1.0645890975962542, 1.4966846336620354, 0.4541370173391847, -1.1285002237720632, 4.319613754198333, 0.6590565197748737, -2.3436948454060653, -4.115820254824023, -0.029778238966182636, 0.795120126366912, 0.1800653822873389, 0.0, 3.1163752731045724, 0.15960718397414111, -0.7346658981606436, -0.1973888096528869, -0.7116415547893532,
+-4.558892315982878, -1.7594021572377623, -1.2652912826383433, 0.9905102682507371, -2.0985063083979023, 1.7063979375020377, 0.6132401678100009, -0.4541370173391852, -1.4966846336620476, -4.319613754198339, 1.1285002237720605, 0.7658930694187083, -2.357095527641499, 1.064589097596253, -5.140784956908144, -0.6590565197748679, 4.115820254824037, 2.3436948454060573, 0.029778238966183125, -0.1800653822873359, -0.7951201263669153, -3.1163752731045724, 0.0, 0.71164155478935, 0.1973888096528901, 0.7346658981606372, -0.15960718397413862,
+-3.2117356080303803, -3.6112813302216713, -0.8266393399665194, 2.520812908731641, 0.14034800771819048, 0.024348115151799948, -3.2260489080343286, -5.655444047050364, -19.909020941069866, 3.0367129695880832, -2.8996213945368607, -5.151973251646951, 0.3986738203099664, -1.6949198009668083, 1.3276813620016823, 3.049025358424062, 0.026012543529633645, 1.271906370130427, 3.57356938337672, -0.4455798406197396, 0.47817325020768053, -0.15960718397414111, -0.71164155478935, 0.0, -1.5581876365522882, -0.3569959936270113, 1.46933179632127,
+-1.9464443253920187, 3.7322529760164143, -1.8518791729839088, -0.3672192491087197, -2.794877724005471, 0.26309226440541583, 3.4458651559413247, -20.899531209320617, -3.556937738652459, -4.606019332038912, 2.4234728017780744, 0.594485025057365, 4.017497542393682, 1.0935648461639937, -1.1041521086202575, -1.071788475275629, 0.6850690633045105, -1.0667948963999776, 1.2732933765745933, -0.4753580795859133, 3.753634765664056, 0.7346658981606436, -0.1973888096528901, 1.5581876365522882, 0.0, -1.4232831095787026, -0.35699599362703105,
+-3.7322529760164014, 1.9464443253919836, 1.8518791729839168, 2.794877724005484, 0.36721924910872045, -3.4458651559413327, -0.26309226440542083, -4.017497542393689, -0.5944850250573608, 1.1041521086202537, -1.0935648461640088, 3.5569377386524654, 20.89953120932059, -2.423472801778076, 4.6060193320388985, 1.0717884752756415, 1.0667948963999712, -0.6850690633045139, -1.2732933765745946, -3.753634765664064, 0.47535807958591664, 0.1973888096528869, -0.7346658981606372, 0.3569959936270113, 1.4232831095787026, 0.0, -1.5581876365522849,
+3.6112813302216593, 3.2117356080303487, 0.8266393399664891, -0.14034800771818173, -2.5208129087316506, 3.2260489080343198, -0.024348115151790604, -0.3986738203099895, 5.151973251646959, -1.3276813620016612, 1.694919800966806, 19.909020941069873, 5.6554440470503735, 2.8996213945368763, -3.03671296958808, -3.0490253584240525, -1.2719063701304292, -0.026012543529641403, -3.5735693833767184, -0.47817325020768164, 0.4455798406197351, 0.7116415547893532, 0.15960718397413862, -1.46933179632127, 0.35699599362703105, 1.5581876365522849, 0.0};
+
+const double p4Dy[729] = {-15.28499617463146, 0.09827147270086124, 0.19654294540174796, 0.2870983239512125, -0.164085376440144, -0.4452349679915834, 0.06989189152237135, -0.15251000125927563, -0.2048955178996692, -0.44232233201278237, -0.024654882058863847, -0.03011871770800668, 0.42075792920998006, -0.12660138709291216, -3.3185622553257907, 0.048845803980856306, -0.13342014677484385, 0.14462674423071498, -0.05553697909937705, -0.006505362292085907, -0.06120785634410891, -0.10900916485152638, 0.11266078234486171, 0.05875484376287875, 0.09694858537476714, 0.1376134946492328, -0.05310883929020566,
+-0.09827147270086124, 0.0, 0.09827147270087347, -0.13396665873213587, -0.13365960525875817, 0.19649327861528584, 2.8733272873342135, 0.1336596052587607, 0.13396665873214064, -2.873327287334207, -0.19649327861528823, -0.052385516640395494, 0.05238551664038741, 0.4176674499539139, -0.41766744995391747, -0.095780940249859, 0.09578094024985785, -9.030965889809071e-16, 0.00567087724473144, -0.0056708772447323225, -2.468104976161084e-16, -0.024952712304370517, -0.05590032556132032, 0.05590032556132042, 0.02495271230436975, 0.03819374161188785, -0.03819374161188903,
+-0.19654294540174796, -0.09827147270087347, 15.28499617463146, 0.20489551789967816, 0.15251000125928516, 0.024654882058868614, 0.44232233201278004, 0.16408537644014445, -0.2870983239512186, -0.06989189152236565, 0.445234967991583, -0.42075792920997346, 0.03011871770800419, 3.3185622553257907, 0.12660138709291832, 0.13342014677484448, -0.04884580398085644, -0.14462674423071606, 0.0065053622920860695, 0.055536979099378284, 0.06120785634410899, -0.0969485853747657, -0.058754843762877665, -0.11266078234486313, 0.1090091648515255, 0.05310883929020579, -0.1376134946492322,
+-1.8343807795523694, 0.8559641188321322, -1.309155674191496, -19.910396398833793, -0.9292089878722894, 0.6009288150227082, 0.1776890838648202, 0.22980299287321443, 1.9242671035439682, -2.9524607667234357, -0.20413569656523223, -0.09619204170148214, -1.581983965239188, 0.18412594919846403, 2.4409147565893874, 0.24116380960165718, -0.7245564881296103, 1.1190995177139629, 0.048708169878006975, 0.7132041988172096, 0.49029775323050717, -1.0907550537346093, -4.0308540050255, -0.774847334935228, -0.07689148379455714, 0.45460866335528777, -0.0875885682237497,
+1.0484041028346944, 0.8540022369858469, -0.9744446123868041, 0.9292089878722894, -19.910396398833793, -0.376789337109576, -2.3244821244241085, -3.163967930478372, 0.22980299287322126, 4.587526524395933, 0.35147442302985465, 0.9621335517719841, 0.32599503457468426, -0.03367993684773616, -2.1884367644869362, 0.0403235838514332, 0.8321111265111371, -1.5367233656862271, -0.17371591411960613, 0.3506367152582226, 0.6124399423887191, -3.8398161180121875, -0.686020015754205, -0.11465722939811551, 0.99365157080289, -0.14771638250483227, -0.2886628025018202,
+2.2538503300374044, -0.9946802760235254, -0.1248069402906035, -0.4761019959741005, 0.2985214737170633, -17.141859608597226, 0.1187941368589855, 0.27846505302302493, -0.1617319891384971, 1.6885086434480594, -1.7017539992643365, -0.605318539140416, 1.700710835767743, 0.2759492722843605, -1.7702761450361306, 0.6941668393814986, -3.674640424508889, -0.5994748509692356, -0.20279671720873876, 0.3963039467276609, 0.097440087462807, 0.4640248521828354, -0.703822673102532, 0.16871993636572868, -0.20287631854527582, 0.7855375215315806, -0.6600584756782898,
+-0.35380388805762664, -14.545240424570872, -2.2391061027550836, -0.14077894981230582, 1.8416334037877937, -0.1187941368589855, -17.141859608597226, 3.6345911200255987, -2.339166352039789, -3.540552290072251, 1.6885086434480605, -0.135048154453527, 0.13258632374176318, -0.8508769996321724, 1.4125593711637054, 0.20031503249770397, -0.44075477678425157, -3.1856839366004435, -0.103592524130115, 0.01158451396669216, 0.2731246543464982, -0.44307657735879197, 0.37031870310967574, -0.16710214998107722, 0.2589921793669143, -0.16267451141902012, 0.17244044951510798,
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fem/fem.hpp

@@ -18,7 +18,6 @@
 #include "fe_coll.hpp"
 #include "eltrans.hpp"
 #include "coefficient.hpp"
-#include "complex_fem.hpp"
 #include "lininteg.hpp"
 #include "nonlininteg.hpp"
 #include "bilininteg.hpp"

fem/gridfunc.cpp

@@ -2310,7 +2310,14 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
       else
       {
          int intorder = 2*fe->GetOrder() + 1; // <----------
-         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+         if (fe->Space() == FunctionSpace::SBPk)
+         {
+            ir = &(fe->GetNodes());
+         }
+         else 
+         {
+            ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+         }
       }
       GetValues(i, *ir, vals);
       T = fes->GetElementTransformation(i);

fem/linearform.hpp

@@ -81,15 +81,6 @@ public:
        Update(FiniteElementSpace *, Vector &, int). */
    LinearForm() { fes = NULL; extern_lfs = 0; }
 
-   /// Construct a LinearForm using previously allocated array @a data.
-   /** The LinearForm does not assume ownership of @a data which is assumed to
-       be of size at least `f->GetVSize()`. Similar to the Vector constructor
-       for externally allocated array, the pointer @a data can be NULL. The data
-       array can be replaced later using the method SetData().
-    */
-   LinearForm(FiniteElementSpace *f, double *data) : Vector(data, f->GetVSize())
-   { fes = f; }
-
    /// Copy assignment. Only the data of the base class Vector is copied.
    /** It is assumed that this object and @a rhs use FiniteElementSpace%s that
        have the same size.

fem/lininteg.cpp

@@ -36,9 +36,16 @@ void DomainLFIntegrator::AssembleRHSElementVect(const FiniteElement &el,
    const IntegrationRule *ir = IntRule;
    if (ir == NULL)
    {
-      // ir = &IntRules.Get(el.GetGeomType(),
-      //                    oa * el.GetOrder() + ob + Tr.OrderW());
-      ir = &IntRules.Get(el.GetGeomType(), oa * el.GetOrder() + ob);
+      if (el.Space() == FunctionSpace::SBPk)
+      {
+         ir = &el.GetNodes();
+      }
+      else 
+      {
+         // ir = &IntRules.Get(el.GetGeomType(),
+         //                    oa * el.GetOrder() + ob + Tr.OrderW());
+         ir = &IntRules.Get(el.GetGeomType(), oa * el.GetOrder() + ob);
+      }
    }
 
    for (int i = 0; i < ir->GetNPoints(); i++)

fem/plinearform.hpp

@@ -45,16 +45,6 @@ public:
    /** The pointer @a pf is not owned by the newly constructed object. */
    ParLinearForm(ParFiniteElementSpace *pf) : LinearForm(pf) { pfes = pf; }
 
-   /// Construct a ParLinearForm using previously allocated array @a data.
-   /** The ParLinearForm does not assume ownership of @a data which is assumed
-       to be of size at least `pf->GetVSize()`. Similar to the LinearForm and
-       Vector constructors for externally allocated array, the pointer @a data
-       can be NULL. The data array can be replaced later using the method
-       SetData().
-    */
-   ParLinearForm(ParFiniteElementSpace *pf, double *data) :
-      LinearForm(pf, data), pfes(pf) { }
-
    /** @brief Create a ParLinearForm on the ParFiniteElementSpace @a *pf, using
        the same integrators as the ParLinearForm @a *plf.
 

general/cuda.cpp

@@ -10,17 +10,27 @@
 // Software Foundation) version 2.1 dated February 1999.
 
 #include "cuda.hpp"
+#include "globals.hpp"
 
 namespace mfem
 {
 
+#ifdef MFEM_USE_CUDA
+void mfem_cuda_error(cudaError_t err, const char *expr, const char *func,
+                     const char *file, int line)
+{
+   mfem::err << "CUDA error: (" << expr << ") failed with error:\n --> "
+             << cudaGetErrorString(err)
+             << "\n ... in function: " << func
+             << "\n ... in file: " << file << ':' << line << '\n';
+   mfem_error();
+}
+#endif
+
 void* CuMemAlloc(void** dptr, size_t bytes)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS != ::cuMemAlloc((CUdeviceptr*)dptr, bytes))
-   {
-      mfem_error("Error in CuMemAlloc");
-   }
+   MFEM_CUDA_CHECK(cudaMalloc(dptr, bytes));
 #endif
    return *dptr;
 }
@@ -28,10 +38,7 @@ void* CuMemAlloc(void** dptr, size_t bytes)
 void* CuMemFree(void *dptr)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS != ::cuMemFree((CUdeviceptr)dptr))
-   {
-      mfem_error("Error in CuMemFree");
-   }
+   MFEM_CUDA_CHECK(cudaFree(dptr));
 #endif
    return dptr;
 }
@@ -39,22 +46,15 @@ void* CuMemFree(void *dptr)
 void* CuMemcpyHtoD(void* dst, const void* src, size_t bytes)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS != ::cuMemcpyHtoD((CUdeviceptr)dst, src, bytes))
-   {
-      mfem_error("Error in CuMemcpyHtoD");
-   }
+   MFEM_CUDA_CHECK(cudaMemcpy(dst, src, bytes, cudaMemcpyHostToDevice));
 #endif
    return dst;
 }
 
-void* CuMemcpyHtoDAsync(void* dst, const void* src, size_t bytes, void *s)
+void* CuMemcpyHtoDAsync(void* dst, const void* src, size_t bytes)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS !=
-       ::cuMemcpyHtoDAsync((CUdeviceptr)dst, src, bytes, (CUstream)s))
-   {
-      mfem_error("Error in CuMemcpyHtoDAsync");
-   }
+   MFEM_CUDA_CHECK(cudaMemcpyAsync(dst, src, bytes, cudaMemcpyHostToDevice));
 #endif
    return dst;
 }
@@ -62,24 +62,15 @@ void* CuMemcpyHtoDAsync(void* dst, const void* src, size_t bytes, void *s)
 void* CuMemcpyDtoD(void* dst, void* src, size_t bytes)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS !=
-       ::cuMemcpyDtoD((CUdeviceptr)dst, (CUdeviceptr)src, bytes))
-   {
-      mfem_error("Error in CuMemcpyDtoD");
-   }
+   MFEM_CUDA_CHECK(cudaMemcpy(dst, src, bytes, cudaMemcpyDeviceToDevice));
 #endif
    return dst;
 }
 
-void* CuMemcpyDtoDAsync(void* dst, void* src, size_t bytes, void *s)
+void* CuMemcpyDtoDAsync(void* dst, void* src, size_t bytes)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS !=
-       ::cuMemcpyDtoDAsync((CUdeviceptr)dst, (CUdeviceptr)src,
-                           bytes, (CUstream)s))
-   {
-      mfem_error("Error in CuMemcpyDtoDAsync");
-   }
+   MFEM_CUDA_CHECK(cudaMemcpyAsync(dst, src, bytes, cudaMemcpyDeviceToDevice));
 #endif
    return dst;
 }
@@ -87,10 +78,7 @@ void* CuMemcpyDtoDAsync(void* dst, void* src, size_t bytes, void *s)
 void* CuMemcpyDtoH(void *dst, void *src, size_t bytes)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS != ::cuMemcpyDtoH(dst, (CUdeviceptr)src, bytes))
-   {
-      mfem_error("Error in CuMemcpyDtoH");
-   }
+   MFEM_CUDA_CHECK(cudaMemcpy(dst, src, bytes, cudaMemcpyDeviceToHost));
 #endif
    return dst;
 }
@@ -98,11 +86,7 @@ void* CuMemcpyDtoH(void *dst, void *src, size_t bytes)
 void* CuMemcpyDtoHAsync(void* dst, void* src, size_t bytes, void *s)
 {
 #ifdef MFEM_USE_CUDA
-   if (CUDA_SUCCESS !=
-       ::cuMemcpyDtoHAsync(dst, (CUdeviceptr)src, bytes, (CUstream)s))
-   {
-      mfem_error("Error in CuMemcpyDtoHAsync");
-   }
+   MFEM_CUDA_CHECK(cudaMemcpyAsync(dst, src, bytes, cudaMemcpyDeviceToHost));
 #endif
    return dst;
 }

general/cuda.hpp

@@ -26,89 +26,33 @@
 #ifdef MFEM_USE_CUDA
 #define MFEM_ATTR_DEVICE __device__
 #define MFEM_ATTR_HOST_DEVICE __host__ __device__
-// Define the CUDA debug macros:
-// - MFEM_CUDA_CHECK_DRV(x) where 'x' returns/is type 'CUresult'
-// - MFEM_CUDA_CHECK_RT(x)  where 'x' returns/is type 'cudaError_t'
-#ifdef MFEM_DEBUG
-#define MFEM_CUDA_CHECK_DRV(x) \
-   do \
-   { \
-      CUresult err = (x); \
-      if (err != CUDA_SUCCESS) \
-      { \
-         const char *error_string; \
-         cuGetErrorString(err, &error_string); \
-         _MFEM_MESSAGE("CUDA error: (" << #x \
-                       << ") failed with error:\n --> " \
-                       << error_string, 0); \
-      } \
-   } \
-   while (0)
-#define MFEM_CUDA_CHECK_RT(x) \
+// Define a CUDA error check macro, MFEM_CUDA_CHECK(x), where x returns/is of
+// type 'cudaError_t'. This macro evaluates 'x' and raises an error if the
+// result is not cudaSuccess.
+#define MFEM_CUDA_CHECK(x) \
    do \
    { \
       cudaError_t err = (x); \
       if (err != cudaSuccess) \
       { \
-         _MFEM_MESSAGE("CUDA error: (" << #x \
-                       << ") failed with error:\n --> " \
-                       << cudaGetErrorString(err), 0); \
+         mfem_cuda_error(err, #x, _MFEM_FUNC_NAME, __FILE__, __LINE__); \
       } \
    } \
    while (0)
-#else
-#define MFEM_CUDA_CHECK_DRV(x) x
-#define MFEM_CUDA_CHECK_RT(x) x
-#endif
 #else // MFEM_USE_CUDA
 #define MFEM_ATTR_DEVICE
 #define MFEM_ATTR_HOST_DEVICE
-typedef int CUdevice;
-typedef int CUcontext;
-typedef void* CUstream;
 #endif // MFEM_USE_CUDA
 
 
 namespace mfem
 {
 
-// Define 'atomicAdd' function.
-#ifdef __CUDA_ARCH__
-#if __CUDA_ARCH__ < 600
-static __device__ inline double atomicAdd(double* address, double val)
-{
-   unsigned long long int* address_as_ull = (unsigned long long int*)address;
-   unsigned long long int old = *address_as_ull, assumed;
-   do
-   {
-      assumed = old;
-      old =
-         atomicCAS(address_as_ull, assumed,
-                   __double_as_longlong(val +
-                                        __longlong_as_double(assumed)));
-      // Note: uses integer comparison to avoid hang in case of NaN
-      // (since NaN != NaN)
-   }
-   while (assumed != old);
-   return __longlong_as_double(old);
-}
-#endif // __CUDA_ARCH__ < 600
-template<typename T> MFEM_ATTR_DEVICE
-inline T AtomicAdd(T volatile *address, T val)
-{
-   return atomicAdd((T *)address, val);
-}
-#else // __CUDA_ARCH__
-template<typename T> inline T AtomicAdd(T volatile *address, T val)
-{
-#ifdef MFEM_USE_OPENMP
-   #pragma omp atomic
+#ifdef MFEM_USE_CUDA
+// Function used by the macro MFEM_CUDA_CHECK.
+void mfem_cuda_error(cudaError_t err, const char *expr, const char *func,
+                     const char *file, int line);
 #endif
-   *address += val;
-   return *address;
-}
-#endif // __CUDA_ARCH__
-
 
 /// Allocates device memory
 void* CuMemAlloc(void **d_ptr, size_t bytes);
@@ -120,20 +64,19 @@ void* CuMemFree(void *d_ptr);
 void* CuMemcpyHtoD(void *d_dst, const void *h_src, size_t bytes);
 
 /// Copies memory from Host to Device
-void* CuMemcpyHtoDAsync(void *d_dst, const void *h_src,
-                        size_t bytes, void *stream);
+void* CuMemcpyHtoDAsync(void *d_dst, const void *h_src, size_t bytes);
 
 /// Copies memory from Device to Device
 void* CuMemcpyDtoD(void *d_dst, void *d_src, size_t bytes);
 
 /// Copies memory from Device to Device
-void* CuMemcpyDtoDAsync(void *d_dst, void *d_src, size_t bytes, void *stream);
+void* CuMemcpyDtoDAsync(void *d_dst, void *d_src, size_t bytes);
 
 /// Copies memory from Device to Host
 void* CuMemcpyDtoH(void *h_dst, void *d_src, size_t bytes);
 
 /// Copies memory from Device to Host
-void* CuMemcpyDtoHAsync(void *h_dst, void *d_src, size_t bytes, void *stream);
+void* CuMemcpyDtoHAsync(void *h_dst, void *d_src, size_t bytes);
 
 } // namespace mfem
 

general/device.cpp

@@ -24,9 +24,6 @@ namespace mfem
 namespace internal
 {
 
-CUstream *cuStream = NULL;
-static CUdevice cuDevice;
-static CUcontext cuContext;
 OccaDevice occaDevice;
 
 // Backends listed by priority, high to low:
@@ -100,14 +97,9 @@ void Device::Print(std::ostream &out)
 #ifdef MFEM_USE_CUDA
 static void DeviceSetup(const int dev, int &ngpu)
 {
-   cudaGetDeviceCount(&ngpu);
-   MFEM_VERIFY(ngpu>0, "No CUDA device found!");
-   cuInit(0);
-   cuDeviceGet(&internal::cuDevice, dev);
-   cuCtxCreate(&internal::cuContext, CU_CTX_SCHED_AUTO, internal::cuDevice);
-   internal::cuStream = new CUstream;
-   MFEM_VERIFY(internal::cuStream, "CUDA stream could not be created!");
-   cuStreamCreate(internal::cuStream, CU_STREAM_DEFAULT);
+   MFEM_CUDA_CHECK(cudaGetDeviceCount(&ngpu));
+   MFEM_VERIFY(ngpu > 0, "No CUDA device found!");
+   MFEM_CUDA_CHECK(cudaSetDevice(dev));
 }
 #endif
 
@@ -125,7 +117,7 @@ static void RajaDeviceSetup(const int dev, int &ngpu)
 #endif
 }
 
-static void OccaDeviceSetup(CUdevice cu_dev, CUcontext cu_ctx)
+static void OccaDeviceSetup(const int dev)
 {
 #ifdef MFEM_USE_OCCA
    const int cpu  = Device::Allows(Backend::OCCA_CPU);
@@ -138,7 +130,8 @@ static void OccaDeviceSetup(CUdevice cu_dev, CUcontext cu_ctx)
    if (cuda)
    {
 #if OCCA_CUDA_ENABLED
-      internal::occaDevice = occa::cuda::wrapDevice(cu_dev, cu_ctx);
+      std::string mode("mode: 'CUDA', device_id : ");
+      internal::occaDevice.setup(mode.append(1,'0'+dev));
 #else
       MFEM_ABORT("the OCCA CUDA backend requires OCCA built with CUDA!");
 #endif
@@ -197,22 +190,10 @@ void Device::Setup(const int device)
                "the OpenMP and RAJA OpenMP backends require MFEM built with"
                " MFEM_USE_OPENMP=YES");
 #endif
-   // The check for MFEM_USE_OCCA is in the function OccaDeviceSetup().
-
-   // We initialize CUDA and/or RAJA_CUDA first so OccaDeviceSetup() can reuse
-   // the same initialized cuDevice and cuContext objects when OCCA_CUDA is
-   // enabled.
    if (Allows(Backend::CUDA)) { CudaDeviceSetup(dev, ngpu); }
    if (Allows(Backend::RAJA_CUDA)) { RajaDeviceSetup(dev, ngpu); }
-   if (Allows(Backend::OCCA_MASK))
-   {
-      OccaDeviceSetup(internal::cuDevice, internal::cuContext);
-   }
-}
-
-Device::~Device()
-{
-   delete internal::cuStream;
+   // The check for MFEM_USE_OCCA is in the function OccaDeviceSetup().
+   if (Allows(Backend::OCCA_MASK)) { OccaDeviceSetup(dev); }
 }
 
 } // mfem

general/device.hpp

@@ -181,8 +181,6 @@ public:
        Backend::*_MASK, or combinations of those. */
    static inline bool Allows(unsigned long b_mask)
    { return Get().allowed_backends & b_mask; }
-
-   ~Device();
 };
 
 } // mfem

general/forall.hpp

@@ -22,6 +22,9 @@
 
 #ifdef MFEM_USE_RAJA
 #include "RAJA/RAJA.hpp"
+#if defined(RAJA_ENABLE_CUDA) && !defined(MFEM_USE_CUDA)
+#error When RAJA is built with CUDA, MFEM_USE_CUDA=YES is required
+#endif
 #endif
 
 namespace mfem
@@ -106,8 +109,7 @@ void CuWrap(const int N, DBODY &&d_body)
    if (N==0) { return; }
    const int GRID = (N+BLOCKS-1)/BLOCKS;
    CuKernel<<<GRID,BLOCKS>>>(N,d_body);
-   const cudaError_t last = cudaGetLastError();
-   MFEM_VERIFY(last == cudaSuccess, cudaGetErrorString(last));
+   MFEM_CUDA_CHECK(cudaGetLastError());
 }
 
 #else  // MFEM_USE_CUDA

general/mem_manager.cpp

@@ -312,7 +312,6 @@ void MemoryManager::Pull(const void *ptr, const std::size_t bytes)
    { mfem_error("Unknown pointer to pull from!"); }
 }
 
-namespace internal { extern CUstream *cuStream; }
 void* MemoryManager::Memcpy(void *dst, const void *src,
                             const std::size_t bytes, const bool async)
 {
@@ -322,7 +321,7 @@ void* MemoryManager::Memcpy(void *dst, const void *src,
    const bool run_on_host = !Device::Allows(Backend::DEVICE_MASK);
    if (run_on_host) { return std::memcpy(dst, src, bytes); }
    if (!async) { return CuMemcpyDtoD(d_dst, d_src, bytes); }
-   return CuMemcpyDtoDAsync(d_dst, d_src, bytes, internal::cuStream);
+   return CuMemcpyDtoDAsync(d_dst, d_src, bytes);
 }
 
 void MemoryManager::RegisterCheck(void *ptr)

general/occa.hpp

@@ -13,7 +13,6 @@
 #define MFEM_OCCA_HPP
 
 #include "../config/config.hpp"
-#include "cuda.hpp" // for CUdevice, CUcontext
 
 #ifdef MFEM_USE_OCCA
 #include <occa.hpp>

linalg/complex_operator.cpp

@@ -10,8 +10,6 @@
 // Software Foundation) version 2.1 dated February 1999.
 
 #include "complex_operator.hpp"
-#include <set>
-#include <map>
 
 namespace mfem
 {
@@ -41,30 +39,6 @@ ComplexOperator::~ComplexOperator()
    delete v_;
 }
 
-Operator & ComplexOperator::real()
-{
-   MFEM_ASSERT(Op_Real_, "ComplexOperator has no real part!");
-   return *Op_Real_;
-}
-
-Operator & ComplexOperator::imag()
-{
-   MFEM_ASSERT(Op_Imag_, "ComplexOperator has no imaginary part!");
-   return *Op_Imag_;
-}
-
-const Operator & ComplexOperator::real() const
-{
-   MFEM_ASSERT(Op_Real_, "ComplexOperator has no real part!");
-   return *Op_Real_;
-}
-
-const Operator & ComplexOperator::imag() const
-{
-   MFEM_ASSERT(Op_Imag_, "ComplexOperator has no imaginary part!");
-   return *Op_Imag_;
-}
-
 void ComplexOperator::Mult(const Vector &x, Vector &y) const
 {
    double * x_data = x.GetData();
@@ -146,30 +120,6 @@ void ComplexOperator::MultTranspose(const Vector &x_r, const Vector &x_i,
 }
 
 
-SparseMatrix & ComplexSparseMatrix::real()
-{
-   MFEM_ASSERT(Op_Real_, "ComplexSparseMatrix has no real part!");
-   return dynamic_cast<SparseMatrix &>(*Op_Real_);
-}
-
-SparseMatrix & ComplexSparseMatrix::imag()
-{
-   MFEM_ASSERT(Op_Imag_, "ComplexSparseMatrix has no imaginary part!");
-   return dynamic_cast<SparseMatrix &>(*Op_Imag_);
-}
-
-const SparseMatrix & ComplexSparseMatrix::real() const
-{
-   MFEM_ASSERT(Op_Real_, "ComplexSparseMatrix has no real part!");
-   return dynamic_cast<const SparseMatrix &>(*Op_Real_);
-}
-
-const SparseMatrix & ComplexSparseMatrix::imag() const
-{
-   MFEM_ASSERT(Op_Imag_, "ComplexSparseMatrix has no imaginary part!");
-   return dynamic_cast<const SparseMatrix &>(*Op_Imag_);
-}
-
 SparseMatrix * ComplexSparseMatrix::GetSystemMatrix() const
 {
    SparseMatrix * A_r = dynamic_cast<SparseMatrix*>(Op_Real_);
@@ -234,358 +184,4 @@ SparseMatrix * ComplexSparseMatrix::GetSystemMatrix() const
    return new SparseMatrix(I, J, D, this->Height(), this->Width());
 }
 
-#ifdef MFEM_USE_MPI
-
-ComplexHypreParMatrix::ComplexHypreParMatrix(HypreParMatrix * A_Real,
-                                             HypreParMatrix * A_Imag,
-                                             bool ownReal, bool ownImag,
-                                             Convention convention)
-   : ComplexOperator(A_Real, A_Imag, ownReal, ownImag, convention)
-{
-   comm_ = (A_Real) ? A_Real->GetComm() :
-           ((A_Imag) ? A_Imag->GetComm() : MPI_COMM_WORLD);
-
-   MPI_Comm_rank(comm_, &myid_);
-   MPI_Comm_size(comm_, &nranks_);
-}
-
-HypreParMatrix & ComplexHypreParMatrix::real()
-{
-   MFEM_ASSERT(Op_Real_, "ComplexHypreParMatrix has no real part!");
-   return dynamic_cast<HypreParMatrix &>(*Op_Real_);
-}
-
-HypreParMatrix & ComplexHypreParMatrix::imag()
-{
-   MFEM_ASSERT(Op_Imag_, "ComplexHypreParMatrix has no imaginary part!");
-   return dynamic_cast<HypreParMatrix &>(*Op_Imag_);
-}
-
-const HypreParMatrix & ComplexHypreParMatrix::real() const
-{
-   MFEM_ASSERT(Op_Real_, "ComplexHypreParMatrix has no real part!");
-   return dynamic_cast<const HypreParMatrix &>(*Op_Real_);
-}
-
-const HypreParMatrix & ComplexHypreParMatrix::imag() const
-{
-   MFEM_ASSERT(Op_Imag_, "ComplexHypreParMatrix has no imaginary part!");
-   return dynamic_cast<const HypreParMatrix &>(*Op_Imag_);
-}
-
-HypreParMatrix * ComplexHypreParMatrix::GetSystemMatrix() const
-{
-   HypreParMatrix * A_r = dynamic_cast<HypreParMatrix*>(Op_Real_);
-   HypreParMatrix * A_i = dynamic_cast<HypreParMatrix*>(Op_Imag_);
-
-   if ( A_r == NULL && A_i == NULL ) { return NULL; }
-
-   HYPRE_Int global_num_rows_r = (A_r) ? A_r->GetGlobalNumRows() : 0;
-   HYPRE_Int global_num_rows_i = (A_i) ? A_i->GetGlobalNumRows() : 0;
-   HYPRE_Int global_num_rows = std::max(global_num_rows_r, global_num_rows_i);
-
-   HYPRE_Int global_num_cols_r = (A_r) ? A_r->GetGlobalNumCols() : 0;
-   HYPRE_Int global_num_cols_i = (A_i) ? A_i->GetGlobalNumCols() : 0;
-   HYPRE_Int global_num_cols = std::max(global_num_cols_r, global_num_cols_i);
-
-   int row_starts_size = (HYPRE_AssumedPartitionCheck()) ? 2 : nranks_ + 1;
-   HYPRE_Int * row_starts = hypre_CTAlloc(HYPRE_Int, row_starts_size);
-   HYPRE_Int * col_starts = hypre_CTAlloc(HYPRE_Int, row_starts_size);
-
-   const HYPRE_Int * row_starts_z = (A_r) ? A_r->RowPart() :
-                                    ((A_i) ? A_i->RowPart() : NULL);
-   const HYPRE_Int * col_starts_z = (A_r) ? A_r->ColPart() :
-                                    ((A_i) ? A_i->ColPart() : NULL);
-
-   for (int i = 0; i < row_starts_size; i++)
-   {
-      row_starts[i] = 2 * row_starts_z[i];
-      col_starts[i] = 2 * col_starts_z[i];
-   }
-
-   SparseMatrix diag_r, diag_i, offd_r, offd_i;
-   HYPRE_Int * cmap_r, * cmap_i;
-
-   int nrows_r = 0, nrows_i = 0, ncols_r = 0, ncols_i = 0;
-   int ncols_offd_r = 0, ncols_offd_i = 0;
-   if (A_r)
-   {
-      A_r->GetDiag(diag_r);
-      A_r->GetOffd(offd_r, cmap_r);
-      nrows_r = diag_r.Height();
-      ncols_r = diag_r.Width();
-      ncols_offd_r = offd_r.Width();
-   }
-   if (A_i)
-   {
-      A_i->GetDiag(diag_i);
-      A_i->GetOffd(offd_i, cmap_i);
-      nrows_i = diag_i.Height();
-      ncols_i = diag_i.Width();
-      ncols_offd_i = offd_i.Width();
-   }
-   int nrows = std::max(nrows_r, nrows_i);
-   int ncols = std::max(ncols_r, ncols_i);
-
-   // Determine the unique set of off-diagonal columns global indices
-   std::set<int> cset;
-   for (int i=0; i<ncols_offd_r; i++)
-   {
-      cset.insert(cmap_r[i]);
-   }
-   for (int i=0; i<ncols_offd_i; i++)
-   {
-      cset.insert(cmap_i[i]);
-   }
-   int num_cols_offd = (int)cset.size();
-
-   // Exatract pointers to the various CSR arrays of the diagonal blocks
-   const int * diag_r_I = (A_r) ? diag_r.GetI() : NULL;
-   const int * diag_i_I = (A_i) ? diag_i.GetI() : NULL;
-
-   const int * diag_r_J = (A_r) ? diag_r.GetJ() : NULL;
-   const int * diag_i_J = (A_i) ? diag_i.GetJ() : NULL;
-
-   const double * diag_r_D = (A_r) ? diag_r.GetData() : NULL;
-   const double * diag_i_D = (A_i) ? diag_i.GetData() : NULL;
-
-   int diag_r_nnz = (diag_r_I) ? diag_r_I[nrows] : 0;
-   int diag_i_nnz = (diag_i_I) ? diag_i_I[nrows] : 0;
-   int diag_nnz = 2 * (diag_r_nnz + diag_i_nnz);
-
-   // Exatract pointers to the various CSR arrays of the off-diagonal blocks
-   const int * offd_r_I = (A_r) ? offd_r.GetI() : NULL;
-   const int * offd_i_I = (A_i) ? offd_i.GetI() : NULL;
-
-   const int * offd_r_J = (A_r) ? offd_r.GetJ() : NULL;
-   const int * offd_i_J = (A_i) ? offd_i.GetJ() : NULL;
-
-   const double * offd_r_D = (A_r) ? offd_r.GetData() : NULL;
-   const double * offd_i_D = (A_i) ? offd_i.GetData() : NULL;
-
-   int offd_r_nnz = (offd_r_I) ? offd_r_I[nrows] : 0;
-   int offd_i_nnz = (offd_i_I) ? offd_i_I[nrows] : 0;
-   int offd_nnz = 2 * (offd_r_nnz + offd_i_nnz);
-
-   // Allocate CSR arrays for the combined matrix
-   HYPRE_Int * diag_I = hypre_CTAlloc(HYPRE_Int, 2 * nrows + 1);
-   HYPRE_Int * diag_J = hypre_CTAlloc(HYPRE_Int, diag_nnz);
-   double    * diag_D = hypre_CTAlloc(double, diag_nnz);
-
-   HYPRE_Int * offd_I = hypre_CTAlloc(HYPRE_Int, 2 * nrows + 1);
-   HYPRE_Int * offd_J = hypre_CTAlloc(HYPRE_Int, offd_nnz);
-   double    * offd_D = hypre_CTAlloc(double, offd_nnz);
-   HYPRE_Int * cmap   = hypre_CTAlloc(HYPRE_Int, 2 * num_cols_offd);
-
-   // Fill the CSR arrays for the diagonal portion of the matrix
-   const double factor = (convention_ == HERMITIAN) ? 1.0 : -1.0;
-
-   diag_I[0] = 0;
-   diag_I[nrows] = diag_r_nnz + diag_i_nnz;
-   for (int i=0; i<nrows; i++)
-   {
-      diag_I[i + 1]         = ((diag_r_I)?diag_r_I[i+1]:0) +
-                              ((diag_i_I)?diag_i_I[i+1]:0);
-      diag_I[i + nrows + 1] = diag_I[i+1] + diag_r_nnz + diag_i_nnz;
-
-      if (diag_r_I)
-      {
-         for (int j=0; j<diag_r_I[i+1] - diag_r_I[i]; j++)
-         {
-            diag_J[diag_I[i] + j] = diag_r_J[diag_r_I[i] + j];
-            diag_D[diag_I[i] + j] = diag_r_D[diag_r_I[i] + j];
-
-            diag_J[diag_I[i+nrows] + j] =
-               diag_r_J[diag_r_I[i] + j] + ncols;
-            diag_D[diag_I[i+nrows] + j] =
-               factor * diag_r_D[diag_r_I[i] + j];
-         }
-      }
-      if (diag_i_I)
-      {
-         const int off_r = (diag_r_I)?(diag_r_I[i+1] - diag_r_I[i]):0;
-         for (int j=0; j<diag_i_I[i+1] - diag_i_I[i]; j++)
-         {
-            diag_J[diag_I[i] + off_r + j] =  diag_i_J[diag_i_I[i] + j] + ncols;
-            diag_D[diag_I[i] + off_r + j] = -diag_i_D[diag_i_I[i] + j];
-
-            diag_J[diag_I[i+nrows] + off_r + j] = diag_i_J[diag_i_I[i] + j];
-            diag_D[diag_I[i+nrows] + off_r + j] =
-               factor * diag_i_D[diag_i_I[i] + j];
-         }
-      }
-   }
-
-   // Determine the mappings describing the layout of off-diagonal columns
-   int num_recv_procs = 0;
-   HYPRE_Int * offd_col_start_stop = NULL;
-   this->getColStartStop(A_r, A_i, num_recv_procs, offd_col_start_stop);
-
-   std::set<int>::iterator sit;
-   std::map<int,int> cmapa, cmapb, cinvmap;
-   for (sit=cset.begin(); sit!=cset.end(); sit++)
-   {
-      int col_orig = *sit;
-      int col_2x2  = -1;
-      int col_size = 0;
-      for (int i=0; i<num_recv_procs; i++)
-      {
-         if (offd_col_start_stop[2*i] <= col_orig &&
-             col_orig < offd_col_start_stop[2*i+1])
-         {
-            col_2x2 = offd_col_start_stop[2*i] + col_orig;
-            col_size = offd_col_start_stop[2*i+1] - offd_col_start_stop[2*i];
-            break;
-         }
-      }
-      cmapa[*sit] = col_2x2;
-      cmapb[*sit] = col_2x2 + col_size;
-      cinvmap[col_2x2] = -1;
-      cinvmap[col_2x2 + col_size] = -1;
-   }
-   delete [] offd_col_start_stop;
-
-   std::map<int, int>::iterator mit;
-   int i = 0;
-   for (mit=cinvmap.begin(); mit!=cinvmap.end(); mit++, i++)
-   {
-      mit->second = i;
-      cmap[i] = mit->first;
-   }
-
-   // Fill the CSR arrays for the off-diagonal portion of the matrix
-   offd_I[0] = 0;
-   offd_I[nrows] = offd_r_nnz + offd_i_nnz;
-   for (int i=0; i<nrows; i++)
-   {
-      offd_I[i + 1]         = ((offd_r_I)?offd_r_I[i+1]:0) +
-                              ((offd_i_I)?offd_i_I[i+1]:0);
-      offd_I[i + nrows + 1] = offd_I[i+1] + offd_r_nnz + offd_i_nnz;
-
-      if (offd_r_I)
-      {
-         const int off_i = (offd_i_I)?(offd_i_I[i+1] - offd_i_I[i]):0;
-         for (int j=0; j<offd_r_I[i+1] - offd_r_I[i]; j++)
-         {
-            offd_J[offd_I[i] + j] =
-               cinvmap[cmapa[cmap_r[offd_r_J[offd_r_I[i] + j]]]];
-            offd_D[offd_I[i] + j] = offd_r_D[offd_r_I[i] + j];
-
-            offd_J[offd_I[i+nrows] + off_i + j] =
-               cinvmap[cmapb[cmap_r[offd_r_J[offd_r_I[i] + j]]]];
-            offd_D[offd_I[i+nrows] + off_i + j] =
-               factor * offd_r_D[offd_r_I[i] + j];
-         }
-      }
-      if (offd_i_I)
-      {
-         const int off_r = (offd_r_I)?(offd_r_I[i+1] - offd_r_I[i]):0;
-         for (int j=0; j<offd_i_I[i+1] - offd_i_I[i]; j++)
-         {
-            offd_J[offd_I[i] + off_r + j] =
-               cinvmap[cmapb[cmap_i[offd_i_J[offd_i_I[i] + j]]]];
-            offd_D[offd_I[i] + off_r + j] = -offd_i_D[offd_i_I[i] + j];
-
-            offd_J[offd_I[i+nrows] + j] =
-               cinvmap[cmapa[cmap_i[offd_i_J[offd_i_I[i] + j]]]];
-            offd_D[offd_I[i+nrows] + j] = factor * offd_i_D[offd_i_I[i] + j];
-         }
-      }
-   }
-
-   // Construct the combined matrix
-   HypreParMatrix * A = new HypreParMatrix(comm_,
-                                           2 * global_num_rows,
-                                           2 * global_num_cols,
-                                           row_starts, col_starts,
-                                           diag_I, diag_J, diag_D,
-                                           offd_I, offd_J, offd_D,
-                                           2 * num_cols_offd, cmap);
-
-   // Give the new matrix ownership of its interanl arrays
-   A->SetOwnerFlags(-1,-1,-1);
-   hypre_CSRMatrixSetDataOwner(((hypre_ParCSRMatrix*)(*A))->diag,1);
-   hypre_CSRMatrixSetDataOwner(((hypre_ParCSRMatrix*)(*A))->offd,1);
-   hypre_ParCSRMatrixSetRowStartsOwner((hypre_ParCSRMatrix*)(*A),1);
-   hypre_ParCSRMatrixSetColStartsOwner((hypre_ParCSRMatrix*)(*A),1);
-
-   return A;
-}
-
-void
-ComplexHypreParMatrix::getColStartStop(const HypreParMatrix * A_r,
-                                       const HypreParMatrix * A_i,
-                                       int & num_recv_procs,
-                                       HYPRE_Int *& offd_col_start_stop) const
-{
-   hypre_ParCSRCommPkg * comm_pkg_r =
-      (A_r) ? hypre_ParCSRMatrixCommPkg((hypre_ParCSRMatrix*)(*A_r)) : NULL;
-   hypre_ParCSRCommPkg * comm_pkg_i =
-      (A_i) ? hypre_ParCSRMatrixCommPkg((hypre_ParCSRMatrix*)(*A_i)) : NULL;
-
-   std::set<HYPRE_Int> send_procs, recv_procs;
-   if ( comm_pkg_r )
-   {
-      for (HYPRE_Int i=0; i<comm_pkg_r->num_sends; i++)
-      {
-         send_procs.insert(comm_pkg_r->send_procs[i]);
-      }
-      for (HYPRE_Int i=0; i<comm_pkg_r->num_recvs; i++)
-      {
-         recv_procs.insert(comm_pkg_r->recv_procs[i]);
-      }
-   }
-   if ( comm_pkg_i )
-   {
-      for (HYPRE_Int i=0; i<comm_pkg_i->num_sends; i++)
-      {
-         send_procs.insert(comm_pkg_i->send_procs[i]);
-      }
-      for (HYPRE_Int i=0; i<comm_pkg_i->num_recvs; i++)
-      {
-         recv_procs.insert(comm_pkg_i->recv_procs[i]);
-      }
-   }
-
-   num_recv_procs = (int)recv_procs.size();
-
-   HYPRE_Int loc_start_stop[2];
-   offd_col_start_stop = new HYPRE_Int[2 * num_recv_procs];
-
-   const HYPRE_Int * row_part = (A_r) ? A_r->RowPart() :
-                                ((A_i) ? A_i->RowPart() : NULL);
-
-   int row_part_ind = (HYPRE_AssumedPartitionCheck()) ? 0 : myid_;
-   loc_start_stop[0] = row_part[row_part_ind];
-   loc_start_stop[1] = row_part[row_part_ind+1];
-
-   MPI_Request * req = new MPI_Request[send_procs.size()+recv_procs.size()];
-   MPI_Status * stat = new MPI_Status[send_procs.size()+recv_procs.size()];
-   int send_count = 0;
-   int recv_count = 0;
-   int tag = 0;
-
-   std::set<HYPRE_Int>::iterator sit;
-   for (sit=send_procs.begin(); sit!=send_procs.end(); sit++)
-   {
-      MPI_Isend(loc_start_stop, 2, HYPRE_MPI_INT,
-                *sit, tag, comm_, &req[send_count]);
-      send_count++;
-   }
-   for (sit=recv_procs.begin(); sit!=recv_procs.end(); sit++)
-   {
-      MPI_Irecv(&offd_col_start_stop[2*recv_count], 2, HYPRE_MPI_INT,
-                *sit, tag, comm_, &req[send_count+recv_count]);
-      recv_count++;
-   }
-
-   MPI_Waitall(send_count+recv_count, req, stat);
-
-   delete [] req;
-   delete [] stat;
-}
-
-
-#endif // MFEM_USE_MPI
-
 }

linalg/complex_operator.hpp

@@ -14,9 +14,6 @@
 
 #include "operator.hpp"
 #include "sparsemat.hpp"
-#ifdef MFEM_USE_MPI
-#include "hypre.hpp"
-#endif
 
 namespace mfem
 {
@@ -30,8 +27,7 @@ namespace mfem
     ComplexOperator allows one to choose a convention upon construction, which
     facilitates symmetry.
 
-    If we let (y_r + i y_i) = (Op_r + i Op_i)(x_r + i x_i) then Matrix-vector
-    products are then computed as:
+    Matrix-vector products are then computed as:
 
     1. When Convention::HERMITIAN is used (default)
     / y_r \   / Op_r -Op_i \ / x_r \
@@ -42,8 +38,6 @@ namespace mfem
     / y_r \   / Op_r -Op_i \ / x_r \
     |     | = |            | |     |
     \-y_i /   \-Op_i -Op_r / \ x_i /
-    In other words, Matrix-vector products with Convention::BLOCK_SYMMETRIC
-    compute the complex conjugate of Op*x.
 
     Either convention can be used with a given complex operator,
     however, each of them is best suited for certain classes of
@@ -88,30 +82,9 @@ public:
 
    virtual ~ComplexOperator();
 
-   /** @brief Check for existence of real or imaginary part of the operator
-
-       These methods do not check that the operators are non-zero but
-       only that the operators have been set.
-    */
-   bool hasRealPart() const { return Op_Real_ != NULL; }
-   bool hasImagPart() const { return Op_Imag_ != NULL; }
-
-   /** @brief Real or imaginary part accessor methods
-
-       The following accessor methods should only be called if the
-       requested part of the opertor is known to exist.  This
-       can be checked with hasRealPart() or hasImagPart().
-   */
-   virtual Operator & real();
-   virtual Operator & imag();
-   virtual const Operator & real() const;
-   virtual const Operator & imag() const;
-
    virtual void Mult(const Vector &x, Vector &y) const;
    virtual void MultTranspose(const Vector &x, Vector &y) const;
 
-   virtual Type GetType() const { return Complex_Operator; }
-
 protected:
    // Let this be hidden from the public interface since the implementation
    // depends on internal members
@@ -154,74 +127,9 @@ public:
       : ComplexOperator(A_Real, A_Imag, ownReal, ownImag, convention)
    {}
 
-   virtual SparseMatrix & real();
-   virtual SparseMatrix & imag();
-
-   virtual const SparseMatrix & real() const;
-   virtual const SparseMatrix & imag() const;
-
-   /** Combine the blocks making up this complex operator into a
-       single SparseMatrix.  The resulting matrix can be passed to
-       solvers which require access to the matrix entries themselves,
-       such as sparse direct solvers, rather than simply the action of
-       the opertor.  Note that this combined operator requires roughly
-       twice the memory of the block structured operator. */
    SparseMatrix * GetSystemMatrix() const;
-
-   virtual Type GetType() const { return MFEM_ComplexSparseMat; }
 };
 
-#ifdef MFEM_USE_MPI
-
-/** @brief Specialization of the ComplexOperator built from a pair of
-    HypreParMatrices.
-
-    The purpose of this specialization is to construct a single
-    HypreParMatrix object which is equivalent to the 2x2 block system
-    that the ComplexOperator mimics. The resulting HypreParMatrix can
-    then be passed along to solvers which require access to the CSR
-    matrix data such as SuperLU, STRUMPACK, or similar sparse linear
-    solvers.
-
-    See ComplexOperator documentation in operator.hpp for more information.
- */
-class ComplexHypreParMatrix : public ComplexOperator
-{
-public:
-   ComplexHypreParMatrix(HypreParMatrix * A_Real, HypreParMatrix * A_Imag,
-                         bool ownReal, bool ownImag,
-                         Convention convention = HERMITIAN);
-
-   virtual HypreParMatrix & real();
-   virtual HypreParMatrix & imag();
-
-   virtual const HypreParMatrix & real() const;
-   virtual const HypreParMatrix & imag() const;
-
-   /** Combine the blocks making up this complex operator into a
-       single HypreParMatrix.  The resulting matrix can be passed to
-       solvers which require access to the matrix entries themselves,
-       such as sparse direct solvers or Hypre preconditioners, rather
-       than simply the action of the opertor.  Note that this combined
-       operator requires roughly twice the memory of the block
-       structured operator. */
-   HypreParMatrix * GetSystemMatrix() const;
-
-   virtual Type GetType() const { return Complex_Hypre_ParCSR; }
-
-private:
-   void getColStartStop(const HypreParMatrix * A_r,
-                        const HypreParMatrix * A_i,
-                        int & num_recv_procs,
-                        HYPRE_Int *& offd_col_start_stop) const;
-
-   MPI_Comm comm_;
-   int myid_;
-   int nranks_;
-};
-
-#endif // MFEM_USE_MPI
-
 }
 
-#endif // MFEM_COMPLEX_OPERATOR
+#endif

linalg/hypre.hpp

@@ -468,13 +468,16 @@ public:
    { internal::hypre_ParCSRMatrixSetConstantValues(A, value); return *this; }
 
    /** Perform the operation `*this += B`, assuming that both matrices use the
-       same row and column partitions and the same col_map_offd arrays. We also
-       assume that the sparsity pattern of `*this` contains that of `B`. */
+       same row and column partitions and the same col_map_offd arrays, or B has
+       an empty off-diagonal block. We also assume that the sparsity pattern of
+       `*this` contains that of `B`. */
    HypreParMatrix &operator+=(const HypreParMatrix &B) { return Add(1.0, B); }
 
    /** Perform the operation `*this += beta*B`, assuming that both matrices use
-       the same row and column partitions and the same col_map_offd arrays. We
-       also assume that the sparsity pattern of `*this` contains that of `B`. */
+       the same row and column partitions and the same col_map_offd arrays, or
+       B has an empty off-diagonal block. We also assume that the sparsity
+       pattern of `*this` contains that of `B`. For a more general case consider
+       the stand-alone function ParAdd described below. */
    HypreParMatrix &Add(const double beta, const HypreParMatrix &B)
    {
       MFEM_VERIFY(internal::hypre_ParCSRMatrixSum(A, beta, B.A) == 0,

linalg/hypre_parcsr.cpp

@@ -1520,10 +1520,14 @@ hypre_ParCSRMatrixSum(hypre_ParCSRMatrix *A,
    hypre_CSRMatrix *A_offd = hypre_ParCSRMatrixOffd(A);
    hypre_CSRMatrix *B_diag = hypre_ParCSRMatrixDiag(B);
    hypre_CSRMatrix *B_offd = hypre_ParCSRMatrixOffd(B);
+   HYPRE_Int ncols_B_offd  = hypre_CSRMatrixNumCols(B_offd);
    HYPRE_Int error;
 
    error = hypre_CSRMatrixSum(A_diag, beta, B_diag);
-   error = error ? error : hypre_CSRMatrixSum(A_offd, beta, B_offd);
+   if (ncols_B_offd > 0) /* treat B_offd as zero if it has no columns */
+   {
+      error = error ? error : hypre_CSRMatrixSum(A_offd, beta, B_offd);
+   }
 
    return error;
 }

linalg/hypre_parcsr.hpp

@@ -115,8 +115,9 @@ hypre_ParCSRMatrixAdd(hypre_ParCSRMatrix *A,
                       hypre_ParCSRMatrix *B);
 
 /** Perform the operation A += beta*B, assuming that both matrices use the same
-    row and column partitions and the same col_map_offd arrays. We also assume
-    that the sparsity pattern of A contains that of B. */
+    row and column partitions and the same col_map_offd arrays, or B has an empty
+    off-diagonal block. We also assume that the sparsity pattern of A contains
+    that of B. */
 HYPRE_Int
 hypre_ParCSRMatrixSum(hypre_ParCSRMatrix *A,
                       HYPRE_Complex       beta,

linalg/operator.hpp

@@ -124,17 +124,14 @@ public:
    enum Type
    {
       ANY_TYPE,         ///< ID for the base class Operator, i.e. any type.
-      MFEM_SPARSEMAT,   ///< ID for class SparseMatrix.
+      MFEM_SPARSEMAT,   ///< ID for class SparseMatrix
       Hypre_ParCSR,     ///< ID for class HypreParMatrix.
       PETSC_MATAIJ,     ///< ID for class PetscParMatrix, MATAIJ format.
       PETSC_MATIS,      ///< ID for class PetscParMatrix, MATIS format.
       PETSC_MATSHELL,   ///< ID for class PetscParMatrix, MATSHELL format.
       PETSC_MATNEST,    ///< ID for class PetscParMatrix, MATNEST format.
       PETSC_MATHYPRE,   ///< ID for class PetscParMatrix, MATHYPRE format.
-      PETSC_MATGENERIC, ///< ID for class PetscParMatrix, unspecified format.
-      Complex_Operator, ///< ID for class ComplexOperator.
-      MFEM_ComplexSparseMat, ///< ID for class ComplexSparseMatrix.
-      Complex_Hypre_ParCSR   ///< ID for class ComplexHypreParMatrix.
+      PETSC_MATGENERIC  ///< ID for class PetscParMatrix, unspecified format.
    };
 
    /// Return the type ID of the Operator class.
@@ -305,24 +302,6 @@ public:
 };
 
 
-/// Scaled Operator B: x -> a A(x).
-class ScaledOperator : public Operator
-{
-private:
-   const Operator &A_;
-   double a_;
-
-public:
-   /// Create a scalar product operator related to A.
-   explicit ScaledOperator(const Operator *A, double a)
-      : Operator(A->Width(), A->Height()), A_(*A), a_(a) { }
-
-   /// Operator application
-   virtual void Mult(const Vector &x, Vector &y) const
-   { A_.Mult(x, y); y *= a_; }
-};
-
-
 /** @brief The transpose of a given operator. Switches the roles of the methods
     Mult() and MultTranspose(). */
 class TransposeOperator : public Operator

linalg/sparsemat.cpp

@@ -38,6 +38,7 @@ SparseMatrix::SparseMatrix(int nrows, int ncols)
      current_row(-1),
      ColPtrJ(NULL),
      ColPtrNode(NULL),
+     At(NULL),
      ownGraph(true),
      ownData(true),
      isSorted(false)
@@ -60,6 +61,7 @@ SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n)
      Rows(NULL),
      ColPtrJ(NULL),
      ColPtrNode(NULL),
+     At(NULL),
      ownGraph(true),
      ownData(true),
      isSorted(false)
@@ -78,6 +80,7 @@ SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n,
      Rows(NULL),
      ColPtrJ(NULL),
      ColPtrNode(NULL),
+     At(NULL),
      ownGraph(ownij),
      ownData(owna),
      isSorted(issorted)
@@ -103,6 +106,7 @@ SparseMatrix::SparseMatrix(int nrows, int ncols, int rowsize)
    , Rows(NULL)
    , ColPtrJ(NULL)
    , ColPtrNode(NULL)
+   , At(NULL)
    , ownGraph(true)
    , ownData(true)
    , isSorted(false)
@@ -183,6 +187,7 @@ SparseMatrix::SparseMatrix(const SparseMatrix &mat, bool copy_graph)
    current_row = -1;
    ColPtrJ = NULL;
    ColPtrNode = NULL;
+   At = NULL;
    isSorted = mat.isSorted;
 }
 
@@ -191,6 +196,7 @@ SparseMatrix::SparseMatrix(const Vector &v)
    , Rows(NULL)
    , ColPtrJ(NULL)
    , ColPtrNode(NULL)
+   , At(NULL)
    , ownGraph(true)
    , ownData(true)
    , isSorted(true)
@@ -245,6 +251,7 @@ void SparseMatrix::SetEmpty()
    current_row = -1;
    ColPtrJ = NULL;
    ColPtrNode = NULL;
+   At = NULL;
 #ifdef MFEM_USE_MEMALLOC
    NodesMem = NULL;
 #endif
@@ -333,7 +340,7 @@ void SparseMatrix::SetWidth(int newWidth)
       // Nothing to be done here
       return;
    }
-   else if ( newWidth == -1)
+   else if (newWidth == -1)
    {
       // Compute the actual width
       width = ActualWidth();
@@ -552,12 +559,10 @@ void SparseMatrix::Mult(const Vector &x, Vector &y) const
 
 void SparseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
 {
-   MFEM_ASSERT(width == x.Size(),
-               "Input vector size (" << x.Size() << ") must match matrix width (" << width
-               << ")");
-   MFEM_ASSERT(height == y.Size(),
-               "Output vector size (" << y.Size() << ") must match matrix height (" << height
-               << ")");
+   MFEM_ASSERT(width == x.Size(), "Input vector size (" << x.Size()
+               << ") must match matrix width (" << width << ")");
+   MFEM_ASSERT(height == y.Size(), "Output vector size (" << y.Size()
+               << ") must match matrix height (" << height << ")");
 
    int i, j, end;
    double *Ap = A, *yp = y.GetData();
@@ -636,12 +641,10 @@ void SparseMatrix::MultTranspose(const Vector &x, Vector &y) const
 void SparseMatrix::AddMultTranspose(const Vector &x, Vector &y,
                                     const double a) const
 {
-   MFEM_ASSERT(height == x.Size(),
-               "Input vector size (" << x.Size() << ") must match matrix height (" << height
-               << ")");
-   MFEM_ASSERT(width == y.Size(),
-               "Output vector size (" << y.Size() << ") must match matrix width (" << width
-               << ")");
+   MFEM_ASSERT(height == x.Size(), "Input vector size (" << x.Size()
+               << ") must match matrix height (" << height << ")");
+   MFEM_ASSERT(width == y.Size(), "Output vector size (" << y.Size()
+               << ") must match matrix width (" << width << ")");
 
    if (A == NULL)
    {
@@ -658,23 +661,40 @@ void SparseMatrix::AddMultTranspose(const Vector &x, Vector &y,
       }
       return;
    }
-   // Prepare the lambda capture and get our pointers from the memory manager
-   const int d_height = height;
-   const DeviceArray d_I(I);
-   const DeviceArray d_J(J);
-   const DeviceVector d_A(A);
-   const DeviceVector d_x(x, x.Size());
-   DeviceVector d_y(y, y.Size());
-   MFEM_FORALL(i, d_height,
+
+   if (At)
    {
-      const double xi = a * d_x[i];
-      const int end = d_I[i+1];
-      for (int j = d_I[i]; j < end; j++)
+      At->AddMult(x, y, a);
+   }
+   else
+   {
+      MFEM_VERIFY(Device::IsDisabled(), "transpose action on device is not "
+                  "enabled; see BuildTranspose() for details.");
+      for (int i = 0; i < height; i++)
       {
-         const int Jj = d_J[j];
-         AtomicAdd(&d_y[Jj], d_A[j] * xi);
+         const double xi = a * x[i];
+         const int end = I[i+1];
+         for (int j = I[i]; j < end; j++)
+         {
+            const int Jj = J[j];
+            y[Jj] += A[j] * xi;
+         }
       }
-   });
+   }
+}
+
+void SparseMatrix::BuildTranspose() const
+{
+   if (At == NULL)
+   {
+      At = Transpose(*this);
+   }
+}
+
+void SparseMatrix::ResetTranspose() const
+{
+   delete At;
+   At = NULL;
 }
 
 void SparseMatrix::PartMult(
@@ -2101,12 +2121,12 @@ void SparseMatrix::Set(const int i, const int j, const double A)
    if ((gi=i) < 0) { gi = -1-gi, s = -1; }
    else { s = 1; }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to set a row " << gi << " outside the matrix height "
                << height);
    if ((gj=j) < 0) { gj = -1-gj, t = -s; }
    else { t = s; }
    MFEM_ASSERT(gj < width,
-               "Trying to insert a column " << gj << " outside the matrix width "
+               "Trying to set a column " << gj << " outside the matrix width "
                << width);
    if (t < 0) { a = -a; }
    _Set_(gi, gj, a);
@@ -2142,7 +2162,7 @@ void SparseMatrix::SetSubMatrix(const Array<int> &rows, const Array<int> &cols,
       if ((gi=rows[i]) < 0) { gi = -1-gi, s = -1; }
       else { s = 1; }
       MFEM_ASSERT(gi < height,
-                  "Trying to insert a row " << gi << " outside the matrix height "
+                  "Trying to set a row " << gi << " outside the matrix height "
                   << height);
       SetColPtr(gi);
       for (j = 0; j < cols.Size(); j++)
@@ -2155,7 +2175,7 @@ void SparseMatrix::SetSubMatrix(const Array<int> &rows, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix width "
+                     "Trying to set a column " << gj << " outside the matrix width "
                      << width);
          if (t < 0) { a = -a; }
          _Set_(gj, a);
@@ -2177,7 +2197,7 @@ void SparseMatrix::SetSubMatrixTranspose(const Array<int> &rows,
       if ((gi=rows[i]) < 0) { gi = -1-gi, s = -1; }
       else { s = 1; }
       MFEM_ASSERT(gi < height,
-                  "Trying to insert a row " << gi << " outside the matrix height "
+                  "Trying to set a row " << gi << " outside the matrix height "
                   << height);
       SetColPtr(gi);
       for (j = 0; j < cols.Size(); j++)
@@ -2190,7 +2210,7 @@ void SparseMatrix::SetSubMatrixTranspose(const Array<int> &rows,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix width "
+                     "Trying to set a column " << gj << " outside the matrix width "
                      << width);
          if (t < 0) { a = -a; }
          _Set_(gj, a);
@@ -2210,7 +2230,7 @@ void SparseMatrix::GetSubMatrix(const Array<int> &rows, const Array<int> &cols,
       if ((gi=rows[i]) < 0) { gi = -1-gi, s = -1; }
       else { s = 1; }
       MFEM_ASSERT(gi < height,
-                  "Trying to insert a row " << gi << " outside the matrix height "
+                  "Trying to read a row " << gi << " outside the matrix height "
                   << height);
       SetColPtr(gi);
       for (j = 0; j < cols.Size(); j++)
@@ -2218,7 +2238,7 @@ void SparseMatrix::GetSubMatrix(const Array<int> &rows, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix width "
+                     "Trying to read a column " << gj << " outside the matrix width "
                      << width);
          a = _Get_(gj);
          subm(i, j) = (t < 0) ? (-a) : (a);
@@ -2236,7 +2256,7 @@ bool SparseMatrix::RowIsEmpty(const int row) const
       gi = -1-gi;
    }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to query a row " << gi << " outside the matrix height "
                << height);
    if (Rows)
    {
@@ -2255,7 +2275,7 @@ int SparseMatrix::GetRow(const int row, Array<int> &cols, Vector &srow) const
 
    if ((gi=row) < 0) { gi = -1-gi; }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to read a row " << gi << " outside the matrix height "
                << height);
    if (Rows)
    {
@@ -2282,7 +2302,7 @@ int SparseMatrix::GetRow(const int row, Array<int> &cols, Vector &srow) const
       j = I[gi];
       cols.MakeRef(J + j, I[gi+1]-j);
       srow.NewDataAndSize(A + j, cols.Size());
-      MFEM_ASSERT(row >= 0, "Row not valid: " << row );
+      MFEM_ASSERT(row >= 0, "Row not valid: " << row << ", height: " << height);
       return 1;
    }
 }
@@ -2296,7 +2316,7 @@ void SparseMatrix::SetRow(const int row, const Array<int> &cols,
    if ((gi=row) < 0) { gi = -1-gi, s = -1; }
    else { s = 1; }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to set a row " << gi << " outside the matrix height "
                << height);
 
    if (!Finalized())
@@ -2307,7 +2327,7 @@ void SparseMatrix::SetRow(const int row, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix"
+                     "Trying to set a column " << gj << " outside the matrix"
                      " width " << width);
          a = srow(j);
          if (t < 0) { a = -a; }
@@ -2325,7 +2345,7 @@ void SparseMatrix::SetRow(const int row, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix"
+                     "Trying to set a column " << gj << " outside the matrix"
                      " width " << width);
 
          J[i] = gj;
@@ -2771,9 +2791,10 @@ void SparseMatrix::Destroy()
       delete NodesMem;
    }
 #endif
+   delete At;
 }
 
-int SparseMatrix::ActualWidth()
+int SparseMatrix::ActualWidth() const
 {
    int awidth = 0;
    if (A)
@@ -2817,8 +2838,10 @@ SparseMatrix *Transpose (const SparseMatrix &A)
       "Finalize must be called before Transpose. Use TransposeRowMatrix instead");
 
    int i, j, end;
-   int m, n, nnz, *A_i, *A_j, *At_i, *At_j;
-   double *A_data, *At_data;
+   const int *A_i, *A_j;
+   int m, n, nnz, *At_i, *At_j;
+   const double *A_data;
+   double *At_data;
 
    m      = A.Height(); // number of rows of A
    n      = A.Width();  // number of columns of A
@@ -2945,8 +2968,10 @@ SparseMatrix *Mult (const SparseMatrix &A, const SparseMatrix &B,
                     SparseMatrix *OAB)
 {
    int nrowsA, ncolsA, nrowsB, ncolsB;
-   int *A_i, *A_j, *B_i, *B_j, *C_i, *C_j, *B_marker;
-   double *A_data, *B_data, *C_data;
+   const int *A_i, *A_j, *B_i, *B_j;
+   int *C_i, *C_j, *B_marker;
+   const double *A_data, *B_data;
+   double *C_data;
    int ia, ib, ic, ja, jb, num_nonzeros;
    int row_start, counter;
    double a_entry, b_entry;
@@ -3259,13 +3284,13 @@ SparseMatrix * Add(double a, const SparseMatrix & A, double b,
    int * C_j;
    double * C_data;
 
-   int * A_i = A.GetI();
-   int * A_j = A.GetJ();
-   double * A_data = A.GetData();
+   const int *A_i = A.GetI();
+   const int *A_j = A.GetJ();
+   const double *A_data = A.GetData();
 
-   int * B_i = B.GetI();
-   int * B_j = B.GetJ();
-   double * B_data = B.GetData();
+   const int *B_i = B.GetI();
+   const int *B_j = B.GetJ();
+   const double *B_data = B.GetData();
 
    int * marker = new int[ncols];
    std::fill(marker, marker+ncols, -1);
@@ -3493,6 +3518,7 @@ void SparseMatrix::Swap(SparseMatrix &other)
    mfem::Swap(current_row, other.current_row);
    mfem::Swap(ColPtrJ, other.ColPtrJ);
    mfem::Swap(ColPtrNode, other.ColPtrNode);
+   mfem::Swap(At, other.At);
 
 #ifdef MFEM_USE_MEMALLOC
    mfem::Swap(NodesMem, other.NodesMem);

linalg/sparsemat.hpp

@@ -64,6 +64,9 @@ protected:
    mutable int* ColPtrJ;
    mutable RowNode ** ColPtrNode;
 
+   /// Transpose of A. Owned. Used to perform MultTranspose() on devices.
+   mutable SparseMatrix *At;
+
 #ifdef MFEM_USE_MEMALLOC
    typedef MemAlloc <RowNode, 1024> RowNodeAlloc;
    RowNodeAlloc * NodesMem;
@@ -97,6 +100,9 @@ public:
 
    /** @brief Create a sparse matrix in CSR format. Ownership of @a i, @a j, and
        @a data is optionally transferred to the SparseMatrix. */
+   /** If the parameter @a data is NULL, then the internal #A array is allocated
+       by this constructor (initializing it with zeros and taking ownership,
+       regardless of the parameter @a owna). */
    SparseMatrix(int *i, int *j, double *data, int m, int n, bool ownij,
                 bool owna, bool issorted);
 
@@ -112,7 +118,7 @@ public:
        ownership. */
    SparseMatrix(const SparseMatrix &mat, bool copy_graph = true);
 
-   /// Create a SparseMatrix with diagonal v, i.e. A = Diag(v)
+   /// Create a SparseMatrix with diagonal @a v, i.e. A = Diag(v)
    SparseMatrix(const Vector & v);
 
 
@@ -134,21 +140,35 @@ public:
    /// Check if the SparseMatrix is empty.
    bool Empty() const { return (A == NULL) && (Rows == NULL); }
 
-   /// Return the array #I
-   inline int *GetI() const { return I; }
-   /// Return the array #J
-   inline int *GetJ() const { return J; }
-   /// Return element data, i.e. array #A
-   inline double *GetData() const { return A; }
-   /// Returns the number of elements in row @a i
+   /// Return the array #I.
+   inline int *GetI() { return I; }
+   /// Return the array #I, const version.
+   inline const int *GetI() const { return I; }
+
+   /// Return the array #J.
+   inline int *GetJ() { return J; }
+   /// Return the array #J, const version.
+   inline const int *GetJ() const { return J; }
+
+   /// Return the element data, i.e. the array #A.
+   inline double *GetData() { return A; }
+   /// Return the element data, i.e. the array #A, const version.
+   inline const double *GetData() const { return A; }
+
+   /// Returns the number of elements in row @a i.
    int RowSize(const int i) const;
-   /// Returns the maximum number of elements among all rows
+
+   /// Returns the maximum number of elements among all rows.
    int MaxRowSize() const;
-   /// Return a pointer to the column indices in a row
+
+   /// Return a pointer to the column indices in a row.
    int *GetRowColumns(const int row);
+   /// Return a pointer to the column indices in a row, const version.
    const int *GetRowColumns(const int row) const;
-   /// Return a pointer to the entries in a row
+
+   /// Return a pointer to the entries in a row.
    double *GetRowEntries(const int row);
+   /// Return a pointer to the entries in a row, const version.
    const double *GetRowEntries(const int row) const;
 
    /// Change the width of a SparseMatrix.
@@ -163,7 +183,7 @@ public:
 
    /// Returns the actual Width of the matrix.
    /*! This method can be called for matrices finalized or not. */
-   int ActualWidth();
+   int ActualWidth() const;
 
    /// Sort the column indices corresponding to each row.
    void SortColumnIndices();
@@ -206,13 +226,45 @@ public:
    void AddMultTranspose(const Vector &x, Vector &y,
                          const double a = 1.0) const;
 
+   /** @brief Build and store internally the transpose of this matrix which will
+       be used in the methods AddMultTranspose() and MultTranspose(). */
+   /** If this method has been called, the internal transpose matrix will be
+       used to perform the action of the transpose matrix in AddMultTranspose(),
+       and MultTranspose().
+
+       Warning: any changes in this matrix will invalidate the internal
+       transpose. To rebuild the transpose, call ResetTranspose() followed by a
+       call to this method. If the internal transpose is already built, this
+       method has no effect.
+
+       When any non-default backend is enabled, i.e. Device::IsEnabled() is
+       true, the methods AddMultTranspose(), and MultTranspose(), require the
+       internal transpose to be built. If that is not the case (i.e. the
+       internal transpose is not built), these methods will raise an error with
+       an appropriate message pointing to this method. When using the default
+       backend, calling this method is optional.
+
+       This method can only be used when the sparse matrix is finalized. */
+   void BuildTranspose() const;
+
+   /** Reset (destroy) the internal transpose matrix. See BuildTranspose() for
+       more details. */
+   void ResetTranspose() const;
+
    void PartMult(const Array<int> &rows, const Vector &x, Vector &y) const;
    void PartAddMult(const Array<int> &rows, const Vector &x, Vector &y,
                     const double a=1.0) const;
 
-   /// y = A * x, but treat all elements as booleans (zero=false, nonzero=true).
+   /// y = A * x, treating all entries as booleans (zero=false, nonzero=true).
+   /** The actual values stored in the data array, #A, are not used - this means
+       and that all entries in the sparsity pattern are considered to be true by
+       this method. */
    void BooleanMult(const Array<int> &x, Array<int> &y) const;
-   /// y = At * x, but treat all elements as booleans (zero=false, nonzero=true).
+
+   /// y = At * x, treating all entries as booleans (zero=false, nonzero=true).
+   /** The actual values stored in the data array, #A, are not used - this means
+       and that all entries in the sparsity pattern are considered to be true by
+       this method. */
    void BooleanMultTranspose(const Array<int> &x, Array<int> &y) const;
 
    /// Compute y^t A x
@@ -452,11 +504,11 @@ SparseMatrix *Transpose(const SparseMatrix &A);
 SparseMatrix *TransposeAbstractSparseMatrix (const AbstractSparseMatrix &A,
                                              int useActualWidth);
 
-/** Matrix product A.B.
-    If OAB is not NULL, we assume it has the structure
-    of A.B and store the result in OAB.
-    If OAB is NULL, we create a new SparseMatrix to store
+/// Matrix product A.B.
+/** If @a OAB is not NULL, we assume it has the structure of A.B and store the
+    result in @a OAB. If @a OAB is NULL, we create a new SparseMatrix to store
     the result and return a pointer to it.
+
     All matrices must be finalized. */
 SparseMatrix *Mult(const SparseMatrix &A, const SparseMatrix &B,
                    SparseMatrix *OAB = NULL);
@@ -555,16 +607,20 @@ inline void SparseMatrix::SetColPtr(const int row) const
 inline void SparseMatrix::ClearColPtr() const
 {
    if (Rows)
+   {
       for (RowNode *node_p = Rows[current_row]; node_p != NULL;
            node_p = node_p->Prev)
       {
          ColPtrNode[node_p->Column] = NULL;
       }
+   }
    else
+   {
       for (int j = I[current_row], end = I[current_row+1]; j < end; j++)
       {
          ColPtrJ[J[j]] = -1;
       }
+   }
 }
 
 inline double &SparseMatrix::SearchRow(const int col)

linalg/vector.cpp

@@ -857,11 +857,11 @@ static double cuVectorMin(const int N, const double *X)
    const int bytes = min_sz*sizeof(double);
    static double *h_min = NULL;
    if (!h_min) { h_min = (double*)calloc(min_sz,sizeof(double)); }
-   static CUdeviceptr gdsr = (CUdeviceptr) NULL;
-   if (!gdsr) { ::cuMemAlloc(&gdsr,bytes); }
+   static void *gdsr = NULL;
+   if (!gdsr) { MFEM_CUDA_CHECK(cudaMalloc(&gdsr, bytes)); }
    cuKernelMin<<<gridSize,blockSize>>>(N, (double*)gdsr, x);
-   MFEM_CUDA_CHECK_RT(cudaGetLastError());
-   ::cuMemcpy((CUdeviceptr)h_min,(CUdeviceptr)gdsr,bytes);
+   MFEM_CUDA_CHECK(cudaGetLastError());
+   MFEM_CUDA_CHECK(cudaMemcpy(h_min, gdsr, bytes, cudaMemcpyDeviceToHost));
    double min = std::numeric_limits<double>::infinity();
    for (int i = 0; i < min_sz; i++) { min = fmin(min, h_min[i]); }
    return min;
@@ -909,19 +909,19 @@ static double cuVectorDot(const int N, const double *X, const double *Y)
       if (h_dot) { free(h_dot); }
       h_dot = (double*)calloc(dot_sz,sizeof(double));
    }
-   static CUdeviceptr gdsr = (CUdeviceptr) NULL;
+   static void *gdsr = NULL;
    if (!gdsr or dot_block_sz!=dot_sz)
    {
-      if (gdsr) { MFEM_CUDA_CHECK_DRV(::cuMemFree(gdsr)); }
-      MFEM_CUDA_CHECK_DRV(::cuMemAlloc(&gdsr,bytes));
+      if (gdsr) { MFEM_CUDA_CHECK(cudaFree(gdsr)); }
+      MFEM_CUDA_CHECK(cudaMalloc(&gdsr,bytes));
    }
    if (dot_block_sz!=dot_sz)
    {
       dot_block_sz = dot_sz;
    }
    cuKernelDot<<<gridSize,blockSize>>>(N, (double*)gdsr, x, y);
-   MFEM_CUDA_CHECK_RT(cudaGetLastError());
-   MFEM_CUDA_CHECK_DRV(::cuMemcpy((CUdeviceptr)h_dot,(CUdeviceptr)gdsr,bytes));
+   MFEM_CUDA_CHECK(cudaGetLastError());
+   MFEM_CUDA_CHECK(cudaMemcpy(h_dot, gdsr, bytes, cudaMemcpyDeviceToHost));
    double dot = 0.0;
    for (int i = 0; i < dot_sz; i++) { dot += h_dot[i]; }
    return dot;

makefile

@@ -211,6 +211,9 @@ ifneq ($(MFEM_USE_CUDA),YES)
    XCOMPILER = $(CXX_XCOMPILER)
    XLINKER   = $(CXX_XLINKER)
 else
+   ifneq ($(MFEM_USE_MM),YES)
+      $(error MFEM_USE_CUDA=YES requires MFEM_USE_MM=YES)
+   endif
    MFEM_CXX ?= $(CUDA_CXX)
    CXXFLAGS += $(CUDA_FLAGS) -ccbin $(CXX_OR_MPICXX)
    XCOMPILER = $(CUDA_XCOMPILER)
@@ -230,7 +233,7 @@ endif
 
 # List of MFEM dependencies, that require the *_LIB variable to be non-empty
 MFEM_REQ_LIB_DEPS = SUPERLU METIS CONDUIT SIDRE LAPACK SUNDIALS MESQUITE\
- SUITESPARSE STRUMPACK GECKO GNUTLS NETCDF PETSC MPFR PUMI CUDA OCCA RAJA
+ SUITESPARSE STRUMPACK GECKO GNUTLS NETCDF PETSC MPFR PUMI OCCA RAJA
 PETSC_ERROR_MSG = $(if $(PETSC_FOUND),,. PETSC config not found: $(PETSC_VARS))
 
 define mfem_check_dependency
@@ -246,7 +249,7 @@ ifeq ($(MAKECMDGOALS),config)
 endif
 
 # List of MFEM dependencies, processed below
-MFEM_DEPENDENCIES = $(MFEM_REQ_LIB_DEPS) LIBUNWIND OPENMP
+MFEM_DEPENDENCIES = $(MFEM_REQ_LIB_DEPS) LIBUNWIND OPENMP CUDA
 
 # List of deprecated MFEM dependencies, processed below
 MFEM_LEGACY_DEPENDENCIES = OPENMP
@@ -319,8 +322,8 @@ MFEM_TEST_MK   ?= @MFEM_DIR@/config/test.mk
 # Use "\n" (interpreted by sed) to add a newline.
 MFEM_CONFIG_EXTRA ?= $(if $(BUILD_DIR_DEF),MFEM_BUILD_DIR ?= @MFEM_DIR@,)
 
-MFEM_SOURCE_DIR  := $(MFEM_REAL_DIR)
-MFEM_INSTALL_DIR := $(BUILD_REAL_DIR)
+MFEM_SOURCE_DIR  = $(MFEM_REAL_DIR)
+MFEM_INSTALL_DIR = $(abspath $(MFEM_PREFIX))
 
 # If we have 'config' target, export variables used by config/makefile
 ifneq (,$(filter config,$(MAKECMDGOALS)))
@@ -344,6 +347,11 @@ ifneq (,$(filter install,$(MAKECMDGOALS)))
    MFEM_LIBS     = $(if $(shared),$(INSTALL_RPATH)) -L@MFEM_LIB_DIR@ -lmfem\
       @MFEM_EXT_LIBS@
    MFEM_LIB_FILE = @MFEM_LIB_DIR@/libmfem.$(if $(shared),$(SO_VER),a)
+   ifeq ($(MFEM_USE_OCCA),YES)
+      ifneq ($(MFEM_INSTALL_DIR),$(abspath $(PREFIX))
+         $(error OCCA is enabled: PREFIX must be set during configuration!)
+      endif
+   endif
    MFEM_PREFIX := $(abspath $(PREFIX))
    MFEM_INC_DIR = $(abspath $(PREFIX_INC))
    MFEM_LIB_DIR = $(abspath $(PREFIX_LIB))
@@ -358,6 +366,7 @@ DIRS = general linalg mesh fem
 SOURCE_FILES = $(foreach dir,$(DIRS),$(wildcard $(SRC)$(dir)/*.cpp))
 RELSRC_FILES = $(patsubst $(SRC)%,%,$(SOURCE_FILES))
 OBJECT_FILES = $(patsubst $(SRC)%,$(BLD)%,$(SOURCE_FILES:.cpp=.o))
+OKL_DIRS = fem
 
 .PHONY: lib all clean distclean install config status info deps serial parallel\
 	debug pdebug cuda pcuda cudebug pcudebug style check test unittest\
@@ -498,7 +507,12 @@ install: $(if $(static),$(BLD)libmfem.a) $(if $(shared),$(BLD)libmfem.$(SO_EXT))
 # install remaining includes in each subdirectory
 	for dir in $(DIRS); do \
 	   mkdir -p $(PREFIX_INC)/mfem/$$dir && \
-	   $(INSTALL) -m 640 $(SRC)$$dir/*.hpp $(SRC)$$dir/*.okl $(PREFIX_INC)/mfem/$$dir; \
+	   $(INSTALL) -m 640 $(SRC)$$dir/*.hpp $(PREFIX_INC)/mfem/$$dir; \
+	done
+# install *.okl files
+	for dir in $(OKL_DIRS); do \
+	   mkdir -p $(PREFIX_INC)/mfem/$$dir && \
+	   $(INSTALL) -m 640 $(SRC)$$dir/*.okl $(PREFIX_INC)/mfem/$$dir; \
 	done
 # install config.mk in $(PREFIX_SHARE)
 	mkdir -p $(PREFIX_SHARE)

mesh/pmesh.cpp

@@ -3090,6 +3090,23 @@ void ParMesh::Rebalance()
                  " meshes.");
    }
 
+   // Make sure the Nodes use a ParFiniteElementSpace
+   if (Nodes && dynamic_cast<ParFiniteElementSpace*>(Nodes->FESpace()) == NULL)
+   {
+      ParFiniteElementSpace *pfes =
+         new ParFiniteElementSpace(*Nodes->FESpace(), *this);
+      ParGridFunction *new_nodes = new ParGridFunction(pfes);
+      *new_nodes = *Nodes;
+      if (Nodes->OwnFEC())
+      {
+         new_nodes->MakeOwner(Nodes->OwnFEC());
+         Nodes->MakeOwner(NULL); // takes away ownership of 'fec' and 'fes'
+         delete Nodes->FESpace();
+      }
+      delete Nodes;
+      Nodes = new_nodes;
+   }
+
    DeleteFaceNbrData();
 
    pncmesh->Rebalance();
@@ -3110,22 +3127,6 @@ void ParMesh::Rebalance()
    last_operation = Mesh::REBALANCE;
    sequence++;
 
-   // Make sure the Nodes use a ParFiniteElementSpace
-   if (Nodes && dynamic_cast<ParFiniteElementSpace*>(Nodes->FESpace()) == NULL)
-   {
-      ParFiniteElementSpace *pfes =
-         new ParFiniteElementSpace(*Nodes->FESpace(), *this);
-      ParGridFunction *new_nodes = new ParGridFunction(pfes);
-      *new_nodes = *Nodes;
-      if (Nodes->OwnFEC())
-      {
-         new_nodes->MakeOwner(Nodes->OwnFEC());
-         Nodes->MakeOwner(NULL); // takes away ownership of 'fec' and 'fes'
-         delete Nodes->FESpace();
-      }
-      delete Nodes;
-      Nodes = new_nodes;
-   }
    UpdateNodes();
 }
 

tests/unit/CMakeLists.txt

@@ -9,11 +9,11 @@
 # terms of the GNU Lesser General Public License (as published by the Free
 # Software Foundation) version 2.1 dated February 1999.
 
-# Include the build directory where mfem.hpp and mfem-performance.hpp are.
-include_directories(BEFORE ${PROJECT_BINARY_DIR})
 # Include the top mfem source directory - needed by some tests, e.g. to
 # #include "general/text.hpp".
 include_directories(BEFORE ${PROJECT_SOURCE_DIR})
+# Include the build directory where mfem.hpp and mfem-performance.hpp are.
+include_directories(BEFORE ${PROJECT_BINARY_DIR})
 # Include the source directory for the unit tests - catch.hpp is there.
 include_directories(BEFORE ${CMAKE_CURRENT_SOURCE_DIR})
 

tests/unit/fem/test_datacollection.cpp

@@ -12,7 +12,13 @@
 #include "mfem.hpp"
 #include "catch.hpp"
 #include <stdio.h>
-#include <unistd.h>  // rmdir
+
+#ifndef _WIN32
+#include <unistd.h> // rmdir
+#else
+#include <direct.h> // _rmdir
+#define rmdir(dir) _rmdir(dir)
+#endif
 
 using namespace mfem;
 

tests/unit/fem/test_inversetransform.cpp

@@ -125,7 +125,7 @@ TEST_CASE("InverseElementTransformation",
       REQUIRE( mesh_file.good() );
 
       const int npts = 100; // number of random points to test
-      const int min_found_pts = 94;
+      const int min_found_pts = 93;
       const int rand_seed = 189548;
       srand(rand_seed);