Generic version of PointMatrixHash::operator()

Miniapp for block preconditioned elasticity with partial and full assembly on GPUs [full-assembly-elast-dev]

.gitignore

@@ -128,6 +128,13 @@ examples/amgx/sol.gf
 examples/amgx/mesh.*
 examples/amgx/sol.*
 
+examples/caliper/ex1
+examples/caliper/ex1p
+examples/caliper/refined.mesh
+examples/caliper/sol.gf
+examples/caliper/mesh.*
+examples/caliper/sol.*
+
 examples/ginkgo/ex1
 examples/ginkgo/refined.mesh
 examples/ginkgo/sol.gf
@@ -266,6 +273,7 @@ miniapps/navier/*_output
 miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
 miniapps/nurbs/nurbs_ex11p
+miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
 miniapps/nurbs/refined.mesh
@@ -275,6 +283,10 @@ miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
 miniapps/nurbs/sin-fit.mesh
 miniapps/nurbs/CurveInt
+miniapps/nurbs/nurbs_naca_cmesh
+miniapps/nurbs/naca-cmesh.mesh
+miniapps/nurbs/glvis_naca-cmesh.mesh
+miniapps/nurbs/Naca_cmesh
 
 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -299,7 +311,7 @@ miniapps/tools/convert-dc
 miniapps/tools/lor-transfer
 miniapps/tools/plor-transfer
 miniapps/tools/get-values
-miniapps/tools/check-tmop-metric
+miniapps/tools/tmop-check-metric
 miniapps/tools/tmop-metric-magnitude
 miniapps/tools/nodal-transfer
 miniapps/tools/ParaView
@@ -330,6 +342,7 @@ miniapps/toys/mondrian.mesh
 miniapps/solvers/block-solvers
 miniapps/solvers/lor_solvers
 miniapps/solvers/plor_solvers
+miniapps/solvers/lor_elast
 miniapps/solvers/ParaView
 miniapps/solvers/mesh.*
 miniapps/solvers/sol.*

CHANGELOG

@@ -11,6 +11,44 @@
 Version 4.6.1 (development)
 ===========================
 
+Discretization improvements
+---------------------------
+- Introduced support for higher order non conformal Nedelec elements on
+  simplices in ParMesh.
+- Introduced support for internal boundary elements in nonconformal adapted
+  meshes.
+
+- Added functionality for construction of cut-surface and cut-volume
+  IntegrationRules through a moment-fitting approach. The cut is specified by
+  the zero level set of a Coefficient. See fem/intrules_cut.hpp and Example 38.
+
+GPU support
+----------------------------
+- Added support for full assembly on simplices.
+- Added functionality for BilinearFormIntegrators to use kernels that work for both
+  tensor and unstructured elements.
+- Added partial assembly for linear elasticity. Does not use sum factorization for now.
+
+New and updated examples and miniapps
+-------------------------------------
+- Added miniapp to demonstrate new elasticity integrator and unstructured element GPU support,
+  and a block diagonal preconditioner using low order refinement. Allows comparison with
+  currently existing legacy mode integrator. See miniapps/solvers/lor_elast.
+
+Miscellaneous
+-------------
+- Added support for single and double precision, with corresponding hypre build.
+  Generalized the floating point type from `double` to `real_t`.
+
+- The ReadCubit Genesis mesh importer has been rewritten to improve readability.
+
+- Updated the Doxygen documentation style, which now requires Doxygen version
+  1.9.8 or later. See the doc/ directory.
+
+- Improved thread safety for global variables in the library, for example
+  IntegrationRules IntRules, RefinedIntRules, GeometryRefiner
+  GlobGeometryRefiner, and FiniteElement::dof2quad_array.
+
 
 Version 4.6, released on September 27, 2023
 ===========================================
@@ -31,6 +69,7 @@ Meshing improvements
   * The edge to knot map for NURBS meshes can be determined automatically. It is
     no longer needed to specify this in the NURBS mesh.
   * Added curve interpolation method for NURBS.
+  * Added new small miniapp for printing of shape functions of a KnotVector
   * See miniapps/nurbs for example meshes and miniapps.
 
 Discretization improvements
@@ -77,6 +116,8 @@ Linear and nonlinear solvers
 
 - Added HIP support to the PETSc and SUNDIALS interfaces.
 
+- Efficient GPU-accelerated LOR assembly now supports surface meshes.
+
 New and updated examples and miniapps
 -------------------------------------
 - Added a new H(div) solver miniapp demonstrating the use of a matrix-free

CMakeLists.txt

@@ -139,10 +139,9 @@ if (MFEM_USE_CUDA)
       set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CMAKE_CXX_COMPILER})
    endif()
    set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} ${CUDA_FLAGS}")
+   find_package(CUDAToolkit REQUIRED)
    set(CUSPARSE_FOUND TRUE)
-   set(CUSPARSE_LIBRARIES "cusparse")
-   set(CUBLAS_FOUND TRUE)
-   set(CUBLAS_LIBRARIES "cublas")
+   get_target_property(CUSPARSE_LIBRARIES CUDA::cusparse LOCATION)
 endif()
 
 if (XSDK_ENABLE_C)
@@ -531,7 +530,7 @@ find_package(Threads REQUIRED)
 set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
     SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
     NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
-    ADIOS2 CUBLAS CUSPARSE MKL_CPARDISO MKL_PARDISO AMGX CALIPER CODIPACK
+    ADIOS2 CUSPARSE MKL_CPARDISO MKL_PARDISO AMGX CALIPER CODIPACK
     BENCHMARK PARELAG MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM ENZYME)
 
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
@@ -641,16 +640,34 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
   foreach(Header mfem.hpp mfem-performance.hpp)
     message(STATUS
       "Writing substitute header --> \"${Header}\"")
-    file(WRITE "${PROJECT_BINARY_DIR}/${Header}"
+    file(WRITE "${PROJECT_BINARY_DIR}/${Header}.tmp"
 "// Auto-generated file.
 #define MFEM_CONFIG_FILE \"${PROJECT_BINARY_DIR}/config/_config.hpp\"
 #include \"${PROJECT_SOURCE_DIR}/${Header}\"
 ")
+
+    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different 
+      "${PROJECT_BINARY_DIR}/${Header}.tmp"
+      "${PROJECT_BINARY_DIR}/${Header}"
+    )
+    execute_process(COMMAND ${CMAKE_COMMAND} -E remove
+      "${PROJECT_BINARY_DIR}/${Header}.tmp"
+    )
+
     # This version will be installed in the top include directory:
-    file(WRITE "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}"
+    file(WRITE "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}.tmp"
 "// Auto-generated file.
 #include \"mfem/${Header}\"
 ")
+
+    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different 
+      "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}.tmp"
+      "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}"
+    )
+    execute_process(COMMAND ${CMAKE_COMMAND} -E remove
+      "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}.tmp"
+    )
+
   endforeach()
 endif()
 

CONTRIBUTING.md

@@ -359,6 +359,8 @@ Before you can start, you need a GitHub account, here are a few suggestions:
     conflicted files in the commit message.
   - All significant new features and changes should be documented in CHANGELOG.
   - New examples and miniapps should have documentation on the MFEM webpage.
+  - The general floating-point type `real_t` should be used, rather than
+    `float` or `double`, except in special cases where only one is possible.
 
 
 ### Pull Requests

INSTALL

@@ -659,8 +659,7 @@ The specific libraries and their options are:
   requires the PT-Scotch and Scalapack libraries as well as ParMETIS, which
   includes METIS 5 in its distribution. Starting with STRUMPACK v2.2.0, ParMETIS
   and PT-Scotch are optional dependencies.
-  The support for STRUMPACK was added in MFEM v3.3.2 and it requires STRUMPACK
-  2.0.0 or later.
+  The support for STRUMPACK was added in MFEM v3.3.2.
   URL: http://portal.nersc.gov/project/sparse/strumpack
   Options: STRUMPACK_OPT, STRUMPACK_LIB.
   Versions: STRUMPACK >= 3.0.0.
@@ -797,7 +796,7 @@ The specific libraries and their options are:
   URL: https://github.com/CEED/libCEED
        https://ceed.exascaleproject.org/libceed
   Options: CEED_DIR, CEED_OPT, CEED_LIB.
-  Versions: libCEED >= 0.10.
+  Versions: libCEED >= 0.12.
 
 - RAJA (optional), used when MFEM_USE_RAJA = YES.
   Beginning with MFEM v4.5.1, only RAJA v2022.10.3+ is supported.

config/cmake/MFEMConfig.cmake.in

@@ -63,6 +63,8 @@ set(MFEM_USE_ALGOIM @MFEM_USE_ALGOIM@)
 set(MFEM_USE_BENCHMARK @MFEM_USE_BENCHMARK@)
 set(MFEM_USE_PARELAG @MFEM_USE_PARELAG@)
 set(MFEM_USE_ENZYME @MFEM_USE_ENZYME@)
+set(MFEM_USE_DOUBLE @MFEM_USE_DOUBLE@)
+set(MFEM_USE_SINGLE @MFEM_USE_SINGLE@)
 
 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")
 set(MFEM_CXX_FLAGS "@CMAKE_CXX_FLAGS@")

config/cmake/config.hpp.in

@@ -201,4 +201,10 @@
 // Enable Enzyme for AD
 #cmakedefine MFEM_USE_ENZYME
 
+// Use double-precision floating point type
+#cmakedefine MFEM_USE_DOUBLE
+
+// Use single-precision floating point type
+#cmakedefine MFEM_USE_SINGLE
+
 #endif // MFEM_CONFIG_HEADER

config/cmake/modules/FindHYPRE.cmake

@@ -14,9 +14,13 @@
 #   - HYPRE_LIBRARIES
 #   - HYPRE_INCLUDE_DIRS
 #   - HYPRE_VERSION
+#   - HYPRE_USING_CUDA (internal)
 #   - HYPRE_USING_HIP (internal)
 
 if (HYPRE_FOUND)
+  if (HYPRE_USING_CUDA)
+    find_package(CUDAToolkit REQUIRED)
+  endif()
   if (HYPRE_USING_HIP)
     find_package(rocsparse REQUIRED)
     find_package(rocrand REQUIRED)
@@ -27,6 +31,20 @@ endif()
 include(MfemCmakeUtilities)
 mfem_find_package(HYPRE HYPRE HYPRE_DIR "include" "HYPRE.h" "lib" "HYPRE"
   "Paths to headers required by HYPRE." "Libraries required by HYPRE."
+  CHECK_BUILD HYPRE_USING_CUDA FALSE
+  "
+#undef HYPRE_USING_CUDA
+#include <HYPRE_config.h>
+
+#ifndef HYPRE_USING_CUDA
+#error HYPRE is built without CUDA.
+#endif
+
+int main()
+{
+   return 0;
+}
+"
   CHECK_BUILD HYPRE_USING_HIP FALSE
   "
 #undef HYPRE_USING_HIP
@@ -57,6 +75,16 @@ if (HYPRE_FOUND AND (NOT HYPRE_VERSION))
   endif()
 endif()
 
+if (HYPRE_FOUND AND HYPRE_USING_CUDA)
+  find_package(CUDAToolkit REQUIRED)
+  get_target_property(CUSPARSE_LIBRARIES CUDA::cusparse LOCATION)
+  get_target_property(CURAND_LIBRARIES CUDA::curand LOCATION)
+  list(APPEND HYPRE_LIBRARIES ${CUSPARSE_LIBRARIES} ${CURAND_LIBRARIES})
+  set(HYPRE_LIBRARIES ${HYPRE_LIBRARIES} CACHE STRING
+      "HYPRE libraries + dependencies." FORCE)
+  message(STATUS "Updated HYPRE_LIBRARIES: ${HYPRE_LIBRARIES}")
+endif()
+
 if (HYPRE_FOUND AND HYPRE_USING_HIP)
   find_package(rocsparse REQUIRED)
   find_package(rocrand REQUIRED)

config/config.hpp.in

@@ -201,4 +201,10 @@
 // Enable the Enzyme LLVM plugin
 // #define MFEM_USE_ENZYME
 
+// Use double-precision floating point type
+// #define MFEM_USE_DOUBLE
+
+// Use single-precision floating point type
+// #define MFEM_USE_SINGLE
+
 #endif // MFEM_CONFIG_HEADER

config/config.mk.in

@@ -64,6 +64,8 @@ MFEM_USE_CODIPACK      = @MFEM_USE_CODIPACK@
 MFEM_USE_BENCHMARK     = @MFEM_USE_BENCHMARK@
 MFEM_USE_PARELAG       = @MFEM_USE_PARELAG@
 MFEM_USE_ENZYME        = @MFEM_USE_ENZYME@
+MFEM_USE_DOUBLE        = @MFEM_USE_DOUBLE@
+MFEM_USE_SINGLE        = @MFEM_USE_SINGLE@
 
 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@

config/defaults.cmake

@@ -66,6 +66,8 @@ option(MFEM_USE_CODIPACK "Enable automatic differentiation (AD) using CoDiPack"
 option(MFEM_USE_BENCHMARK "Enable Google Benchmark" OFF)
 option(MFEM_USE_PARELAG "Enable ParELAG" OFF)
 option(MFEM_USE_ENZYME "Enable Enzyme" OFF)
+option(MFEM_USE_DOUBLE "Double precision" ON)
+option(MFEM_USE_SINGLE "Single precision" OFF)
 
 # Optional overrides for autodetected MPIEXEC and MPIEXEC_NUMPROC_FLAG
 # set(MFEM_MPIEXEC "mpirun" CACHE STRING "Command for running MPI tests")
@@ -106,12 +108,7 @@ set(HYPRE_DIR "${MFEM_DIR}/../hypre/src/hypre" CACHE PATH
 # If hypre was compiled to depend on BLAS and LAPACK:
 # set(HYPRE_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
 #     "Packages that HYPRE depends on.")
-if (MFEM_USE_CUDA)
-   # This is only necessary when hypre is built with cuda:
-   set(HYPRE_REQUIRED_LIBRARIES "-lcusparse" "-lcurand" CACHE STRING
-       "Libraries that HYPRE depends on.")
-endif()
-# HIP dependency for HYPRE is handled in FindHYPRE.cmake.
+# CUDA and HIP dependencies for HYPRE are handled in FindHYPRE.cmake.
 
 set(METIS_DIR "${MFEM_DIR}/../metis-4.0" CACHE PATH "Path to the METIS library.")
 
@@ -157,7 +154,8 @@ set(STRUMPACK_DIR "${MFEM_DIR}/../STRUMPACK-build" CACHE PATH
 # STRUMPACK may also depend on "OpenMP", depending on how it was compiled.
 # Starting with v2.2.0 of STRUMPACK, ParMETIS and Scotch are optional.
 set(STRUMPACK_REQUIRED_PACKAGES "MPI" "MPI_Fortran" "ParMETIS" "METIS"
-    "ScaLAPACK" "Scotch/ptscotch/ptscotcherr/scotch/scotcherr" CACHE STRING
+    "Scotch/ptscotch/ptscotcherr/scotch/scotcherr"
+    "ScaLAPACK" "LAPACK" "BLAS" CACHE STRING
     "Additional packages required by STRUMPACK.")
 # If the MPI package does not find all required Fortran libraries:
 # set(STRUMPACK_REQUIRED_LIBRARIES "gfortran" "mpi_mpifh" CACHE STRING

config/defaults.mk

@@ -167,6 +167,8 @@ MFEM_USE_CODIPACK      = NO
 MFEM_USE_BENCHMARK     = NO
 MFEM_USE_PARELAG       = NO
 MFEM_USE_ENZYME        = NO
+MFEM_USE_DOUBLE        = YES
+MFEM_USE_SINGLE        = NO
 
 # MPI library compile and link flags
 # These settings are used only when building MFEM with MPI + HIP
@@ -331,16 +333,30 @@ STRUMPACK_OPT = -I$(STRUMPACK_DIR)/include $(SCOTCH_OPT)
 STRUMPACK_LIB = -L$(STRUMPACK_DIR)/lib -lstrumpack $(MPI_FORTRAN_LIB)\
  $(SCOTCH_LIB) $(SCALAPACK_LIB)
 
-# Ginkgo library configuration (currently not needed)
+# Ginkgo library configuration
 GINKGO_DIR = @MFEM_DIR@/../ginkgo/install
+GINKGO_SEARCH_DIR = $(subst @MFEM_DIR@,$(MFEM_DIR),$(GINKGO_DIR))
 GINKGO_BUILD_TYPE=Release
 ifeq ($(MFEM_USE_GINKGO),YES)
    BASE_FLAGS = -std=c++14
 endif
 GINKGO_OPT = -isystem $(GINKGO_DIR)/include
-GINKGO_LIB_DIR = $(sort $(dir $(wildcard $(GINKGO_DIR)/lib*/libginkgo*.a  $(GINKGO_DIR)/lib*/libginkgo*.so $(GINKGO_DIR)/lib*/libginkgo*.dylib $(GINKGO_DIR)/lib*/libginkgo*.dll)))
-ALL_GINKGO_LIBS_DEBUG = $(notdir $(basename $(wildcard $(GINKGO_DIR)/lib*/libginkgo*d.a  $(GINKGO_DIR)/lib*/libginkgo*d.so $(GINKGO_DIR)/lib*/libginkgo*d.dylib $(GINKGO_DIR)/lib*/libginkgo*d.dll)))
-ALL_GINKGO_LIBS = $(notdir $(basename $(wildcard $(GINKGO_DIR)/lib*/libginkgo*.a  $(GINKGO_DIR)/lib*/libginkgo*.so $(GINKGO_DIR)/lib*/libginkgo*.dylib $(GINKGO_DIR)/lib*/libginkgo*.dll)))
+GINKGO_LIB_DIR = $(sort $(dir $(wildcard\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.a\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.so\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.dylib\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.dll)))
+GINKGO_LINK_LIB_DIR = $(GINKGO_DIR)$(subst $(GINKGO_SEARCH_DIR),,$(GINKGO_LIB_DIR))
+ALL_GINKGO_LIBS_DEBUG = $(notdir $(basename $(wildcard\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*d.a\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*d.so\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*d.dylib\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*d.dll)))
+ALL_GINKGO_LIBS = $(notdir $(basename $(wildcard\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.a\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.so\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.dylib\
+ $(GINKGO_SEARCH_DIR)/lib*/libginkgo*.dll)))
 ALL_GINKGO_LIBS_RELEASE = $(filter-out $(ALL_GINKGO_LIBS_DEBUG),$(ALL_GINKGO_LIBS))
 GINKGO_LINK = $(subst libginkgo,-lginkgo,$(ALL_GINKGO_LIBS_RELEASE))
 ifeq ($(GINKGO_BUILD_TYPE),Debug)
@@ -349,7 +365,8 @@ ifeq ($(GINKGO_BUILD_TYPE),Debug)
   endif
 else
 endif
-GINKGO_LIB = $(XLINKER)-rpath,$(GINKGO_LIB_DIR) -L$(GINKGO_LIB_DIR) $(GINKGO_LINK)
+GINKGO_LIB = $(XLINKER)-rpath,$(GINKGO_LINK_LIB_DIR) -L$(GINKGO_LINK_LIB_DIR)\
+ $(GINKGO_LINK)
 
 # AmgX library configuration
 AMGX_DIR = @MFEM_DIR@/../amgx

config/makefile

@@ -38,14 +38,14 @@ all: header config-mk
 MPI = $(MFEM_USE_MPI:NO=)
 GHV_CXX ?= $(MFEM_CXX)
 GHV = get_hypre_version
-GHV_FLAGS = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(HYPRE_OPT))
+GHV_FLAGS = $(MFEM_CXXFLAGS) $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(HYPRE_OPT))
 SMX = $(if $(MFEM_USE_PUMI:NO=),MFEM_USE_SIMMETRIX)
 SMX_PATH = $(PUMI_DIR)/include/gmi_sim.h
 SMX_FILE = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(SMX_PATH))
 MUMPS = $(MFEM_USE_MUMPS:NO=)
 GMV_CXX ?= $(MFEM_CXX)
 GMV = get_mumps_version
-GMV_FLAGS = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(MUMPS_OPT))
+GMV_FLAGS = $(MFEM_CXXFLAGS) $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(MUMPS_OPT))
 
 $(GHV): $(SRC)$(GHV).cpp
 	$(call mfem-info, Determining HYPRE version ...)
@@ -110,3 +110,4 @@ config-mk:
 
 clean:
 	rm -f $(CONFIG_HPP) $(CONFIG_MK) sample-runs-build.log
+	rm -f $(GHV) $(GHV).out $(GMV) $(GMV).out

config/sample-runs.sh

@@ -315,7 +315,7 @@ function extract_sample_runs()
    sruns=`grep -v "^//.*  mpirun .* ${app}" "${src}" |
           grep "^//.*  ${app}" |
           sed -e "s/.*  ${app}/${vg_app}/g"`
-   runs="${sruns}${pruns}"
+   runs="${sruns}"$'\n'"${pruns}"
    if [ "$skip_gen_meshes" == "yes" ]; then
       runs=`printf "%s" "$runs" | grep -v ".* -m .*\.gen"`
    fi

doc/CodeDocumentation.dox

@@ -112,6 +112,7 @@ namespace mfem {
  * - <a class="el" href="ex36p_8cpp_source.html">Example 36p</a>: parallel Proximal Galerkin FEM for the obstacle problem
  * - <a class="el" href="ex37_8cpp_source.html">Example 37</a>: Topology optimization
  * - <a class="el" href="ex37p_8cpp_source.html">Example 37p</a>: parallel topology optimization
+ * - <a class="el" href="ex38_8cpp_source.html">Example 38</a>: cut-surface and cut-volume integration
  *
  * <H4>AmgX Examples</H4>
  * - Variants of Examples
@@ -215,6 +216,7 @@ namespace mfem {
  * - <a class="el" href="generate__random__field_8cpp_source.html">SPDE Solvers</a>: SPDE solver random field generation
  * - <a class="el" href="pdiffusion_8cpp_source.html">DPG Diffusion example</a>: DPG formulation for the diffusion problem
  * - <a class="el" href="pmaxwell_8cpp_source.html">DPG Maxwell example</a>: DPG formulation for the indefinite Maxwell problem
+ * - <a class="el" href="lor__elast_8cpp_source.html">LOR Elasticity</a>: solve linear elasticity with LOR preconditioning on GPUs
  *
  * See also the <a class="el" href="https://mfem.org/examples/">examples documentation</a> online.
  */

doc/README

@@ -14,7 +14,7 @@ If not already available, Doxygen can be downloaded from
 
    http://www.doxygen.org
 
-We recommend using version 1.8 or later.
+We recommend using version 1.9.8 or later.
 
 To build the documentation, simply type "make" in the doc/ directory. This will
 create the file CodeDocumentation.html, which can be viewed in any web browser.

doc/css/customization.css

@@ -0,0 +1,3 @@
+html {
+    --content-maxwidth: auto;
+}

doc/html/header.html

@@ -0,0 +1,78 @@
+<!-- HTML header for doxygen 1.9.6-->
+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
+<html xmlns="http://www.w3.org/1999/xhtml" lang="$langISO">
+<head>
+<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
+<meta http-equiv="X-UA-Compatible" content="IE=11"/>
+<meta name="generator" content="Doxygen $doxygenversion"/>
+<meta name="viewport" content="width=device-width, initial-scale=1"/>
+<!--BEGIN PROJECT_NAME--><title>$projectname: $title</title><!--END PROJECT_NAME-->
+<!--BEGIN !PROJECT_NAME--><title>$title</title><!--END !PROJECT_NAME-->
+<link href="$relpath^tabs.css" rel="stylesheet" type="text/css"/>
+<!--BEGIN DISABLE_INDEX-->
+  <!--BEGIN FULL_SIDEBAR-->
+<script type="text/javascript">var page_layout=1;</script>
+  <!--END FULL_SIDEBAR-->
+<!--END DISABLE_INDEX-->
+<script type="text/javascript" src="$relpath^jquery.js"></script>
+<script type="text/javascript" src="$relpath^dynsections.js"></script>
+$treeview
+$search
+$mathjax
+$darkmode
+<link href="$relpath^$stylesheet" rel="stylesheet" type="text/css" />
+$extrastylesheet
+<script type="text/javascript" src="$relpath^doxygen-awesome-darkmode-toggle.js"></script>
+<script type="text/javascript">
+    DoxygenAwesomeDarkModeToggle.init()
+</script>
+</head>
+<body>
+<!--BEGIN DISABLE_INDEX-->
+  <!--BEGIN FULL_SIDEBAR-->
+<div id="side-nav" class="ui-resizable side-nav-resizable"><!-- do not remove this div, it is closed by doxygen! -->
+  <!--END FULL_SIDEBAR-->
+<!--END DISABLE_INDEX-->
+
+<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
+
+<!--BEGIN TITLEAREA-->
+<div id="titlearea">
+<table cellspacing="0" cellpadding="0">
+ <tbody>
+ <tr id="projectrow">
+  <!--BEGIN PROJECT_LOGO-->
+  <td id="projectlogo"><img alt="Logo" src="$relpath^$projectlogo"/></td>
+  <!--END PROJECT_LOGO-->
+  <!--BEGIN PROJECT_NAME-->
+  <td id="projectalign">
+   <div id="projectname">$projectname<!--BEGIN PROJECT_NUMBER--><span id="projectnumber">&#160;$projectnumber</span><!--END PROJECT_NUMBER-->
+   </div>
+   <!--BEGIN PROJECT_BRIEF--><div id="projectbrief">$projectbrief</div><!--END PROJECT_BRIEF-->
+  </td>
+  <!--END PROJECT_NAME-->
+  <!--BEGIN !PROJECT_NAME-->
+   <!--BEGIN PROJECT_BRIEF-->
+    <td>
+    <div id="projectbrief">$projectbrief</div>
+    </td>
+   <!--END PROJECT_BRIEF-->
+  <!--END !PROJECT_NAME-->
+  <!--BEGIN DISABLE_INDEX-->
+   <!--BEGIN SEARCHENGINE-->
+     <!--BEGIN !FULL_SIDEBAR-->
+    <td>$searchbox</td>
+     <!--END !FULL_SIDEBAR-->
+   <!--END SEARCHENGINE-->
+  <!--END DISABLE_INDEX-->
+ </tr>
+  <!--BEGIN SEARCHENGINE-->
+   <!--BEGIN FULL_SIDEBAR-->
+   <tr><td colspan="2">$searchbox</td></tr>
+   <!--END FULL_SIDEBAR-->
+  <!--END SEARCHENGINE-->
+ </tbody>
+</table>
+</div>
+<!--END TITLEAREA-->
+<!-- end header part -->

doc/js/doxygen-awesome-darkmode-toggle.js

@@ -0,0 +1,157 @@
+/**
+
+Doxygen Awesome
+https://github.com/jothepro/doxygen-awesome-css
+
+MIT License
+
+Copyright (c) 2021 - 2023 jothepro
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+
+*/
+
+class DoxygenAwesomeDarkModeToggle extends HTMLElement {
+    // SVG icons from https://fonts.google.com/icons
+    // Licensed under the Apache 2.0 license:
+    // https://www.apache.org/licenses/LICENSE-2.0.html
+    static lightModeIcon = `<svg xmlns="http://www.w3.org/2000/svg" enable-background="new 0 0 24 24" height="24px" viewBox="0 0 24 24" width="24px" fill="#FCBF00"><rect fill="none" height="24" width="24"/><circle cx="12" cy="12" opacity=".3" r="3"/><path d="M12,9c1.65,0,3,1.35,3,3s-1.35,3-3,3s-3-1.35-3-3S10.35,9,12,9 M12,7c-2.76,0-5,2.24-5,5s2.24,5,5,5s5-2.24,5-5 S14.76,7,12,7L12,7z M2,13l2,0c0.55,0,1-0.45,1-1s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S1.45,13,2,13z M20,13l2,0c0.55,0,1-0.45,1-1 s-0.45-1-1-1l-2,0c-0.55,0-1,0.45-1,1S19.45,13,20,13z M11,2v2c0,0.55,0.45,1,1,1s1-0.45,1-1V2c0-0.55-0.45-1-1-1S11,1.45,11,2z M11,20v2c0,0.55,0.45,1,1,1s1-0.45,1-1v-2c0-0.55-0.45-1-1-1C11.45,19,11,19.45,11,20z M5.99,4.58c-0.39-0.39-1.03-0.39-1.41,0 c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0s0.39-1.03,0-1.41L5.99,4.58z M18.36,16.95 c-0.39-0.39-1.03-0.39-1.41,0c-0.39,0.39-0.39,1.03,0,1.41l1.06,1.06c0.39,0.39,1.03,0.39,1.41,0c0.39-0.39,0.39-1.03,0-1.41 L18.36,16.95z M19.42,5.99c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06c-0.39,0.39-0.39,1.03,0,1.41 s1.03,0.39,1.41,0L19.42,5.99z M7.05,18.36c0.39-0.39,0.39-1.03,0-1.41c-0.39-0.39-1.03-0.39-1.41,0l-1.06,1.06 c-0.39,0.39-0.39,1.03,0,1.41s1.03,0.39,1.41,0L7.05,18.36z"/></svg>`
+    static darkModeIcon = `<svg xmlns="http://www.w3.org/2000/svg" enable-background="new 0 0 24 24" height="24px" viewBox="0 0 24 24" width="24px" fill="#FE9700"><rect fill="none" height="24" width="24"/><path d="M9.37,5.51C9.19,6.15,9.1,6.82,9.1,7.5c0,4.08,3.32,7.4,7.4,7.4c0.68,0,1.35-0.09,1.99-0.27 C17.45,17.19,14.93,19,12,19c-3.86,0-7-3.14-7-7C5,9.07,6.81,6.55,9.37,5.51z" opacity=".3"/><path d="M9.37,5.51C9.19,6.15,9.1,6.82,9.1,7.5c0,4.08,3.32,7.4,7.4,7.4c0.68,0,1.35-0.09,1.99-0.27C17.45,17.19,14.93,19,12,19 c-3.86,0-7-3.14-7-7C5,9.07,6.81,6.55,9.37,5.51z M12,3c-4.97,0-9,4.03-9,9s4.03,9,9,9s9-4.03,9-9c0-0.46-0.04-0.92-0.1-1.36 c-0.98,1.37-2.58,2.26-4.4,2.26c-2.98,0-5.4-2.42-5.4-5.4c0-1.81,0.89-3.42,2.26-4.4C12.92,3.04,12.46,3,12,3L12,3z"/></svg>`
+    static title = "Toggle Light/Dark Mode"
+
+    static prefersLightModeInDarkModeKey = "prefers-light-mode-in-dark-mode"
+    static prefersDarkModeInLightModeKey = "prefers-dark-mode-in-light-mode"
+
+    static _staticConstructor = function() {
+        DoxygenAwesomeDarkModeToggle.enableDarkMode(DoxygenAwesomeDarkModeToggle.userPreference)
+        // Update the color scheme when the browsers preference changes
+        // without user interaction on the website.
+        window.matchMedia('(prefers-color-scheme: dark)').addEventListener('change', event => {
+            DoxygenAwesomeDarkModeToggle.onSystemPreferenceChanged()
+        })
+        // Update the color scheme when the tab is made visible again.
+        // It is possible that the appearance was changed in another tab 
+        // while this tab was in the background.
+        document.addEventListener("visibilitychange", visibilityState => {
+            if (document.visibilityState === 'visible') {
+                DoxygenAwesomeDarkModeToggle.onSystemPreferenceChanged()
+            }
+        });
+    }()
+
+    static init() {
+        $(function() {
+            $(document).ready(function() {
+                const toggleButton = document.createElement('doxygen-awesome-dark-mode-toggle')
+                toggleButton.title = DoxygenAwesomeDarkModeToggle.title
+                toggleButton.updateIcon()
+
+                window.matchMedia('(prefers-color-scheme: dark)').addEventListener('change', event => {
+                    toggleButton.updateIcon()
+                })
+                document.addEventListener("visibilitychange", visibilityState => {
+                    if (document.visibilityState === 'visible') {
+                        toggleButton.updateIcon()
+                    }
+                });
+
+                $(document).ready(function(){
+                    document.getElementById("MSearchBox").parentNode.appendChild(toggleButton)
+                })
+                $(window).resize(function(){
+                    document.getElementById("MSearchBox").parentNode.appendChild(toggleButton)
+                })
+            })
+        })
+    }
+
+    constructor() {
+        super();
+        this.onclick=this.toggleDarkMode
+    }
+
+    /**
+     * @returns `true` for dark-mode, `false` for light-mode system preference
+     */
+    static get systemPreference() {
+        return window.matchMedia('(prefers-color-scheme: dark)').matches
+    }
+
+    /**
+     * @returns `true` for dark-mode, `false` for light-mode user preference
+     */
+    static get userPreference() {
+        return (!DoxygenAwesomeDarkModeToggle.systemPreference && localStorage.getItem(DoxygenAwesomeDarkModeToggle.prefersDarkModeInLightModeKey)) || 
+        (DoxygenAwesomeDarkModeToggle.systemPreference && !localStorage.getItem(DoxygenAwesomeDarkModeToggle.prefersLightModeInDarkModeKey))
+    }
+
+    static set userPreference(userPreference) {
+        DoxygenAwesomeDarkModeToggle.darkModeEnabled = userPreference
+        if(!userPreference) {
+            if(DoxygenAwesomeDarkModeToggle.systemPreference) {
+                localStorage.setItem(DoxygenAwesomeDarkModeToggle.prefersLightModeInDarkModeKey, true)
+            } else {
+                localStorage.removeItem(DoxygenAwesomeDarkModeToggle.prefersDarkModeInLightModeKey)
+            }
+        } else {
+            if(!DoxygenAwesomeDarkModeToggle.systemPreference) {
+                localStorage.setItem(DoxygenAwesomeDarkModeToggle.prefersDarkModeInLightModeKey, true)
+            } else {
+                localStorage.removeItem(DoxygenAwesomeDarkModeToggle.prefersLightModeInDarkModeKey)
+            }
+        }
+        DoxygenAwesomeDarkModeToggle.onUserPreferenceChanged()
+    }
+
+    static enableDarkMode(enable) {
+        if(enable) {
+            DoxygenAwesomeDarkModeToggle.darkModeEnabled = true
+            document.documentElement.classList.add("dark-mode")
+            document.documentElement.classList.remove("light-mode")
+        } else {
+            DoxygenAwesomeDarkModeToggle.darkModeEnabled = false
+            document.documentElement.classList.remove("dark-mode")
+            document.documentElement.classList.add("light-mode")
+        }
+    }
+
+    static onSystemPreferenceChanged() {
+        DoxygenAwesomeDarkModeToggle.darkModeEnabled = DoxygenAwesomeDarkModeToggle.userPreference
+        DoxygenAwesomeDarkModeToggle.enableDarkMode(DoxygenAwesomeDarkModeToggle.darkModeEnabled)
+    }
+
+    static onUserPreferenceChanged() {
+        DoxygenAwesomeDarkModeToggle.enableDarkMode(DoxygenAwesomeDarkModeToggle.darkModeEnabled)
+    }
+
+    toggleDarkMode() {
+        DoxygenAwesomeDarkModeToggle.userPreference = !DoxygenAwesomeDarkModeToggle.userPreference
+        this.updateIcon()
+    }
+
+    updateIcon() {
+        if(DoxygenAwesomeDarkModeToggle.darkModeEnabled) {
+            this.innerHTML = DoxygenAwesomeDarkModeToggle.darkModeIcon
+        } else {
+            this.innerHTML = DoxygenAwesomeDarkModeToggle.lightModeIcon
+        }
+    }
+}
+
+customElements.define("doxygen-awesome-dark-mode-toggle", DoxygenAwesomeDarkModeToggle);

doc/makefile

@@ -16,7 +16,7 @@ DOXYGEN_CONF = CodeDocumentation.conf
 # doxygen uses: graphviz, latex
 html: $(DOXYGEN_CONF)
 	@# Generate the html documentation
-	@( cat $(DOXYGEN_CONF) ; echo "$(MFEM_DOXYGEN_FLAGS)" ) | doxygen -
+	@( cat $(DOXYGEN_CONF) ; printf "$(MFEM_DOXYGEN_FLAGS)\n" ) | doxygen -
 	@echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > CodeDocumentation.html
 	@cat warnings.log 1>&2
 	@# Generate the log of undocumented methods

examples/CMakeLists.txt

@@ -45,6 +45,12 @@ list(APPEND ALL_EXE_SRCS
   ex37.cpp
   )
 
+if(MFEM_USE_LAPACK)
+list(APPEND ALL_EXE_SRCS
+  ex38.cpp
+  )
+endif()
+
 if (MFEM_USE_MPI)
   list(APPEND ALL_EXE_SRCS
     ex0p.cpp

examples/ex10.cpp

@@ -62,7 +62,7 @@ protected:
 
    BilinearForm M, S;
    NonlinearForm H;
-   double viscosity;
+   real_t viscosity;
    HyperelasticModel *model;
 
    CGSolver M_solver; // Krylov solver for inverting the mass matrix M
@@ -84,16 +84,16 @@ protected:
 
 public:
    HyperelasticOperator(FiniteElementSpace &f, Array<int> &ess_bdr,
-                        double visc, double mu, double K);
+                        real_t visc, real_t mu, real_t K);
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
    /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &x, Vector &k);
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
-   double ElasticEnergy(const Vector &x) const;
-   double KineticEnergy(const Vector &v) const;
+   real_t ElasticEnergy(const Vector &x) const;
+   real_t KineticEnergy(const Vector &v) const;
    void GetElasticEnergyDensity(const GridFunction &x, GridFunction &w) const;
 
    virtual ~HyperelasticOperator();
@@ -109,7 +109,7 @@ private:
    BilinearForm *M, *S;
    NonlinearForm *H;
    mutable SparseMatrix *Jacobian;
-   double dt;
+   real_t dt;
    const Vector *v, *x;
    mutable Vector w, z;
 
@@ -117,7 +117,7 @@ public:
    ReducedSystemOperator(BilinearForm *M_, BilinearForm *S_, NonlinearForm *H_);
 
    /// Set current dt, v, x values - needed to compute action and Jacobian.
-   void SetParameters(double dt_, const Vector *v_, const Vector *x_);
+   void SetParameters(real_t dt_, const Vector *v_, const Vector *x_);
 
    /// Compute y = H(x + dt (v + dt k)) + M k + S (v + dt k).
    virtual void Mult(const Vector &k, Vector &y) const;
@@ -141,7 +141,7 @@ private:
 public:
    ElasticEnergyCoefficient(HyperelasticModel &m, const GridFunction &x_)
       : model(m), x(x_) { }
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
    virtual ~ElasticEnergyCoefficient() { }
 };
 
@@ -161,11 +161,11 @@ int main(int argc, char *argv[])
    int ref_levels = 2;
    int order = 2;
    int ode_solver_type = 3;
-   double t_final = 300.0;
-   double dt = 3.0;
-   double visc = 1e-2;
-   double mu = 0.25;
-   double K = 5.0;
+   real_t t_final = 300.0;
+   real_t dt = 3.0;
+   real_t visc = 1e-2;
+   real_t mu = 0.25;
+   real_t K = 5.0;
    bool visualization = true;
    int vis_steps = 1;
 
@@ -205,6 +205,10 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
+#ifdef MFEM_USE_SINGLE
+   MFEM_ABORT("This example is not supported in single precision.");
+#endif
+
    // 2. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
@@ -309,13 +313,13 @@ int main(int argc, char *argv[])
            << " Press space (in the GLVis window) to resume it.\n";
    }
 
-   double ee0 = oper.ElasticEnergy(x.GetTrueVector());
-   double ke0 = oper.KineticEnergy(v.GetTrueVector());
+   real_t ee0 = oper.ElasticEnergy(x.GetTrueVector());
+   real_t ke0 = oper.KineticEnergy(v.GetTrueVector());
    cout << "initial elastic energy (EE) = " << ee0 << endl;
    cout << "initial kinetic energy (KE) = " << ke0 << endl;
    cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
 
-   double t = 0.0;
+   real_t t = 0.0;
    oper.SetTime(t);
    ode_solver->Init(oper);
 
@@ -324,7 +328,7 @@ int main(int argc, char *argv[])
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       ode_solver->Step(vx, t, dt_real);
 
@@ -332,8 +336,8 @@ int main(int argc, char *argv[])
 
       if (last_step || (ti % vis_steps) == 0)
       {
-         double ee = oper.ElasticEnergy(x.GetTrueVector());
-         double ke = oper.KineticEnergy(v.GetTrueVector());
+         real_t ee = oper.ElasticEnergy(x.GetTrueVector());
+         real_t ke = oper.KineticEnergy(v.GetTrueVector());
 
          cout << "step " << ti << ", t = " << t << ", EE = " << ee << ", KE = "
               << ke << ", ΔTE = " << (ee+ke)-(ee0+ke0) << endl;
@@ -419,7 +423,7 @@ ReducedSystemOperator::ReducedSystemOperator(
      dt(0.0), v(NULL), x(NULL), w(height), z(height)
 { }
 
-void ReducedSystemOperator::SetParameters(double dt_, const Vector *v_,
+void ReducedSystemOperator::SetParameters(real_t dt_, const Vector *v_,
                                           const Vector *x_)
 {
    dt = dt_;  v = v_;  x = x_;
@@ -453,16 +457,16 @@ ReducedSystemOperator::~ReducedSystemOperator()
 
 
 HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
-                                           Array<int> &ess_bdr, double visc,
-                                           double mu, double K)
-   : TimeDependentOperator(2*f.GetTrueVSize(), 0.0), fespace(f),
+                                           Array<int> &ess_bdr, real_t visc,
+                                           real_t mu, real_t K)
+   : TimeDependentOperator(2*f.GetTrueVSize(), (real_t) 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
      viscosity(visc), z(height/2)
 {
-   const double rel_tol = 1e-8;
+   const real_t rel_tol = 1e-8;
    const int skip_zero_entries = 0;
 
-   const double ref_density = 1.0; // density in the reference configuration
+   const real_t ref_density = 1.0; // density in the reference configuration
    ConstantCoefficient rho0(ref_density);
    M.AddDomainIntegrator(new VectorMassIntegrator(rho0));
    M.Assemble(skip_zero_entries);
@@ -533,7 +537,7 @@ void HyperelasticOperator::Mult(const Vector &vx, Vector &dvx_dt) const
    dx_dt = v;
 }
 
-void HyperelasticOperator::ImplicitSolve(const double dt,
+void HyperelasticOperator::ImplicitSolve(const real_t dt,
                                          const Vector &vx, Vector &dvx_dt)
 {
    int sc = height/2;
@@ -555,12 +559,12 @@ void HyperelasticOperator::ImplicitSolve(const double dt,
    add(v, dt, dv_dt, dx_dt);
 }
 
-double HyperelasticOperator::ElasticEnergy(const Vector &x) const
+real_t HyperelasticOperator::ElasticEnergy(const Vector &x) const
 {
    return H.GetEnergy(x);
 }
 
-double HyperelasticOperator::KineticEnergy(const Vector &v) const
+real_t HyperelasticOperator::KineticEnergy(const Vector &v) const
 {
    return 0.5*M.InnerProduct(v, v);
 }
@@ -581,7 +585,7 @@ HyperelasticOperator::~HyperelasticOperator()
 }
 
 
-double ElasticEnergyCoefficient::Eval(ElementTransformation &T,
+real_t ElasticEnergyCoefficient::Eval(ElementTransformation &T,
                                       const IntegrationPoint &ip)
 {
    model.SetTransformation(T);
@@ -601,7 +605,7 @@ void InitialDeformation(const Vector &x, Vector &y)
 void InitialVelocity(const Vector &x, Vector &v)
 {
    const int dim = x.Size();
-   const double s = 0.1/64.;
+   const real_t s = 0.1/64.;
 
    v = 0.0;
    v(dim-1) = s*x(0)*x(0)*(8.0-x(0));

examples/ex10p.cpp

@@ -63,7 +63,7 @@ protected:
 
    ParBilinearForm M, S;
    ParNonlinearForm H;
-   double viscosity;
+   real_t viscosity;
    HyperelasticModel *model;
 
    HypreParMatrix *Mmat; // Mass matrix from ParallelAssemble()
@@ -86,16 +86,16 @@ protected:
 
 public:
    HyperelasticOperator(ParFiniteElementSpace &f, Array<int> &ess_bdr,
-                        double visc, double mu, double K);
+                        real_t visc, real_t mu, real_t K);
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
    /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &x, Vector &k);
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
-   double ElasticEnergy(const ParGridFunction &x) const;
-   double KineticEnergy(const ParGridFunction &v) const;
+   real_t ElasticEnergy(const ParGridFunction &x) const;
+   real_t KineticEnergy(const ParGridFunction &v) const;
    void GetElasticEnergyDensity(const ParGridFunction &x,
                                 ParGridFunction &w) const;
 
@@ -112,7 +112,7 @@ private:
    ParBilinearForm *M, *S;
    ParNonlinearForm *H;
    mutable HypreParMatrix *Jacobian;
-   double dt;
+   real_t dt;
    const Vector *v, *x;
    mutable Vector w, z;
    const Array<int> &ess_tdof_list;
@@ -122,7 +122,7 @@ public:
                          ParNonlinearForm *H_, const Array<int> &ess_tdof_list);
 
    /// Set current dt, v, x values - needed to compute action and Jacobian.
-   void SetParameters(double dt_, const Vector *v_, const Vector *x_);
+   void SetParameters(real_t dt_, const Vector *v_, const Vector *x_);
 
    /// Compute y = H(x + dt (v + dt k)) + M k + S (v + dt k).
    virtual void Mult(const Vector &k, Vector &y) const;
@@ -146,7 +146,7 @@ private:
 public:
    ElasticEnergyCoefficient(HyperelasticModel &m, const ParGridFunction &x_)
       : model(m), x(x_) { }
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
    virtual ~ElasticEnergyCoefficient() { }
 };
 
@@ -173,11 +173,11 @@ int main(int argc, char *argv[])
    int par_ref_levels = 0;
    int order = 2;
    int ode_solver_type = 3;
-   double t_final = 300.0;
-   double dt = 3.0;
-   double visc = 1e-2;
-   double mu = 0.25;
-   double K = 5.0;
+   real_t t_final = 300.0;
+   real_t dt = 3.0;
+   real_t visc = 1e-2;
+   real_t mu = 0.25;
+   real_t K = 5.0;
    bool adaptive_lin_rtol = true;
    bool visualization = true;
    int vis_steps = 1;
@@ -229,6 +229,10 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
+#ifdef MFEM_USE_SINGLE
+   MFEM_ABORT("This example is not supported in single precision.");
+#endif
+
    // 3. Read the serial mesh from the given mesh file on all processors. We can
    //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
    //    with the same code.
@@ -358,8 +362,8 @@ int main(int argc, char *argv[])
       }
    }
 
-   double ee0 = oper.ElasticEnergy(x_gf);
-   double ke0 = oper.KineticEnergy(v_gf);
+   real_t ee0 = oper.ElasticEnergy(x_gf);
+   real_t ke0 = oper.KineticEnergy(v_gf);
    if (myid == 0)
    {
       cout << "initial elastic energy (EE) = " << ee0 << endl;
@@ -367,7 +371,7 @@ int main(int argc, char *argv[])
       cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
    }
 
-   double t = 0.0;
+   real_t t = 0.0;
    oper.SetTime(t);
    ode_solver->Init(oper);
 
@@ -376,7 +380,7 @@ int main(int argc, char *argv[])
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       ode_solver->Step(vx, t, dt_real);
 
@@ -386,8 +390,8 @@ int main(int argc, char *argv[])
       {
          v_gf.SetFromTrueVector(); x_gf.SetFromTrueVector();
 
-         double ee = oper.ElasticEnergy(x_gf);
-         double ke = oper.KineticEnergy(v_gf);
+         real_t ee = oper.ElasticEnergy(x_gf);
+         real_t ke = oper.KineticEnergy(v_gf);
 
          if (myid == 0)
          {
@@ -485,7 +489,7 @@ ReducedSystemOperator::ReducedSystemOperator(
      ess_tdof_list(ess_tdof_list_)
 { }
 
-void ReducedSystemOperator::SetParameters(double dt_, const Vector *v_,
+void ReducedSystemOperator::SetParameters(real_t dt_, const Vector *v_,
                                           const Vector *x_)
 {
    dt = dt_;  v = v_;  x = x_;
@@ -523,17 +527,17 @@ ReducedSystemOperator::~ReducedSystemOperator()
 
 
 HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
-                                           Array<int> &ess_bdr, double visc,
-                                           double mu, double K)
-   : TimeDependentOperator(2*f.TrueVSize(), 0.0), fespace(f),
+                                           Array<int> &ess_bdr, real_t visc,
+                                           real_t mu, real_t K)
+   : TimeDependentOperator(2*f.TrueVSize(), (real_t) 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
      viscosity(visc), M_solver(f.GetComm()), newton_solver(f.GetComm()),
      z(height/2)
 {
-   const double rel_tol = 1e-8;
+   const real_t rel_tol = 1e-8;
    const int skip_zero_entries = 0;
 
-   const double ref_density = 1.0; // density in the reference configuration
+   const real_t ref_density = 1.0; // density in the reference configuration
    ConstantCoefficient rho0(ref_density);
    M.AddDomainIntegrator(new VectorMassIntegrator(rho0));
    M.Assemble(skip_zero_entries);
@@ -607,7 +611,7 @@ void HyperelasticOperator::Mult(const Vector &vx, Vector &dvx_dt) const
    dx_dt = v;
 }
 
-void HyperelasticOperator::ImplicitSolve(const double dt,
+void HyperelasticOperator::ImplicitSolve(const real_t dt,
                                          const Vector &vx, Vector &dvx_dt)
 {
    int sc = height/2;
@@ -629,17 +633,17 @@ void HyperelasticOperator::ImplicitSolve(const double dt,
    add(v, dt, dv_dt, dx_dt);
 }
 
-double HyperelasticOperator::ElasticEnergy(const ParGridFunction &x) const
+real_t HyperelasticOperator::ElasticEnergy(const ParGridFunction &x) const
 {
    return H.GetEnergy(x);
 }
 
-double HyperelasticOperator::KineticEnergy(const ParGridFunction &v) const
+real_t HyperelasticOperator::KineticEnergy(const ParGridFunction &v) const
 {
-   double loc_energy = 0.5*M.InnerProduct(v, v);
-   double energy;
-   MPI_Allreduce(&loc_energy, &energy, 1, MPI_DOUBLE, MPI_SUM,
-                 fespace.GetComm());
+   real_t loc_energy = 0.5*M.InnerProduct(v, v);
+   real_t energy;
+   MPI_Allreduce(&loc_energy, &energy, 1, MPITypeMap<real_t>::mpi_type,
+                 MPI_SUM, fespace.GetComm());
    return energy;
 }
 
@@ -660,7 +664,7 @@ HyperelasticOperator::~HyperelasticOperator()
 }
 
 
-double ElasticEnergyCoefficient::Eval(ElementTransformation &T,
+real_t ElasticEnergyCoefficient::Eval(ElementTransformation &T,
                                       const IntegrationPoint &ip)
 {
    model.SetTransformation(T);
@@ -680,7 +684,7 @@ void InitialDeformation(const Vector &x, Vector &y)
 void InitialVelocity(const Vector &x, Vector &v)
 {
    const int dim = x.Size();
-   const double s = 0.1/64.;
+   const real_t s = 0.1/64.;
 
    v = 0.0;
    v(dim-1) = s*x(0)*x(0)*(8.0-x(0));

examples/ex11p.cpp

@@ -211,7 +211,7 @@ int main(int argc, char *argv[])
    m->AddDomainIntegrator(new MassIntegrator(one));
    m->Assemble();
    // shift the eigenvalue corresponding to eliminated dofs to a large value
-   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<real_t>::min());
    m->Finalize();
 
    HypreParMatrix *A = a->ParallelAssemble();
@@ -262,12 +262,13 @@ int main(int argc, char *argv[])
 #ifdef MFEM_USE_STRUMPACK
       if (sp_solver)
       {
-         STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+         STRUMPACKSolver * strumpack = new STRUMPACKSolver(MPI_COMM_WORLD, argc, argv);
          strumpack->SetPrintFactorStatistics(true);
          strumpack->SetPrintSolveStatistics(false);
          strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
          strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
-         strumpack->DisableMatching();
+         strumpack->SetMatching(strumpack::MatchingJob::NONE);
+         strumpack->SetCompression(strumpack::CompressionType::NONE);
          strumpack->SetOperator(*Arow);
          strumpack->SetFromCommandLine();
          precond = strumpack;
@@ -299,7 +300,7 @@ int main(int argc, char *argv[])
    // 9. Compute the eigenmodes and extract the array of eigenvalues. Define a
    //    parallel grid function to represent each of the eigenmodes returned by
    //    the solver.
-   Array<double> eigenvalues;
+   Array<real_t> eigenvalues;
    lobpcg->Solve();
    lobpcg->GetEigenvalues(eigenvalues);
    ParGridFunction x(fespace);

examples/ex12p.cpp

@@ -206,7 +206,7 @@ int main(int argc, char *argv[])
    m->AddDomainIntegrator(new VectorMassIntegrator());
    m->Assemble();
    // shift the eigenvalue corresponding to eliminated dofs to a large value
-   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<real_t>::min());
    m->Finalize();
    if (myid == 0)
    {
@@ -247,7 +247,7 @@ int main(int argc, char *argv[])
    // 10. Compute the eigenmodes and extract the array of eigenvalues. Define a
    //     parallel grid function to represent each of the eigenmodes returned by
    //     the solver.
-   Array<double> eigenvalues;
+   Array<real_t> eigenvalues;
    lobpcg->Solve();
    lobpcg->GetEigenvalues(eigenvalues);
    ParGridFunction x(fespace);

examples/ex13p.cpp

@@ -5,6 +5,7 @@
 // Sample runs:  mpirun -np 4 ex13p -m ../data/star.mesh
 //               mpirun -np 4 ex13p -m ../data/square-disc.mesh -o 2 -n 4
 //               mpirun -np 4 ex13p -m ../data/beam-tet.mesh
+//               mpirun -np 4 ex13p -m ../data/beam-tet.mesh -nc -o 2 -rs 1
 //               mpirun -np 4 ex13p -m ../data/beam-hex.mesh
 //               mpirun -np 4 ex13p -m ../data/escher.mesh
 //               mpirun -np 4 ex13p -m ../data/fichera.mesh
@@ -54,6 +55,7 @@ int main(int argc, char *argv[])
    int par_ref_levels = 1;
    int order = 1;
    int nev = 5;
+   bool nc = false;
    bool visualization = 1;
    const char *device_config = "cpu";
 
@@ -69,6 +71,9 @@ int main(int argc, char *argv[])
                   " isoparametric space.");
    args.AddOption(&nev, "-n", "--num-eigs",
                   "Number of desired eigenmodes.");
+   args.AddOption(&nc, "-nc", "--non-conforming", "-c",
+                  "--conforming",
+                  "Mark the mesh as nonconforming before partitioning.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -98,6 +103,10 @@ int main(int argc, char *argv[])
    //    and volume meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
+   if (nc)
+   {
+      mesh->EnsureNCMesh(true);
+   }
 
    // 5. Refine the serial mesh on all processors to increase the resolution. In
    //    this example we do 'ref_levels' of uniform refinement (2 by default, or
@@ -161,7 +170,7 @@ int main(int argc, char *argv[])
    m->AddDomainIntegrator(new VectorFEMassIntegrator(one));
    m->Assemble();
    // shift the eigenvalue corresponding to eliminated dofs to a large value
-   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<real_t>::min());
    m->Finalize();
 
    HypreParMatrix *A = a->ParallelAssemble();
@@ -189,7 +198,7 @@ int main(int argc, char *argv[])
    // 10. Compute the eigenmodes and extract the array of eigenvalues. Define a
    //     parallel grid function to represent each of the eigenmodes returned by
    //     the solver.
-   Array<double> eigenvalues;
+   Array<real_t> eigenvalues;
    ame->Solve();
    ame->GetEigenvalues(eigenvalues);
    ParGridFunction x(fespace);

examples/ex14.cpp

@@ -43,9 +43,9 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int ref_levels = -1;
    int order = 1;
-   double sigma = -1.0;
-   double kappa = -1.0;
-   double eta = 0.0;
+   real_t sigma = -1.0;
+   real_t kappa = -1.0;
+   real_t eta = 0.0;
    bool visualization = 1;
 
    OptionsParser args(argc, argv);

examples/ex14p.cpp

@@ -44,7 +44,7 @@ public:
       pmesh(m),
       pgf(f) {}
 
-   void MonitorSolution(int i, double norm, const Vector &x, bool final)
+   void MonitorSolution(int i, real_t norm, const Vector &x, bool final)
    {
       char vishost[] = "localhost";
       int  visport   = 19916;
@@ -81,9 +81,9 @@ int main(int argc, char *argv[])
    int ser_ref_levels = -1;
    int par_ref_levels = 2;
    int order = 1;
-   double sigma = -1.0;
-   double kappa = -1.0;
-   double eta = 0.0;
+   real_t sigma = -1.0;
+   real_t kappa = -1.0;
+   real_t eta = 0.0;
    bool visualization = 1;
 
    OptionsParser args(argc, argv);

examples/ex15.cpp

@@ -63,8 +63,8 @@ int problem;
 int nfeatures;
 
 // Prescribed time-dependent boundary and right-hand side functions.
-double bdr_func(const Vector &pt, double t);
-double rhs_func(const Vector &pt, double t);
+real_t bdr_func(const Vector &pt, real_t t);
+real_t rhs_func(const Vector &pt, real_t t);
 
 // Update the finite element space, interpolate the solution and perform
 // parallel load balancing.
@@ -79,9 +79,9 @@ int main(int argc, char *argv[])
    nfeatures = 1;
    const char *mesh_file = "../data/star-hilbert.mesh";
    int order = 2;
-   double t_final = 1.0;
-   double max_elem_error = 5.0e-3;
-   double hysteresis = 0.15; // derefinement safety coefficient
+   real_t t_final = 1.0;
+   real_t max_elem_error = 5.0e-3;
+   real_t hysteresis = 0.15; // derefinement safety coefficient
    int ref_levels = 0;
    int nc_limit = 3;         // maximum level of hanging nodes
    bool visualization = true;
@@ -247,7 +247,7 @@ int main(int argc, char *argv[])
    //     refine the mesh as many times as necessary. Then we derefine any
    //     elements which have very small errors.
    x = 0.0;
-   for (double time = 0.0; time < t_final + 1e-10; time += 0.01)
+   for (real_t time = 0.0; time < t_final + 1e-10; time += 0.01)
    {
       cout << "\nTime " << time << "\n\nRefinement:" << endl;
 
@@ -366,47 +366,47 @@ void UpdateProblem(Mesh &mesh, FiniteElementSpace &fespace,
 }
 
 
-const double alpha = 0.02;
+const real_t alpha = 0.02;
 
 // Spherical front with a Gaussian cross section and radius t
-double front(double x, double y, double z, double t, int)
+real_t front(real_t x, real_t y, real_t z, real_t t, int)
 {
-   double r = sqrt(x*x + y*y + z*z);
+   real_t r = sqrt(x*x + y*y + z*z);
    return exp(-0.5*pow((r - t)/alpha, 2));
 }
 
-double front_laplace(double x, double y, double z, double t, int dim)
+real_t front_laplace(real_t x, real_t y, real_t z, real_t t, int dim)
 {
-   double x2 = x*x, y2 = y*y, z2 = z*z, t2 = t*t;
-   double r = sqrt(x2 + y2 + z2);
-   double a2 = alpha*alpha, a4 = a2*a2;
+   real_t x2 = x*x, y2 = y*y, z2 = z*z, t2 = t*t;
+   real_t r = sqrt(x2 + y2 + z2);
+   real_t a2 = alpha*alpha, a4 = a2*a2;
    return -exp(-0.5*pow((r - t)/alpha, 2)) / a4 *
           (-2*t*(x2 + y2 + z2 - (dim-1)*a2/2)/r + x2 + y2 + z2 + t2 - dim*a2);
 }
 
 // Smooth spherical step function with radius t
-double ball(double x, double y, double z, double t, int)
+real_t ball(real_t x, real_t y, real_t z, real_t t, int)
 {
-   double r = sqrt(x*x + y*y + z*z);
+   real_t r = sqrt(x*x + y*y + z*z);
    return -atan(2*(r - t)/alpha);
 }
 
-double ball_laplace(double x, double y, double z, double t, int dim)
+real_t ball_laplace(real_t x, real_t y, real_t z, real_t t, int dim)
 {
-   double x2 = x*x, y2 = y*y, z2 = z*z, t2 = 4*t*t;
-   double r = sqrt(x2 + y2 + z2);
-   double a2 = alpha*alpha;
-   double den = pow(-a2 - 4*(x2 + y2 + z2 - 2*r*t) - t2, 2.0);
+   real_t x2 = x*x, y2 = y*y, z2 = z*z, t2 = 4*t*t;
+   real_t r = sqrt(x2 + y2 + z2);
+   real_t a2 = alpha*alpha;
+   real_t den = pow(-a2 - 4*(x2 + y2 + z2 - 2*r*t) - t2, 2.0);
    return (dim == 2) ? 2*alpha*(a2 + t2 - 4*x2 - 4*y2)/r/den
           /*      */ : 4*alpha*(a2 + t2 - 4*r*t)/r/den;
 }
 
 // Composes several features into one function
 template<typename F0, typename F1>
-double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
+real_t composite_func(const Vector &pt, real_t t, F0 f0, F1 f1)
 {
    int dim = pt.Size();
-   double x = pt(0), y = pt(1), z = 0.0;
+   real_t x = pt(0), y = pt(1), z = 0.0;
    if (dim == 3) { z = pt(2); }
 
    if (problem == 0)
@@ -417,11 +417,11 @@ double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
       }
       else
       {
-         double sum = 0.0;
+         real_t sum = 0.0;
          for (int i = 0; i < nfeatures; i++)
          {
-            double x0 = 0.5*cos(2*M_PI * i / nfeatures);
-            double y0 = 0.5*sin(2*M_PI * i / nfeatures);
+            real_t x0 = 0.5*cos(2*M_PI * i / nfeatures);
+            real_t y0 = 0.5*sin(2*M_PI * i / nfeatures);
             sum += f0(x - x0, y - y0, z, t, dim);
          }
          return sum;
@@ -429,11 +429,11 @@ double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
    }
    else
    {
-      double sum = 0.0;
+      real_t sum = 0.0;
       for (int i = 0; i < nfeatures; i++)
       {
-         double x0 = 0.5*cos(2*M_PI * i / nfeatures + M_PI*t);
-         double y0 = 0.5*sin(2*M_PI * i / nfeatures + M_PI*t);
+         real_t x0 = 0.5*cos(2*M_PI * i / nfeatures + M_PI*t);
+         real_t y0 = 0.5*sin(2*M_PI * i / nfeatures + M_PI*t);
          sum += f1(x - x0, y - y0, z, 0.25, dim);
       }
       return sum;
@@ -441,13 +441,13 @@ double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
 }
 
 // Exact solution, used for the Dirichlet BC.
-double bdr_func(const Vector &pt, double t)
+real_t bdr_func(const Vector &pt, real_t t)
 {
    return composite_func(pt, t, front, ball);
 }
 
 // Laplace of the exact solution, used for the right hand side.
-double rhs_func(const Vector &pt, double t)
+real_t rhs_func(const Vector &pt, real_t t)
 {
    return composite_func(pt, t, front_laplace, ball_laplace);
 }

examples/ex15p.cpp

@@ -13,6 +13,7 @@
 //               mpirun -np 4 ex15p -m ../data/square-disc-nurbs.mesh
 //               mpirun -np 4 ex15p -m ../data/disc-nurbs.mesh
 //               mpirun -np 4 ex15p -m ../data/fichera.mesh -tf 0.5
+//               mpirun -np 4 ex15p -m ../data/fichera-mixed.mesh -tf 0.5
 //               mpirun -np 4 ex15p -m ../data/ball-nurbs.mesh -tf 0.5
 //               mpirun -np 4 ex15p -m ../data/mobius-strip.mesh
 //               mpirun -np 4 ex15p -m ../data/amr-quad.mesh
@@ -67,8 +68,8 @@ int problem;
 int nfeatures;
 
 // Prescribed time-dependent boundary and right-hand side functions.
-double bdr_func(const Vector &pt, double t);
-double rhs_func(const Vector &pt, double t);
+real_t bdr_func(const Vector &pt, real_t t);
+real_t rhs_func(const Vector &pt, real_t t);
 
 // Update the finite element space, interpolate the solution and perform
 // parallel load balancing.
@@ -90,9 +91,9 @@ int main(int argc, char *argv[])
    nfeatures = 1;
    const char *mesh_file = "../data/star-hilbert.mesh";
    int order = 2;
-   double t_final = 1.0;
-   double max_elem_error = 1.0e-4;
-   double hysteresis = 0.25; // derefinement safety coefficient
+   real_t t_final = 1.0;
+   real_t max_elem_error = 1.0e-4;
+   real_t hysteresis = 0.25; // derefinement safety coefficient
    int ref_levels = 0;
    int nc_limit = 3;         // maximum level of hanging nodes
    bool visualization = true;
@@ -281,7 +282,7 @@ int main(int argc, char *argv[])
    //     solve the problem on the current mesh, visualize the solution and
    //     refine the mesh as many times as necessary. Then we derefine any
    //     elements which have very small errors.
-   for (double time = 0.0; time < t_final + 1e-10; time += 0.01)
+   for (real_t time = 0.0; time < t_final + 1e-10; time += 0.01)
    {
       if (myid == 0)
       {
@@ -426,47 +427,47 @@ void UpdateAndRebalance(ParMesh &pmesh, ParFiniteElementSpace &fespace,
 }
 
 
-const double alpha = 0.02;
+const real_t alpha = 0.02;
 
 // Spherical front with a Gaussian cross section and radius t
-double front(double x, double y, double z, double t, int)
+real_t front(real_t x, real_t y, real_t z, real_t t, int)
 {
-   double r = sqrt(x*x + y*y + z*z);
+   real_t r = sqrt(x*x + y*y + z*z);
    return exp(-0.5*pow((r - t)/alpha, 2));
 }
 
-double front_laplace(double x, double y, double z, double t, int dim)
+real_t front_laplace(real_t x, real_t y, real_t z, real_t t, int dim)
 {
-   double x2 = x*x, y2 = y*y, z2 = z*z, t2 = t*t;
-   double r = sqrt(x2 + y2 + z2);
-   double a2 = alpha*alpha, a4 = a2*a2;
+   real_t x2 = x*x, y2 = y*y, z2 = z*z, t2 = t*t;
+   real_t r = sqrt(x2 + y2 + z2);
+   real_t a2 = alpha*alpha, a4 = a2*a2;
    return -exp(-0.5*pow((r - t)/alpha, 2)) / a4 *
           (-2*t*(x2 + y2 + z2 - (dim-1)*a2/2)/r + x2 + y2 + z2 + t2 - dim*a2);
 }
 
 // Smooth spherical step function with radius t
-double ball(double x, double y, double z, double t, int)
+real_t ball(real_t x, real_t y, real_t z, real_t t, int)
 {
-   double r = sqrt(x*x + y*y + z*z);
+   real_t r = sqrt(x*x + y*y + z*z);
    return -atan(2*(r - t)/alpha);
 }
 
-double ball_laplace(double x, double y, double z, double t, int dim)
+real_t ball_laplace(real_t x, real_t y, real_t z, real_t t, int dim)
 {
-   double x2 = x*x, y2 = y*y, z2 = z*z, t2 = 4*t*t;
-   double r = sqrt(x2 + y2 + z2);
-   double a2 = alpha*alpha;
-   double den = pow(-a2 - 4*(x2 + y2 + z2 - 2*r*t) - t2, 2.0);
+   real_t x2 = x*x, y2 = y*y, z2 = z*z, t2 = 4*t*t;
+   real_t r = sqrt(x2 + y2 + z2);
+   real_t a2 = alpha*alpha;
+   real_t den = pow(-a2 - 4*(x2 + y2 + z2 - 2*r*t) - t2, 2.0);
    return (dim == 2) ? 2*alpha*(a2 + t2 - 4*x2 - 4*y2)/r/den
           /*      */ : 4*alpha*(a2 + t2 - 4*r*t)/r/den;
 }
 
 // Composes several features into one function
 template<typename F0, typename F1>
-double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
+real_t composite_func(const Vector &pt, real_t t, F0 f0, F1 f1)
 {
    int dim = pt.Size();
-   double x = pt(0), y = pt(1), z = 0.0;
+   real_t x = pt(0), y = pt(1), z = 0.0;
    if (dim == 3) { z = pt(2); }
 
    if (problem == 0)
@@ -477,11 +478,11 @@ double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
       }
       else
       {
-         double sum = 0.0;
+         real_t sum = 0.0;
          for (int i = 0; i < nfeatures; i++)
          {
-            double x0 = 0.5*cos(2*M_PI * i / nfeatures);
-            double y0 = 0.5*sin(2*M_PI * i / nfeatures);
+            real_t x0 = 0.5*cos(2*M_PI * i / nfeatures);
+            real_t y0 = 0.5*sin(2*M_PI * i / nfeatures);
             sum += f0(x - x0, y - y0, z, t, dim);
          }
          return sum;
@@ -489,11 +490,11 @@ double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
    }
    else
    {
-      double sum = 0.0;
+      real_t sum = 0.0;
       for (int i = 0; i < nfeatures; i++)
       {
-         double x0 = 0.5*cos(2*M_PI * i / nfeatures + M_PI*t);
-         double y0 = 0.5*sin(2*M_PI * i / nfeatures + M_PI*t);
+         real_t x0 = 0.5*cos(2*M_PI * i / nfeatures + M_PI*t);
+         real_t y0 = 0.5*sin(2*M_PI * i / nfeatures + M_PI*t);
          sum += f1(x - x0, y - y0, z, 0.25, dim);
       }
       return sum;
@@ -501,13 +502,13 @@ double composite_func(const Vector &pt, double t, F0 f0, F1 f1)
 }
 
 // Exact solution, used for the Dirichlet BC.
-double bdr_func(const Vector &pt, double t)
+real_t bdr_func(const Vector &pt, real_t t)
 {
    return composite_func(pt, t, front, ball);
 }
 
 // Laplace of the exact solution, used for the right hand side.
-double rhs_func(const Vector &pt, double t)
+real_t rhs_func(const Vector &pt, real_t t)
 {
    return composite_func(pt, t, front_laplace, ball_laplace);
 }

examples/ex16.cpp

@@ -60,7 +60,7 @@ protected:
 
    SparseMatrix Mmat, Kmat;
    SparseMatrix *T; // T = M + dt K
-   double current_dt;
+   real_t current_dt;
 
    CGSolver M_solver; // Krylov solver for inverting the mass matrix M
    DSmoother M_prec;  // Preconditioner for the mass matrix M
@@ -68,18 +68,18 @@ protected:
    CGSolver T_solver; // Implicit solver for T = M + dt K
    DSmoother T_prec;  // Preconditioner for the implicit solver
 
-   double alpha, kappa;
+   real_t alpha, kappa;
 
    mutable Vector z; // auxiliary vector
 
 public:
-   ConductionOperator(FiniteElementSpace &f, double alpha, double kappa,
+   ConductionOperator(FiniteElementSpace &f, real_t alpha, real_t kappa,
                       const Vector &u);
 
    virtual void Mult(const Vector &u, Vector &du_dt) const;
    /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   virtual void ImplicitSolve(const real_t dt, const Vector &u, Vector &k);
 
    /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
    void SetParameters(const Vector &u);
@@ -87,7 +87,7 @@ public:
    virtual ~ConductionOperator();
 };
 
-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x);
 
 int main(int argc, char *argv[])
 {
@@ -96,10 +96,10 @@ int main(int argc, char *argv[])
    int ref_levels = 2;
    int order = 2;
    int ode_solver_type = 3;
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
@@ -246,7 +246,7 @@ int main(int argc, char *argv[])
    // 8. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
    ode_solver->Init(oper);
-   double t = 0.0;
+   real_t t = 0.0;
 
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -293,12 +293,12 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), current_dt(0.0), z(height)
+ConductionOperator::ConductionOperator(FiniteElementSpace &f, real_t al,
+                                       real_t kap, const Vector &u)
+   : TimeDependentOperator(f.GetTrueVSize(), (real_t) 0.0), fespace(f),
+     M(NULL), K(NULL), T(NULL), current_dt(0.0), z(height)
 {
-   const double rel_tol = 1e-8;
+   const real_t rel_tol = 1e-8;
 
    M = new BilinearForm(&fespace);
    M->AddDomainIntegrator(new MassIntegrator());
@@ -336,7 +336,7 @@ void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
    M_solver.Mult(z, du_dt);
 }
 
-void ConductionOperator::ImplicitSolve(const double dt,
+void ConductionOperator::ImplicitSolve(const real_t dt,
                                        const Vector &u, Vector &du_dt)
 {
    // Solve the equation:
@@ -382,7 +382,7 @@ ConductionOperator::~ConductionOperator()
    delete K;
 }
 
-double InitialTemperature(const Vector &x)
+real_t InitialTemperature(const Vector &x)
 {
    if (x.Norml2() < 0.5)
    {

examples/ex16p.cpp

@@ -62,7 +62,7 @@ protected:
    HypreParMatrix Mmat;
    HypreParMatrix Kmat;
    HypreParMatrix *T; // T = M + dt K
-   double current_dt;
+   real_t current_dt;
 
    CGSolver M_solver;    // Krylov solver for inverting the mass matrix M
    HypreSmoother M_prec; // Preconditioner for the mass matrix M
@@ -70,18 +70,18 @@ protected:
    CGSolver T_solver;    // Implicit solver for T = M + dt K
    HypreSmoother T_prec; // Preconditioner for the implicit solver
 
-   double alpha, kappa;
+   real_t alpha, kappa;
 
    mutable Vector z; // auxiliary vector
 
 public:
-   ConductionOperator(ParFiniteElementSpace &f, double alpha, double kappa,
+   ConductionOperator(ParFiniteElementSpace &f, real_t alpha, real_t kappa,
                       const Vector &u);
 
    virtual void Mult(const Vector &u, Vector &du_dt) const;
    /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   virtual void ImplicitSolve(const real_t dt, const Vector &u, Vector &k);
 
    /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
    void SetParameters(const Vector &u);
@@ -89,7 +89,7 @@ public:
    virtual ~ConductionOperator();
 };
 
-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x);
 
 int main(int argc, char *argv[])
 {
@@ -105,10 +105,10 @@ int main(int argc, char *argv[])
    int par_ref_levels = 1;
    int order = 2;
    int ode_solver_type = 3;
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
    bool visualization = true;
    bool visit = false;
    int vis_steps = 5;
@@ -313,7 +313,7 @@ int main(int argc, char *argv[])
    // 10. Perform time-integration (looping over the time iterations, ti, with a
    //     time-step dt).
    ode_solver->Init(oper);
-   double t = 0.0;
+   real_t t = 0.0;
 
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -382,13 +382,13 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), current_dt(0.0),
+ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, real_t al,
+                                       real_t kap, const Vector &u)
+   : TimeDependentOperator(f.GetTrueVSize(), (real_t) 0.0), fespace(f),
+     M(NULL), K(NULL), T(NULL), current_dt(0.0),
      M_solver(f.GetComm()), T_solver(f.GetComm()), z(height)
 {
-   const double rel_tol = 1e-8;
+   const real_t rel_tol = 1e-8;
 
    M = new ParBilinearForm(&fespace);
    M->AddDomainIntegrator(new MassIntegrator());
@@ -427,7 +427,7 @@ void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
    M_solver.Mult(z, du_dt);
 }
 
-void ConductionOperator::ImplicitSolve(const double dt,
+void ConductionOperator::ImplicitSolve(const real_t dt,
                                        const Vector &u, Vector &du_dt)
 {
    // Solve the equation:
@@ -473,7 +473,7 @@ ConductionOperator::~ConductionOperator()
    delete K;
 }
 
-double InitialTemperature(const Vector &x)
+real_t InitialTemperature(const Vector &x)
 {
    if (x.Norml2() < 0.5)
    {

examples/ex17.cpp

@@ -69,7 +69,7 @@ public:
    void SetDisplacement(GridFunction &u_) { u = &u_; }
    void SetComponent(int i, int j) { si = i; sj = j; }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 // Simple GLVis visualization manager.
@@ -104,8 +104,8 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/beam-tri.mesh";
    int ref_levels = -1;
    int order = 1;
-   double alpha = -1.0;
-   double kappa = -1.0;
+   real_t alpha = -1.0;
+   real_t kappa = -1.0;
    bool visualization = 1;
 
    OptionsParser args(argc, argv);
@@ -245,7 +245,7 @@ int main(int argc, char *argv[])
    //     solve the system Ax=b with PCG for the symmetric formulation, or GMRES
    //     for the non-symmetric.
    GSSmoother M(A);
-   const double rtol = 1e-6;
+   const real_t rtol = 1e-6;
    if (alpha == -1.0)
    {
       PCG(A, M, B, X, 3, 5000, rtol*rtol, 0.0);
@@ -337,17 +337,17 @@ void InitDisplacement(const Vector &x, Vector &u)
 }
 
 
-double StressCoefficient::Eval(ElementTransformation &T,
+real_t StressCoefficient::Eval(ElementTransformation &T,
                                const IntegrationPoint &ip)
 {
    MFEM_ASSERT(u != NULL, "displacement field is not set");
 
-   double L = lambda.Eval(T, ip);
-   double M = mu.Eval(T, ip);
+   real_t L = lambda.Eval(T, ip);
+   real_t M = mu.Eval(T, ip);
    u->GetVectorGradient(T, grad);
    if (si == sj)
    {
-      double div_u = grad.Trace();
+      real_t div_u = grad.Trace();
       return L*div_u + 2*M*grad(si,si);
    }
    else

examples/ex17p.cpp

@@ -69,7 +69,7 @@ public:
    void SetDisplacement(GridFunction &u_) { u = &u_; }
    void SetComponent(int i, int j) { si = i; sj = j; }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 // Simple GLVis visualization manager.
@@ -108,8 +108,8 @@ int main(int argc, char *argv[])
    int ser_ref_levels = -1;
    int par_ref_levels = 1;
    int order = 1;
-   double alpha = -1.0;
-   double kappa = -1.0;
+   real_t alpha = -1.0;
+   real_t kappa = -1.0;
    bool amg_elast = false;
    bool visualization = 1;
 
@@ -268,7 +268,7 @@ int main(int argc, char *argv[])
    // 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
    //     solve the system Ax=b with PCG for the symmetric formulation, or GMRES
    //     for the non-symmetric.
-   const double rtol = 1e-6;
+   const real_t rtol = 1e-6;
    HypreBoomerAMG amg(A);
    if (amg_elast)
    {
@@ -376,17 +376,17 @@ void InitDisplacement(const Vector &x, Vector &u)
 }
 
 
-double StressCoefficient::Eval(ElementTransformation &T,
+real_t StressCoefficient::Eval(ElementTransformation &T,
                                const IntegrationPoint &ip)
 {
    MFEM_ASSERT(u != NULL, "displacement field is not set");
 
-   double L = lambda.Eval(T, ip);
-   double M = mu.Eval(T, ip);
+   real_t L = lambda.Eval(T, ip);
+   real_t M = mu.Eval(T, ip);
    u->GetVectorGradient(T, grad);
    if (si == sj)
    {
-      double div_u = grad.Trace();
+      real_t div_u = grad.Trace();
       return L*div_u + 2*M*grad(si,si);
    }
    else

examples/ex18.cpp

@@ -52,11 +52,11 @@ int problem;
 
 // Equation constant parameters.
 const int num_equation = 4;
-const double specific_heat_ratio = 1.4;
-const double gas_constant = 1.0;
+const real_t specific_heat_ratio = 1.4;
+const real_t gas_constant = 1.0;
 
 // Maximum characteristic speed (updated by integrators)
-double max_char_speed;
+real_t max_char_speed;
 
 int main(int argc, char *argv[])
 {
@@ -66,9 +66,9 @@ int main(int argc, char *argv[])
    int ref_levels = 1;
    int order = 3;
    int ode_solver_type = 4;
-   double t_final = 2.0;
-   double dt = -0.01;
-   double cfl = 0.3;
+   real_t t_final = 2.0;
+   real_t dt = -0.01;
+   real_t cfl = 0.3;
    bool visualization = true;
    int vis_steps = 50;
 
@@ -228,7 +228,7 @@ int main(int argc, char *argv[])
    }
 
    // Determine the minimum element size.
-   double hmin = 0.0;
+   real_t hmin = 0.0;
    if (cfl > 0)
    {
       hmin = mesh.GetElementSize(0, 1);
@@ -242,7 +242,7 @@ int main(int argc, char *argv[])
    tic_toc.Clear();
    tic_toc.Start();
 
-   double t = 0.0;
+   real_t t = 0.0;
    euler.SetTime(t);
    ode_solver->Init(euler);
 
@@ -260,7 +260,7 @@ int main(int argc, char *argv[])
    bool done = false;
    for (int ti = 0; !done; )
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       ode_solver->Step(sol, t, dt_real);
       if (cfl > 0)
@@ -298,7 +298,7 @@ int main(int argc, char *argv[])
    // 10. Compute the L2 solution error summed for all components.
    if (t_final == 2.0)
    {
-      const double error = sol.ComputeLpError(2, u0);
+      const real_t error = sol.ComputeLpError(2, u0);
       cout << "Solution error: " << error << endl;
    }
 

examples/ex18.hpp

@@ -9,11 +9,11 @@ using namespace mfem;
 extern int problem;
 
 // Maximum characteristic speed (updated by integrators)
-extern double max_char_speed;
+extern real_t max_char_speed;
 
 extern const int num_equation;
-extern const double specific_heat_ratio;
-extern const double gas_constant;
+extern const real_t specific_heat_ratio;
+extern const real_t gas_constant;
 
 // Time-dependent operator for the right-hand side of the ODE representing the
 // DG weak form.
@@ -52,7 +52,7 @@ private:
 
 public:
    RiemannSolver();
-   double Eval(const Vector &state1, const Vector &state2,
+   real_t Eval(const Vector &state1, const Vector &state2,
                const Vector &nor, Vector &flux);
 };
 
@@ -149,13 +149,13 @@ void FE_Evolution::Mult(const Vector &x, Vector &y) const
 bool StateIsPhysical(const Vector &state, const int dim);
 
 // Pressure (EOS) computation
-inline double ComputePressure(const Vector &state, int dim)
+inline real_t ComputePressure(const Vector &state, int dim)
 {
-   const double den = state(0);
+   const real_t den = state(0);
    const Vector den_vel(state.GetData() + 1, dim);
-   const double den_energy = state(1 + dim);
+   const real_t den_energy = state(1 + dim);
 
-   double den_vel2 = 0;
+   real_t den_vel2 = 0;
    for (int d = 0; d < dim; d++) { den_vel2 += den_vel(d) * den_vel(d); }
    den_vel2 /= den;
 
@@ -165,13 +165,13 @@ inline double ComputePressure(const Vector &state, int dim)
 // Compute the vector flux F(u)
 void ComputeFlux(const Vector &state, int dim, DenseMatrix &flux)
 {
-   const double den = state(0);
+   const real_t den = state(0);
    const Vector den_vel(state.GetData() + 1, dim);
-   const double den_energy = state(1 + dim);
+   const real_t den_energy = state(1 + dim);
 
    MFEM_ASSERT(StateIsPhysical(state, dim), "");
 
-   const double pres = ComputePressure(state, dim);
+   const real_t pres = ComputePressure(state, dim);
 
    for (int d = 0; d < dim; d++)
    {
@@ -183,7 +183,7 @@ void ComputeFlux(const Vector &state, int dim, DenseMatrix &flux)
       flux(1+d, d) += pres;
    }
 
-   const double H = (den_energy + pres) / den;
+   const real_t H = (den_energy + pres) / den;
    for (int d = 0; d < dim; d++)
    {
       flux(1+dim, d) = den_vel(d) * H;
@@ -196,15 +196,15 @@ void ComputeFluxDotN(const Vector &state, const Vector &nor,
 {
    // NOTE: nor in general is not a unit normal
    const int dim = nor.Size();
-   const double den = state(0);
+   const real_t den = state(0);
    const Vector den_vel(state.GetData() + 1, dim);
-   const double den_energy = state(1 + dim);
+   const real_t den_energy = state(1 + dim);
 
    MFEM_ASSERT(StateIsPhysical(state, dim), "");
 
-   const double pres = ComputePressure(state, dim);
+   const real_t pres = ComputePressure(state, dim);
 
-   double den_velN = 0;
+   real_t den_velN = 0;
    for (int d = 0; d < dim; d++) { den_velN += den_vel(d) * nor(d); }
 
    fluxN(0) = den_velN;
@@ -213,23 +213,23 @@ void ComputeFluxDotN(const Vector &state, const Vector &nor,
       fluxN(1+d) = den_velN * den_vel(d) / den + pres * nor(d);
    }
 
-   const double H = (den_energy + pres) / den;
+   const real_t H = (den_energy + pres) / den;
    fluxN(1 + dim) = den_velN * H;
 }
 
 // Compute the maximum characteristic speed.
-inline double ComputeMaxCharSpeed(const Vector &state, const int dim)
+inline real_t ComputeMaxCharSpeed(const Vector &state, const int dim)
 {
-   const double den = state(0);
+   const real_t den = state(0);
    const Vector den_vel(state.GetData() + 1, dim);
 
-   double den_vel2 = 0;
+   real_t den_vel2 = 0;
    for (int d = 0; d < dim; d++) { den_vel2 += den_vel(d) * den_vel(d); }
    den_vel2 /= den;
 
-   const double pres = ComputePressure(state, dim);
-   const double sound = sqrt(specific_heat_ratio * pres / den);
-   const double vel = sqrt(den_vel2 / den);
+   const real_t pres = ComputePressure(state, dim);
+   const real_t sound = sqrt(specific_heat_ratio * pres / den);
+   const real_t vel = sqrt(den_vel2 / den);
 
    return vel + sound;
 }
@@ -254,7 +254,7 @@ void FE_Evolution::GetFlux(const DenseMatrix &x_, DenseTensor &flux_) const
       }
 
       // Update max char speed
-      const double mcs = ComputeMaxCharSpeed(state, flux_dim);
+      const real_t mcs = ComputeMaxCharSpeed(state, flux_dim);
       if (mcs > max_char_speed) { max_char_speed = mcs; }
    }
 }
@@ -264,7 +264,7 @@ RiemannSolver::RiemannSolver() :
    flux1(num_equation),
    flux2(num_equation) { }
 
-double RiemannSolver::Eval(const Vector &state1, const Vector &state2,
+real_t RiemannSolver::Eval(const Vector &state1, const Vector &state2,
                            const Vector &nor, Vector &flux)
 {
    // NOTE: nor in general is not a unit normal
@@ -273,15 +273,15 @@ double RiemannSolver::Eval(const Vector &state1, const Vector &state2,
    MFEM_ASSERT(StateIsPhysical(state1, dim), "");
    MFEM_ASSERT(StateIsPhysical(state2, dim), "");
 
-   const double maxE1 = ComputeMaxCharSpeed(state1, dim);
-   const double maxE2 = ComputeMaxCharSpeed(state2, dim);
+   const real_t maxE1 = ComputeMaxCharSpeed(state1, dim);
+   const real_t maxE2 = ComputeMaxCharSpeed(state2, dim);
 
-   const double maxE = max(maxE1, maxE2);
+   const real_t maxE = max(maxE1, maxE2);
 
    ComputeFluxDotN(state1, nor, flux1);
    ComputeFluxDotN(state2, nor, flux2);
 
-   double normag = 0;
+   real_t normag = 0;
    for (int i = 0; i < dim; i++)
    {
       normag += nor(i) * nor(i);
@@ -359,7 +359,7 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
 
       // Get the normal vector and the flux on the face
       CalcOrtho(Tr.Jacobian(), nor);
-      const double mcs = rsolver.Eval(funval1, funval2, nor, fluxN);
+      const real_t mcs = rsolver.Eval(funval1, funval2, nor, fluxN);
 
       // Update max char speed
       if (mcs > max_char_speed) { max_char_speed = mcs; }
@@ -382,9 +382,9 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
 // Check that the state is physical - enabled in debug mode
 bool StateIsPhysical(const Vector &state, const int dim)
 {
-   const double den = state(0);
+   const real_t den = state(0);
    const Vector den_vel(state.GetData() + 1, dim);
-   const double den_energy = state(1 + dim);
+   const real_t den_energy = state(1 + dim);
 
    if (den < 0)
    {
@@ -407,11 +407,11 @@ bool StateIsPhysical(const Vector &state, const int dim)
       return false;
    }
 
-   double den_vel2 = 0;
+   real_t den_vel2 = 0;
    for (int i = 0; i < dim; i++) { den_vel2 += den_vel(i) * den_vel(i); }
    den_vel2 /= den;
 
-   const double pres = (specific_heat_ratio - 1.0) * (den_energy - 0.5 * den_vel2);
+   const real_t pres = (specific_heat_ratio - 1.0) * (den_energy - 0.5 * den_vel2);
 
    if (pres <= 0)
    {
@@ -431,7 +431,7 @@ void InitialCondition(const Vector &x, Vector &y)
 {
    MFEM_ASSERT(x.Size() == 2, "");
 
-   double radius = 0, Minf = 0, beta = 0;
+   real_t radius = 0, Minf = 0, beta = 0;
    if (problem == 1)
    {
       // "Fast vortex"
@@ -452,36 +452,36 @@ void InitialCondition(const Vector &x, Vector &y)
                  "Options are: 1 - fast vortex, 2 - slow vortex");
    }
 
-   const double xc = 0.0, yc = 0.0;
+   const real_t xc = 0.0, yc = 0.0;
 
    // Nice units
-   const double vel_inf = 1.;
-   const double den_inf = 1.;
+   const real_t vel_inf = 1.;
+   const real_t den_inf = 1.;
 
    // Derive remainder of background state from this and Minf
-   const double pres_inf = (den_inf / specific_heat_ratio) * (vel_inf / Minf) *
+   const real_t pres_inf = (den_inf / specific_heat_ratio) * (vel_inf / Minf) *
                            (vel_inf / Minf);
-   const double temp_inf = pres_inf / (den_inf * gas_constant);
+   const real_t temp_inf = pres_inf / (den_inf * gas_constant);
 
-   double r2rad = 0.0;
+   real_t r2rad = 0.0;
    r2rad += (x(0) - xc) * (x(0) - xc);
    r2rad += (x(1) - yc) * (x(1) - yc);
    r2rad /= (radius * radius);
 
-   const double shrinv1 = 1.0 / (specific_heat_ratio - 1.);
+   const real_t shrinv1 = 1.0 / (specific_heat_ratio - 1.);
 
-   const double velX = vel_inf * (1 - beta * (x(1) - yc) / radius * exp(
+   const real_t velX = vel_inf * (1 - beta * (x(1) - yc) / radius * exp(
                                      -0.5 * r2rad));
-   const double velY = vel_inf * beta * (x(0) - xc) / radius * exp(-0.5 * r2rad);
-   const double vel2 = velX * velX + velY * velY;
+   const real_t velY = vel_inf * beta * (x(0) - xc) / radius * exp(-0.5 * r2rad);
+   const real_t vel2 = velX * velX + velY * velY;
 
-   const double specific_heat = gas_constant * specific_heat_ratio * shrinv1;
-   const double temp = temp_inf - 0.5 * (vel_inf * beta) *
+   const real_t specific_heat = gas_constant * specific_heat_ratio * shrinv1;
+   const real_t temp = temp_inf - 0.5 * (vel_inf * beta) *
                        (vel_inf * beta) / specific_heat * exp(-r2rad);
 
-   const double den = den_inf * pow(temp/temp_inf, shrinv1);
-   const double pres = den * gas_constant * temp;
-   const double energy = shrinv1 * pres / den + 0.5 * vel2;
+   const real_t den = den_inf * pow(temp/temp_inf, shrinv1);
+   const real_t pres = den * gas_constant * temp;
+   const real_t energy = shrinv1 * pres / den + 0.5 * vel2;
 
    y(0) = den;
    y(1) = den * velX;

examples/ex18p.cpp

@@ -52,11 +52,11 @@ int problem;
 
 // Equation constant parameters.
 const int num_equation = 4;
-const double specific_heat_ratio = 1.4;
-const double gas_constant = 1.0;
+const real_t specific_heat_ratio = 1.4;
+const real_t gas_constant = 1.0;
 
 // Maximum characteristic speed (updated by integrators)
-double max_char_speed;
+real_t max_char_speed;
 
 int main(int argc, char *argv[])
 {
@@ -71,9 +71,9 @@ int main(int argc, char *argv[])
    int par_ref_levels = 1;
    int order = 3;
    int ode_solver_type = 4;
-   double t_final = 2.0;
-   double dt = -0.01;
-   double cfl = 0.3;
+   real_t t_final = 2.0;
+   real_t dt = -0.01;
+   real_t cfl = 0.3;
    bool visualization = true;
    int vis_steps = 50;
 
@@ -270,23 +270,24 @@ int main(int argc, char *argv[])
    }
 
    // Determine the minimum element size.
-   double hmin;
+   real_t hmin;
    if (cfl > 0)
    {
-      double my_hmin = pmesh.GetElementSize(0, 1);
+      real_t my_hmin = pmesh.GetElementSize(0, 1);
       for (int i = 1; i < pmesh.GetNE(); i++)
       {
          my_hmin = min(pmesh.GetElementSize(i, 1), my_hmin);
       }
       // Reduce to find the global minimum element size
-      MPI_Allreduce(&my_hmin, &hmin, 1, MPI_DOUBLE, MPI_MIN, pmesh.GetComm());
+      MPI_Allreduce(&my_hmin, &hmin, 1, MPITypeMap<real_t>::mpi_type,
+                    MPI_MIN, pmesh.GetComm());
    }
 
    // Start the timer.
    tic_toc.Clear();
    tic_toc.Start();
 
-   double t = 0.0;
+   real_t t = 0.0;
    euler.SetTime(t);
    ode_solver->Init(euler);
 
@@ -299,9 +300,9 @@ int main(int argc, char *argv[])
       A.Mult(sol, z);
       // Reduce to find the global maximum wave speed
       {
-         double all_max_char_speed;
-         MPI_Allreduce(&max_char_speed, &all_max_char_speed,
-                       1, MPI_DOUBLE, MPI_MAX, pmesh.GetComm());
+         real_t all_max_char_speed;
+         MPI_Allreduce(&max_char_speed, &all_max_char_speed, 1,
+                       MPITypeMap<real_t>::mpi_type, MPI_MAX, pmesh.GetComm());
          max_char_speed = all_max_char_speed;
       }
       dt = cfl * hmin / max_char_speed / (2*order+1);
@@ -311,16 +312,16 @@ int main(int argc, char *argv[])
    bool done = false;
    for (int ti = 0; !done; )
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
 
       ode_solver->Step(sol, t, dt_real);
       if (cfl > 0)
       {
          // Reduce to find the global maximum wave speed
          {
-            double all_max_char_speed;
-            MPI_Allreduce(&max_char_speed, &all_max_char_speed,
-                          1, MPI_DOUBLE, MPI_MAX, pmesh.GetComm());
+            real_t all_max_char_speed;
+            MPI_Allreduce(&max_char_speed, &all_max_char_speed, 1,
+                          MPITypeMap<real_t>::mpi_type, MPI_MAX, pmesh.GetComm());
             max_char_speed = all_max_char_speed;
          }
          dt = cfl * hmin / max_char_speed / (2*order+1);
@@ -366,7 +367,7 @@ int main(int argc, char *argv[])
    // 12. Compute the L2 solution error summed for all components.
    if (t_final == 2.0)
    {
-      const double error = sol.ComputeLpError(2, u0);
+      const real_t error = sol.ComputeLpError(2, u0);
       if (Mpi::Root())
       {
          cout << "Solution error: " << error << endl;

examples/ex19.cpp

@@ -48,15 +48,15 @@ public:
       print_level = print_lvl;
    }
 
-   virtual void MonitorResidual(int it, double norm, const Vector &r, bool final);
+   virtual void MonitorResidual(int it, real_t norm, const Vector &r, bool final);
 
 private:
    const std::string prefix;
    int print_level;
-   mutable double norm0;
+   mutable real_t norm0;
 };
 
-void GeneralResidualMonitor::MonitorResidual(int it, double norm,
+void GeneralResidualMonitor::MonitorResidual(int it, real_t norm,
                                              const Vector &r, bool final)
 {
    if (print_level == 1 || (print_level == 3 && (final || it == 0)))
@@ -103,7 +103,7 @@ protected:
    BlockOperator *jacobian;
 
    // Scaling factor for the pressure mass matrix in the block preconditioner
-   double gamma;
+   real_t gamma;
 
    // Objects for the block preconditioner application
    SparseMatrix *pressure_mass;
@@ -157,7 +157,7 @@ protected:
 
 public:
    RubberOperator(Array<FiniteElementSpace *> &fes, Array<Array<int> *>&ess_bdr,
-                  Array<int> &block_trueOffsets, double rel_tol, double abs_tol,
+                  Array<int> &block_trueOffsets, real_t rel_tol, real_t abs_tol,
                   int iter, Coefficient &mu);
 
    // Required to use the native newton solver
@@ -187,10 +187,10 @@ int main(int argc, char *argv[])
    int ref_levels = 0;
    int order = 2;
    bool visualization = true;
-   double newton_rel_tol = 1e-4;
-   double newton_abs_tol = 1e-6;
+   real_t newton_rel_tol = 1e-4;
+   real_t newton_abs_tol = 1e-6;
    int newton_iter = 500;
-   double mu = 1.0;
+   real_t mu = 1.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -449,8 +449,8 @@ JacobianPreconditioner::~JacobianPreconditioner()
 RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
                                Array<Array<int> *> &ess_bdr,
                                Array<int> &offsets,
-                               double rel_tol,
-                               double abs_tol,
+                               real_t rel_tol,
+                               real_t abs_tol,
                                int iter,
                                Coefficient &c_mu)
    : Operator(fes[0]->GetTrueVSize() + fes[1]->GetTrueVSize()),

examples/ex19p.cpp

@@ -62,15 +62,15 @@ public:
 #endif
    }
 
-   virtual void MonitorResidual(int it, double norm, const Vector &r, bool final);
+   virtual void MonitorResidual(int it, real_t norm, const Vector &r, bool final);
 
 private:
    const std::string prefix;
    int print_level;
-   mutable double norm0;
+   mutable real_t norm0;
 };
 
-void GeneralResidualMonitor::MonitorResidual(int it, double norm,
+void GeneralResidualMonitor::MonitorResidual(int it, real_t norm,
                                              const Vector &r, bool final)
 {
    if (print_level == 1 || (print_level == 3 && (final || it == 0)))
@@ -117,7 +117,7 @@ protected:
    BlockOperator *jacobian;
 
    // Scaling factor for the pressure mass matrix in the block preconditioner
-   double gamma;
+   real_t gamma;
 
    // Objects for the block preconditioner application
    Operator *pressure_mass;
@@ -171,7 +171,7 @@ protected:
 
 public:
    RubberOperator(Array<ParFiniteElementSpace *> &fes, Array<Array<int> *>&ess_bdr,
-                  Array<int> &block_trueOffsets, double rel_tol, double abs_tol,
+                  Array<int> &block_trueOffsets, real_t rel_tol, real_t abs_tol,
                   int iter, Coefficient &mu);
 
    // Required to use the native newton solver
@@ -214,10 +214,10 @@ int main(int argc, char *argv[])
    int par_ref_levels = 0;
    int order = 2;
    bool visualization = true;
-   double newton_rel_tol = 1e-4;
-   double newton_abs_tol = 1e-6;
+   real_t newton_rel_tol = 1e-4;
+   real_t newton_abs_tol = 1e-6;
    int newton_iter = 500;
-   double mu = 1.0;
+   real_t mu = 1.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -524,8 +524,8 @@ JacobianPreconditioner::~JacobianPreconditioner()
 RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
                                Array<Array<int> *> &ess_bdr,
                                Array<int> &trueOffsets,
-                               double rel_tol,
-                               double abs_tol,
+                               real_t rel_tol,
+                               real_t abs_tol,
                                int iter,
                                Coefficient &c_mu)
    : Operator(fes[0]->TrueVSize() + fes[1]->TrueVSize()),

examples/ex20.cpp

@@ -69,11 +69,11 @@ using namespace mfem;
 
 // Constants used in the Hamiltonian
 static int prob_ = 0;
-static double m_ = 1.0;
-static double k_ = 1.0;
+static real_t m_ = 1.0;
+static real_t k_ = 1.0;
 
 // Hamiltonian functional, see below for implementation
-double hamiltonian(double q, double p, double t);
+real_t hamiltonian(real_t q, real_t p, real_t t);
 
 class GradT : public Operator
 {
@@ -94,7 +94,7 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    int order  = 1;
    int nsteps = 100;
-   double dt  = 0.1;
+   real_t dt  = 0.1;
    bool visualization = true;
    bool gnuplot = false;
 
@@ -136,7 +136,7 @@ int main(int argc, char *argv[])
    siaSolver.Init(P,F);
 
    // 3. Set the initial conditions
-   double t = 0.0;
+   real_t t = 0.0;
    Vector q(1), p(1);
    Vector e(nsteps+1);
    q(0) = 0.0;
@@ -160,7 +160,7 @@ int main(int argc, char *argv[])
    Vector x1(3); x1 = 0.0;
 
    // 6. Perform time-stepping
-   double e_mean = 0.0;
+   real_t e_mean = 0.0;
 
    for (int i = 0; i < nsteps; i++)
    {
@@ -210,13 +210,13 @@ int main(int argc, char *argv[])
 
    // 7. Compute and display mean and standard deviation of the energy
    e_mean /= (nsteps + 1);
-   double e_var = 0.0;
+   real_t e_var = 0.0;
    for (int i=0; i<=nsteps; i++)
    {
       e_var += pow(e[i] - e_mean, 2);
    }
    e_var /= (nsteps + 1);
-   double e_sd = sqrt(e_var);
+   real_t e_sd = sqrt(e_var);
    cout << endl << "Mean and standard deviation of the energy" << endl;
    cout << e_mean << "\t" << e_sd << endl;
 
@@ -256,9 +256,9 @@ int main(int argc, char *argv[])
    }
 }
 
-double hamiltonian(double q, double p, double t)
+real_t hamiltonian(real_t q, real_t p, real_t t)
 {
-   double h = 1.0 - 0.5 / m_ + 0.5 * p * p / m_;
+   real_t h = 1.0 - 0.5 / m_ + 0.5 * p * p / m_;
    switch (prob_)
    {
       case 1:

examples/ex20p.cpp

@@ -74,11 +74,11 @@ using namespace mfem;
 
 // Constants used in the Hamiltonian
 static int prob_ = 0;
-static double m_ = 1.0;
-static double k_ = 1.0;
+static real_t m_ = 1.0;
+static real_t k_ = 1.0;
 
 // Hamiltonian functional, see below for implementation
-double hamiltonian(double q, double p, double t);
+real_t hamiltonian(real_t q, real_t p, real_t t);
 
 class GradT : public Operator
 {
@@ -106,7 +106,7 @@ int main(int argc, char *argv[])
    // 2. Parse command-line options.
    int order  = 1;
    int nsteps = 100;
-   double dt  = 0.1;
+   real_t dt  = 0.1;
    bool visualization = true;
    bool gnuplot = false;
 
@@ -154,11 +154,11 @@ int main(int argc, char *argv[])
    siaSolver.Init(P,F);
 
    // 4. Set the initial conditions
-   double t = 0.0;
+   real_t t = 0.0;
    Vector q(1), p(1);
    Vector e(nsteps+1);
-   q(0) = sin(2.0*M_PI*(double)myid/num_procs);
-   p(0) = cos(2.0*M_PI*(double)myid/num_procs);
+   q(0) = sin(2.0*M_PI*(real_t)myid/num_procs);
+   p(0) = cos(2.0*M_PI*(real_t)myid/num_procs);
 
    // 5. Prepare GnuPlot output file if needed
    ostringstream oss;
@@ -181,7 +181,7 @@ int main(int argc, char *argv[])
    Vector x1(3); x1 = 0.0;
 
    // 7. Perform time-stepping
-   double e_mean = 0.0;
+   real_t e_mean = 0.0;
 
    for (int i = 0; i < nsteps; i++)
    {
@@ -238,20 +238,21 @@ int main(int argc, char *argv[])
 
    // 8. Compute and display mean and standard deviation of the energy
    e_mean /= (nsteps + 1);
-   double e_var = 0.0;
+   real_t e_var = 0.0;
    for (int i = 0; i <= nsteps; i++)
    {
       e_var += pow(e[i] - e_mean, 2);
    }
    e_var /= (nsteps + 1);
-   double e_sd = sqrt(e_var);
+   real_t e_sd = sqrt(e_var);
 
-   double e_loc_stats[2];
-   double *e_stats = (myid == 0) ? new double[2 * num_procs] : (double*)NULL;
+   real_t e_loc_stats[2];
+   real_t *e_stats = (myid == 0) ? new real_t[2 * num_procs] : (real_t*)NULL;
 
    e_loc_stats[0] = e_mean;
    e_loc_stats[1] = e_sd;
-   MPI_Gather(e_loc_stats, 2, MPI_DOUBLE, e_stats, 2, MPI_DOUBLE, 0, comm);
+   MPI_Gather(e_loc_stats, 2, MPITypeMap<real_t>::mpi_type, e_stats, 2,
+              MPITypeMap<real_t>::mpi_type, 0, comm);
 
    if (myid == 0)
    {
@@ -324,9 +325,9 @@ int main(int argc, char *argv[])
    }
 }
 
-double hamiltonian(double q, double p, double t)
+real_t hamiltonian(real_t q, real_t p, real_t t)
 {
-   double h = 1.0 - 0.5 / m_ + 0.5 * p * p / m_;
+   real_t h = 1.0 - 0.5 / m_ + 0.5 * p * p / m_;
    switch (prob_)
    {
       case 1:

examples/ex22.cpp

@@ -57,13 +57,13 @@
 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;
+static real_t mu_ = 1.0;
+static real_t epsilon_ = 1.0;
+static real_t sigma_ = 20.0;
+static real_t omega_ = 10.0;
 
-double u0_real_exact(const Vector &);
-double u0_imag_exact(const Vector &);
+real_t u0_real_exact(const Vector &);
+real_t u0_imag_exact(const Vector &);
 
 void u1_real_exact(const Vector &, Vector &);
 void u1_imag_exact(const Vector &, Vector &);
@@ -80,8 +80,8 @@ int main(int argc, char *argv[])
    int ref_levels = 0;
    int order = 1;
    int prob = 0;
-   double freq = -1.0;
-   double a_coef = 0.0;
+   real_t freq = -1.0;
+   real_t a_coef = 0.0;
    bool visualization = 1;
    bool herm_conv = true;
    bool exact_sol = true;
@@ -412,7 +412,7 @@ int main(int argc, char *argv[])
                break; // This should be unreachable
          }
       }
-      double s = (prob != 1) ? 1.0 : -1.0;
+      real_t s = (prob != 1) ? 1.0 : -1.0;
       pc_i = new ScaledOperator(pc_r,
                                 (conv == ComplexOperator::HERMITIAN) ?
                                 s:-s);
@@ -436,8 +436,8 @@ int main(int argc, char *argv[])
 
    if (exact_sol)
    {
-      double err_r = -1.0;
-      double err_i = -1.0;
+      real_t err_r = -1.0;
+      real_t err_i = -1.0;
 
       switch (prob)
       {
@@ -524,7 +524,7 @@ int main(int argc, char *argv[])
       int i = 0;
       while (sol_sock)
       {
-         double t = (double)(i % num_frames) / num_frames;
+         real_t t = (real_t)(i % num_frames) / num_frames;
          ostringstream oss;
          oss << "Harmonic Solution (t = " << t << " T)";
 
@@ -555,21 +555,21 @@ bool check_for_inline_mesh(const char * mesh_file)
    return s0 == "inline-";
 }
 
-complex<double> u0_exact(const Vector &x)
+complex<real_t> 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);
+   complex<real_t> i(0.0, 1.0);
+   complex<real_t> alpha = (epsilon_ * omega_ - i * sigma_);
+   complex<real_t> kappa = std::sqrt(mu_ * omega_* alpha);
    return std::exp(-i * kappa * x[dim - 1]);
 }
 
-double u0_real_exact(const Vector &x)
+real_t u0_real_exact(const Vector &x)
 {
    return u0_exact(x).real();
 }
 
-double u0_imag_exact(const Vector &x)
+real_t u0_imag_exact(const Vector &x)
 {
    return u0_exact(x).imag();
 }

examples/ex22p.cpp

@@ -57,13 +57,13 @@
 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;
+static real_t mu_ = 1.0;
+static real_t epsilon_ = 1.0;
+static real_t sigma_ = 20.0;
+static real_t omega_ = 10.0;
 
-double u0_real_exact(const Vector &);
-double u0_imag_exact(const Vector &);
+real_t u0_real_exact(const Vector &);
+real_t u0_imag_exact(const Vector &);
 
 void u1_real_exact(const Vector &, Vector &);
 void u1_imag_exact(const Vector &, Vector &);
@@ -87,8 +87,8 @@ int main(int argc, char *argv[])
    int par_ref_levels = 1;
    int order = 1;
    int prob = 0;
-   double freq = -1.0;
-   double a_coef = 0.0;
+   real_t freq = -1.0;
+   real_t a_coef = 0.0;
    bool visualization = 1;
    bool herm_conv = true;
    bool exact_sol = true;
@@ -475,8 +475,8 @@ int main(int argc, char *argv[])
 
    if (exact_sol)
    {
-      double err_r = -1.0;
-      double err_i = -1.0;
+      real_t err_r = -1.0;
+      real_t err_i = -1.0;
 
       switch (prob)
       {
@@ -576,7 +576,7 @@ int main(int argc, char *argv[])
       int i = 0;
       while (sol_sock)
       {
-         double t = (double)(i % num_frames) / num_frames;
+         real_t t = (real_t)(i % num_frames) / num_frames;
          ostringstream oss;
          oss << "Harmonic Solution (t = " << t << " T)";
 
@@ -608,21 +608,21 @@ bool check_for_inline_mesh(const char * mesh_file)
    return s0 == "inline-";
 }
 
-complex<double> u0_exact(const Vector &x)
+complex<real_t> 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);
+   complex<real_t> i(0.0, 1.0);
+   complex<real_t> alpha = (epsilon_ * omega_ - i * sigma_);
+   complex<real_t> kappa = std::sqrt(mu_ * omega_* alpha);
    return std::exp(-i * kappa * x[dim - 1]);
 }
 
-double u0_real_exact(const Vector &x)
+real_t u0_real_exact(const Vector &x)
 {
    return u0_exact(x).real();
 }
 
-double u0_imag_exact(const Vector &x)
+real_t u0_imag_exact(const Vector &x)
 {
    return u0_exact(x).imag();
 }

examples/ex23.cpp

@@ -26,13 +26,12 @@
 using namespace std;
 using namespace mfem;
 
-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the wave model can be written as:
  *
  *     d^2u/dt^2 = M^{-1}(-Ku)
  *
- *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
- *  (\kappa + \alpha u).
+ *  where u is the vector representing the temperature, M is the mass,
+ *  and K is the stiffness matrix.
  *
  *  Class WaveOperator represents the right-hand side of the above ODE.
  */
@@ -47,7 +46,7 @@ protected:
 
    SparseMatrix Mmat, Kmat, Kmat0;
    SparseMatrix *T; // T = M + dt K
-   double current_dt;
+   real_t current_dt;
 
    CGSolver M_solver; // Krylov solver for inverting the mass matrix M
    DSmoother M_prec;  // Preconditioner for the mass matrix M
@@ -59,7 +58,7 @@ protected:
    mutable Vector z; // auxiliary vector
 
 public:
-   WaveOperator(FiniteElementSpace &f, Array<int> &ess_bdr,double speed);
+   WaveOperator(FiniteElementSpace &f, Array<int> &ess_bdr, real_t speed);
 
    using SecondOrderTimeDependentOperator::Mult;
    virtual void Mult(const Vector &u, const Vector &du_dt,
@@ -69,7 +68,7 @@ public:
        d2udt2 = f(u + fac0*d2udt2,dudt + fac1*d2udt2, t),
        for the unknown d2udt2. */
    using SecondOrderTimeDependentOperator::ImplicitSolve;
-   virtual void ImplicitSolve(const double fac0, const double fac1,
+   virtual void ImplicitSolve(const real_t fac0, const real_t fac1,
                               const Vector &u, const Vector &dudt, Vector &d2udt2);
 
    ///
@@ -80,12 +79,11 @@ public:
 
 
 WaveOperator::WaveOperator(FiniteElementSpace &f,
-                           Array<int> &ess_bdr, double speed)
-   : SecondOrderTimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL),
-     K(NULL),
-     T(NULL), current_dt(0.0), z(height)
+                           Array<int> &ess_bdr, real_t speed)
+   : SecondOrderTimeDependentOperator(f.GetTrueVSize(), (real_t) 0.0),
+     fespace(f), M(NULL), K(NULL), T(NULL), current_dt(0.0), z(height)
 {
-   const double rel_tol = 1e-8;
+   const real_t rel_tol = 1e-8;
 
    fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
 
@@ -133,7 +131,7 @@ void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
    M_solver.Mult(z, d2udt2);
 }
 
-void WaveOperator::ImplicitSolve(const double fac0, const double fac1,
+void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
                                  const Vector &u, const Vector &dudt, Vector &d2udt2)
 {
    // Solve the equation:
@@ -168,12 +166,12 @@ WaveOperator::~WaveOperator()
    delete c2;
 }
 
-double InitialSolution(const Vector &x)
+real_t InitialSolution(const Vector &x)
 {
    return exp(-x.Norml2()*x.Norml2()*30);
 }
 
-double InitialRate(const Vector &x)
+real_t InitialRate(const Vector &x)
 {
    return 0.0;
 }
@@ -187,9 +185,9 @@ int main(int argc, char *argv[])
    int ref_levels = 2;
    int order = 2;
    int ode_solver_type = 10;
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double speed = 1.0;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t speed = 1.0;
    bool visualization = true;
    bool visit = true;
    bool dirichlet = true;
@@ -301,7 +299,7 @@ int main(int argc, char *argv[])
    Vector dudt;
    dudt_gf.GetTrueDofs(dudt);
 
-   // 7. Initialize the conduction operator and the visualization.
+   // 7. Initialize the wave operator and the visualization.
    Array<int> ess_bdr;
    if (mesh->bdr_attributes.Size())
    {
@@ -356,7 +354,7 @@ int main(int argc, char *argv[])
       else
       {
          sout.precision(precision);
-         sout << "solution\n" << *mesh << dudt_gf;
+         sout << "solution\n" << *mesh << u_gf;
          sout << "pause\n";
          sout << flush;
          cout << "GLVis visualization paused."
@@ -367,7 +365,7 @@ int main(int argc, char *argv[])
    // 8. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
    ode_solver->Init(oper);
-   double t = 0.0;
+   real_t t = 0.0;
 
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)

examples/ex24.cpp

@@ -44,14 +44,14 @@
 using namespace std;
 using namespace mfem;
 
-double p_exact(const Vector &x);
+real_t p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
-double div_gradp_exact(const Vector &x);
+real_t div_gradp_exact(const Vector &x);
 void v_exact(const Vector &x, Vector &v);
 void curlv_exact(const Vector &x, Vector &cv);
 
 int dim;
-double freq = 1.0, kappa;
+real_t freq = 1.0, kappa;
 
 int main(int argc, char *argv[])
 {
@@ -304,9 +304,9 @@ int main(int argc, char *argv[])
    // 12. Compute and print the L_2 norm of the error.
    if (prob == 0)
    {
-      double errSol = x.ComputeL2Error(gradp_coef);
-      double errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
-      double errProj = exact_proj.ComputeL2Error(gradp_coef);
+      real_t errSol = x.ComputeL2Error(gradp_coef);
+      real_t errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
+      real_t errProj = exact_proj.ComputeL2Error(gradp_coef);
 
       cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
            "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
@@ -317,9 +317,9 @@ int main(int argc, char *argv[])
    }
    else if (prob == 1)
    {
-      double errSol = x.ComputeL2Error(curlv_coef);
-      double errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
-      double errProj = exact_proj.ComputeL2Error(curlv_coef);
+      real_t errSol = x.ComputeL2Error(curlv_coef);
+      real_t errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
+      real_t errProj = exact_proj.ComputeL2Error(curlv_coef);
 
       cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in H(div): "
            "|| E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
@@ -337,9 +337,9 @@ int main(int argc, char *argv[])
          irs[i] = &(IntRules.Get(i, order_quad));
       }
 
-      double errSol = x.ComputeL2Error(divgradp_coef, irs);
-      double errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
-      double errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
+      real_t errSol = x.ComputeL2Error(divgradp_coef, irs);
+      real_t errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
+      real_t errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
 
       cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
            "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
@@ -376,7 +376,7 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double p_exact(const Vector &x)
+real_t p_exact(const Vector &x)
 {
    if (dim == 3)
    {
@@ -406,7 +406,7 @@ void gradp_exact(const Vector &x, Vector &f)
    }
 }
 
-double div_gradp_exact(const Vector &x)
+real_t div_gradp_exact(const Vector &x)
 {
    if (dim == 3)
    {

examples/ex24p.cpp

@@ -44,14 +44,14 @@
 using namespace std;
 using namespace mfem;
 
-double p_exact(const Vector &x);
+real_t p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
-double div_gradp_exact(const Vector &x);
+real_t div_gradp_exact(const Vector &x);
 void v_exact(const Vector &x, Vector &v);
 void curlv_exact(const Vector &x, Vector &cv);
 
 int dim;
-double freq = 1.0, kappa;
+real_t freq = 1.0, kappa;
 
 int main(int argc, char *argv[])
 {
@@ -352,9 +352,9 @@ int main(int argc, char *argv[])
    // 14. Compute and print the L_2 norm of the error.
    if (prob == 0)
    {
-      double errSol = x.ComputeL2Error(gradp_coef);
-      double errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
-      double errProj = exact_proj.ComputeL2Error(gradp_coef);
+      real_t errSol = x.ComputeL2Error(gradp_coef);
+      real_t errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
+      real_t errProj = exact_proj.ComputeL2Error(gradp_coef);
 
       if (myid == 0)
       {
@@ -368,9 +368,9 @@ int main(int argc, char *argv[])
    }
    else if (prob == 1)
    {
-      double errSol = x.ComputeL2Error(curlv_coef);
-      double errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
-      double errProj = exact_proj.ComputeL2Error(curlv_coef);
+      real_t errSol = x.ComputeL2Error(curlv_coef);
+      real_t errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
+      real_t errProj = exact_proj.ComputeL2Error(curlv_coef);
 
       if (myid == 0)
       {
@@ -391,9 +391,9 @@ int main(int argc, char *argv[])
          irs[i] = &(IntRules.Get(i, order_quad));
       }
 
-      double errSol = x.ComputeL2Error(divgradp_coef, irs);
-      double errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
-      double errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
+      real_t errSol = x.ComputeL2Error(divgradp_coef, irs);
+      real_t errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
+      real_t errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
 
       if (myid == 0)
       {
@@ -441,7 +441,7 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double p_exact(const Vector &x)
+real_t p_exact(const Vector &x)
 {
    if (dim == 3)
    {
@@ -471,7 +471,7 @@ void gradp_exact(const Vector &x, Vector &f)
    }
 }
 
-double div_gradp_exact(const Vector &x)
+real_t div_gradp_exact(const Vector &x)
 {
    if (dim == 3)
    {

examples/ex25.cpp

@@ -53,13 +53,13 @@ private:
    int dim;
 
    // Length of the PML Region in each direction
-   Array2D<double> length;
+   Array2D<real_t> length;
 
    // Computational Domain Boundary
-   Array2D<double> comp_dom_bdr;
+   Array2D<real_t> comp_dom_bdr;
 
    // Domain Boundary
-   Array2D<double> dom_bdr;
+   Array2D<real_t> dom_bdr;
 
    // Integer Array identifying elements in the PML
    // 0: in the PML, 1: not in the PML
@@ -70,13 +70,13 @@ private:
 
 public:
    // Constructor
-   PML(Mesh *mesh_,Array2D<double> length_);
+   PML(Mesh *mesh_,Array2D<real_t> length_);
 
    // Return Computational Domain Boundary
-   Array2D<double> GetCompDomainBdr() {return comp_dom_bdr;}
+   Array2D<real_t> GetCompDomainBdr() {return comp_dom_bdr;}
 
    // Return Domain Boundary
-   Array2D<double> GetDomainBdr() {return dom_bdr;}
+   Array2D<real_t> GetDomainBdr() {return dom_bdr;}
 
    // Return Markers list for elements
    Array<int> * GetMarkedPMLElements() {return &elems;}
@@ -85,7 +85,7 @@ public:
    void SetAttributes(Mesh *mesh_);
 
    // PML complex stretching function
-   void StretchFunction(const Vector &x, vector<complex<double>> &dxs);
+   void StretchFunction(const Vector &x, vector<complex<real_t>> &dxs);
 };
 
 // Class for returning the PML coefficients of the bilinear form
@@ -106,7 +106,7 @@ public:
    virtual void Eval(Vector &K, ElementTransformation &T,
                      const IntegrationPoint &ip)
    {
-      double x[3];
+      real_t x[3];
       Vector transip(x, 3);
       T.Transform(ip, transip);
       K.SetSize(vdim);
@@ -114,7 +114,7 @@ public:
    }
 };
 
-void maxwell_solution(const Vector &x, vector<complex<double>> &Eval);
+void maxwell_solution(const Vector &x, vector<complex<real_t>> &Eval);
 
 void E_bdr_data_Re(const Vector &x, Vector &E);
 void E_bdr_data_Im(const Vector &x, Vector &E);
@@ -134,12 +134,12 @@ void detJ_inv_JT_J_Re(const Vector &x, PML * pml, Vector &D);
 void detJ_inv_JT_J_Im(const Vector &x, PML * pml, Vector &D);
 void detJ_inv_JT_J_abs(const Vector &x, PML * pml, Vector &D);
 
-Array2D<double> comp_domain_bdr;
-Array2D<double> domain_bdr;
+Array2D<real_t> comp_domain_bdr;
+Array2D<real_t> domain_bdr;
 
-double mu = 1.0;
-double epsilon = 1.0;
-double omega;
+real_t mu = 1.0;
+real_t epsilon = 1.0;
+real_t omega;
 int dim;
 bool exact_known = false;
 
@@ -160,7 +160,7 @@ int main(int argc, char *argv[])
    int order = 1;
    int ref_levels = 3;
    int iprob = 4;
-   double freq = 5.0;
+   real_t freq = 5.0;
    bool herm_conv = true;
    bool umf_solver = false;
    bool visualization = 1;
@@ -244,7 +244,7 @@ int main(int argc, char *argv[])
    omega = 2.0 * M_PI * freq;
 
    // Setup PML length
-   Array2D<double> length(dim, 2); length = 0.0;
+   Array2D<real_t> length(dim, 2); length = 0.0;
 
    // 4. Setup the Cartesian PML region.
    switch (prob)
@@ -470,7 +470,7 @@ int main(int argc, char *argv[])
 
       std::unique_ptr<Operator> pc_r;
       std::unique_ptr<Operator> pc_i;
-      double s = (conv == ComplexOperator::HERMITIAN) ? -1.0 : 1.0;
+      real_t s = (conv == ComplexOperator::HERMITIAN) ? -1.0 : 1.0;
       if (pa)
       {
          // Jacobi Smoother
@@ -519,14 +519,14 @@ int main(int argc, char *argv[])
          irs[i] = &(IntRules.Get(i, order_quad));
       }
 
-      double L2Error_Re = x.real().ComputeL2Error(E_ex_Re, irs,
+      real_t L2Error_Re = x.real().ComputeL2Error(E_ex_Re, irs,
                                                   pml->GetMarkedPMLElements());
-      double L2Error_Im = x.imag().ComputeL2Error(E_ex_Im, irs,
+      real_t L2Error_Im = x.imag().ComputeL2Error(E_ex_Im, irs,
                                                   pml->GetMarkedPMLElements());
 
       ComplexGridFunction x_gf0(fespace);
       x_gf0 = 0.0;
-      double norm_E_Re, norm_E_Im;
+      real_t norm_E_Re, norm_E_Im;
       norm_E_Re = x_gf0.real().ComputeL2Error(E_ex_Re, irs,
                                               pml->GetMarkedPMLElements());
       norm_E_Im = x_gf0.imag().ComputeL2Error(E_ex_Im, irs,
@@ -593,7 +593,7 @@ int main(int argc, char *argv[])
       int i = 0;
       while (sol_sock)
       {
-         double t = (double)(i % num_frames) / num_frames;
+         real_t t = (real_t)(i % num_frames) / num_frames;
          ostringstream oss;
          oss << "Harmonic Solution (t = " << t << " T)";
 
@@ -617,20 +617,20 @@ int main(int argc, char *argv[])
 void source(const Vector &x, Vector &f)
 {
    Vector center(dim);
-   double r = 0.0;
+   real_t r = 0.0;
    for (int i = 0; i < dim; ++i)
    {
       center(i) = 0.5 * (comp_domain_bdr(i, 0) + comp_domain_bdr(i, 1));
       r += pow(x[i] - center[i], 2.);
    }
-   double n = 5.0 * omega * sqrt(epsilon * mu) / M_PI;
-   double coeff = pow(n, 2) / M_PI;
-   double alpha = -pow(n, 2) * r;
+   real_t n = 5.0 * omega * sqrt(epsilon * mu) / M_PI;
+   real_t coeff = pow(n, 2) / M_PI;
+   real_t alpha = -pow(n, 2) * r;
    f = 0.0;
    f[0] = coeff * exp(alpha);
 }
 
-void maxwell_solution(const Vector &x, vector<complex<double>> &E)
+void maxwell_solution(const Vector &x, vector<complex<real_t>> &E)
 {
    // Initialize
    for (int i = 0; i < dim; ++i)
@@ -638,8 +638,8 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
       E[i] = 0.0;
    }
 
-   complex<double> zi = complex<double>(0., 1.);
-   double k = omega * sqrt(epsilon * mu);
+   complex<real_t> zi = complex<real_t>(0., 1.);
+   real_t k = omega * sqrt(epsilon * mu);
    switch (prob)
    {
       case disc:
@@ -654,58 +654,58 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
 
          if (dim == 2)
          {
-            double x0 = x(0) + shift(0);
-            double x1 = x(1) + shift(1);
-            double r = sqrt(x0 * x0 + x1 * x1);
-            double beta = k * r;
+            real_t x0 = x(0) + shift(0);
+            real_t x1 = x(1) + shift(1);
+            real_t r = sqrt(x0 * x0 + x1 * x1);
+            real_t beta = k * r;
 
             // Bessel functions
-            complex<double> Ho, Ho_r, Ho_rr;
-            Ho = jn(0, beta) + zi * yn(0, beta);
-            Ho_r = -k * (jn(1, beta) + zi * yn(1, beta));
-            Ho_rr = -k * k * (1.0 / beta *
-                              (jn(1, beta) + zi * yn(1, beta)) -
-                              (jn(2, beta) + zi * yn(2, beta)));
+            complex<real_t> Ho, Ho_r, Ho_rr;
+            Ho = jn(0, beta) + (complex<double>) zi * yn(0, beta);
+            Ho_r = -k * complex<real_t>(jn(1, beta) + (complex<double>) zi * yn(1, beta));
+            Ho_rr = -k * k * (real_t(1) / beta *
+                              complex<real_t>(jn(1, beta) + (complex<double>) zi * yn(1, beta)) -
+                              complex<real_t>(jn(2, beta) + (complex<double>) zi * yn(2, beta)));
 
             // First derivatives
-            double r_x = x0 / r;
-            double r_y = x1 / r;
-            double r_xy = -(r_x / r) * r_y;
-            double r_xx = (1.0 / r) * (1.0 - r_x * r_x);
+            real_t r_x = x0 / r;
+            real_t r_y = x1 / r;
+            real_t r_xy = -(r_x / r) * r_y;
+            real_t r_xx = (1.0 / r) * (1.0 - r_x * r_x);
 
-            complex<double> val, val_xx, val_xy;
-            val = 0.25 * zi * Ho;
-            val_xx = 0.25 * zi * (r_xx * Ho_r + r_x * r_x * Ho_rr);
-            val_xy = 0.25 * zi * (r_xy * Ho_r + r_x * r_y * Ho_rr);
+            complex<real_t> val, val_xx, val_xy;
+            val = real_t(0.25) * zi * Ho;
+            val_xx = real_t(0.25) * zi * (r_xx * Ho_r + r_x * r_x * Ho_rr);
+            val_xy = real_t(0.25) * zi * (r_xy * Ho_r + r_x * r_y * Ho_rr);
             E[0] = zi / k * (k * k * val + val_xx);
             E[1] = zi / k * val_xy;
          }
          else if (dim == 3)
          {
-            double x0 = x(0) + shift(0);
-            double x1 = x(1) + shift(1);
-            double x2 = x(2) + shift(2);
-            double r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
+            real_t x0 = x(0) + shift(0);
+            real_t x1 = x(1) + shift(1);
+            real_t x2 = x(2) + shift(2);
+            real_t r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
 
-            double r_x = x0 / r;
-            double r_y = x1 / r;
-            double r_z = x2 / r;
-            double r_xx = (1.0 / r) * (1.0 - r_x * r_x);
-            double r_yx = -(r_y / r) * r_x;
-            double r_zx = -(r_z / r) * r_x;
+            real_t r_x = x0 / r;
+            real_t r_y = x1 / r;
+            real_t r_z = x2 / r;
+            real_t r_xx = (1.0 / r) * (1.0 - r_x * r_x);
+            real_t r_yx = -(r_y / r) * r_x;
+            real_t r_zx = -(r_z / r) * r_x;
 
-            complex<double> val, val_r, val_rr;
+            complex<real_t> val, val_r, val_rr;
             val = exp(zi * k * r) / r;
-            val_r = val / r * (zi * k * r - 1.0);
+            val_r = val / r * (zi * k * r - real_t(1));
             val_rr = val / (r * r) * (-k * k * r * r
-                                      - 2.0 * zi * k * r + 2.0);
+                                      - real_t(2) * zi * k * r + real_t(2));
 
-            complex<double> val_xx, val_yx, val_zx;
+            complex<real_t> val_xx, val_yx, val_zx;
             val_xx = val_rr * r_x * r_x + val_r * r_xx;
             val_yx = val_rr * r_x * r_y + val_r * r_yx;
             val_zx = val_rr * r_x * r_z + val_r * r_zx;
 
-            complex<double> alpha = zi * k / 4.0 / M_PI / k / k;
+            complex<real_t> alpha = zi * k / real_t(4) / (real_t) M_PI / k / k;
             E[0] = alpha * (k * k * val + val_xx);
             E[1] = alpha * val_yx;
             E[2] = alpha * val_zx;
@@ -717,12 +717,12 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
          // T_10 mode
          if (dim == 3)
          {
-            double k10 = sqrt(k * k - M_PI * M_PI);
-            E[1] = -zi * k / M_PI * sin(M_PI*x(2))*exp(zi * k10 * x(0));
+            real_t k10 = sqrt(k * k - M_PI * M_PI);
+            E[1] = -zi * k / (real_t) M_PI * sin((real_t) M_PI*x(2))*exp(zi * k10 * x(0));
          }
          else if (dim == 2)
          {
-            E[1] = -zi * k / M_PI * exp(zi * k * x(0));
+            E[1] = -zi * k / (real_t) M_PI * exp(zi * k * x(0));
          }
          break;
       }
@@ -733,7 +733,7 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
 
 void E_exact_Re(const Vector &x, Vector &E)
 {
-   vector<complex<double>> Eval(E.Size());
+   vector<complex<real_t>> Eval(E.Size());
    maxwell_solution(x, Eval);
    for (int i = 0; i < dim; ++i)
    {
@@ -743,7 +743,7 @@ void E_exact_Re(const Vector &x, Vector &E)
 
 void E_exact_Im(const Vector &x, Vector &E)
 {
-   vector<complex<double>> Eval(E.Size());
+   vector<complex<real_t>> Eval(E.Size());
    maxwell_solution(x, Eval);
    for (int i = 0; i < dim; ++i)
    {
@@ -768,7 +768,7 @@ void E_bdr_data_Re(const Vector &x, Vector &E)
    }
    if (!in_pml)
    {
-      vector<complex<double>> Eval(E.Size());
+      vector<complex<real_t>> Eval(E.Size());
       maxwell_solution(x, Eval);
       for (int i = 0; i < dim; ++i)
       {
@@ -795,7 +795,7 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
    }
    if (!in_pml)
    {
-      vector<complex<double>> Eval(E.Size());
+      vector<complex<real_t>> Eval(E.Size());
       maxwell_solution(x, Eval);
       for (int i = 0; i < dim; ++i)
       {
@@ -806,8 +806,8 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
 
 void detJ_JT_J_inv_Re(const Vector &x, PML * pml, Vector &D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det(1.0, 0.0);
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det(1.0, 0.0);
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -817,14 +817,14 @@ void detJ_JT_J_inv_Re(const Vector &x, PML * pml, Vector &D)
 
    for (int i = 0; i < dim; ++i)
    {
-      D(i) = (det / pow(dxs[i], 2)).real();
+      D(i) = (det / pow(dxs[i], real_t(2))).real();
    }
 }
 
 void detJ_JT_J_inv_Im(const Vector &x, PML * pml, Vector &D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -834,14 +834,14 @@ void detJ_JT_J_inv_Im(const Vector &x, PML * pml, Vector &D)
 
    for (int i = 0; i < dim; ++i)
    {
-      D(i) = (det / pow(dxs[i], 2)).imag();
+      D(i) = (det / pow(dxs[i], real_t(2))).imag();
    }
 }
 
 void detJ_JT_J_inv_abs(const Vector &x, PML * pml, Vector &D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -851,14 +851,14 @@ void detJ_JT_J_inv_abs(const Vector &x, PML * pml, Vector &D)
 
    for (int i = 0; i < dim; ++i)
    {
-      D(i) = abs(det / pow(dxs[i], 2));
+      D(i) = abs(det / pow(dxs[i], real_t(2)));
    }
 }
 
 void detJ_inv_JT_J_Re(const Vector &x, PML * pml, Vector &D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det(1.0, 0.0);
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det(1.0, 0.0);
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -869,21 +869,21 @@ void detJ_inv_JT_J_Re(const Vector &x, PML * pml, Vector &D)
    // in the 2D case the coefficient is scalar 1/det(J)
    if (dim == 2)
    {
-      D = (1.0 / det).real();
+      D = (real_t(1) / det).real();
    }
    else
    {
       for (int i = 0; i < dim; ++i)
       {
-         D(i) = (pow(dxs[i], 2) / det).real();
+         D(i) = (pow(dxs[i], real_t(2)) / det).real();
       }
    }
 }
 
 void detJ_inv_JT_J_Im(const Vector &x, PML * pml, Vector &D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -893,21 +893,21 @@ void detJ_inv_JT_J_Im(const Vector &x, PML * pml, Vector &D)
 
    if (dim == 2)
    {
-      D = (1.0 / det).imag();
+      D = (real_t(1) / det).imag();
    }
    else
    {
       for (int i = 0; i < dim; ++i)
       {
-         D(i) = (pow(dxs[i], 2) / det).imag();
+         D(i) = (pow(dxs[i], real_t(2)) / det).imag();
       }
    }
 }
 
 void detJ_inv_JT_J_abs(const Vector &x, PML * pml, Vector &D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -917,18 +917,18 @@ void detJ_inv_JT_J_abs(const Vector &x, PML * pml, Vector &D)
 
    if (dim == 2)
    {
-      D = abs(1.0 / det);
+      D = abs(real_t(1) / det);
    }
    else
    {
       for (int i = 0; i < dim; ++i)
       {
-         D(i) = abs(pow(dxs[i], 2) / det);
+         D(i) = abs(pow(dxs[i], real_t(2)) / det);
       }
    }
 }
 
-PML::PML(Mesh *mesh_, Array2D<double> length_)
+PML::PML(Mesh *mesh_, Array2D<real_t> length_)
    : mesh(mesh_), length(length_)
 {
    dim = mesh->Dimension();
@@ -979,7 +979,7 @@ void PML::SetAttributes(Mesh *mesh_)
       for (int iv = 0; iv < nrvert; ++iv)
       {
          int vert_idx = vertices[iv];
-         double *coords = mesh_->GetVertex(vert_idx);
+         real_t *coords = mesh_->GetVertex(vert_idx);
          for (int comp = 0; comp < dim; ++comp)
          {
             if (coords[comp] > comp_dom_bdr(comp, 1) ||
@@ -1000,14 +1000,14 @@ void PML::SetAttributes(Mesh *mesh_)
 }
 
 void PML::StretchFunction(const Vector &x,
-                          vector<complex<double>> &dxs)
+                          vector<complex<real_t>> &dxs)
 {
-   complex<double> zi = complex<double>(0., 1.);
+   complex<real_t> zi = complex<real_t>(0., 1.);
 
-   double n = 2.0;
-   double c = 5.0;
-   double coeff;
-   double k = omega * sqrt(epsilon * mu);
+   real_t n = 2.0;
+   real_t c = 5.0;
+   real_t coeff;
+   real_t k = omega * sqrt(epsilon * mu);
 
    // Stretch in each direction independently
    for (int i = 0; i < dim; ++i)
@@ -1016,14 +1016,14 @@ void PML::StretchFunction(const Vector &x,
       if (x(i) >= comp_domain_bdr(i, 1))
       {
          coeff = n * c / k / pow(length(i, 1), n);
-         dxs[i] = 1.0 + zi * coeff *
-                  abs(pow(x(i) - comp_domain_bdr(i, 1), n - 1.0));
+         dxs[i] = real_t(1) + zi * coeff *
+                  abs(pow(x(i) - comp_domain_bdr(i, 1), n - real_t(1)));
       }
       if (x(i) <= comp_domain_bdr(i, 0))
       {
          coeff = n * c / k / pow(length(i, 0), n);
-         dxs[i] = 1.0 + zi * coeff *
-                  abs(pow(x(i) - comp_domain_bdr(i, 0), n - 1.0));
+         dxs[i] = real_t(1) + zi * coeff *
+                  abs(pow(x(i) - comp_domain_bdr(i, 0), n - real_t(1)));
       }
    }
 }

examples/ex25p.cpp

@@ -52,13 +52,13 @@ private:
    int dim;
 
    // Length of the PML Region in each direction
-   Array2D<double> length;
+   Array2D<real_t> length;
 
    // Computational Domain Boundary
-   Array2D<double> comp_dom_bdr;
+   Array2D<real_t> comp_dom_bdr;
 
    // Domain Boundary
-   Array2D<double> dom_bdr;
+   Array2D<real_t> dom_bdr;
 
    // Integer Array identifying elements in the PML
    // 0: in the PML, 1: not in the PML
@@ -69,13 +69,13 @@ private:
 
 public:
    // Constructor
-   PML(Mesh *mesh_,Array2D<double> length_);
+   PML(Mesh *mesh_,Array2D<real_t> length_);
 
    // Return Computational Domain Boundary
-   Array2D<double> GetCompDomainBdr() {return comp_dom_bdr;}
+   Array2D<real_t> GetCompDomainBdr() {return comp_dom_bdr;}
 
    // Return Domain Boundary
-   Array2D<double> GetDomainBdr() {return dom_bdr;}
+   Array2D<real_t> GetDomainBdr() {return dom_bdr;}
 
    // Return Markers list for elements
    Array<int> * GetMarkedPMLElements() {return &elems;}
@@ -84,7 +84,7 @@ public:
    void SetAttributes(ParMesh *pmesh);
 
    // PML complex stretching function
-   void StretchFunction(const Vector &x, vector<complex<double>> &dxs);
+   void StretchFunction(const Vector &x, vector<complex<real_t>> &dxs);
 };
 
 // Class for returning the PML coefficients of the bilinear form
@@ -105,7 +105,7 @@ public:
    virtual void Eval(Vector &K, ElementTransformation &T,
                      const IntegrationPoint &ip)
    {
-      double x[3];
+      real_t x[3];
       Vector transip(x, 3);
       T.Transform(ip, transip);
       K.SetSize(vdim);
@@ -113,7 +113,7 @@ public:
    }
 };
 
-void maxwell_solution(const Vector &x, vector<complex<double>> &Eval);
+void maxwell_solution(const Vector &x, vector<complex<real_t>> &Eval);
 
 void E_bdr_data_Re(const Vector &x, Vector &E);
 void E_bdr_data_Im(const Vector &x, Vector &E);
@@ -133,12 +133,12 @@ void detJ_inv_JT_J_Re(const Vector &x, PML * pml, Vector & D);
 void detJ_inv_JT_J_Im(const Vector &x, PML * pml, Vector & D);
 void detJ_inv_JT_J_abs(const Vector &x, PML * pml, Vector & D);
 
-Array2D<double> comp_domain_bdr;
-Array2D<double> domain_bdr;
+Array2D<real_t> comp_domain_bdr;
+Array2D<real_t> domain_bdr;
 
-double mu = 1.0;
-double epsilon = 1.0;
-double omega;
+real_t mu = 1.0;
+real_t epsilon = 1.0;
+real_t omega;
 int dim;
 bool exact_known = false;
 
@@ -166,10 +166,11 @@ int main(int argc, char *argv[])
    int ref_levels = 1;
    int par_ref_levels = 2;
    int iprob = 4;
-   double freq = 5.0;
+   real_t freq = 5.0;
    bool herm_conv = true;
    bool slu_solver  = false;
    bool mumps_solver = false;
+   bool strumpack_solver = false;
    bool visualization = 1;
    bool pa = false;
    const char *device_config = "cpu";
@@ -200,6 +201,11 @@ int main(int argc, char *argv[])
 #ifdef MFEM_USE_MUMPS
    args.AddOption(&mumps_solver, "-mumps", "--mumps-solver", "-no-mumps",
                   "--no-mumps-solver", "Use the MUMPS Solver.");
+#endif
+#ifdef MFEM_USE_STRUMPACK
+   args.AddOption(&strumpack_solver, "-strumpack", "--strumpack-solver",
+                  "-no-strumpack", "--no-strumpack-solver",
+                  "Use the STRUMPACK Solver.");
 #endif
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
@@ -209,13 +215,14 @@ int main(int argc, char *argv[])
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.Parse();
-   if (slu_solver && mumps_solver)
+   if (slu_solver + mumps_solver + strumpack_solver > 1)
    {
       if (myid == 0)
-         cout << "WARNING: Both SuperLU and MUMPS have been selected,"
-              << " please choose either one." << endl
+         cout << "WARNING: More than one of SuperLU, MUMPS, and STRUMPACK have"
+              << " been selected, please choose only one." << endl
               << "         Defaulting to SuperLU." << endl;
       mumps_solver = false;
+      strumpack_solver = false;
    }
 
    if (iprob > 4) { iprob = 4; }
@@ -271,7 +278,7 @@ int main(int argc, char *argv[])
    omega = 2.0 * M_PI * freq;
 
    // Setup PML length
-   Array2D<double> length(dim, 2); length = 0.0;
+   Array2D<real_t> length(dim, 2); length = 0.0;
 
    // 5. Setup the Cartesian PML region.
    switch (prob)
@@ -474,6 +481,24 @@ int main(int argc, char *argv[])
       delete A;
    }
 #endif
+#ifdef MFEM_USE_STRUMPACK
+   if (!pa && strumpack_solver)
+   {
+      HypreParMatrix *A = Ah.As<ComplexHypreParMatrix>()->GetSystemMatrix();
+      STRUMPACKRowLocMatrix SA(*A);
+      STRUMPACKSolver strumpack(MPI_COMM_WORLD, argc, argv);
+      strumpack.SetPrintFactorStatistics(false);
+      strumpack.SetPrintSolveStatistics(false);
+      strumpack.SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+      strumpack.SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+      strumpack.SetMatching(strumpack::MatchingJob::NONE);
+      strumpack.SetCompression(strumpack::CompressionType::NONE);
+      strumpack.SetFromCommandLine();
+      strumpack.SetOperator(SA);
+      strumpack.Mult(B, X);
+      delete A;
+   }
+#endif
 #ifdef MFEM_USE_MUMPS
    if (!pa && mumps_solver)
    {
@@ -493,7 +518,7 @@ int main(int argc, char *argv[])
    //
    //    In PML:   1/mu (abs(1/det(J) J^T J) Curl E, Curl F)
    //              + omega^2 * epsilon (abs(det(J) * (J^T J)^-1) * E, F)
-   if (pa || (!slu_solver && !mumps_solver))
+   if (pa || (!slu_solver && !mumps_solver && !strumpack_solver))
    {
       ConstantCoefficient absomeg(pow(omega, 2) * epsilon);
       RestrictedCoefficient restr_absomeg(absomeg,attr);
@@ -574,14 +599,14 @@ int main(int argc, char *argv[])
          irs[i] = &(IntRules.Get(i, order_quad));
       }
 
-      double L2Error_Re = x.real().ComputeL2Error(E_ex_Re, irs,
+      real_t L2Error_Re = x.real().ComputeL2Error(E_ex_Re, irs,
                                                   pml->GetMarkedPMLElements());
-      double L2Error_Im = x.imag().ComputeL2Error(E_ex_Im, irs,
+      real_t L2Error_Im = x.imag().ComputeL2Error(E_ex_Im, irs,
                                                   pml->GetMarkedPMLElements());
 
       ParComplexGridFunction x_gf0(fespace);
       x_gf0 = 0.0;
-      double norm_E_Re, norm_E_Im;
+      real_t norm_E_Re, norm_E_Im;
       norm_E_Re = x_gf0.real().ComputeL2Error(E_ex_Re, irs,
                                               pml->GetMarkedPMLElements());
       norm_E_Im = x_gf0.imag().ComputeL2Error(E_ex_Im, irs,
@@ -669,7 +694,7 @@ int main(int argc, char *argv[])
          int i = 0;
          while (sol_sock)
          {
-            double t = (double)(i % num_frames) / num_frames;
+            real_t t = (real_t)(i % num_frames) / num_frames;
             ostringstream oss;
             oss << "Harmonic Solution (t = " << t << " T)";
 
@@ -693,20 +718,20 @@ int main(int argc, char *argv[])
 void source(const Vector &x, Vector &f)
 {
    Vector center(dim);
-   double r = 0.0;
+   real_t r = 0.0;
    for (int i = 0; i < dim; ++i)
    {
       center(i) = 0.5 * (comp_domain_bdr(i, 0) + comp_domain_bdr(i, 1));
       r += pow(x[i] - center[i], 2.);
    }
-   double n = 5.0 * omega * sqrt(epsilon * mu) / M_PI;
-   double coeff = pow(n, 2) / M_PI;
-   double alpha = -pow(n, 2) * r;
+   real_t n = 5.0 * omega * sqrt(epsilon * mu) / M_PI;
+   real_t coeff = pow(n, 2) / M_PI;
+   real_t alpha = -pow(n, 2) * r;
    f = 0.0;
    f[0] = coeff * exp(alpha);
 }
 
-void maxwell_solution(const Vector &x, vector<complex<double>> &E)
+void maxwell_solution(const Vector &x, vector<complex<real_t>> &E)
 {
    // Initialize
    for (int i = 0; i < dim; ++i)
@@ -714,8 +739,8 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
       E[i] = 0.0;
    }
 
-   complex<double> zi = complex<double>(0., 1.);
-   double k = omega * sqrt(epsilon * mu);
+   complex<real_t> zi = complex<real_t>(0., 1.);
+   real_t k = omega * sqrt(epsilon * mu);
    switch (prob)
    {
       case disc:
@@ -730,58 +755,58 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
 
          if (dim == 2)
          {
-            double x0 = x(0) + shift(0);
-            double x1 = x(1) + shift(1);
-            double r = sqrt(x0 * x0 + x1 * x1);
-            double beta = k * r;
+            real_t x0 = x(0) + shift(0);
+            real_t x1 = x(1) + shift(1);
+            real_t r = sqrt(x0 * x0 + x1 * x1);
+            real_t beta = k * r;
 
             // Bessel functions
-            complex<double> Ho, Ho_r, Ho_rr;
-            Ho = jn(0, beta) + zi * yn(0, beta);
-            Ho_r = -k * (jn(1, beta) + zi * yn(1, beta));
-            Ho_rr = -k * k * (1.0 / beta *
-                              (jn(1, beta) + zi * yn(1, beta)) -
-                              (jn(2, beta) + zi * yn(2, beta)));
+            complex<real_t> Ho, Ho_r, Ho_rr;
+            Ho = jn(0, beta) + (complex<double>) zi * yn(0, beta);
+            Ho_r = -k * complex<real_t>(jn(1, beta) + (complex<double>) zi * yn(1, beta));
+            Ho_rr = -k * k * complex<real_t>(1.0 / beta *
+                                             (jn(1, beta) + (complex<double>) zi * yn(1, beta)) -
+                                             (jn(2, beta) + (complex<double>) zi * yn(2, beta)));
 
             // First derivatives
-            double r_x = x0 / r;
-            double r_y = x1 / r;
-            double r_xy = -(r_x / r) * r_y;
-            double r_xx = (1.0 / r) * (1.0 - r_x * r_x);
+            real_t r_x = x0 / r;
+            real_t r_y = x1 / r;
+            real_t r_xy = -(r_x / r) * r_y;
+            real_t r_xx = (1.0 / r) * (1.0 - r_x * r_x);
 
-            complex<double> val, val_xx, val_xy;
-            val = 0.25 * zi * Ho;
-            val_xx = 0.25 * zi * (r_xx * Ho_r + r_x * r_x * Ho_rr);
-            val_xy = 0.25 * zi * (r_xy * Ho_r + r_x * r_y * Ho_rr);
+            complex<real_t> val, val_xx, val_xy;
+            val = real_t(0.25) * zi * Ho;
+            val_xx = real_t(0.25) * zi * (r_xx * Ho_r + r_x * r_x * Ho_rr);
+            val_xy = real_t(0.25) * zi * (r_xy * Ho_r + r_x * r_y * Ho_rr);
             E[0] = zi / k * (k * k * val + val_xx);
             E[1] = zi / k * val_xy;
          }
          else if (dim == 3)
          {
-            double x0 = x(0) + shift(0);
-            double x1 = x(1) + shift(1);
-            double x2 = x(2) + shift(2);
-            double r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
+            real_t x0 = x(0) + shift(0);
+            real_t x1 = x(1) + shift(1);
+            real_t x2 = x(2) + shift(2);
+            real_t r = sqrt(x0 * x0 + x1 * x1 + x2 * x2);
 
-            double r_x = x0 / r;
-            double r_y = x1 / r;
-            double r_z = x2 / r;
-            double r_xx = (1.0 / r) * (1.0 - r_x * r_x);
-            double r_yx = -(r_y / r) * r_x;
-            double r_zx = -(r_z / r) * r_x;
+            real_t r_x = x0 / r;
+            real_t r_y = x1 / r;
+            real_t r_z = x2 / r;
+            real_t r_xx = (1.0 / r) * (1.0 - r_x * r_x);
+            real_t r_yx = -(r_y / r) * r_x;
+            real_t r_zx = -(r_z / r) * r_x;
 
-            complex<double> val, val_r, val_rr;
+            complex<real_t> val, val_r, val_rr;
             val = exp(zi * k * r) / r;
-            val_r = val / r * (zi * k * r - 1.0);
+            val_r = val / r * (zi * k * r - real_t(1));
             val_rr = val / (r * r) * (-k * k * r * r
-                                      - 2.0 * zi * k * r + 2.0);
+                                      - real_t(2) * zi * k * r + real_t(2));
 
-            complex<double> val_xx, val_yx, val_zx;
+            complex<real_t> val_xx, val_yx, val_zx;
             val_xx = val_rr * r_x * r_x + val_r * r_xx;
             val_yx = val_rr * r_x * r_y + val_r * r_yx;
             val_zx = val_rr * r_x * r_z + val_r * r_zx;
 
-            complex<double> alpha = zi * k / 4.0 / M_PI / k / k;
+            complex<real_t> alpha = zi * k / real_t(4) / (real_t) M_PI / k / k;
             E[0] = alpha * (k * k * val + val_xx);
             E[1] = alpha * val_yx;
             E[2] = alpha * val_zx;
@@ -793,12 +818,12 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
          // T_10 mode
          if (dim == 3)
          {
-            double k10 = sqrt(k * k - M_PI * M_PI);
-            E[1] = -zi * k / M_PI * sin(M_PI*x(2))*exp(zi * k10 * x(0));
+            real_t k10 = sqrt(k * k - M_PI * M_PI);
+            E[1] = -zi * k / (real_t) M_PI * sin((real_t) M_PI*x(2))*exp(zi * k10 * x(0));
          }
          else if (dim == 2)
          {
-            E[1] = -zi * k / M_PI * exp(zi * k * x(0));
+            E[1] = -zi * k / (real_t) M_PI * exp(zi * k * x(0));
          }
          break;
       }
@@ -809,7 +834,7 @@ void maxwell_solution(const Vector &x, vector<complex<double>> &E)
 
 void E_exact_Re(const Vector &x, Vector &E)
 {
-   vector<complex<double>> Eval(E.Size());
+   vector<complex<real_t>> Eval(E.Size());
    maxwell_solution(x, Eval);
    for (int i = 0; i < dim; ++i)
    {
@@ -819,7 +844,7 @@ void E_exact_Re(const Vector &x, Vector &E)
 
 void E_exact_Im(const Vector &x, Vector &E)
 {
-   vector<complex<double>> Eval(E.Size());
+   vector<complex<real_t>> Eval(E.Size());
    maxwell_solution(x, Eval);
    for (int i = 0; i < dim; ++i)
    {
@@ -844,7 +869,7 @@ void E_bdr_data_Re(const Vector &x, Vector &E)
    }
    if (!in_pml)
    {
-      vector<complex<double>> Eval(E.Size());
+      vector<complex<real_t>> Eval(E.Size());
       maxwell_solution(x, Eval);
       for (int i = 0; i < dim; ++i)
       {
@@ -871,7 +896,7 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
    }
    if (!in_pml)
    {
-      vector<complex<double>> Eval(E.Size());
+      vector<complex<real_t>> Eval(E.Size());
       maxwell_solution(x, Eval);
       for (int i = 0; i < dim; ++i)
       {
@@ -882,8 +907,8 @@ void E_bdr_data_Im(const Vector &x, Vector &E)
 
 void detJ_JT_J_inv_Re(const Vector &x, PML * pml, Vector & D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det(1.0, 0.0);
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det(1.0, 0.0);
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -893,14 +918,14 @@ void detJ_JT_J_inv_Re(const Vector &x, PML * pml, Vector & D)
 
    for (int i = 0; i < dim; ++i)
    {
-      D(i) = (det / pow(dxs[i], 2)).real();
+      D(i) = (det / pow(dxs[i], real_t(2))).real();
    }
 }
 
 void detJ_JT_J_inv_Im(const Vector &x, PML * pml, Vector & D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -910,14 +935,14 @@ void detJ_JT_J_inv_Im(const Vector &x, PML * pml, Vector & D)
 
    for (int i = 0; i < dim; ++i)
    {
-      D(i) = (det / pow(dxs[i], 2)).imag();
+      D(i) = (det / pow(dxs[i], real_t(2))).imag();
    }
 }
 
 void detJ_JT_J_inv_abs(const Vector &x, PML * pml, Vector & D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -927,14 +952,14 @@ void detJ_JT_J_inv_abs(const Vector &x, PML * pml, Vector & D)
 
    for (int i = 0; i < dim; ++i)
    {
-      D(i) = abs(det / pow(dxs[i], 2));
+      D(i) = abs(det / pow(dxs[i], real_t(2)));
    }
 }
 
 void detJ_inv_JT_J_Re(const Vector &x, PML * pml, Vector & D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det(1.0, 0.0);
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det(1.0, 0.0);
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -945,21 +970,21 @@ void detJ_inv_JT_J_Re(const Vector &x, PML * pml, Vector & D)
    // in the 2D case the coefficient is scalar 1/det(J)
    if (dim == 2)
    {
-      D = (1.0 / det).real();
+      D = (real_t(1) / det).real();
    }
    else
    {
       for (int i = 0; i < dim; ++i)
       {
-         D(i) = (pow(dxs[i], 2) / det).real();
+         D(i) = (pow(dxs[i], real_t(2)) / det).real();
       }
    }
 }
 
 void detJ_inv_JT_J_Im(const Vector &x, PML * pml, Vector & D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -969,21 +994,21 @@ void detJ_inv_JT_J_Im(const Vector &x, PML * pml, Vector & D)
 
    if (dim == 2)
    {
-      D = (1.0 / det).imag();
+      D = (real_t(1) / det).imag();
    }
    else
    {
       for (int i = 0; i < dim; ++i)
       {
-         D(i) = (pow(dxs[i], 2) / det).imag();
+         D(i) = (pow(dxs[i], real_t(2)) / det).imag();
       }
    }
 }
 
 void detJ_inv_JT_J_abs(const Vector &x, PML * pml, Vector & D)
 {
-   vector<complex<double>> dxs(dim);
-   complex<double> det = 1.0;
+   vector<complex<real_t>> dxs(dim);
+   complex<real_t> det = 1.0;
    pml->StretchFunction(x, dxs);
 
    for (int i = 0; i < dim; ++i)
@@ -993,18 +1018,18 @@ void detJ_inv_JT_J_abs(const Vector &x, PML * pml, Vector & D)
 
    if (dim == 2)
    {
-      D = abs(1.0 / det);
+      D = abs(real_t(1) / det);
    }
    else
    {
       for (int i = 0; i < dim; ++i)
       {
-         D(i) = abs(pow(dxs[i], 2) / det);
+         D(i) = abs(pow(dxs[i], real_t(2)) / det);
       }
    }
 }
 
-PML::PML(Mesh *mesh_, Array2D<double> length_)
+PML::PML(Mesh *mesh_, Array2D<real_t> length_)
    : mesh(mesh_), length(length_)
 {
    dim = mesh->Dimension();
@@ -1056,7 +1081,7 @@ void PML::SetAttributes(ParMesh *pmesh)
       for (int iv = 0; iv < nrvert; ++iv)
       {
          int vert_idx = vertices[iv];
-         double *coords = pmesh->GetVertex(vert_idx);
+         real_t *coords = pmesh->GetVertex(vert_idx);
          for (int comp = 0; comp < dim; ++comp)
          {
             if (coords[comp] > comp_dom_bdr(comp, 1) ||
@@ -1077,14 +1102,14 @@ void PML::SetAttributes(ParMesh *pmesh)
 }
 
 void PML::StretchFunction(const Vector &x,
-                          vector<complex<double>> &dxs)
+                          vector<complex<real_t>> &dxs)
 {
-   complex<double> zi = complex<double>(0., 1.);
+   complex<real_t> zi = complex<real_t>(0., 1.);
 
-   double n = 2.0;
-   double c = 5.0;
-   double coeff;
-   double k = omega * sqrt(epsilon * mu);
+   real_t n = 2.0;
+   real_t c = 5.0;
+   real_t coeff;
+   real_t k = omega * sqrt(epsilon * mu);
 
    // Stretch in each direction independently
    for (int i = 0; i < dim; ++i)
@@ -1093,14 +1118,14 @@ void PML::StretchFunction(const Vector &x,
       if (x(i) >= comp_domain_bdr(i, 1))
       {
          coeff = n * c / k / pow(length(i, 1), n);
-         dxs[i] = 1.0 + zi * coeff *
-                  abs(pow(x(i) - comp_domain_bdr(i, 1), n - 1.0));
+         dxs[i] = real_t(1) + zi * coeff *
+                  abs(pow(x(i) - comp_domain_bdr(i, 1), n - real_t(1)));
       }
       if (x(i) <= comp_domain_bdr(i, 0))
       {
          coeff = n * c / k / pow(length(i, 0), n);
-         dxs[i] = 1.0 + zi * coeff *
-                  abs(pow(x(i) - comp_domain_bdr(i, 0), n - 1.0));
+         dxs[i] = real_t(1) + zi * coeff *
+                  abs(pow(x(i) - comp_domain_bdr(i, 0), n - real_t(1)));
       }
    }
 }

examples/ex27.cpp

@@ -63,7 +63,7 @@
 using namespace std;
 using namespace mfem;
 
-static double a_ = 0.2;
+static real_t a_ = 0.2;
 
 // Normal to hole with boundary attribute 4
 void n4Vec(const Vector &x, Vector &n) { n = x; n[0] -= 0.5; n /= -n.Norml2(); }
@@ -73,25 +73,25 @@ Mesh * GenerateSerialMesh(int ref);
 // Compute the average value of alpha*n.Grad(sol) + beta*sol over the boundary
 // attributes marked in bdr_marker. Also computes the L2 norm of
 // alpha*n.Grad(sol) + beta*sol - gamma over the same boundary.
-double IntegrateBC(const GridFunction &sol, const Array<int> &bdr_marker,
-                   double alpha, double beta, double gamma,
-                   double &error);
+real_t IntegrateBC(const GridFunction &sol, const Array<int> &bdr_marker,
+                   real_t alpha, real_t beta, real_t gamma,
+                   real_t &error);
 
 int main(int argc, char *argv[])
 {
    // 1. Parse command-line options.
    int ser_ref_levels = 2;
    int order = 1;
-   double sigma = -1.0;
-   double kappa = -1.0;
+   real_t sigma = -1.0;
+   real_t kappa = -1.0;
    bool h1 = true;
    bool visualization = true;
 
-   double mat_val = 1.0;
-   double dbc_val = 0.0;
-   double nbc_val = 1.0;
-   double rbc_a_val = 1.0; // du/dn + a * u = b
-   double rbc_b_val = 1.0;
+   real_t mat_val = 1.0;
+   real_t dbc_val = 0.0;
+   real_t nbc_val = 1.0;
+   real_t rbc_a_val = 1.0; // du/dn + a * u = b
+   real_t rbc_b_val = 1.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&h1, "-h1", "--continuous", "-dg", "--discontinuous",
@@ -302,7 +302,7 @@ int main(int argc, char *argv[])
    {
       // Integrate the solution on the Dirichlet boundary and compare to the
       // expected value.
-      double error, avg = IntegrateBC(u, dbc_bdr, 0.0, 1.0, dbc_val, error);
+      real_t error, avg = IntegrateBC(u, dbc_bdr, 0.0, 1.0, dbc_val, error);
 
       bool hom_dbc = (dbc_val == 0.0);
       error /=  hom_dbc ? 1.0 : fabs(dbc_val);
@@ -314,7 +314,7 @@ int main(int argc, char *argv[])
    {
       // Integrate n.Grad(u) on the inhomogeneous Neumann boundary and compare
       // to the expected value.
-      double error, avg = IntegrateBC(u, nbc_bdr, 1.0, 0.0, nbc_val, error);
+      real_t error, avg = IntegrateBC(u, nbc_bdr, 1.0, 0.0, nbc_val, error);
 
       bool hom_nbc = (nbc_val == 0.0);
       error /=  hom_nbc ? 1.0 : fabs(nbc_val);
@@ -330,7 +330,7 @@ int main(int argc, char *argv[])
       nbc0_bdr = 0;
       nbc0_bdr[3] = 1;
 
-      double error, avg = IntegrateBC(u, nbc0_bdr, 1.0, 0.0, 0.0, error);
+      real_t error, avg = IntegrateBC(u, nbc0_bdr, 1.0, 0.0, 0.0, error);
 
       bool hom_nbc = true;
       mfem::out << "Average of n.Grad(u) on Gamma_nbc0:\t"
@@ -341,8 +341,8 @@ int main(int argc, char *argv[])
    {
       // Integrate n.Grad(u) + a * u on the Robin boundary and compare to the
       // expected value.
-      double error;
-      double avg = IntegrateBC(u, rbc_bdr, 1.0, rbc_a_val, rbc_b_val, error);
+      real_t error;
+      real_t avg = IntegrateBC(u, rbc_bdr, 1.0, rbc_a_val, rbc_b_val, error);
 
       bool hom_rbc = (rbc_b_val == 0.0);
       error /=  hom_rbc ? 1.0 : fabs(rbc_b_val);
@@ -383,22 +383,22 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-void quad_trans(double u, double v, double &x, double &y, bool log = false)
+void quad_trans(real_t u, real_t v, real_t &x, real_t &y, bool log = false)
 {
-   double a = a_; // Radius of disc
+   real_t a = a_; // Radius of disc
 
-   double d = 4.0 * a * (M_SQRT2 - 2.0 * a) * (1.0 - 2.0 * v);
+   real_t d = 4.0 * a * (M_SQRT2 - 2.0 * a) * (1.0 - 2.0 * v);
 
-   double v0 = (1.0 + M_SQRT2) * (M_SQRT2 * a - 2.0 * v) *
+   real_t v0 = (1.0 + M_SQRT2) * (M_SQRT2 * a - 2.0 * v) *
                ((4.0 - 3 * M_SQRT2) * a +
                 (8.0 * (M_SQRT2 - 1.0) * a - 2.0) * v) / d;
 
-   double r = 2.0 * ((M_SQRT2 - 1.0) * a * a * (1.0 - 4.0 *v) +
+   real_t r = 2.0 * ((M_SQRT2 - 1.0) * a * a * (1.0 - 4.0 *v) +
                      2.0 * (1.0 + M_SQRT2 *
                             (1.0 + 2.0 * (2.0 * a - M_SQRT2 - 1.0) * a)) * v * v
                     ) / d;
 
-   double t = asin(v / r) * u / v;
+   real_t t = asin(v / r) * u / v;
    if (log)
    {
       mfem::out << "u, v, r, v0, t "
@@ -411,7 +411,7 @@ void quad_trans(double u, double v, double &x, double &y, bool log = false)
 
 void trans(const Vector &u, Vector &x)
 {
-   double tol = 1e-4;
+   real_t tol = 1e-4;
 
    if (u[1] > 0.5 - tol || u[1] < -0.5 + tol)
    {
@@ -542,8 +542,8 @@ Mesh * GenerateSerialMesh(int ref)
       vi[0] = o +  3; vi[1] = o +  4; mesh->AddBdrSegment(vi, 3 + i);
    }
 
-   double d[2];
-   double a = a_ / M_SQRT2;
+   real_t d[2];
+   real_t a = a_ / M_SQRT2;
 
    d[0] = -1.0; d[1] = -0.5; mesh->AddVertex(d);
    d[0] = -1.0; d[1] =  0.0; mesh->AddVertex(d);
@@ -636,12 +636,12 @@ Mesh * GenerateSerialMesh(int ref)
    return mesh;
 }
 
-double IntegrateBC(const GridFunction &x, const Array<int> &bdr,
-                   double alpha, double beta, double gamma,
-                   double &error)
+real_t IntegrateBC(const GridFunction &x, const Array<int> &bdr,
+                   real_t alpha, real_t beta, real_t gamma,
+                   real_t &error)
 {
-   double nrm = 0.0;
-   double avg = 0.0;
+   real_t nrm = 0.0;
+   real_t avg = 0.0;
    error = 0.0;
 
    const bool a_is_zero = alpha == 0.0;
@@ -683,8 +683,8 @@ double IntegrateBC(const GridFunction &x, const Array<int> &bdr,
          IntegrationPoint eip;
          FTr->Loc1.Transform(ip, eip);
          FTr->Face->SetIntPoint(&ip);
-         double face_weight = FTr->Face->Weight();
-         double val = 0.0;
+         real_t face_weight = FTr->Face->Weight();
+         real_t val = 0.0;
          if (!a_is_zero)
          {
             FTr->Elem1->SetIntPoint(&eip);

examples/ex27p.cpp

@@ -63,7 +63,7 @@
 using namespace std;
 using namespace mfem;
 
-static double a_ = 0.2;
+static real_t a_ = 0.2;
 
 // Normal to hole with boundary attribute 4
 void n4Vec(const Vector &x, Vector &n) { n = x; n[0] -= 0.5; n /= -n.Norml2(); }
@@ -73,9 +73,9 @@ Mesh * GenerateSerialMesh(int ref);
 // Compute the average value of alpha*n.Grad(sol) + beta*sol over the boundary
 // attributes marked in bdr_marker. Also computes the L2 norm of
 // alpha*n.Grad(sol) + beta*sol - gamma over the same boundary.
-double IntegrateBC(const ParGridFunction &sol, const Array<int> &bdr_marker,
-                   double alpha, double beta, double gamma,
-                   double &error);
+real_t IntegrateBC(const ParGridFunction &sol, const Array<int> &bdr_marker,
+                   real_t alpha, real_t beta, real_t gamma,
+                   real_t &error);
 
 int main(int argc, char *argv[])
 {
@@ -88,16 +88,16 @@ int main(int argc, char *argv[])
    int ser_ref_levels = 2;
    int par_ref_levels = 1;
    int order = 1;
-   double sigma = -1.0;
-   double kappa = -1.0;
+   real_t sigma = -1.0;
+   real_t kappa = -1.0;
    bool h1 = true;
    bool visualization = true;
 
-   double mat_val = 1.0;
-   double dbc_val = 0.0;
-   double nbc_val = 1.0;
-   double rbc_a_val = 1.0; // du/dn + a * u = b
-   double rbc_b_val = 1.0;
+   real_t mat_val = 1.0;
+   real_t dbc_val = 0.0;
+   real_t nbc_val = 1.0;
+   real_t rbc_a_val = 1.0; // du/dn + a * u = b
+   real_t rbc_b_val = 1.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&h1, "-h1", "--continuous", "-dg", "--discontinuous",
@@ -322,7 +322,7 @@ int main(int argc, char *argv[])
    {
       // Integrate the solution on the Dirichlet boundary and compare to the
       // expected value.
-      double error, avg = IntegrateBC(u, dbc_bdr, 0.0, 1.0, dbc_val, error);
+      real_t error, avg = IntegrateBC(u, dbc_bdr, 0.0, 1.0, dbc_val, error);
 
       bool hom_dbc = (dbc_val == 0.0);
       error /=  hom_dbc ? 1.0 : fabs(dbc_val);
@@ -334,7 +334,7 @@ int main(int argc, char *argv[])
    {
       // Integrate n.Grad(u) on the inhomogeneous Neumann boundary and compare
       // to the expected value.
-      double error, avg = IntegrateBC(u, nbc_bdr, 1.0, 0.0, nbc_val, error);
+      real_t error, avg = IntegrateBC(u, nbc_bdr, 1.0, 0.0, nbc_val, error);
 
       bool hom_nbc = (nbc_val == 0.0);
       error /=  hom_nbc ? 1.0 : fabs(nbc_val);
@@ -350,7 +350,7 @@ int main(int argc, char *argv[])
       nbc0_bdr = 0;
       nbc0_bdr[3] = 1;
 
-      double error, avg = IntegrateBC(u, nbc0_bdr, 1.0, 0.0, 0.0, error);
+      real_t error, avg = IntegrateBC(u, nbc0_bdr, 1.0, 0.0, 0.0, error);
 
       bool hom_nbc = true;
       mfem::out << "Average of n.Grad(u) on Gamma_nbc0:\t"
@@ -361,7 +361,7 @@ int main(int argc, char *argv[])
    {
       // Integrate n.Grad(u) + a * u on the Robin boundary and compare to the
       // expected value.
-      double error, avg = IntegrateBC(u, rbc_bdr, 1.0, rbc_a_val, rbc_b_val,
+      real_t error, avg = IntegrateBC(u, rbc_bdr, 1.0, rbc_a_val, rbc_b_val,
                                       error);
 
       bool hom_rbc = (rbc_b_val == 0.0);
@@ -409,22 +409,22 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-void quad_trans(double u, double v, double &x, double &y, bool log = false)
+void quad_trans(real_t u, real_t v, real_t &x, real_t &y, bool log = false)
 {
-   double a = a_; // Radius of disc
+   real_t a = a_; // Radius of disc
 
-   double d = 4.0 * a * (M_SQRT2 - 2.0 * a) * (1.0 - 2.0 * v);
+   real_t d = 4.0 * a * (M_SQRT2 - 2.0 * a) * (1.0 - 2.0 * v);
 
-   double v0 = (1.0 + M_SQRT2) * (M_SQRT2 * a - 2.0 * v) *
+   real_t v0 = (1.0 + M_SQRT2) * (M_SQRT2 * a - 2.0 * v) *
                ((4.0 - 3 * M_SQRT2) * a +
                 (8.0 * (M_SQRT2 - 1.0) * a - 2.0) * v) / d;
 
-   double r = 2.0 * ((M_SQRT2 - 1.0) * a * a * (1.0 - 4.0 *v) +
+   real_t r = 2.0 * ((M_SQRT2 - 1.0) * a * a * (1.0 - 4.0 *v) +
                      2.0 * (1.0 + M_SQRT2 *
                             (1.0 + 2.0 * (2.0 * a - M_SQRT2 - 1.0) * a)) * v * v
                     ) / d;
 
-   double t = asin(v / r) * u / v;
+   real_t t = asin(v / r) * u / v;
    if (log)
    {
       mfem::out << "u, v, r, v0, t "
@@ -437,7 +437,7 @@ void quad_trans(double u, double v, double &x, double &y, bool log = false)
 
 void trans(const Vector &u, Vector &x)
 {
-   double tol = 1e-4;
+   real_t tol = 1e-4;
 
    if (u[1] > 0.5 - tol || u[1] < -0.5 + tol)
    {
@@ -568,8 +568,8 @@ Mesh * GenerateSerialMesh(int ref)
       vi[0] = o +  3; vi[1] = o +  4; mesh->AddBdrSegment(vi, 3 + i);
    }
 
-   double d[2];
-   double a = a_ / M_SQRT2;
+   real_t d[2];
+   real_t a = a_ / M_SQRT2;
 
    d[0] = -1.0; d[1] = -0.5; mesh->AddVertex(d);
    d[0] = -1.0; d[1] =  0.0; mesh->AddVertex(d);
@@ -662,14 +662,14 @@ Mesh * GenerateSerialMesh(int ref)
    return mesh;
 }
 
-double IntegrateBC(const ParGridFunction &x, const Array<int> &bdr,
-                   double alpha, double beta, double gamma,
-                   double &glb_err)
+real_t IntegrateBC(const ParGridFunction &x, const Array<int> &bdr,
+                   real_t alpha, real_t beta, real_t gamma,
+                   real_t &glb_err)
 {
-   double loc_vals[3];
-   double &nrm = loc_vals[0];
-   double &avg = loc_vals[1];
-   double &error = loc_vals[2];
+   real_t loc_vals[3];
+   real_t &nrm = loc_vals[0];
+   real_t &avg = loc_vals[1];
+   real_t &error = loc_vals[2];
 
    nrm = 0.0;
    avg = 0.0;
@@ -714,8 +714,8 @@ double IntegrateBC(const ParGridFunction &x, const Array<int> &bdr,
          IntegrationPoint eip;
          FTr->Loc1.Transform(ip, eip);
          FTr->Face->SetIntPoint(&ip);
-         double face_weight = FTr->Face->Weight();
-         double val = 0.0;
+         real_t face_weight = FTr->Face->Weight();
+         real_t val = 0.0;
          if (!a_is_zero)
          {
             FTr->Elem1->SetIntPoint(&eip);
@@ -741,11 +741,12 @@ double IntegrateBC(const ParGridFunction &x, const Array<int> &bdr,
       }
    }
 
-   double glb_vals[3];
-   MPI_Allreduce(loc_vals, glb_vals, 3, MPI_DOUBLE, MPI_SUM, fes.GetComm());
+   real_t glb_vals[3];
+   MPI_Allreduce(loc_vals, glb_vals, 3, MPITypeMap<real_t>::mpi_type,
+                 MPI_SUM, fes.GetComm());
 
-   double glb_nrm = glb_vals[0];
-   double glb_avg = glb_vals[1];
+   real_t glb_nrm = glb_vals[0];
+   real_t glb_avg = glb_vals[1];
    glb_err = glb_vals[2];
 
    // Normalize by the length of the boundary

examples/ex28.cpp

@@ -35,7 +35,7 @@ using namespace mfem;
 // Return a mesh with a single element with vertices (0, 0), (1, 0), (1, 1),
 // (offset, 1) to demonstrate boundary conditions on a surface that is not
 // axis-aligned.
-Mesh * build_trapezoid_mesh(double offset)
+Mesh * build_trapezoid_mesh(real_t offset)
 {
    MFEM_VERIFY(offset < 0.9, "offset is too large!");
 
@@ -45,7 +45,7 @@ Mesh * build_trapezoid_mesh(double offset)
    Mesh * mesh = new Mesh(dimension, nvt, 1, nbe);
 
    // vertices
-   double vc[dimension];
+   real_t vc[dimension];
    vc[0] = 0.0; vc[1] = 0.0;
    mesh->AddVertex(vc);
    vc[0] = 1.0; vc[1] = 0.0;
@@ -81,7 +81,7 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    int order = 1;
    bool visualization = 1;
-   double offset = 0.3;
+   real_t offset = 0.3;
    bool visit = false;
 
    OptionsParser args(argc, argv);

examples/ex28p.cpp

@@ -38,7 +38,7 @@ using namespace mfem;
 // Return a mesh with a single element with vertices (0, 0), (1, 0), (1, 1),
 // (offset, 1) to demonstrate boundary conditions on a surface that is not
 // axis-aligned.
-Mesh * build_trapezoid_mesh(double offset)
+Mesh * build_trapezoid_mesh(real_t offset)
 {
    MFEM_VERIFY(offset < 0.9, "offset is too large!");
 
@@ -48,7 +48,7 @@ Mesh * build_trapezoid_mesh(double offset)
    Mesh * mesh = new Mesh(dimension, nvt, 1, nbe);
 
    // vertices
-   double vc[dimension];
+   real_t vc[dimension];
    vc[0] = 0.0; vc[1] = 0.0;
    mesh->AddVertex(vc);
    vc[0] = 1.0; vc[1] = 0.0;
@@ -97,9 +97,9 @@ int main(int argc, char *argv[])
    int order = 1;
    bool visualization = 1;
    bool reorder_space = false;
-   double offset = 0.3;
+   real_t offset = 0.3;
    bool visit = false;
-   double penalty = 0.0;
+   real_t penalty = 0.0;
 
    OptionsParser args(argc, argv);
    args.AddOption(&order, "-o", "--order",

examples/ex29.cpp

@@ -34,7 +34,7 @@ void trans(const Vector &x, Vector &r);
 
 void sigmaFunc(const Vector &x, DenseMatrix &s);
 
-double uExact(const Vector &x)
+real_t uExact(const Vector &x)
 {
    return (0.25 * (2.0 + x[0]) - x[2]) * (x[2] + 0.25 * (2.0 + x[0]));
 }
@@ -167,7 +167,7 @@ int main(int argc, char *argv[])
 
    // 13. Compute error in the solution and its flux
    FunctionCoefficient uCoef(uExact);
-   double error = x.ComputeL2Error(uCoef);
+   real_t error = x.ComputeL2Error(uCoef);
 
    cout << "|u - u_h|_2 = " << error << endl;
 
@@ -176,7 +176,7 @@ int main(int argc, char *argv[])
    x.ComputeFlux(*integ, flux); flux *= -1.0;
 
    VectorFunctionCoefficient fluxCoef(3, fluxExact);
-   double flux_err = flux.ComputeL2Error(fluxCoef);
+   real_t flux_err = flux.ComputeL2Error(fluxCoef);
 
    cout << "|f - f_h|_2 = " << flux_err << endl;
 
@@ -304,8 +304,8 @@ void trans(const Vector &x, Vector &r)
 {
    r.SetSize(3);
 
-   double tol = 1e-6;
-   double theta = 0.0;
+   real_t tol = 1e-6;
+   real_t theta = 0.0;
    if (fabs(x[1] + 1.0) < tol)
    {
       theta = 0.25 * M_PI * (x[0] - 2.0);
@@ -337,7 +337,7 @@ void trans(const Vector &x, Vector &r)
 void sigmaFunc(const Vector &x, DenseMatrix &s)
 {
    s.SetSize(3);
-   double a = 17.0 - 2.0 * x[0] * (1.0 + x[0]);
+   real_t a = 17.0 - 2.0 * x[0] * (1.0 + x[0]);
    s(0,0) = 0.5 + x[0] * x[0] * (8.0 / a - 0.5);
    s(0,1) = x[0] * x[1] * (8.0 / a - 0.5);
    s(0,2) = 0.0;

examples/ex29p.cpp

@@ -34,7 +34,7 @@ void trans(const Vector &x, Vector &r);
 
 void sigmaFunc(const Vector &x, DenseMatrix &s);
 
-double uExact(const Vector &x)
+real_t uExact(const Vector &x)
 {
    return (0.25 * (2.0 + x[0]) - x[2]) * (x[2] + 0.25 * (2.0 + x[0]));
 }
@@ -201,7 +201,7 @@ int main(int argc, char *argv[])
 
    // 15. Compute error in the solution and its flux
    FunctionCoefficient uCoef(uExact);
-   double error = x.ComputeL2Error(uCoef);
+   real_t error = x.ComputeL2Error(uCoef);
 
    if (myid == 0) { cout << "|u - u_h|_2 = " << error << endl; }
 
@@ -210,7 +210,7 @@ int main(int argc, char *argv[])
    x.ComputeFlux(*integ, flux); flux *= -1.0;
 
    VectorFunctionCoefficient fluxCoef(3, fluxExact);
-   double flux_err = flux.ComputeL2Error(fluxCoef);
+   real_t flux_err = flux.ComputeL2Error(fluxCoef);
 
    if (myid == 0) { cout << "|f - f_h|_2 = " << flux_err << endl; }
 
@@ -349,8 +349,8 @@ void trans(const Vector &x, Vector &r)
 {
    r.SetSize(3);
 
-   double tol = 1e-6;
-   double theta = 0.0;
+   real_t tol = 1e-6;
+   real_t theta = 0.0;
    if (fabs(x[1] + 1.0) < tol)
    {
       theta = 0.25 * M_PI * (x[0] - 2.0);
@@ -382,7 +382,7 @@ void trans(const Vector &x, Vector &r)
 void sigmaFunc(const Vector &x, DenseMatrix &s)
 {
    s.SetSize(3);
-   double a = 17.0 - 2.0 * x[0] * (1.0 + x[0]);
+   real_t a = 17.0 - 2.0 * x[0] * (1.0 + x[0]);
    s(0,0) = 0.5 + x[0] * x[0] * (8.0 / a - 0.5);
    s(0,1) = x[0] * x[1] * (8.0 / a - 0.5);
    s(0,2) = 0.0;

examples/ex3.cpp

@@ -53,7 +53,7 @@ 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;
+real_t freq = 1.0, kappa;
 int dim;
 
 int main(int argc, char *argv[])
@@ -63,6 +63,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool static_cond = false;
    bool pa = false;
+   bool nc = false;
    const char *device_config = "cpu";
    bool visualization = 1;
 
@@ -77,6 +78,9 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&nc, "-nc", "--non-conforming", "-c",
+                  "--conforming",
+                  "Mark the mesh as nonconforming before partitioning.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -102,6 +106,11 @@ int main(int argc, char *argv[])
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    dim = mesh->Dimension();
    int sdim = mesh->SpaceDimension();
+   if (nc)
+   {
+      // Can set to false to use conformal refinement for simplices.
+      mesh->EnsureNCMesh(true);
+   }
 
    // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the

examples/ex30.cpp

@@ -42,9 +42,9 @@ using namespace std;
 using namespace mfem;
 
 // Piecewise-affine function which is sometimes mesh-conforming
-double affine_function(const Vector &p)
+real_t affine_function(const Vector &p)
 {
-   double x = p(0), y = p(1);
+   real_t x = p(0), y = p(1);
    if (x < 0.0)
    {
       return 1.0 + x + y;
@@ -56,7 +56,7 @@ double affine_function(const Vector &p)
 }
 
 // Piecewise-constant function which is never mesh-conforming
-double jump_function(const Vector &p)
+real_t jump_function(const Vector &p)
 {
    if (p.Normlp(2.0) > 0.4 && p.Normlp(2.0) < 0.6)
    {
@@ -70,17 +70,17 @@ double jump_function(const Vector &p)
 
 // Singular function derived from the Laplacian of the "steep wavefront" problem
 // in [2].
-double singular_function(const Vector &p)
+real_t singular_function(const Vector &p)
 {
-   double x = p(0), y = p(1);
-   double alpha = 1000.0;
-   double xc = 0.75, yc = 0.5;
-   double r0 = 0.7;
-   double r = sqrt(pow(x - xc,2.0) + pow(y - yc,2.0));
-   double num = - ( alpha - pow(alpha,3) * (pow(r,2) - pow(r0,2)) );
-   double denom = pow(r * ( pow(alpha,2) * pow(r0,2) + pow(alpha,2) * pow(r,2) \
+   real_t x = p(0), y = p(1);
+   real_t alpha = 1000.0;
+   real_t xc = 0.75, yc = 0.5;
+   real_t r0 = 0.7;
+   real_t r = sqrt(pow(x - xc,2.0) + pow(y - yc,2.0));
+   real_t num = - ( alpha - pow(alpha,3) * (pow(r,2) - pow(r0,2)) );
+   real_t denom = pow(r * ( pow(alpha,2) * pow(r0,2) + pow(alpha,2) * pow(r,2) \
                             - 2 * pow(alpha,2) * r0 * r + 1.0 ),2);
-   denom = max(denom,1e-8);
+   denom = std::max(denom, (real_t) 1.0e-8);
    return num / denom;
 }
 
@@ -91,9 +91,9 @@ int main(int argc, char *argv[])
    int order = 1;
    int nc_limit = 1;
    int max_elems = 100*1000;
-   double double_max_elems = double(max_elems);
+   real_t double_max_elems = real_t(max_elems);
    bool visualization = true;
-   double osc_threshold = 1e-3;
+   real_t osc_threshold = 1e-3;
    int enriched_order = 5;
 
    OptionsParser args(argc, argv);

examples/ex30p.cpp

@@ -42,9 +42,9 @@ using namespace std;
 using namespace mfem;
 
 // Piecewise-affine function which is sometimes mesh-conforming
-double affine_function(const Vector &p)
+real_t affine_function(const Vector &p)
 {
-   double x = p(0), y = p(1);
+   real_t x = p(0), y = p(1);
    if (x < 0.0)
    {
       return 1.0 + x + y;
@@ -56,7 +56,7 @@ double affine_function(const Vector &p)
 }
 
 // Piecewise-constant function which is never mesh-conforming
-double jump_function(const Vector &p)
+real_t jump_function(const Vector &p)
 {
    if (p.Normlp(2.0) > 0.4 && p.Normlp(2.0) < 0.6)
    {
@@ -70,17 +70,17 @@ double jump_function(const Vector &p)
 
 // Singular function derived from the Laplacian of the "steep wavefront" problem
 // in [2].
-double singular_function(const Vector &p)
+real_t singular_function(const Vector &p)
 {
-   double x = p(0), y = p(1);
-   double alpha = 1000.0;
-   double xc = 0.75, yc = 0.5;
-   double r0 = 0.7;
-   double r = sqrt(pow(x - xc,2.0) + pow(y - yc,2.0));
-   double num = - ( alpha - pow(alpha,3) * (pow(r,2) - pow(r0,2)) );
-   double denom = pow(r * ( pow(alpha,2) * pow(r0,2) + pow(alpha,2) * pow(r,2) \
+   real_t x = p(0), y = p(1);
+   real_t alpha = 1000.0;
+   real_t xc = 0.75, yc = 0.5;
+   real_t r0 = 0.7;
+   real_t r = sqrt(pow(x - xc,2.0) + pow(y - yc,2.0));
+   real_t num = - ( alpha - pow(alpha,3) * (pow(r,2) - pow(r0,2)) );
+   real_t denom = pow(r * ( pow(alpha,2) * pow(r0,2) + pow(alpha,2) * pow(r,2) \
                             - 2 * pow(alpha,2) * r0 * r + 1.0 ),2);
-   denom = max(denom,1e-8);
+   denom = std::max(denom, (real_t) 1.0e-8);
    return num / denom;
 }
 
@@ -97,10 +97,10 @@ int main(int argc, char *argv[])
    int order = 1;
    int nc_limit = 1;
    int max_elems = 1e5;
-   double double_max_elems = double(max_elems);
+   real_t double_max_elems = real_t(max_elems);
    bool visualization = true;
    bool nc_simplices = true;
-   double osc_threshold = 1e-3;
+   real_t osc_threshold = 1e-3;
    int enriched_order = 5;
 
    OptionsParser args(argc, argv);
@@ -199,7 +199,7 @@ int main(int argc, char *argv[])
    coeffrefiner.PreprocessMesh(pmesh);
 
    int globalNE = pmesh.GetGlobalNE();
-   double osc = coeffrefiner.GetOsc();
+   real_t osc = coeffrefiner.GetOsc();
    if (myid == 0)
    {
       mfem::out << "\n";

examples/ex31.cpp

@@ -39,7 +39,7 @@ using namespace mfem;
 void E_exact(const Vector &, Vector &);
 void CurlE_exact(const Vector &, Vector &);
 void f_exact(const Vector &, Vector &);
-double freq = 1.0, kappa;
+real_t freq = 1.0, kappa;
 int dim;
 
 int main(int argc, char *argv[])
@@ -177,7 +177,7 @@ int main(int argc, char *argv[])
 
    // 13. Compute and print the H(Curl) norm of the error.
    {
-      double error = sol.ComputeHCurlError(&E, &CurlE);
+      real_t error = sol.ComputeHCurlError(&E, &CurlE);
       cout << "\n|| E_h - E ||_{H(Curl)} = " << error << '\n' << endl;
    }
 
@@ -376,8 +376,8 @@ void CurlE_exact(const Vector &x, Vector &dE)
 {
    if (dim == 1)
    {
-      double c4 = cos(kappa * x(0) + 0.4 * M_PI);
-      double c9 = cos(kappa * x(0) + 0.9 * M_PI);
+      real_t c4 = cos(kappa * x(0) + 0.4 * M_PI);
+      real_t c9 = cos(kappa * x(0) + 0.9 * M_PI);
 
       dE(0) =  0.0;
       dE(1) = -1.3 * c9;
@@ -386,9 +386,9 @@ void CurlE_exact(const Vector &x, Vector &dE)
    }
    else if (dim == 2)
    {
-      double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
 
       dE(0) =  1.3 * c9;
       dE(1) = -1.3 * c9;
@@ -397,13 +397,13 @@ void CurlE_exact(const Vector &x, Vector &dE)
    }
    else
    {
-      double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
-      double sk = sin(kappa * x(2));
-      double ck = cos(kappa * x(2));
+      real_t s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t sk = sin(kappa * x(2));
+      real_t ck = cos(kappa * x(2));
 
       dE(0) =  1.2 * s4 * sk + 1.3 * M_SQRT1_2 * c9 * ck;
       dE(1) = -1.1 * s0 * sk - 1.3 * M_SQRT1_2 * c9 * ck;
@@ -416,9 +416,9 @@ void f_exact(const Vector &x, Vector &f)
 {
    if (dim == 1)
    {
-      double s0 = sin(kappa * x(0) + 0.0 * M_PI);
-      double s4 = sin(kappa * x(0) + 0.4 * M_PI);
-      double s9 = sin(kappa * x(0) + 0.9 * M_PI);
+      real_t s0 = sin(kappa * x(0) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * x(0) + 0.4 * M_PI);
+      real_t s9 = sin(kappa * x(0) + 0.9 * M_PI);
 
       f(0) = 2.2 * s0 + 1.2 * M_SQRT1_2 * s4;
       f(1) = 1.2 * (2.0 + kappa * kappa) * s4 +
@@ -427,9 +427,9 @@ void f_exact(const Vector &x, Vector &f)
    }
    else if (dim == 2)
    {
-      double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
 
       f(0) = 0.55 * (4.0 + kappa * kappa) * s0 +
              0.6 * (M_SQRT2 - kappa * kappa) * s4;
@@ -440,14 +440,14 @@ void f_exact(const Vector &x, Vector &f)
    }
    else
    {
-      double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
-      double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
-      double sk = sin(kappa * x(2));
-      double ck = cos(kappa * x(2));
+      real_t s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t sk = sin(kappa * x(2));
+      real_t ck = cos(kappa * x(2));
 
       f(0) = 0.55 * (4.0 + 3.0 * kappa * kappa) * s0 * ck +
              0.6 * (M_SQRT2 - kappa * kappa) * s4 * ck -

examples/ex31p.cpp

@@ -39,7 +39,7 @@ using namespace mfem;
 void E_exact(const Vector &, Vector &);
 void CurlE_exact(const Vector &, Vector &);
 void f_exact(const Vector &, Vector &);
-double freq = 1.0, kappa;
+real_t freq = 1.0, kappa;
 int dim;
 
 int main(int argc, char *argv[])
@@ -224,7 +224,7 @@ int main(int argc, char *argv[])
 
    // 14. Compute and print the H(Curl) norm of the error.
    {
-      double error = sol.ComputeHCurlError(&E, &CurlE);
+      real_t error = sol.ComputeHCurlError(&E, &CurlE);
       if (Mpi::Root())
       {
          cout << "\n|| E_h - E ||_{H(Curl)} = " << error << '\n' << endl;
@@ -442,8 +442,8 @@ void CurlE_exact(const Vector &x, Vector &dE)
 {
    if (dim == 1)
    {
-      double c4 = cos(kappa * x(0) + 0.4 * M_PI);
-      double c9 = cos(kappa * x(0) + 0.9 * M_PI);
+      real_t c4 = cos(kappa * x(0) + 0.4 * M_PI);
+      real_t c9 = cos(kappa * x(0) + 0.9 * M_PI);
 
       dE(0) =  0.0;
       dE(1) = -1.3 * c9;
@@ -452,9 +452,9 @@ void CurlE_exact(const Vector &x, Vector &dE)
    }
    else if (dim == 2)
    {
-      double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
 
       dE(0) =  1.3 * c9;
       dE(1) = -1.3 * c9;
@@ -463,13 +463,13 @@ void CurlE_exact(const Vector &x, Vector &dE)
    }
    else
    {
-      double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
-      double sk = sin(kappa * x(2));
-      double ck = cos(kappa * x(2));
+      real_t s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t sk = sin(kappa * x(2));
+      real_t ck = cos(kappa * x(2));
 
       dE(0) =  1.2 * s4 * sk + 1.3 * M_SQRT1_2 * c9 * ck;
       dE(1) = -1.1 * s0 * sk - 1.3 * M_SQRT1_2 * c9 * ck;
@@ -482,9 +482,9 @@ void f_exact(const Vector &x, Vector &f)
 {
    if (dim == 1)
    {
-      double s0 = sin(kappa * x(0) + 0.0 * M_PI);
-      double s4 = sin(kappa * x(0) + 0.4 * M_PI);
-      double s9 = sin(kappa * x(0) + 0.9 * M_PI);
+      real_t s0 = sin(kappa * x(0) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * x(0) + 0.4 * M_PI);
+      real_t s9 = sin(kappa * x(0) + 0.9 * M_PI);
 
       f(0) = 2.2 * s0 + 1.2 * M_SQRT1_2 * s4;
       f(1) = 1.2 * (2.0 + kappa * kappa) * s4 +
@@ -493,9 +493,9 @@ void f_exact(const Vector &x, Vector &f)
    }
    else if (dim == 2)
    {
-      double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
 
       f(0) = 0.55 * (4.0 + kappa * kappa) * s0 +
              0.6 * (M_SQRT2 - kappa * kappa) * s4;
@@ -506,14 +506,14 @@ void f_exact(const Vector &x, Vector &f)
    }
    else
    {
-      double s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
-      double s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
-      double s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
-      double c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
-      double sk = sin(kappa * x(2));
-      double ck = cos(kappa * x(2));
+      real_t s0 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t c0 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.0 * M_PI);
+      real_t s4 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t c4 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.4 * M_PI);
+      real_t s9 = sin(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t c9 = cos(kappa * M_SQRT1_2 * (x(0) + x(1)) + 0.9 * M_PI);
+      real_t sk = sin(kappa * x(2));
+      real_t ck = cos(kappa * x(2));
 
       f(0) = 0.55 * (4.0 + 3.0 * kappa * kappa) * s0 * ck +
              0.6 * (M_SQRT2 - kappa * kappa) * s4 * ck -

examples/ex32p.cpp

@@ -35,8 +35,8 @@
 using namespace std;
 using namespace mfem;
 
-double GetVectorMax(int vdim, const ParGridFunction &x);
-double GetScalarMax(const ParGridFunction &x);
+real_t GetVectorMax(int vdim, const ParGridFunction &x);
+real_t GetScalarMax(const ParGridFunction &x);
 
 int main(int argc, char *argv[])
 {
@@ -140,7 +140,7 @@ int main(int argc, char *argv[])
    //    extract the corresponding parallel matrices A and M.
    HypreParMatrix *A = NULL;
    HypreParMatrix *M = NULL;
-   double shift = 0.0;
+   real_t shift = 0.0;
    {
       DenseMatrix epsilonMat(3);
       epsilonMat(0,0) = 2.0; epsilonMat(1,1) = 2.0; epsilonMat(2,2) = 2.0;
@@ -178,7 +178,7 @@ int main(int argc, char *argv[])
       m.AddDomainIntegrator(new VectorFEMassIntegrator(epsilon));
       m.Assemble();
       // shift the eigenvalue corresponding to eliminated dofs to a large value
-      m.EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+      m.EliminateEssentialBCDiag(ess_bdr, numeric_limits<real_t>::min());
       m.Finalize();
 
       A = a.ParallelAssemble();
@@ -204,7 +204,7 @@ int main(int argc, char *argv[])
    // 9. Compute the eigenmodes and extract the array of eigenvalues. Define
    //    parallel grid functions to represent each of the eigenmodes returned by
    //    the solver and their derivatives.
-   Array<double> eigenvalues;
+   Array<real_t> eigenvalues;
    ame->Solve();
    ame->GetEigenvalues(eigenvalues);
    ParGridFunction x(&fespace_nd);
@@ -308,10 +308,10 @@ int main(int argc, char *argv[])
                yComp.ProjectCoefficient(yCoef);
                zComp.ProjectCoefficient(zCoef);
 
-               double max_x = GetScalarMax(xComp);
-               double max_y = GetScalarMax(yComp);
-               double max_z = GetScalarMax(zComp);
-               double max_r = std::max(max_x, std::max(max_y, max_z));
+               real_t max_x = GetScalarMax(xComp);
+               real_t max_y = GetScalarMax(yComp);
+               real_t max_z = GetScalarMax(zComp);
+               real_t max_r = std::max(max_x, std::max(max_y, max_z));
 
                ostringstream x_cmd;
                x_cmd << " window_title 'Eigenmode " << i+1 << '/' << nev
@@ -368,7 +368,7 @@ int main(int argc, char *argv[])
                dyComp.ProjectCoefficient(dyCoef);
                dzComp.ProjectCoefficient(dzCoef);
 
-               double min_d = max_r / (bbMax[0] - bbMin[0]);
+               real_t min_d = max_r / (bbMax[0] - bbMin[0]);
 
                max_y = GetScalarMax(dyComp);
                max_z = GetScalarMax(dzComp);
@@ -480,9 +480,9 @@ int main(int argc, char *argv[])
                xyComp.ProjectCoefficient(xyCoef);
                zComp.ProjectCoefficient(zCoef);
 
-               double max_v = GetVectorMax(2, xyComp);
-               double max_s = GetScalarMax(zComp);
-               double max_r = std::max(max_v, max_s);
+               real_t max_v = GetVectorMax(2, xyComp);
+               real_t max_s = GetScalarMax(zComp);
+               real_t max_r = std::max(max_v, max_s);
 
                ostringstream xy_cmd;
                xy_cmd << " window_title 'Eigenmode " << i+1 << '/' << nev
@@ -523,7 +523,7 @@ int main(int argc, char *argv[])
                dxyComp.ProjectCoefficient(dxyCoef);
                dzComp.ProjectCoefficient(dzCoef);
 
-               double min_d = max_r / std::min(bbMax[0] - bbMin[0],
+               real_t min_d = max_r / std::min(bbMax[0] - bbMin[0],
                                                bbMax[1] - bbMin[1]);
 
                max_v = GetVectorMax(2, dxyComp);
@@ -649,17 +649,17 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double GetVectorMax(int vdim, const ParGridFunction &x)
+real_t GetVectorMax(int vdim, const ParGridFunction &x)
 {
    Vector zeroVec(vdim); zeroVec = 0.0;
    VectorConstantCoefficient zero(zeroVec);
-   double nrm = x.ComputeMaxError(zero);
+   real_t nrm = x.ComputeMaxError(zero);
    return nrm;
 }
 
-double GetScalarMax(const ParGridFunction &x)
+real_t GetScalarMax(const ParGridFunction &x)
 {
    ConstantCoefficient zero(0.0);
-   double nrm = x.ComputeMaxError(zero);
+   real_t nrm = x.ComputeMaxError(zero);
    return nrm;
 }

examples/ex33.cpp

@@ -90,7 +90,7 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    int num_refs = 3;
-   double alpha = 0.5;
+   real_t alpha = 0.5;
    bool visualization = true;
    bool verification = false;
 
@@ -118,13 +118,17 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
-   Array<double> coeffs, poles;
+#ifdef MFEM_USE_SINGLE
+   MFEM_ABORT("This example is not supported in single precision.");
+#endif
+
+   Array<real_t> coeffs, poles;
    int progress_steps = 1;
 
    // 2. Compute the rational expansion coefficients that define the
    //    integer-order PDEs.
    const int power_of_laplace = (int)floor(alpha);
-   double exponent_to_approximate = alpha - power_of_laplace;
+   real_t exponent_to_approximate = alpha - power_of_laplace;
    bool integer_order = false;
    // Check if alpha is an integer or not.
    if (abs(exponent_to_approximate) > 1e-12)
@@ -135,7 +139,7 @@ int main(int argc, char *argv[])
       ComputePartialFractionApproximation(exponent_to_approximate, coeffs,
                                           poles);
 
-      // If the example is build without LAPACK, the exponent_to_approximate
+      // If the example is built without LAPACK, the exponent_to_approximate
       // might be modified by the function call above.
       alpha = exponent_to_approximate + power_of_laplace;
    }
@@ -173,7 +177,7 @@ int main(int argc, char *argv[])
    // 7. Define diffusion coefficient, load, and solution GridFunction.
    auto func = [&alpha](const Vector &x)
    {
-      double val = 1.0;
+      real_t val = 1.0;
       for (int i=0; i<x.Size(); i++)
       {
          val *= sin(M_PI*x(i));
@@ -364,7 +368,7 @@ int main(int argc, char *argv[])
    {
       auto solution = [] (const Vector &x)
       {
-         double val = 1.0;
+         real_t val = 1.0;
          for (int i=0; i<x.Size(); i++)
          {
             val *= sin(M_PI*x(i));
@@ -372,7 +376,7 @@ int main(int argc, char *argv[])
          return val;
       };
       FunctionCoefficient sol(solution);
-      double l2_error = u.ComputeL2Error(sol);
+      real_t l2_error = u.ComputeL2Error(sol);
 
       string analytic_solution,expected_mesh;
       switch (dim)

examples/ex33.hpp

@@ -50,8 +50,8 @@ using namespace mfem;
 
     See pg. A1501 of Nakatsukasa et al. [1]. */
 void RationalApproximation_AAA(const Vector &val, const Vector &pt,
-                               Array<double> &z, Array<double> &f, Vector &w,
-                               double tol, int max_order)
+                               Array<real_t> &z, Array<real_t> &f, Vector &w,
+                               real_t tol, int max_order)
 {
 
    // number of sample points
@@ -67,11 +67,11 @@ void RationalApproximation_AAA(const Vector &val, const Vector &pt,
    DenseMatrix C, Ctemp, A, Am;
    // auxiliary arrays and vectors
    Vector f_vec;
-   Array<double> c_i;
+   Array<real_t> c_i;
 
    // mean of the value vector
    Vector R(val.Size());
-   double mean_val = val.Sum()/size;
+   real_t mean_val = val.Sum()/size;
 
    for (int i = 0; i<R.Size(); i++) { R(i) = mean_val; }
 
@@ -79,10 +79,10 @@ void RationalApproximation_AAA(const Vector &val, const Vector &pt,
    {
       // select next support point
       int idx = 0;
-      double tmp_max = 0;
+      real_t tmp_max = 0;
       for (int j = 0; j < size; j++)
       {
-         double tmp = abs(val(j)-R(j));
+         real_t tmp = abs(val(j)-R(j));
          if (tmp > tmp_max)
          {
             tmp_max = tmp;
@@ -98,7 +98,7 @@ void RationalApproximation_AAA(const Vector &val, const Vector &pt,
       J.DeleteFirst(idx);
 
       // next column in Cauchy matrix
-      Array<double> C_tmp(size);
+      Array<real_t> C_tmp(size);
       for (int j = 0; j < size; j++)
       {
          C_tmp[j] = 1.0/(pt(j)-pt(idx));
@@ -173,7 +173,7 @@ void RationalApproximation_AAA(const Vector &val, const Vector &pt,
 
     See pg. A1501 of Nakatsukasa et al. [1]. */
 void ComputePolesAndZeros(const Vector &z, const Vector &f, const Vector &w,
-                          Array<double> & poles, Array<double> & zeros, double &scale)
+                          Array<real_t> & poles, Array<real_t> & zeros, real_t &scale)
 {
    // Initialization
    poles.SetSize(0);
@@ -242,8 +242,8 @@ void ComputePolesAndZeros(const Vector &z, const Vector &f, const Vector &w,
     @param[in]  zeros   Array of zeros
     @param[in]  scale   Scaling constant
     @param[out] coeffs  Coefficients c_i */
-void PartialFractionExpansion(double scale, Array<double> & poles,
-                              Array<double> & zeros, Array<double> & coeffs)
+void PartialFractionExpansion(real_t scale, Array<real_t> & poles,
+                              Array<real_t> & zeros, Array<real_t> & coeffs)
 {
    int psize = poles.Size();
    int zsize = zeros.Size();
@@ -259,13 +259,13 @@ void PartialFractionExpansion(double scale, Array<double> & poles,
 
    for (int i=0; i<psize; i++)
    {
-      double tmp_numer=1.0;
+      real_t tmp_numer=1.0;
       for (int j=0; j<zsize; j++)
       {
          tmp_numer *= poles[i]-zeros[j];
       }
 
-      double tmp_denom=1.0;
+      real_t tmp_denom=1.0;
       for (int k=0; k<psize; k++)
       {
          if (k != i) { tmp_denom *= poles[i]-poles[k]; }
@@ -292,10 +292,10 @@ void PartialFractionExpansion(double scale, Array<double> & poles,
            @a alpha != 0.99, then @a alpha = 0.5 is used by default.
 
    See pg. A1501 of Nakatsukasa et al. [1]. */
-void ComputePartialFractionApproximation(double & alpha,
-                                         Array<double> & coeffs, Array<double> & poles,
-                                         double lmax = 1000.,
-                                         double tol=1e-10, int npoints = 1000,
+void ComputePartialFractionApproximation(real_t & alpha,
+                                         Array<real_t> & coeffs, Array<real_t> & poles,
+                                         real_t lmax = 1000.,
+                                         real_t tol=1e-10, int npoints = 1000,
                                          int max_order = 100)
 {
    MFEM_VERIFY(alpha < 1., "alpha must be less than 1");
@@ -320,26 +320,26 @@ void ComputePartialFractionApproximation(double & alpha,
             << "\nThe default is alpha = 0.5.\n" << string(80, '=') << "\n"
             << endl;
    }
-   const double eps = std::numeric_limits<double>::epsilon();
+   const real_t eps = std::numeric_limits<real_t>::epsilon();
 
    if (abs(alpha - 0.33) < eps)
    {
-      coeffs = Array<double> ({1.821898e+03, 9.101221e+01, 2.650611e+01,
+      coeffs = Array<real_t> ({1.821898e+03, 9.101221e+01, 2.650611e+01,
                                1.174937e+01, 6.140444e+00, 3.441713e+00,
                                1.985735e+00, 1.162634e+00, 6.891560e-01,
                                4.111574e-01, 2.298736e-01});
-      poles = Array<double> ({-4.155583e+04, -2.956285e+03, -8.331715e+02,
+      poles = Array<real_t> ({-4.155583e+04, -2.956285e+03, -8.331715e+02,
                               -3.139332e+02, -1.303448e+02, -5.563385e+01,
                               -2.356255e+01, -9.595516e+00, -3.552160e+00,
                               -1.032136e+00, -1.241480e-01});
    }
    else if (abs(alpha - 0.99) < eps)
    {
-      coeffs = Array<double>({2.919591e-02, 1.419750e-02, 1.065798e-02,
+      coeffs = Array<real_t>({2.919591e-02, 1.419750e-02, 1.065798e-02,
                               9.395094e-03, 8.915329e-03, 8.822991e-03,
                               9.058247e-03, 9.814521e-03, 1.180396e-02,
                               1.834554e-02, 9.840482e-01});
-      poles = Array<double> ({-1.069683e+04, -1.769370e+03, -5.718374e+02,
+      poles = Array<real_t> ({-1.069683e+04, -1.769370e+03, -5.718374e+02,
                               -2.242095e+02, -9.419132e+01, -4.031012e+01,
                               -1.701525e+01, -6.810088e+00, -2.382810e+00,
                               -5.700059e-01, -1.384324e-03});
@@ -350,11 +350,11 @@ void ComputePartialFractionApproximation(double & alpha,
       {
          alpha = 0.5;
       }
-      coeffs = Array<double>({2.290262e+02, 2.641819e+01, 1.005566e+01,
+      coeffs = Array<real_t>({2.290262e+02, 2.641819e+01, 1.005566e+01,
                               5.390411e+00, 3.340725e+00, 2.211205e+00,
                               1.508883e+00, 1.049474e+00, 7.462709e-01,
                               5.482686e-01, 4.232510e-01, 3.578967e-01});
-      poles = Array<double>({-3.168211e+04, -3.236077e+03, -9.868287e+02,
+      poles = Array<real_t>({-3.168211e+04, -3.236077e+03, -9.868287e+02,
                              -3.945597e+02, -1.738889e+02, -7.925178e+01,
                              -3.624992e+01, -1.629196e+01, -6.982956e+00,
                              -2.679984e+00, -7.782607e-01, -7.649166e-02});
@@ -372,15 +372,15 @@ void ComputePartialFractionApproximation(double & alpha,
 
    Vector x(npoints);
    Vector val(npoints);
-   double dx = lmax / (double)(npoints-1);
+   real_t dx = lmax / (real_t)(npoints-1);
    for (int i = 0; i<npoints; i++)
    {
-      x(i) = dx * (double)i;
+      x(i) = dx * (real_t)i;
       val(i) = pow(x(i),1.-alpha);
    }
 
    // Apply triple-A algorithm to f(x) = x^{1-a}
-   Array<double> z, f;
+   Array<real_t> z, f;
    Vector w;
    RationalApproximation_AAA(val,x,z,f,w,tol,max_order);
 
@@ -389,8 +389,8 @@ void ComputePartialFractionApproximation(double & alpha,
    vecf.SetDataAndSize(f.GetData(), f.Size());
 
    // Compute poles and zeros for RA of f(x) = x^{1-a}
-   double scale;
-   Array<double> zeros;
+   real_t scale;
+   Array<real_t> zeros;
    ComputePolesAndZeros(vecz, vecf, w, poles, zeros, scale);
 
    // Remove the zero at x=0, thus, delivering a RA for f(x) = x^{-a}

examples/ex33p.cpp

@@ -96,7 +96,7 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    int num_refs = 3;
-   double alpha = 0.5;
+   real_t alpha = 0.5;
    bool visualization = true;
    bool verification = false;
 
@@ -127,13 +127,17 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   Array<double> coeffs, poles;
+#ifdef MFEM_USE_SINGLE
+   MFEM_ABORT("This example is not supported in single precision.");
+#endif
+
+   Array<real_t> coeffs, poles;
    int progress_steps = 1;
 
    // 2. Compute the rational expansion coefficients that define the
    //    integer-order PDEs.
    const int power_of_laplace = floor(alpha);
-   double exponent_to_approximate = alpha - power_of_laplace;
+   real_t exponent_to_approximate = alpha - power_of_laplace;
    bool integer_order = false;
    // Check if alpha is an integer or not.
    if (abs(exponent_to_approximate) > 1e-12)
@@ -193,7 +197,7 @@ int main(int argc, char *argv[])
    // 7. Define diffusion coefficient, load, and solution GridFunction.
    auto func = [&alpha](const Vector &x)
    {
-      double val = 1.0;
+      real_t val = 1.0;
       for (int i=0; i<x.Size(); i++)
       {
          val *= sin(M_PI*x(i));
@@ -398,7 +402,7 @@ int main(int argc, char *argv[])
    {
       auto solution = [] (const Vector &x)
       {
-         double val = 1.0;
+         real_t val = 1.0;
          for (int i=0; i<x.Size(); i++)
          {
             val *= sin(M_PI*x(i));
@@ -406,7 +410,7 @@ int main(int argc, char *argv[])
          return val;
       };
       FunctionCoefficient sol(solution);
-      double l2_error = u.ComputeL2Error(sol);
+      real_t l2_error = u.ComputeL2Error(sol);
 
       if (Mpi::Root())
       {

examples/ex34.cpp

@@ -69,7 +69,7 @@ int main(int argc, char *argv[])
    Array<int> jn_zero_attr;
    int ref_levels = 1;
    int order = 1;
-   double delta_const = 1e-6;
+   real_t delta_const = 1e-6;
    bool mixed = true;
    bool static_cond = false;
    const char *device_config = "cpu";

examples/ex34p.cpp

@@ -73,7 +73,7 @@ int main(int argc, char *argv[])
    int ser_ref_levels = 1;
    int par_ref_levels = 1;
    int order = 1;
-   double delta_const = 1e-6;
+   real_t delta_const = 1e-6;
    bool mixed = true;
    bool static_cond = false;
    bool pa = false;

examples/ex35p.cpp

@@ -55,9 +55,9 @@
 using namespace std;
 using namespace mfem;
 
-static double mu_ = 1.0;
-static double epsilon_ = 1.0;
-static double sigma_ = 2.0;
+static real_t mu_ = 1.0;
+static real_t epsilon_ = 1.0;
+static real_t sigma_ = 2.0;
 
 void SetPortBC(int prob, int dim, int mode, ParGridFunction &port_bc);
 
@@ -77,9 +77,9 @@ int main(int argc, char *argv[])
    Array<int> port_bc_attr;
    int prob = 0;
    int mode = 1;
-   double freq = -1.0;
-   double omega = 2.0 * M_PI;
-   double a_coef = 0.0;
+   real_t freq = -1.0;
+   real_t omega = 2.0 * M_PI;
+   real_t a_coef = 0.0;
    bool herm_conv = true;
    bool slu_solver  = false;
    bool visualization = 1;
@@ -587,7 +587,7 @@ int main(int argc, char *argv[])
       int i = 0;
       while (sol_sock)
       {
-         double t = (double)(i % num_frames) / num_frames;
+         real_t t = (real_t)(i % num_frames) / num_frames;
          ostringstream oss;
          oss << "Harmonic Solution (t = " << t << " T)";
 
@@ -637,7 +637,7 @@ void ScalarWaveGuide(int mode, ParGridFunction &x)
    m.AddDomainIntegrator(new MassIntegrator);
    m.Assemble();
    // shift the eigenvalue corresponding to eliminated dofs to a large value
-   m.EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+   m.EliminateEssentialBCDiag(ess_bdr, numeric_limits<real_t>::min());
    m.Finalize();
 
    HypreParMatrix *A = a.ParallelAssemble();
@@ -694,7 +694,7 @@ void VectorWaveGuide(int mode, ParGridFunction &x)
    m.AddDomainIntegrator(new VectorFEMassIntegrator);
    m.Assemble();
    // shift the eigenvalue corresponding to eliminated dofs to a large value
-   m.EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+   m.EliminateEssentialBCDiag(ess_bdr, numeric_limits<real_t>::min());
    m.Finalize();
 
    HypreParMatrix *A = a.ParallelAssemble();

examples/ex36.cpp

@@ -37,8 +37,8 @@
 using namespace std;
 using namespace mfem;
 
-double spherical_obstacle(const Vector &pt);
-double exact_solution_obstacle(const Vector &pt);
+real_t spherical_obstacle(const Vector &pt);
+real_t exact_solution_obstacle(const Vector &pt);
 void exact_solution_gradient_obstacle(const Vector &pt, Vector &grad);
 
 class LogarithmGridFunctionCoefficient : public Coefficient
@@ -46,14 +46,14 @@ class LogarithmGridFunctionCoefficient : public Coefficient
 protected:
    GridFunction *u; // grid function
    Coefficient *obstacle;
-   double min_val;
+   real_t min_val;
 
 public:
    LogarithmGridFunctionCoefficient(GridFunction &u_, Coefficient &obst_,
-                                    double min_val_=-36)
+                                    real_t min_val_=-36)
       : u(&u_), obstacle(&obst_), min_val(min_val_) { }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 class ExponentialGridFunctionCoefficient : public Coefficient
@@ -61,15 +61,15 @@ class ExponentialGridFunctionCoefficient : public Coefficient
 protected:
    GridFunction *u;
    Coefficient *obstacle;
-   double min_val;
-   double max_val;
+   real_t min_val;
+   real_t max_val;
 
 public:
    ExponentialGridFunctionCoefficient(GridFunction &u_, Coefficient &obst_,
-                                      double min_val_=0.0, double max_val_=1e6)
+                                      real_t min_val_=0.0, real_t max_val_=1e6)
       : u(&u_), obstacle(&obst_), min_val(min_val_), max_val(max_val_) { }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 int main(int argc, char *argv[])
@@ -78,8 +78,8 @@ int main(int argc, char *argv[])
    int order = 1;
    int max_it = 10;
    int ref_levels = 3;
-   double alpha = 1.0;
-   double tol = 1e-5;
+   real_t alpha = 1.0;
+   real_t tol = 1e-5;
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -124,7 +124,7 @@ int main(int argc, char *argv[])
 
    // 3C. Rescale the domain to a unit circle (radius = 1).
    GridFunction *nodes = mesh.GetNodes();
-   double scale = 2*sqrt(2);
+   real_t scale = 2*sqrt(2);
    *nodes /= scale;
 
    // 4. Define the necessary finite element spaces on the mesh.
@@ -159,8 +159,8 @@ int main(int argc, char *argv[])
    // 6. Define an initial guess for the solution.
    auto IC_func = [](const Vector &x)
    {
-      double r0 = 1.0;
-      double rr = 0.0;
+      real_t r0 = 1.0;
+      real_t rr = 0.0;
       for (int i=0; i<x.Size(); i++)
       {
          rr += x(i)*x(i);
@@ -211,7 +211,7 @@ int main(int argc, char *argv[])
    // 10. Iterate
    int k;
    int total_iterations = 0;
-   double increment_u = 0.1;
+   real_t increment_u = 0.1;
    for (k = 0; k < max_it; k++)
    {
       GridFunction u_tmp(&H1fes);
@@ -300,10 +300,10 @@ int main(int argc, char *argv[])
          delta_psi_gf.MakeRef(&L2fes, x.GetBlock(1), 0);
 
          u_tmp -= u_gf;
-         double Newton_update_size = u_tmp.ComputeL2Error(zero);
+         real_t Newton_update_size = u_tmp.ComputeL2Error(zero);
          u_tmp = u_gf;
 
-         double gamma = 1.0;
+         real_t gamma = 1.0;
          delta_psi_gf *= gamma;
          psi_gf += delta_psi_gf;
 
@@ -337,7 +337,7 @@ int main(int argc, char *argv[])
          break;
       }
 
-      double H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
+      real_t H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
       mfem::out << "H1-error  (|| u - uₕᵏ||)       = " << H1_error << endl;
 
    }
@@ -362,13 +362,13 @@ int main(int argc, char *argv[])
    }
 
    {
-      double L2_error = u_gf.ComputeL2Error(exact_coef);
-      double H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
+      real_t L2_error = u_gf.ComputeL2Error(exact_coef);
+      real_t H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
 
       ExponentialGridFunctionCoefficient u_alt_cf(psi_gf,obstacle);
       GridFunction u_alt_gf(&L2fes);
       u_alt_gf.ProjectCoefficient(u_alt_cf);
-      double L2_error_alt = u_alt_gf.ComputeL2Error(exact_coef);
+      real_t L2_error_alt = u_alt_gf.ComputeL2Error(exact_coef);
 
       mfem::out << "\n Final L2-error (|| u - uₕ||)          = " << L2_error <<
                 endl;
@@ -380,35 +380,35 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double LogarithmGridFunctionCoefficient::Eval(ElementTransformation &T,
+real_t LogarithmGridFunctionCoefficient::Eval(ElementTransformation &T,
                                               const IntegrationPoint &ip)
 {
    MFEM_ASSERT(u != NULL, "grid function is not set");
 
-   double val = u->GetValue(T, ip) - obstacle->Eval(T, ip);
+   real_t val = u->GetValue(T, ip) - obstacle->Eval(T, ip);
    return max(min_val, log(val));
 }
 
-double ExponentialGridFunctionCoefficient::Eval(ElementTransformation &T,
+real_t ExponentialGridFunctionCoefficient::Eval(ElementTransformation &T,
                                                 const IntegrationPoint &ip)
 {
    MFEM_ASSERT(u != NULL, "grid function is not set");
 
-   double val = u->GetValue(T, ip);
+   real_t val = u->GetValue(T, ip);
    return min(max_val, max(min_val, exp(val) + obstacle->Eval(T, ip)));
 }
 
-double spherical_obstacle(const Vector &pt)
+real_t spherical_obstacle(const Vector &pt)
 {
-   double x = pt(0), y = pt(1);
-   double r = sqrt(x*x + y*y);
-   double r0 = 0.5;
-   double beta = 0.9;
+   real_t x = pt(0), y = pt(1);
+   real_t r = sqrt(x*x + y*y);
+   real_t r0 = 0.5;
+   real_t beta = 0.9;
 
-   double b = r0*beta;
-   double tmp = sqrt(r0*r0 - b*b);
-   double B = tmp + b*b/tmp;
-   double C = -b/tmp;
+   real_t b = r0*beta;
+   real_t tmp = sqrt(r0*r0 - b*b);
+   real_t B = tmp + b*b/tmp;
+   real_t C = -b/tmp;
 
    if (r > b)
    {
@@ -420,13 +420,13 @@ double spherical_obstacle(const Vector &pt)
    }
 }
 
-double exact_solution_obstacle(const Vector &pt)
+real_t exact_solution_obstacle(const Vector &pt)
 {
-   double x = pt(0), y = pt(1);
-   double r = sqrt(x*x + y*y);
-   double r0 = 0.5;
-   double a =  0.348982574111686;
-   double A = -0.340129705945858;
+   real_t x = pt(0), y = pt(1);
+   real_t r = sqrt(x*x + y*y);
+   real_t r0 = 0.5;
+   real_t a =  0.348982574111686;
+   real_t A = -0.340129705945858;
 
    if (r > a)
    {
@@ -440,11 +440,11 @@ double exact_solution_obstacle(const Vector &pt)
 
 void exact_solution_gradient_obstacle(const Vector &pt, Vector &grad)
 {
-   double x = pt(0), y = pt(1);
-   double r = sqrt(x*x + y*y);
-   double r0 = 0.5;
-   double a =  0.348982574111686;
-   double A = -0.340129705945858;
+   real_t x = pt(0), y = pt(1);
+   real_t r = sqrt(x*x + y*y);
+   real_t r0 = 0.5;
+   real_t a =  0.348982574111686;
+   real_t A = -0.340129705945858;
 
    if (r > a)
    {

examples/ex36p.cpp

@@ -37,8 +37,8 @@
 using namespace std;
 using namespace mfem;
 
-double spherical_obstacle(const Vector &pt);
-double exact_solution_obstacle(const Vector &pt);
+real_t spherical_obstacle(const Vector &pt);
+real_t exact_solution_obstacle(const Vector &pt);
 void exact_solution_gradient_obstacle(const Vector &pt, Vector &grad);
 
 class LogarithmGridFunctionCoefficient : public Coefficient
@@ -46,14 +46,14 @@ class LogarithmGridFunctionCoefficient : public Coefficient
 protected:
    GridFunction *u; // grid function
    Coefficient *obstacle;
-   double min_val;
+   real_t min_val;
 
 public:
    LogarithmGridFunctionCoefficient(GridFunction &u_, Coefficient &obst_,
-                                    double min_val_=-36)
+                                    real_t min_val_=-36)
       : u(&u_), obstacle(&obst_), min_val(min_val_) { }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 class ExponentialGridFunctionCoefficient : public Coefficient
@@ -61,15 +61,15 @@ class ExponentialGridFunctionCoefficient : public Coefficient
 protected:
    GridFunction *u;
    Coefficient *obstacle;
-   double min_val;
-   double max_val;
+   real_t min_val;
+   real_t max_val;
 
 public:
    ExponentialGridFunctionCoefficient(GridFunction &u_, Coefficient &obst_,
-                                      double min_val_=0.0, double max_val_=1e6)
+                                      real_t min_val_=0.0, real_t max_val_=1e6)
       : u(&u_), obstacle(&obst_), min_val(min_val_), max_val(max_val_) { }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
 };
 
 int main(int argc, char *argv[])
@@ -84,8 +84,8 @@ int main(int argc, char *argv[])
    int order = 1;
    int max_it = 10;
    int ref_levels = 3;
-   double alpha = 1.0;
-   double tol = 1e-5;
+   real_t alpha = 1.0;
+   real_t tol = 1e-5;
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -136,7 +136,7 @@ int main(int argc, char *argv[])
 
    // 3C. Rescale the domain to a unit circle (radius = 1).
    GridFunction *nodes = mesh.GetNodes();
-   double scale = 2*sqrt(2);
+   real_t scale = 2*sqrt(2);
    *nodes /= scale;
 
    ParMesh pmesh(MPI_COMM_WORLD, mesh);
@@ -192,8 +192,8 @@ int main(int argc, char *argv[])
    // 6. Define an initial guess for the solution.
    auto IC_func = [](const Vector &x)
    {
-      double r0 = 1.0;
-      double rr = 0.0;
+      real_t r0 = 1.0;
+      real_t rr = 0.0;
       for (int i=0; i<x.Size(); i++)
       {
          rr += x(i)*x(i);
@@ -243,7 +243,7 @@ int main(int argc, char *argv[])
    // 10. Iterate
    int k;
    int total_iterations = 0;
-   double increment_u = 0.1;
+   real_t increment_u = 0.1;
    for (k = 0; k < max_it; k++)
    {
       ParGridFunction u_tmp(&H1fes);
@@ -346,10 +346,10 @@ int main(int argc, char *argv[])
          delta_psi_gf.SetFromTrueDofs(tx.GetBlock(1));
 
          u_tmp -= u_gf;
-         double Newton_update_size = u_tmp.ComputeL2Error(zero);
+         real_t Newton_update_size = u_tmp.ComputeL2Error(zero);
          u_tmp = u_gf;
 
-         double gamma = 1.0;
+         real_t gamma = 1.0;
          delta_psi_gf *= gamma;
          psi_gf += delta_psi_gf;
 
@@ -391,7 +391,7 @@ int main(int argc, char *argv[])
          break;
       }
 
-      double H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
+      real_t H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
       if (myid == 0)
       {
          mfem::out << "H1-error  (|| u - uₕᵏ||)       = " << H1_error << endl;
@@ -423,13 +423,13 @@ int main(int argc, char *argv[])
    }
 
    {
-      double L2_error = u_gf.ComputeL2Error(exact_coef);
-      double H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
+      real_t L2_error = u_gf.ComputeL2Error(exact_coef);
+      real_t H1_error = u_gf.ComputeH1Error(&exact_coef,&exact_grad_coef);
 
       ExponentialGridFunctionCoefficient u_alt_cf(psi_gf,obstacle);
       ParGridFunction u_alt_gf(&L2fes);
       u_alt_gf.ProjectCoefficient(u_alt_cf);
-      double L2_error_alt = u_alt_gf.ComputeL2Error(exact_coef);
+      real_t L2_error_alt = u_alt_gf.ComputeL2Error(exact_coef);
 
       if (myid == 0)
       {
@@ -444,35 +444,35 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double LogarithmGridFunctionCoefficient::Eval(ElementTransformation &T,
+real_t LogarithmGridFunctionCoefficient::Eval(ElementTransformation &T,
                                               const IntegrationPoint &ip)
 {
    MFEM_ASSERT(u != NULL, "grid function is not set");
 
-   double val = u->GetValue(T, ip) - obstacle->Eval(T, ip);
+   real_t val = u->GetValue(T, ip) - obstacle->Eval(T, ip);
    return max(min_val, log(val));
 }
 
-double ExponentialGridFunctionCoefficient::Eval(ElementTransformation &T,
+real_t ExponentialGridFunctionCoefficient::Eval(ElementTransformation &T,
                                                 const IntegrationPoint &ip)
 {
    MFEM_ASSERT(u != NULL, "grid function is not set");
 
-   double val = u->GetValue(T, ip);
+   real_t val = u->GetValue(T, ip);
    return min(max_val, max(min_val, exp(val) + obstacle->Eval(T, ip)));
 }
 
-double spherical_obstacle(const Vector &pt)
+real_t spherical_obstacle(const Vector &pt)
 {
-   double x = pt(0), y = pt(1);
-   double r = sqrt(x*x + y*y);
-   double r0 = 0.5;
-   double beta = 0.9;
+   real_t x = pt(0), y = pt(1);
+   real_t r = sqrt(x*x + y*y);
+   real_t r0 = 0.5;
+   real_t beta = 0.9;
 
-   double b = r0*beta;
-   double tmp = sqrt(r0*r0 - b*b);
-   double B = tmp + b*b/tmp;
-   double C = -b/tmp;
+   real_t b = r0*beta;
+   real_t tmp = sqrt(r0*r0 - b*b);
+   real_t B = tmp + b*b/tmp;
+   real_t C = -b/tmp;
 
    if (r > b)
    {
@@ -484,13 +484,13 @@ double spherical_obstacle(const Vector &pt)
    }
 }
 
-double exact_solution_obstacle(const Vector &pt)
+real_t exact_solution_obstacle(const Vector &pt)
 {
-   double x = pt(0), y = pt(1);
-   double r = sqrt(x*x + y*y);
-   double r0 = 0.5;
-   double a =  0.348982574111686;
-   double A = -0.340129705945858;
+   real_t x = pt(0), y = pt(1);
+   real_t r = sqrt(x*x + y*y);
+   real_t r0 = 0.5;
+   real_t a =  0.348982574111686;
+   real_t A = -0.340129705945858;
 
    if (r > a)
    {
@@ -504,11 +504,11 @@ double exact_solution_obstacle(const Vector &pt)
 
 void exact_solution_gradient_obstacle(const Vector &pt, Vector &grad)
 {
-   double x = pt(0), y = pt(1);
-   double r = sqrt(x*x + y*y);
-   double r0 = 0.5;
-   double a =  0.348982574111686;
-   double A = -0.340129705945858;
+   real_t x = pt(0), y = pt(1);
+   real_t r = sqrt(x*x + y*y);
+   real_t r0 = 0.5;
+   real_t a =  0.348982574111686;
+   real_t A = -0.340129705945858;
 
    if (r > a)
    {

examples/ex37.cpp

@@ -67,9 +67,9 @@ using namespace mfem;
  * @param target_volume θ vol(Ω)
  * @param tol Newton iteration tolerance
  * @param max_its Newton maximum iteration number
- * @return double Final volume, ∫_Ω sigmoid(ψ)
+ * @return real_t Final volume, ∫_Ω sigmoid(ψ)
  */
-double proj(GridFunction &psi, double target_volume, double tol=1e-12,
+real_t proj(GridFunction &psi, real_t target_volume, real_t tol=1e-12,
             int max_its=10)
 {
    MappedGridFunctionCoefficient sigmoid_psi(&psi, sigmoid);
@@ -84,12 +84,12 @@ double proj(GridFunction &psi, double target_volume, double tol=1e-12,
    for (int k=0; k<max_its; k++) // Newton iteration
    {
       int_sigmoid_psi.Assemble(); // Recompute f(c) with updated ψ
-      const double f = int_sigmoid_psi.Sum() - target_volume;
+      const real_t f = int_sigmoid_psi.Sum() - target_volume;
 
       int_der_sigmoid_psi.Assemble(); // Recompute df(c) with updated ψ
-      const double df = int_der_sigmoid_psi.Sum();
+      const real_t df = int_der_sigmoid_psi.Sum();
 
-      const double dc = -f/df;
+      const real_t dc = -f/df;
       psi += dc;
       if (abs(dc) < tol) { done = true; break; }
    }
@@ -179,15 +179,15 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    int ref_levels = 5;
    int order = 2;
-   double alpha = 1.0;
-   double epsilon = 0.01;
-   double vol_fraction = 0.5;
+   real_t alpha = 1.0;
+   real_t epsilon = 0.01;
+   real_t vol_fraction = 0.5;
    int max_it = 1e3;
-   double itol = 1e-1;
-   double ntol = 1e-4;
-   double rho_min = 1e-6;
-   double lambda = 1.0;
-   double mu = 1.0;
+   real_t itol = 1e-1;
+   real_t ntol = 1e-4;
+   real_t rho_min = 1e-6;
+   real_t lambda = 1.0;
+   real_t mu = 1.0;
    bool glvis_visualization = true;
    bool paraview_output = false;
 
@@ -239,8 +239,8 @@ int main(int argc, char *argv[])
       Array<int> vertices;
       be->GetVertices(vertices);
 
-      double * coords1 = mesh.GetVertex(vertices[0]);
-      double * coords2 = mesh.GetVertex(vertices[1]);
+      real_t * coords1 = mesh.GetVertex(vertices[0]);
+      real_t * coords2 = mesh.GetVertex(vertices[1]);
 
       Vector center(2);
       center(0) = 0.5*(coords1[0] + coords2[0]);
@@ -312,7 +312,7 @@ int main(int argc, char *argv[])
    ElasticitySolver->SetupFEM();
    Vector center(2); center(0) = 2.9; center(1) = 0.5;
    Vector force(2); force(0) = 0.0; force(1) = -1.0;
-   double r = 0.05;
+   real_t r = 0.05;
    VolumeForceCoefficient vforce_cf(r,center,force);
    ElasticitySolver->SetRHSCoefficient(&vforce_cf);
    ElasticitySolver->SetEssentialBoundary(ess_bdr);
@@ -353,8 +353,8 @@ int main(int argc, char *argv[])
    LinearForm vol_form(&control_fes);
    vol_form.AddDomainIntegrator(new DomainLFIntegrator(one));
    vol_form.Assemble();
-   double domain_volume = vol_form(onegf);
-   const double target_volume = domain_volume * vol_fraction;
+   real_t domain_volume = vol_form(onegf);
+   const real_t target_volume = domain_volume * vol_fraction;
 
    // 10. Connect to GLVis. Prepare for VisIt output.
    char vishost[] = "localhost";
@@ -385,7 +385,7 @@ int main(int argc, char *argv[])
    // 11. Iterate:
    for (int k = 1; k <= max_it; k++)
    {
-      if (k > 1) { alpha *= ((double) k) / ((double) k-1); }
+      if (k > 1) { alpha *= ((real_t) k) / ((real_t) k-1); }
 
       mfem::out << "\nStep = " << k << std::endl;
 
@@ -422,14 +422,14 @@ int main(int argc, char *argv[])
 
       // Step 5 - Update design variable ψ ← proj(ψ - αG)
       psi.Add(-alpha, grad);
-      const double material_volume = proj(psi, target_volume);
+      const real_t material_volume = proj(psi, target_volume);
 
       // Compute ||ρ - ρ_old|| in control fes.
-      double norm_increment = zerogf.ComputeL1Error(succ_diff_rho);
-      double norm_reduced_gradient = norm_increment/alpha;
+      real_t norm_increment = zerogf.ComputeL1Error(succ_diff_rho);
+      real_t norm_reduced_gradient = norm_increment/alpha;
       psi_old = psi;
 
-      double compliance = (*(ElasticitySolver->GetLinearForm()))(u);
+      real_t compliance = (*(ElasticitySolver->GetLinearForm()))(u);
       mfem::out << "norm of the reduced gradient = " << norm_reduced_gradient <<
                 std::endl;
       mfem::out << "norm of the increment = " << norm_increment << endl;
@@ -449,7 +449,7 @@ int main(int argc, char *argv[])
       {
          rho_gf.ProjectCoefficient(rho);
          paraview_dc.SetCycle(k);
-         paraview_dc.SetTime((double)k);
+         paraview_dc.SetTime((real_t)k);
          paraview_dc.Save();
       }
 

examples/ex37.hpp

@@ -9,15 +9,15 @@ namespace mfem
 {
 
 /// @brief Inverse sigmoid function
-double inv_sigmoid(double x)
+real_t inv_sigmoid(real_t x)
 {
-   double tol = 1e-12;
-   x = std::min(std::max(tol,x),1.0-tol);
+   real_t tol = 1e-12;
+   x = std::min(std::max(tol,x), real_t(1.0)-tol);
    return std::log(x/(1.0-x));
 }
 
 /// @brief Sigmoid function
-double sigmoid(double x)
+real_t sigmoid(real_t x)
 {
    if (x >= 0)
    {
@@ -30,9 +30,9 @@ double sigmoid(double x)
 }
 
 /// @brief Derivative of sigmoid function
-double der_sigmoid(double x)
+real_t der_sigmoid(real_t x)
 {
-   double tmp = sigmoid(-x);
+   real_t tmp = sigmoid(-x);
    return tmp - std::pow(tmp,2);
 }
 
@@ -40,24 +40,24 @@ double der_sigmoid(double x)
 class MappedGridFunctionCoefficient : public GridFunctionCoefficient
 {
 protected:
-   std::function<double(const double)> fun; // f:R → R
+   std::function<real_t(const real_t)> fun; // f:R → R
 public:
    MappedGridFunctionCoefficient()
       :GridFunctionCoefficient(),
-       fun([](double x) {return x;}) {}
+       fun([](real_t x) {return x;}) {}
    MappedGridFunctionCoefficient(const GridFunction *gf,
-                                 std::function<double(const double)> fun_,
+                                 std::function<real_t(const real_t)> fun_,
                                  int comp=1)
       :GridFunctionCoefficient(gf, comp),
        fun(fun_) {}
 
 
-   virtual double Eval(ElementTransformation &T,
+   virtual real_t Eval(ElementTransformation &T,
                        const IntegrationPoint &ip)
    {
       return fun(GridFunctionCoefficient::Eval(T, ip));
    }
-   void SetFunction(std::function<double(const double)> fun_) { fun = fun_; }
+   void SetFunction(std::function<real_t(const real_t)> fun_) { fun = fun_; }
 };
 
 
@@ -67,30 +67,30 @@ class DiffMappedGridFunctionCoefficient : public GridFunctionCoefficient
 protected:
    const GridFunction *OtherGridF;
    GridFunctionCoefficient OtherGridF_cf;
-   std::function<double(const double)> fun; // f:R → R
+   std::function<real_t(const real_t)> fun; // f:R → R
 public:
    DiffMappedGridFunctionCoefficient()
       :GridFunctionCoefficient(),
        OtherGridF(nullptr),
        OtherGridF_cf(),
-       fun([](double x) {return x;}) {}
+       fun([](real_t x) {return x;}) {}
    DiffMappedGridFunctionCoefficient(const GridFunction *gf,
                                      const GridFunction *other_gf,
-                                     std::function<double(const double)> fun_,
+                                     std::function<real_t(const real_t)> fun_,
                                      int comp=1)
       :GridFunctionCoefficient(gf, comp),
        OtherGridF(other_gf),
        OtherGridF_cf(OtherGridF),
        fun(fun_) {}
 
-   virtual double Eval(ElementTransformation &T,
+   virtual real_t Eval(ElementTransformation &T,
                        const IntegrationPoint &ip)
    {
-      const double value1 = fun(GridFunctionCoefficient::Eval(T, ip));
-      const double value2 = fun(OtherGridF_cf.Eval(T, ip));
+      const real_t value1 = fun(GridFunctionCoefficient::Eval(T, ip));
+      const real_t value2 = fun(OtherGridF_cf.Eval(T, ip));
       return value1 - value2;
    }
-   void SetFunction(std::function<double(const double)> fun_) { fun = fun_; }
+   void SetFunction(std::function<real_t(const real_t)> fun_) { fun = fun_; }
 };
 
 /// @brief Solid isotropic material penalization (SIMP) coefficient
@@ -98,20 +98,20 @@ class SIMPInterpolationCoefficient : public Coefficient
 {
 protected:
    GridFunction *rho_filter;
-   double min_val;
-   double max_val;
-   double exponent;
+   real_t min_val;
+   real_t max_val;
+   real_t exponent;
 
 public:
-   SIMPInterpolationCoefficient(GridFunction *rho_filter_, double min_val_= 1e-6,
-                                double max_val_ = 1.0, double exponent_ = 3)
+   SIMPInterpolationCoefficient(GridFunction *rho_filter_, real_t min_val_= 1e-6,
+                                real_t max_val_ = 1.0, real_t exponent_ = 3)
       : rho_filter(rho_filter_), min_val(min_val_), max_val(max_val_),
         exponent(exponent_) { }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
    {
-      double val = rho_filter->GetValue(T, ip);
-      double coeff = min_val + pow(val,exponent)*(max_val-min_val);
+      real_t val = rho_filter->GetValue(T, ip);
+      real_t coeff = min_val + pow(val,exponent)*(max_val-min_val);
       return coeff;
    }
 };
@@ -126,13 +126,13 @@ protected:
    GridFunction *u = nullptr; // displacement
    GridFunction *rho_filter = nullptr; // filter density
    DenseMatrix grad; // auxiliary matrix, used in Eval
-   double exponent;
-   double rho_min;
+   real_t exponent;
+   real_t rho_min;
 
 public:
    StrainEnergyDensityCoefficient(Coefficient *lambda_, Coefficient *mu_,
-                                  GridFunction * u_, GridFunction * rho_filter_, double rho_min_=1e-6,
-                                  double exponent_ = 3.0)
+                                  GridFunction * u_, GridFunction * rho_filter_, real_t rho_min_=1e-6,
+                                  real_t exponent_ = 3.0)
       : lambda(lambda_), mu(mu_),  u(u_), rho_filter(rho_filter_),
         exponent(exponent_), rho_min(rho_min_)
    {
@@ -142,13 +142,13 @@ public:
       MFEM_ASSERT(rho_filter, "density field is not set");
    }
 
-   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
    {
-      double L = lambda->Eval(T, ip);
-      double M = mu->Eval(T, ip);
+      real_t L = lambda->Eval(T, ip);
+      real_t M = mu->Eval(T, ip);
       u->GetVectorGradient(T, grad);
-      double div_u = grad.Trace();
-      double density = L*div_u*div_u;
+      real_t div_u = grad.Trace();
+      real_t density = L*div_u*div_u;
       int dim = T.GetSpaceDim();
       for (int i=0; i<dim; i++)
       {
@@ -157,7 +157,7 @@ public:
             density += M*grad(i,j)*(grad(i,j)+grad(j,i));
          }
       }
-      double val = rho_filter->GetValue(T,ip);
+      real_t val = rho_filter->GetValue(T,ip);
 
       return -exponent * pow(val, exponent-1.0) * (1-rho_min) * density;
    }
@@ -167,11 +167,11 @@ public:
 class VolumeForceCoefficient : public VectorCoefficient
 {
 private:
-   double r;
+   real_t r;
    Vector center;
    Vector force;
 public:
-   VolumeForceCoefficient(double r_,Vector &  center_, Vector & force_) :
+   VolumeForceCoefficient(real_t r_,Vector &  center_, Vector & force_) :
       VectorCoefficient(center_.Size()), r(r_), center(center_), force(force_) { }
 
    using VectorCoefficient::Eval;
@@ -186,7 +186,7 @@ public:
          xx[i]=xx[i]-center[i];
       }
 
-      double cr=xx.Norml2();
+      real_t cr=xx.Norml2();
       V.SetSize(T.GetDimension());
       if (cr <= r)
       {
@@ -198,7 +198,7 @@ public:
       }
    }
 
-   void Set(double r_,Vector & center_, Vector & force_)
+   void Set(real_t r_,Vector & center_, Vector & force_)
    {
       r=r_;
       center = center_;

examples/ex37p.cpp

@@ -66,9 +66,9 @@ using namespace mfem;
  * @param target_volume θ vol(Ω)
  * @param tol Newton iteration tolerance
  * @param max_its Newton maximum iteration number
- * @return double Final volume, ∫_Ω sigmoid(ψ)
+ * @return real_t Final volume, ∫_Ω sigmoid(ψ)
  */
-double proj(ParGridFunction &psi, double target_volume, double tol=1e-12,
+real_t proj(ParGridFunction &psi, real_t target_volume, real_t tol=1e-12,
             int max_its=10)
 {
    MappedGridFunctionCoefficient sigmoid_psi(&psi, sigmoid);
@@ -83,15 +83,17 @@ double proj(ParGridFunction &psi, double target_volume, double tol=1e-12,
    for (int k=0; k<max_its; k++) // Newton iteration
    {
       int_sigmoid_psi.Assemble(); // Recompute f(c) with updated ψ
-      double f = int_sigmoid_psi.Sum();
-      MPI_Allreduce(MPI_IN_PLACE, &f, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+      real_t f = int_sigmoid_psi.Sum();
+      MPI_Allreduce(MPI_IN_PLACE, &f, 1, MPITypeMap<real_t>::mpi_type,
+                    MPI_SUM, MPI_COMM_WORLD);
       f -= target_volume;
 
       int_der_sigmoid_psi.Assemble(); // Recompute df(c) with updated ψ
-      double df = int_der_sigmoid_psi.Sum();
-      MPI_Allreduce(MPI_IN_PLACE, &df, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+      real_t df = int_der_sigmoid_psi.Sum();
+      MPI_Allreduce(MPI_IN_PLACE, &df, 1, MPITypeMap<real_t>::mpi_type,
+                    MPI_SUM, MPI_COMM_WORLD);
 
-      const double dc = -f/df;
+      const real_t dc = -f/df;
       psi += dc;
       if (abs(dc) < tol) { done = true; break; }
    }
@@ -101,9 +103,9 @@ double proj(ParGridFunction &psi, double target_volume, double tol=1e-12,
                    "Result may not be accurate.");
    }
    int_sigmoid_psi.Assemble();
-   double material_volume = int_sigmoid_psi.Sum();
-   MPI_Allreduce(MPI_IN_PLACE, &material_volume, 1, MPI_DOUBLE, MPI_SUM,
-                 MPI_COMM_WORLD);
+   real_t material_volume = int_sigmoid_psi.Sum();
+   MPI_Allreduce(MPI_IN_PLACE, &material_volume, 1,
+                 MPITypeMap<real_t>::mpi_type, MPI_SUM, MPI_COMM_WORLD);
    return material_volume;
 }
 
@@ -190,15 +192,15 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    int ref_levels = 5;
    int order = 2;
-   double alpha = 1.0;
-   double epsilon = 0.01;
-   double vol_fraction = 0.5;
+   real_t alpha = 1.0;
+   real_t epsilon = 0.01;
+   real_t vol_fraction = 0.5;
    int max_it = 1e3;
-   double itol = 1e-1;
-   double ntol = 1e-4;
-   double rho_min = 1e-6;
-   double lambda = 1.0;
-   double mu = 1.0;
+   real_t itol = 1e-1;
+   real_t ntol = 1e-4;
+   real_t rho_min = 1e-6;
+   real_t lambda = 1.0;
+   real_t mu = 1.0;
    bool glvis_visualization = true;
    bool paraview_output = false;
 
@@ -258,8 +260,8 @@ int main(int argc, char *argv[])
       Array<int> vertices;
       be->GetVertices(vertices);
 
-      double * coords1 = mesh.GetVertex(vertices[0]);
-      double * coords2 = mesh.GetVertex(vertices[1]);
+      real_t * coords1 = mesh.GetVertex(vertices[0]);
+      real_t * coords2 = mesh.GetVertex(vertices[1]);
 
       Vector center(2);
       center(0) = 0.5*(coords1[0] + coords2[0]);
@@ -337,7 +339,7 @@ int main(int argc, char *argv[])
    ElasticitySolver->SetupFEM();
    Vector center(2); center(0) = 2.9; center(1) = 0.5;
    Vector force(2); force(0) = 0.0; force(1) = -1.0;
-   double r = 0.05;
+   real_t r = 0.05;
    VolumeForceCoefficient vforce_cf(r,center,force);
    ElasticitySolver->SetRHSCoefficient(&vforce_cf);
    ElasticitySolver->SetEssentialBoundary(ess_bdr);
@@ -378,8 +380,8 @@ int main(int argc, char *argv[])
    ParLinearForm vol_form(&control_fes);
    vol_form.AddDomainIntegrator(new DomainLFIntegrator(one));
    vol_form.Assemble();
-   double domain_volume = vol_form(onegf);
-   const double target_volume = domain_volume * vol_fraction;
+   real_t domain_volume = vol_form(onegf);
+   const real_t target_volume = domain_volume * vol_fraction;
 
    // 10. Connect to GLVis. Prepare for VisIt output.
    char vishost[] = "localhost";
@@ -410,7 +412,7 @@ int main(int argc, char *argv[])
    // 11. Iterate:
    for (int k = 1; k <= max_it; k++)
    {
-      if (k > 1) { alpha *= ((double) k) / ((double) k-1); }
+      if (k > 1) { alpha *= ((real_t) k) / ((real_t) k-1); }
 
       if (myid == 0)
       {
@@ -450,15 +452,16 @@ int main(int argc, char *argv[])
 
       // Step 5 - Update design variable ψ ← proj(ψ - αG)
       psi.Add(-alpha, grad);
-      const double material_volume = proj(psi, target_volume);
+      const real_t material_volume = proj(psi, target_volume);
 
       // Compute ||ρ - ρ_old|| in control fes.
-      double norm_increment = zerogf.ComputeL1Error(succ_diff_rho);
-      double norm_reduced_gradient = norm_increment/alpha;
+      real_t norm_increment = zerogf.ComputeL1Error(succ_diff_rho);
+      real_t norm_reduced_gradient = norm_increment/alpha;
       psi_old = psi;
 
-      double compliance = (*(ElasticitySolver->GetLinearForm()))(u);
-      MPI_Allreduce(MPI_IN_PLACE,&compliance,1,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD);
+      real_t compliance = (*(ElasticitySolver->GetLinearForm()))(u);
+      MPI_Allreduce(MPI_IN_PLACE, &compliance, 1, MPITypeMap<real_t>::mpi_type,
+                    MPI_SUM, MPI_COMM_WORLD);
       if (myid == 0)
       {
          mfem::out << "norm of the reduced gradient = " << norm_reduced_gradient << endl;
@@ -480,7 +483,7 @@ int main(int argc, char *argv[])
       {
          rho_gf.ProjectCoefficient(rho);
          paraview_dc.SetCycle(k);
-         paraview_dc.SetTime((double)k);
+         paraview_dc.SetTime((real_t)k);
          paraview_dc.Save();
       }
 

examples/ex38.cpp

@@ -0,0 +1,696 @@
+//                                MFEM Example 38
+//
+// Compile with: make ex38
+//
+// Sample runs:
+// (since all sample runs require LAPACK, the * symbol is used to exclude them
+// from the automatically generated internal MFEM tests).
+//              * ex38
+//              * ex38 -i volumetric1d
+//              * ex38 -i surface2d
+//              * ex38 -i surface2d -o 4 -r 5
+//              * ex38 -i volumetric2d
+//              * ex38 -i volumetric2d -o 4 -r 5
+//              * ex38 -i surface3d
+//              * ex38 -i surface3d -o 4 -r 5
+//              * ex38 -i volumetric3d
+//              * ex38 -i volumetric3d -o 4 -r 5
+//
+// Description: This example code demonstrates the use of MFEM to integrate
+//              functions over implicit interfaces and subdomains bounded by
+//              implicit interfaces.
+//
+//              The quadrature rules are constructed by means of moment-fitting.
+//              The interface is given by the zero isoline of a level-set
+//              function ϕ and the subdomain is given as the domain where ϕ>0
+//              holds. The algorithm for construction of the quadrature rules
+//              was introduced by Mueller, Kummer and Oberlack [1].
+//
+//              This example also showcases how to set up integrators using the
+//              integration rules on implicit surfaces and subdomains.
+//
+// [1] Mueller, B., Kummer, F. and Oberlack, M. (2013) Highly accurate surface
+//     and volume integration on implicit domains by means of moment-fitting.
+//     Int. J. Numer. Meth. Engr. (96) 512-528. DOI:10.1002/nme.4569
+
+#include "mfem.hpp"
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+/// @brief Integration rule the example should demonstrate
+enum class IntegrationType { Volumetric1D, Surface2D, Volumetric2D,
+                             Surface3D, Volumetric3D
+                           };
+IntegrationType itype;
+
+/// @brief Level-set function defining the implicit interface
+real_t lvlset(const Vector& X)
+{
+   switch (itype)
+   {
+      case IntegrationType::Volumetric1D:
+         return .55 - X(0);
+      case IntegrationType::Surface2D:
+         return 1. - (pow(X(0), 2.) + pow(X(1), 2.));
+      case IntegrationType::Volumetric2D:
+         return 1. - (pow(X(0) / 1.5, 2.) + pow(X(1) / .75, 2.));
+      case IntegrationType::Surface3D:
+         return 1. - (pow(X(0), 2.) + pow(X(1), 2.) + pow(X(2), 2.));
+      case IntegrationType::Volumetric3D:
+         return 1. - (pow(X(0) / 1.5, 2.) + pow(X(1) / .75, 2.) + pow(X(2) / .5, 2.));
+      default:
+         return 1.;
+   }
+}
+
+/// @brief Function that should be integrated
+real_t integrand(const Vector& X)
+{
+   switch (itype)
+   {
+      case IntegrationType::Volumetric1D:
+         return 1.;
+      case IntegrationType::Surface2D:
+         return 3. * pow(X(0), 2.) - pow(X(1), 2.);
+      case IntegrationType::Volumetric2D:
+         return 1.;
+      case IntegrationType::Surface3D:
+         return 4. - 3. * pow(X(0), 2.) + 2. * pow(X(1), 2.) - pow(X(2), 2.);
+      case IntegrationType::Volumetric3D:
+         return 1.;
+      default:
+         return 0.;
+   }
+}
+
+/// @brief Analytic surface integral
+real_t Surface()
+{
+   switch (itype)
+   {
+      case IntegrationType::Volumetric1D:
+         return 1.;
+      case IntegrationType::Surface2D:
+         return 2. * M_PI;
+      case IntegrationType::Volumetric2D:
+         return 7.26633616541076;
+      case IntegrationType::Surface3D:
+         return 40. / 3. * M_PI;
+      case IntegrationType::Volumetric3D:
+         return 9.90182151329315;
+      default:
+         return 0.;
+   }
+}
+
+/// @brief Analytic volume integral over subdomain with positive level-set
+real_t Volume()
+{
+   switch (itype)
+   {
+      case IntegrationType::Volumetric1D:
+         return .55;
+      case IntegrationType::Surface2D:
+         return NAN;
+      case IntegrationType::Volumetric2D:
+         return 9. / 8. * M_PI;
+      case IntegrationType::Surface3D:
+         return NAN;
+      case IntegrationType::Volumetric3D:
+         return 3. / 4. * M_PI;
+      default:
+         return 0.;
+   }
+}
+
+#ifdef MFEM_USE_LAPACK
+/**
+ @brief Class for surface IntegrationRule
+
+ This class demonstrates how IntegrationRules computed as CutIntegrationRules
+ can be saved to reduce the impact by computing them from scratch each time.
+ */
+class SIntegrationRule : public IntegrationRule
+{
+protected:
+   /// @brief Space Dimension of the IntegrationRule
+   int dim;
+   /// @brief Column-wise matrix of the quadtrature weights
+   DenseMatrix Weights;
+   /// @brief Column-wise matrix of the transformation weights of the normal
+   DenseMatrix SurfaceWeights;
+
+public:
+   /**
+    @brief Constructor of SIntegrationRule
+
+    The surface integrationRules are computed and saved in the constructor.
+
+    @param [in] Order Order of the IntegrationRule
+    @param [in] LvlSet Level-set defining the implicit interface
+    @param [in] lsOrder Polynomial degree for approx of level-set function
+    @param [in] mesh Pointer to the mesh that is used
+   */
+   SIntegrationRule(int Order, Coefficient& LvlSet, int lsOrder, Mesh* mesh)
+   {
+      dim = mesh->Dimension();
+
+      IsoparametricTransformation Tr;
+      MomentFittingIntRules MFIRs(Order, LvlSet, lsOrder);
+      mesh->GetElementTransformation(0, &Tr);
+      IntegrationRule ir;
+      MFIRs.GetSurfaceIntegrationRule(Tr, ir);
+      if (dim >1)
+      {
+         Weights.SetSize(ir.GetNPoints(), mesh->GetNE());
+      }
+      else
+      {
+         Weights.SetSize(2, mesh->GetNE());
+      }
+      SurfaceWeights.SetSize(ir.GetNPoints(), mesh->GetNE());
+      Vector w;
+      MFIRs.GetSurfaceWeights(Tr, ir, w);
+      SurfaceWeights.SetCol(0, w);
+      SetSize(ir.GetNPoints());
+
+      for (int ip = 0; ip < GetNPoints(); ip++)
+      {
+         IntPoint(ip).index = ip;
+         IntegrationPoint &intp = IntPoint(ip);
+         intp.x = ir.IntPoint(ip).x;
+         intp.y = ir.IntPoint(ip).y;
+         intp.z = ir.IntPoint(ip).z;
+         if (dim > 1)
+         {
+            Weights(ip, 0) = ir.IntPoint(ip).weight;
+         }
+         else
+         {
+            Weights(0, 0) = ir.IntPoint(ip).x;
+            Weights(1, 0) = ir.IntPoint(ip).weight;
+         }
+      }
+
+
+      for (int elem = 1; elem < mesh->GetNE(); elem++)
+      {
+         mesh->GetElementTransformation(elem, &Tr);
+         MFIRs.GetSurfaceIntegrationRule(Tr, ir);
+         Vector w;
+         MFIRs.GetSurfaceWeights(Tr, ir, w);
+         SurfaceWeights.SetCol(elem, w);
+
+         for (int ip = 0; ip < GetNPoints(); ip++)
+         {
+            if (dim > 1)
+            {
+               Weights(ip, elem) = ir.IntPoint(ip).weight;
+            }
+            else
+            {
+               Weights(0, elem) = ir.IntPoint(ip).x;
+               Weights(1, elem) = ir.IntPoint(ip).weight;
+            }
+         }
+      }
+   }
+
+   /**
+    @brief Set the weights for the given element and multiply them with the
+    transformation of the interface
+    */
+   void SetElementinclSurfaceWeight(int Element)
+   {
+      if (dim == 1)
+      {
+         IntegrationPoint &intp = IntPoint(0);
+         intp.x = Weights(0, Element);
+         intp.weight = Weights(1, Element);
+         cout << intp.x << " " << Element << endl;
+      }
+      else
+         for (int ip = 0; ip < GetNPoints(); ip++)
+         {
+            IntegrationPoint &intp = IntPoint(ip);
+            intp.weight = Weights(ip, Element) * SurfaceWeights(ip, Element);
+         }
+   }
+
+   /// @brief Set the weights for the given element
+   void SetElement(int Element)
+   {
+      if (dim == 1)
+      {
+         IntegrationPoint &intp = IntPoint(0);
+         intp.x = Weights(0, Element);
+         intp.weight = Weights(1, Element);
+      }
+      else
+         for (int ip = 0; ip < GetNPoints(); ip++)
+         {
+            IntegrationPoint &intp = IntPoint(ip);
+            intp.weight = Weights(ip, Element);
+         }
+   }
+
+   /// @brief Destructor of SIntegrationRule
+   ~SIntegrationRule() {}
+};
+
+/**
+ @brief Class for volume IntegrationRule
+
+ This class demonstrates how IntegrationRules computed as CutIntegrationRules
+ can be saved to reduce the impact by computing them from scratch each time.
+ */
+class CIntegrationRule : public IntegrationRule
+{
+protected:
+   /// @brief Space Dimension of the IntegrationRule
+   int dim;
+   /// @brief Column-wise matrix of the quadtrature weights
+   DenseMatrix Weights;
+
+public:
+   /**
+    @brief Constructor of CIntegrationRule
+
+    The volume integrationRules are computed and saved in the constructor.
+
+    @param [in] Order Order of the IntegrationRule
+    @param [in] LvlSet Level-set defining the implicit interface
+    @param [in] lsOrder Polynomial degree for approx of level-set function
+    @param [in] mesh Pointer to the mesh that is used
+   */
+   CIntegrationRule(int Order, Coefficient& LvlSet, int lsOrder, Mesh* mesh)
+   {
+      dim = mesh->Dimension();
+
+      IsoparametricTransformation Tr;
+      MomentFittingIntRules MFIRs(Order, LvlSet, lsOrder);
+      mesh->GetElementTransformation(0, &Tr);
+      IntegrationRule ir;
+      MFIRs.GetVolumeIntegrationRule(Tr, ir);
+      if (dim > 1)
+      {
+         Weights.SetSize(ir.GetNPoints(), mesh->GetNE());
+      }
+      else
+      {
+         Weights.SetSize(2 * ir.GetNPoints(), mesh->GetNE());
+      }
+
+      SetSize(ir.GetNPoints());
+      for (int ip = 0; ip < GetNPoints(); ip++)
+      {
+         IntPoint(ip).index = ip;
+         IntegrationPoint &intp = IntPoint(ip);
+         intp.x = ir.IntPoint(ip).x;
+         intp.y = ir.IntPoint(ip).y;
+         intp.z = ir.IntPoint(ip).z;
+         if (dim > 1)
+         {
+            Weights(ip, 0) = ir.IntPoint(ip).weight;
+         }
+         else
+         {
+            Weights(2 * ip, 0) = ir.IntPoint(ip).x;
+            Weights(2 * ip + 1, 0) = ir.IntPoint(ip).weight;
+         }
+      }
+
+      for (int elem = 1; elem < mesh->GetNE(); elem++)
+      {
+         mesh->GetElementTransformation(elem, &Tr);
+         MFIRs.GetVolumeIntegrationRule(Tr, ir);
+
+         for (int ip = 0; ip < GetNPoints(); ip++)
+         {
+            if (dim > 1)
+            {
+               Weights(ip, elem) = ir.IntPoint(ip).weight;
+            }
+            else
+            {
+               Weights(2 * ip, elem) = ir.IntPoint(ip).x;
+               Weights(2 * ip + 1, elem) = ir.IntPoint(ip).weight;
+            }
+         }
+      }
+   }
+
+   /// @brief Set the weights for the given element
+   void SetElement(int Element)
+   {
+      if (dim == 1)
+         for (int ip = 0; ip < GetNPoints(); ip++)
+         {
+            IntegrationPoint &intp = IntPoint(ip);
+            intp.x = Weights(2 * ip, Element);
+            intp.weight = Weights(2 * ip + 1, Element);
+         }
+      else
+         for (int ip = 0; ip < GetNPoints(); ip++)
+         {
+            IntegrationPoint &intp = IntPoint(ip);
+            intp.weight = Weights(ip, Element);
+         }
+   }
+
+   /// @brief Destructor of CIntegrationRule
+   ~CIntegrationRule() {}
+};
+/**
+ @brief Class for surface linearform integrator
+
+ Integrator to demonstrate the use of the surface integration rule on an
+ implicit surface defined by a level-set.
+ */
+class SurfaceLFIntegrator : public LinearFormIntegrator
+{
+protected:
+   /// @brief vector to evaluate the basis functions
+   Vector shape;
+
+   /// @brief surface integration rule
+   SIntegrationRule* SIntRule;
+
+   /// @brief coefficient representing the level-set defining the interface
+   Coefficient &LevelSet;
+
+   /// @brief coefficient representing the integrand
+   Coefficient &Q;
+
+public:
+   /**
+    @brief Constructor for the surface linear form integrator
+
+    Constructor for the surface linear form integrator to demonstrate the use
+    of the surface integration rule by means of moment-fitting.
+
+    @param [in] q coefficient representing the inegrand
+    @param [in] levelset level-set defining the implicit interfac
+    @param [in] ir surface integrtion rule to be used
+    */
+   SurfaceLFIntegrator(Coefficient &q, Coefficient &levelset,
+                       SIntegrationRule* ir)
+      : LinearFormIntegrator(), SIntRule(ir), LevelSet(levelset), Q(q) { }
+
+   /**
+    @brief Assembly of the element vector
+
+    Assemble the element vector of for the right hand side on the element given
+    by the FiniteElement and ElementTransformation.
+
+    @param [in] el finite Element the vector belongs to
+    @param [in] Tr transformation of finite element
+    @param [out] elvect vector containing the
+   */
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect) override
+   {
+      int dof = el.GetDof();
+      shape.SetSize(dof);
+      elvect.SetSize(dof);
+      elvect = 0.;
+
+      // Update the surface integration rule for the current element
+      SIntRule->SetElementinclSurfaceWeight(Tr.ElementNo);
+
+      for (int ip = 0; ip < SIntRule->GetNPoints(); ip++)
+      {
+         Tr.SetIntPoint((&(SIntRule->IntPoint(ip))));
+         real_t val = Tr.Weight() * Q.Eval(Tr, SIntRule->IntPoint(ip));
+         el.CalcShape(SIntRule->IntPoint(ip), shape);
+         add(elvect, SIntRule->IntPoint(ip).weight * val, shape, elvect);
+      }
+   }
+};
+
+/**
+ @brief Class for subdomain linearform integrator
+
+ Integrator to demonstrate the use of the subdomain integration rule within
+ an area defined by an implicit surface defined by a level-set.
+ */
+class SubdomainLFIntegrator : public LinearFormIntegrator
+{
+protected:
+   /// @brief vector to evaluate the basis functions
+   Vector shape;
+
+   /// @brief surface integration rule
+   CIntegrationRule* CIntRule;
+
+   /// @brief coefficient representing the level-set defining the interface
+   Coefficient &LevelSet;
+
+   /// @brief coefficient representing the integrand
+   Coefficient &Q;
+
+public:
+   /**
+    @brief Constructor for the volumetric subdomain linear form integrator
+
+    Constructor for the subdomain linear form integrator to demonstrate the use
+    of the volumetric subdomain integration rule by means of moment-fitting.
+
+    @param [in] q coefficient representing the inegrand
+    @param [in] levelset level-set defining the implicit interfac
+    @param [in] ir subdomain integrtion rule to be used
+    */
+   SubdomainLFIntegrator(Coefficient &q, Coefficient &levelset,
+                         CIntegrationRule* ir)
+      : LinearFormIntegrator(), CIntRule(ir), LevelSet(levelset), Q(q) { }
+
+   /**
+    @brief Assembly of the element vector
+
+    Assemble the element vector of for the right hand side on the element given
+    by the FiniteElement and ElementTransformation.
+
+    @param [in] el finite Element the vector belongs to
+    @param [in] Tr transformation of finite element
+    @param [out] elvect vector containing the
+   */
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect) override
+   {
+      int dof = el.GetDof();
+      shape.SetSize(dof);
+      elvect.SetSize(dof);
+      elvect = 0.;
+
+      // Update the subdomain integration rule
+      CIntRule->SetElement(Tr.ElementNo);
+
+      for (int ip = 0; ip < CIntRule->GetNPoints(); ip++)
+      {
+         Tr.SetIntPoint((&(CIntRule->IntPoint(ip))));
+         real_t val = Tr.Weight()
+                      * Q.Eval(Tr, CIntRule->IntPoint(ip));
+         el.CalcPhysShape(Tr, shape);
+         add(elvect, CIntRule->IntPoint(ip).weight * val, shape, elvect);
+      }
+   }
+};
+#endif // MFEM_USE_LAPACK
+
+int main(int argc, char *argv[])
+{
+#ifndef MFEM_USE_LAPACK
+   cout << "MFEM must be built with LAPACK for this example." << endl;
+   return EXIT_FAILURE;
+#else
+   // 1. Parse he command-line options.
+   int ref_levels = 3;
+   int order = 2;
+   const char *inttype = "surface2d";
+   bool visualization = true;
+   itype = IntegrationType::Surface2D;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&order, "-o", "--order", "Order of quadrature rule");
+   args.AddOption(&ref_levels, "-r", "--refine", "Number of meh refinements");
+   args.AddOption(&inttype, "-i", "--integrationtype",
+                  "IntegrationType to demonstrate");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.ParseCheck();
+
+   if (strcmp(inttype, "volumetric1d") == 0
+       || strcmp(inttype, "Volumetric1D") == 0)
+   {
+      itype = IntegrationType::Volumetric1D;
+   }
+   else if (strcmp(inttype, "surface2d") == 0
+            || strcmp(inttype, "Surface2D") == 0)
+   {
+      itype = IntegrationType::Surface2D;
+   }
+   else if (strcmp(inttype, "volumetric2d") == 0
+            || strcmp(inttype, "Volumetric2D") == 0)
+   {
+      itype = IntegrationType::Volumetric2D;
+   }
+   else if (strcmp(inttype, "surface3d") == 0
+            || strcmp(inttype, "Surface3d") == 0)
+   {
+      itype = IntegrationType::Surface3D;
+   }
+   else if (strcmp(inttype, "volumetric3d") == 0
+            || strcmp(inttype, "Volumetric3d") == 0)
+   {
+      itype = IntegrationType::Volumetric3D;
+   }
+
+   // 2. Construct and refine the mesh.
+   Mesh *mesh;
+   if (itype == IntegrationType::Volumetric1D)
+   {
+      mesh = new Mesh("../data/inline-segment.mesh");
+   }
+   if (itype == IntegrationType::Surface2D
+       || itype == IntegrationType::Volumetric2D)
+   {
+      mesh = new Mesh(2, 4, 1, 0, 2);
+      mesh->AddVertex(-1.6,-1.6);
+      mesh->AddVertex(1.6,-1.6);
+      mesh->AddVertex(1.6,1.6);
+      mesh->AddVertex(-1.6,1.6);
+      mesh->AddQuad(0,1,2,3);
+      mesh->FinalizeQuadMesh(1, 0, 1);
+   }
+   else if (itype == IntegrationType::Surface3D
+            || itype == IntegrationType::Volumetric3D)
+   {
+      mesh = new Mesh(3, 8, 1, 0, 3);
+      mesh->AddVertex(-1.6,-1.6,-1.6);
+      mesh->AddVertex(1.6,-1.6,-1.6);
+      mesh->AddVertex(1.6,1.6,-1.6);
+      mesh->AddVertex(-1.6,1.6,-1.6);
+      mesh->AddVertex(-1.6,-1.6,1.6);
+      mesh->AddVertex(1.6,-1.6,1.6);
+      mesh->AddVertex(1.6,1.6,1.6);
+      mesh->AddVertex(-1.6,1.6,1.6);
+      mesh->AddHex(0,1,2,3,4,5,6,7);
+      mesh->FinalizeHexMesh(1, 0, 1);
+   }
+
+   for (int lev = 0; lev < ref_levels; lev++)
+   {
+      mesh->UniformRefinement();
+   }
+
+   // 3. Define the necessary finite element space on the mesh.
+   H1_FECollection fe_coll(1, mesh->Dimension());
+   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, &fe_coll);
+
+   // 4. Construction Coefficients for the level set and the integrand.
+   FunctionCoefficient levelset(lvlset);
+   FunctionCoefficient u(integrand);
+
+   // 5. Define the necessary Integration rules on element 0.
+   IsoparametricTransformation Tr;
+   mesh->GetElementTransformation(0, &Tr);
+   SIntegrationRule* sir = new SIntegrationRule(order, levelset, 2, mesh);
+   CIntegrationRule* cir = NULL;
+   if (itype == IntegrationType::Volumetric1D
+       || itype == IntegrationType::Volumetric2D
+       || itype == IntegrationType::Volumetric3D)
+   {
+      cir = new CIntegrationRule(order, levelset, 2, mesh);
+   }
+
+   // 6. Define and assemble the linear forms on the finite element space.
+   LinearForm surface(fespace);
+   LinearForm volume(fespace);
+
+   surface.AddDomainIntegrator(new SurfaceLFIntegrator(u, levelset, sir));
+   surface.Assemble();
+
+   if (itype == IntegrationType::Volumetric1D
+       || itype == IntegrationType::Volumetric2D
+       || itype == IntegrationType::Volumetric3D)
+   {
+      volume.AddDomainIntegrator(new SubdomainLFIntegrator(u, levelset, cir));
+      volume.Assemble();
+   }
+
+   // 7. Print information, computed values and errors to the console.
+   int qorder = 0;
+   int nbasis = 2 * (order + 1) + (int)(order * (order + 1) / 2);
+   IntegrationRules irs(0, Quadrature1D::GaussLegendre);
+   IntegrationRule ir = irs.Get(Geometry::SQUARE, qorder);
+   for (; ir.GetNPoints() <= nbasis; qorder++)
+   {
+      ir = irs.Get(Geometry::SQUARE, qorder);
+   }
+   cout << "============================================" << endl;
+   cout << "Mesh size dx:                       ";
+   if (itype != IntegrationType::Volumetric1D)
+   {
+      cout << 3.2 / pow(2., (real_t)ref_levels) << endl;
+   }
+   else
+   {
+      cout << .25 / pow(2., (real_t)ref_levels) << endl;
+   }
+   if (itype == IntegrationType::Surface2D
+       || itype == IntegrationType::Volumetric2D)
+   {
+      cout << "Number of div free basis functions: " << nbasis << endl;
+      cout << "Number of quadrature points:        " << ir.GetNPoints() << endl;
+   }
+   cout << scientific << setprecision(2);
+   cout << "============================================" << endl;
+   cout << "Computed value of surface integral: " << surface.Sum() << endl;
+   cout << "True value of surface integral:     " << Surface() << endl;
+   cout << "Absolute Error (Surface):            ";
+   cout << abs(surface.Sum() - Surface()) << endl;
+   cout << "Relative Error (Surface):           ";
+   cout << abs(surface.Sum() - Surface()) / Surface() << endl;
+   if (itype == IntegrationType::Volumetric1D
+       || itype == IntegrationType::Volumetric2D
+       || itype == IntegrationType::Volumetric3D)
+   {
+      cout << "--------------------------------------------" << endl;
+      cout << "Computed value of volume integral:  " << volume.Sum() << endl;
+      cout << "True value of volume integral:      " << Volume() << endl;
+      cout << "Absolute Error (Volume):             ";
+      cout << abs(volume.Sum() - Volume()) << endl;
+      cout << "Relative Error (Volume):            ";
+      cout << abs(volume.Sum() - Volume()) / Volume() << endl;
+   }
+   cout << "============================================" << endl;
+
+   // 8. Plot the level-set function on a high order finite element space.
+   if (visualization)
+   {
+      H1_FECollection fe_coll2(5, mesh->Dimension());
+      FiniteElementSpace fespace2(mesh, &fe_coll2);
+      FunctionCoefficient levelset_coeff(levelset);
+      GridFunction lgf(&fespace2);
+      lgf.ProjectCoefficient(levelset_coeff);
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "solution\n" << *mesh << lgf << flush;
+      sol_sock << "keys pppppppppppppppppppppppppppcmmlRj\n";
+      sol_sock << "levellines " << 0. << " " << 0. << " " << 1 << "\n" << flush;
+   }
+
+   delete sir;
+   delete cir;
+   delete fespace;
+   delete mesh;
+   return EXIT_SUCCESS;
+#endif //MFEM_USE_LAPACK
+}

examples/ex3p.cpp

@@ -5,6 +5,7 @@
 // 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-tet.mesh -nc -o 2
 //               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
 //               mpirun -np 4 ex3p -m ../data/beam-hex.mesh -o 2 -pa
 //               mpirun -np 4 ex3p -m ../data/escher.mesh
@@ -54,7 +55,7 @@ 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;
+real_t freq = 1.0, kappa;
 int dim;
 
 int main(int argc, char *argv[])
@@ -70,6 +71,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool static_cond = false;
    bool pa = false;
+   bool nc = false;
    const char *device_config = "cpu";
    bool visualization = true;
 #ifdef MFEM_USE_AMGX
@@ -87,6 +89,9 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&nc, "-nc", "--non-conforming", "-c",
+                  "--conforming",
+                  "Mark the mesh as nonconforming before partitioning.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
@@ -124,6 +129,11 @@ int main(int argc, char *argv[])
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    dim = mesh->Dimension();
    int sdim = mesh->SpaceDimension();
+   if (nc)
+   {
+      // Can set to false to use conformal refinement for simplices.
+      mesh->EnsureNCMesh(true);
+   }
 
    // 5. Refine the serial mesh on all processors to increase the resolution. In
    //    this example we do 'ref_levels' of uniform refinement. We choose
@@ -253,7 +263,7 @@ int main(int argc, char *argv[])
 
    // 15. Compute and print the L^2 norm of the error.
    {
-      double error = x.ComputeL2Error(E);
+      real_t error = x.ComputeL2Error(E);
       if (myid == 0)
       {
          cout << "\n|| E_h - E ||_{L^2} = " << error << '\n' << endl;

examples/ex4.cpp

@@ -54,7 +54,7 @@ using namespace mfem;
 // Exact solution, F, and r.h.s., f. See below for implementation.
 void F_exact(const Vector &, Vector &);
 void f_exact(const Vector &, Vector &);
-double freq = 1.0, kappa;
+real_t freq = 1.0, kappa;
 
 int main(int argc, char *argv[])
 {
@@ -269,9 +269,9 @@ void F_exact(const Vector &p, Vector &F)
 {
    int dim = p.Size();
 
-   double x = p(0);
-   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
+   real_t x = p(0);
+   real_t y = p(1);
+   // real_t z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
 
    F(0) = cos(kappa*x)*sin(kappa*y);
    F(1) = cos(kappa*y)*sin(kappa*x);
@@ -286,11 +286,11 @@ void f_exact(const Vector &p, Vector &f)
 {
    int dim = p.Size();
 
-   double x = p(0);
-   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
+   real_t x = p(0);
+   real_t y = p(1);
+   // real_t z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
 
-   double temp = 1 + 2*kappa*kappa;
+   real_t temp = 1 + 2*kappa*kappa;
 
    f(0) = temp*cos(kappa*x)*sin(kappa*y);
    f(1) = temp*cos(kappa*y)*sin(kappa*x);

examples/ex4p.cpp

@@ -54,7 +54,7 @@ using namespace mfem;
 // Exact solution, F, and r.h.s., f. See below for implementation.
 void F_exact(const Vector &, Vector &);
 void f_exact(const Vector &, Vector &);
-double freq = 1.0, kappa;
+real_t freq = 1.0, kappa;
 
 int main(int argc, char *argv[])
 {
@@ -255,7 +255,7 @@ int main(int argc, char *argv[])
 
    // 15. Compute and print the L^2 norm of the error.
    {
-      double error = x.ComputeL2Error(F);
+      real_t error = x.ComputeL2Error(F);
       if (myid == 0)
       {
          cout << "\n|| F_h - F ||_{L^2} = " << error << '\n' << endl;
@@ -311,9 +311,9 @@ void F_exact(const Vector &p, Vector &F)
 {
    int dim = p.Size();
 
-   double x = p(0);
-   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
+   real_t x = p(0);
+   real_t y = p(1);
+   // real_t z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
 
    F(0) = cos(kappa*x)*sin(kappa*y);
    F(1) = cos(kappa*y)*sin(kappa*x);
@@ -328,11 +328,11 @@ void f_exact(const Vector &p, Vector &f)
 {
    int dim = p.Size();
 
-   double x = p(0);
-   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
+   real_t x = p(0);
+   real_t y = p(1);
+   // real_t z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
 
-   double temp = 1 + 2*kappa*kappa;
+   real_t temp = 1 + 2*kappa*kappa;
 
    f(0) = temp*cos(kappa*x)*sin(kappa*y);
    f(1) = temp*cos(kappa*y)*sin(kappa*x);

examples/ex5.cpp

@@ -45,10 +45,10 @@ using namespace mfem;
 
 // Define the analytical solution and forcing terms / boundary conditions
 void uFun_ex(const Vector & x, Vector & u);
-double pFun_ex(const Vector & x);
+real_t pFun_ex(const Vector & x);
 void fFun(const Vector & x, Vector & f);
-double gFun(const Vector & x);
-double f_natural(const Vector & x);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
 
 int main(int argc, char *argv[])
 {
@@ -270,8 +270,8 @@ int main(int argc, char *argv[])
    // 11. Solve the linear system with MINRES.
    //     Check the norm of the unpreconditioned residual.
    int maxIter(1000);
-   double rtol(1.e-6);
-   double atol(1.e-10);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
 
    chrono.Clear();
    chrono.Start();
@@ -313,10 +313,10 @@ int main(int argc, char *argv[])
       irs[i] = &(IntRules.Get(i, order_quad));
    }
 
-   double err_u  = u.ComputeL2Error(ucoeff, irs);
-   double norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
-   double err_p  = p.ComputeL2Error(pcoeff, irs);
-   double norm_p = ComputeLpNorm(2., pcoeff, *mesh, irs);
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
+   real_t err_p  = p.ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeLpNorm(2., pcoeff, *mesh, irs);
 
    std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
    std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
@@ -391,9 +391,9 @@ int main(int argc, char *argv[])
 
 void uFun_ex(const Vector & x, Vector & u)
 {
-   double xi(x(0));
-   double yi(x(1));
-   double zi(0.0);
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
    if (x.Size() == 3)
    {
       zi = x(2);
@@ -409,11 +409,11 @@ void uFun_ex(const Vector & x, Vector & u)
 }
 
 // Change if needed
-double pFun_ex(const Vector & x)
+real_t pFun_ex(const Vector & x)
 {
-   double xi(x(0));
-   double yi(x(1));
-   double zi(0.0);
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
 
    if (x.Size() == 3)
    {
@@ -428,7 +428,7 @@ void fFun(const Vector & x, Vector & f)
    f = 0.0;
 }
 
-double gFun(const Vector & x)
+real_t gFun(const Vector & x)
 {
    if (x.Size() == 3)
    {
@@ -440,7 +440,7 @@ double gFun(const Vector & x)
    }
 }
 
-double f_natural(const Vector & x)
+real_t f_natural(const Vector & x)
 {
    return (-pFun_ex(x));
 }

examples/ex5p.cpp

@@ -46,10 +46,10 @@ using namespace mfem;
 
 // Define the analytical solution and forcing terms / boundary conditions
 void uFun_ex(const Vector & x, Vector & u);
-double pFun_ex(const Vector & x);
+real_t pFun_ex(const Vector & x);
 void fFun(const Vector & x, Vector & f);
-double gFun(const Vector & x);
-double f_natural(const Vector & x);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
 
 int main(int argc, char *argv[])
 {
@@ -326,8 +326,8 @@ int main(int argc, char *argv[])
    // 13. Solve the linear system with MINRES.
    //     Check the norm of the unpreconditioned residual.
    int maxIter(pa ? 1000 : 500);
-   double rtol(1.e-6);
-   double atol(1.e-10);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
 
    chrono.Clear();
    chrono.Start();
@@ -371,10 +371,10 @@ int main(int argc, char *argv[])
       irs[i] = &(IntRules.Get(i, order_quad));
    }
 
-   double err_u  = u->ComputeL2Error(ucoeff, irs);
-   double norm_u = ComputeGlobalLpNorm(2, ucoeff, *pmesh, irs);
-   double err_p  = p->ComputeL2Error(pcoeff, irs);
-   double norm_p = ComputeGlobalLpNorm(2, pcoeff, *pmesh, irs);
+   real_t err_u  = u->ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeGlobalLpNorm(2, ucoeff, *pmesh, irs);
+   real_t err_p  = p->ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeGlobalLpNorm(2, pcoeff, *pmesh, irs);
 
    if (verbose)
    {
@@ -493,9 +493,9 @@ int main(int argc, char *argv[])
 
 void uFun_ex(const Vector & x, Vector & u)
 {
-   double xi(x(0));
-   double yi(x(1));
-   double zi(0.0);
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
    if (x.Size() == 3)
    {
       zi = x(2);
@@ -511,11 +511,11 @@ void uFun_ex(const Vector & x, Vector & u)
 }
 
 // Change if needed
-double pFun_ex(const Vector & x)
+real_t pFun_ex(const Vector & x)
 {
-   double xi(x(0));
-   double yi(x(1));
-   double zi(0.0);
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
 
    if (x.Size() == 3)
    {
@@ -530,7 +530,7 @@ void fFun(const Vector & x, Vector & f)
    f = 0.0;
 }
 
-double gFun(const Vector & x)
+real_t gFun(const Vector & x)
 {
    if (x.Size() == 3)
    {
@@ -542,7 +542,7 @@ double gFun(const Vector & x)
    }
 }
 
-double f_natural(const Vector & x)
+real_t f_natural(const Vector & x)
 {
    return (-pFun_ex(x));
 }

examples/ex7.cpp

@@ -28,8 +28,8 @@ using namespace std;
 using namespace mfem;
 
 // Exact solution and r.h.s., see below for implementation.
-double analytic_solution(const Vector &x);
-double analytic_rhs(const Vector &x);
+real_t analytic_solution(const Vector &x);
+real_t analytic_rhs(const Vector &x);
 void SnapNodes(Mesh &mesh);
 
 int main(int argc, char *argv[])
@@ -81,7 +81,7 @@ int main(int argc, char *argv[])
 
    if (elem_type == 0) // inscribed octahedron
    {
-      const double tri_v[6][3] =
+      const real_t tri_v[6][3] =
       {
          { 1,  0,  0}, { 0,  1,  0}, {-1,  0,  0},
          { 0, -1,  0}, { 0,  0,  1}, { 0,  0, -1}
@@ -105,7 +105,7 @@ int main(int argc, char *argv[])
    }
    else // inscribed cube
    {
-      const double quad_v[8][3] =
+      const real_t quad_v[8][3] =
       {
          {-1, -1, -1}, {+1, -1, -1}, {+1, +1, -1}, {-1, +1, -1},
          {-1, -1, +1}, {+1, -1, +1}, {+1, +1, +1}, {-1, +1, +1}
@@ -249,15 +249,15 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double analytic_solution(const Vector &x)
+real_t analytic_solution(const Vector &x)
 {
-   double l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
+   real_t l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
    return x(0)*x(1)/l2;
 }
 
-double analytic_rhs(const Vector &x)
+real_t analytic_rhs(const Vector &x)
 {
-   double l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
+   real_t l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
    return 7*x(0)*x(1)/l2;
 }
 

examples/ex7p.cpp

@@ -28,8 +28,8 @@ using namespace std;
 using namespace mfem;
 
 // Exact solution and r.h.s., see below for implementation.
-double analytic_solution(const Vector &x);
-double analytic_rhs(const Vector &x);
+real_t analytic_solution(const Vector &x);
+real_t analytic_rhs(const Vector &x);
 void SnapNodes(Mesh &mesh);
 
 int main(int argc, char *argv[])
@@ -101,7 +101,7 @@ int main(int argc, char *argv[])
 
    if (elem_type == 0) // inscribed octahedron
    {
-      const double tri_v[6][3] =
+      const real_t tri_v[6][3] =
       {
          { 1,  0,  0}, { 0,  1,  0}, {-1,  0,  0},
          { 0, -1,  0}, { 0,  0,  1}, { 0,  0, -1}
@@ -125,7 +125,7 @@ int main(int argc, char *argv[])
    }
    else // inscribed cube
    {
-      const double quad_v[8][3] =
+      const real_t quad_v[8][3] =
       {
          {-1, -1, -1}, {+1, -1, -1}, {+1, +1, -1}, {-1, +1, -1},
          {-1, -1, +1}, {+1, -1, +1}, {+1, +1, +1}, {-1, +1, +1}
@@ -281,7 +281,7 @@ int main(int argc, char *argv[])
    delete b;
 
    // 12. Compute and print the L^2 norm of the error.
-   double error = x.ComputeL2Error(sol_coef);
+   real_t error = x.ComputeL2Error(sol_coef);
    if (myid == 0)
    {
       cout << "\nL2 norm of error: " << error << endl;
@@ -323,15 +323,15 @@ int main(int argc, char *argv[])
    return 0;
 }
 
-double analytic_solution(const Vector &x)
+real_t analytic_solution(const Vector &x)
 {
-   double l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
+   real_t l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
    return x(0)*x(1)/l2;
 }
 
-double analytic_rhs(const Vector &x)
+real_t analytic_rhs(const Vector &x)
 {
-   double l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
+   real_t l2 = x(0)*x(0) + x(1)*x(1) + x(2)*x(2);
    return 7*x(0)*x(1)/l2;
 }
 

examples/ex8.cpp

@@ -206,7 +206,7 @@ int main(int argc, char *argv[])
    SparseMatrix * Shat = RAP(matBhat, matSinv, matBhat);
 
 #ifndef MFEM_USE_SUITESPARSE
-   const double prec_rtol = 1e-3;
+   const real_t prec_rtol = 1e-3;
    const int prec_maxit = 200;
    CGSolver *S0inv = new CGSolver;
    S0inv->SetOperator(matS0);
@@ -240,7 +240,7 @@ int main(int argc, char *argv[])
       Vector LSres(s_test);
       B.Mult(x, LSres);
       LSres -= F;
-      double res = sqrt(matSinv.InnerProduct(LSres, LSres));
+      real_t res = sqrt(matSinv.InnerProduct(LSres, LSres));
       cout << "\n|| B0*x0 + Bhat*xhat - F ||_{S^-1} = " << res << endl;
    }
 

examples/ex8p.cpp

@@ -283,7 +283,7 @@ int main(int argc, char *argv[])
       B.Mult(x, LSres);
       LSres -= *trueF;
       matSinv->Mult(LSres, tmp);
-      double res = sqrt(InnerProduct(LSres, tmp));
+      real_t res = sqrt(InnerProduct(LSres, tmp));
       if (myid == 0)
       {
          cout << "\n|| B0*x0 + Bhat*xhat - F ||_{S^-1} = " << res << endl;

examples/ex9.cpp

@@ -58,10 +58,10 @@ int problem;
 void velocity_function(const Vector &x, Vector &v);
 
 // Initial condition
-double u0_function(const Vector &x);
+real_t u0_function(const Vector &x);
 
 // Inflow boundary condition
-double inflow_function(const Vector &x);
+real_t inflow_function(const Vector &x);
 
 // Mesh bounding box
 Vector bb_min, bb_max;
@@ -72,7 +72,7 @@ private:
    SparseMatrix &M, &K, A;
    GMRESSolver linear_solver;
    BlockILU prec;
-   double dt;
+   real_t dt;
 public:
    DG_Solver(SparseMatrix &M_, SparseMatrix &K_, const FiniteElementSpace &fes)
       : M(M_),
@@ -89,7 +89,7 @@ public:
       linear_solver.SetPreconditioner(prec);
    }
 
-   void SetTimeStep(double dt_)
+   void SetTimeStep(real_t dt_)
    {
       if (dt_ != dt)
       {
@@ -135,7 +135,7 @@ public:
    FE_Evolution(BilinearForm &M_, BilinearForm &K_, const Vector &b_);
 
    virtual void Mult(const Vector &x, Vector &y) const;
-   virtual void ImplicitSolve(const double dt, const Vector &x, Vector &k);
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
    virtual ~FE_Evolution();
 };
@@ -153,8 +153,8 @@ int main(int argc, char *argv[])
    bool fa = false;
    const char *device_config = "cpu";
    int ode_solver_type = 4;
-   double t_final = 10.0;
-   double dt = 0.01;
+   real_t t_final = 10.0;
+   real_t dt = 0.01;
    bool visualization = true;
    bool visit = false;
    bool paraview = false;
@@ -293,7 +293,7 @@ int main(int argc, char *argv[])
       k.SetAssemblyLevel(AssemblyLevel::FULL);
    }
    m.AddDomainIntegrator(new MassIntegrator);
-   constexpr double alpha = -1.0;
+   constexpr real_t alpha = -1.0;
    k.AddDomainIntegrator(new ConvectionIntegrator(velocity, alpha));
    k.AddInteriorFaceIntegrator(
       new NonconservativeDGTraceIntegrator(velocity, alpha));
@@ -393,14 +393,14 @@ int main(int argc, char *argv[])
    //    iterations, ti, with a time-step dt).
    FE_Evolution adv(m, k, b);
 
-   double t = 0.0;
+   real_t t = 0.0;
    adv.SetTime(t);
    ode_solver->Init(adv);
 
    bool done = false;
    for (int ti = 0; !done; )
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
       ode_solver->Step(u, t, dt_real);
       ti++;
 
@@ -450,7 +450,8 @@ int main(int argc, char *argv[])
 
 // Implementation of class FE_Evolution
 FE_Evolution::FE_Evolution(BilinearForm &M_, BilinearForm &K_, const Vector &b_)
-   : TimeDependentOperator(M_.Height()), M(M_), K(K_), b(b_), z(M_.Height())
+   : TimeDependentOperator(M_.FESpace()->GetTrueVSize()),
+     M(M_), K(K_), b(b_), z(height)
 {
    Array<int> ess_tdof_list;
    if (M.GetAssemblyLevel() == AssemblyLevel::LEGACY)
@@ -481,7 +482,7 @@ void FE_Evolution::Mult(const Vector &x, Vector &y) const
    M_solver.Mult(z, y);
 }
 
-void FE_Evolution::ImplicitSolve(const double dt, const Vector &x, Vector &k)
+void FE_Evolution::ImplicitSolve(const real_t dt, const Vector &x, Vector &k)
 {
    MFEM_VERIFY(dg_solver != NULL,
                "Implicit time integration is not supported with partial assembly");
@@ -506,7 +507,7 @@ void velocity_function(const Vector &x, Vector &v)
    Vector X(dim);
    for (int i = 0; i < dim; i++)
    {
-      double center = (bb_min[i] + bb_max[i]) * 0.5;
+      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
       X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
    }
 
@@ -528,7 +529,7 @@ void velocity_function(const Vector &x, Vector &v)
       case 2:
       {
          // Clockwise rotation in 2D around the origin
-         const double w = M_PI/2;
+         const real_t w = M_PI/2;
          switch (dim)
          {
             case 1: v(0) = 1.0; break;
@@ -540,8 +541,8 @@ void velocity_function(const Vector &x, Vector &v)
       case 3:
       {
          // Clockwise twisting rotation in 2D around the origin
-         const double w = M_PI/2;
-         double d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
+         const real_t w = M_PI/2;
+         real_t d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
          d = d*d;
          switch (dim)
          {
@@ -555,7 +556,7 @@ void velocity_function(const Vector &x, Vector &v)
 }
 
 // Initial condition
-double u0_function(const Vector &x)
+real_t u0_function(const Vector &x)
 {
    int dim = x.Size();
 
@@ -563,7 +564,7 @@ double u0_function(const Vector &x)
    Vector X(dim);
    for (int i = 0; i < dim; i++)
    {
-      double center = (bb_min[i] + bb_max[i]) * 0.5;
+      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
       X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
    }
 
@@ -579,28 +580,28 @@ double u0_function(const Vector &x)
             case 2:
             case 3:
             {
-               double rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
+               real_t rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
                if (dim == 3)
                {
-                  const double s = (1. + 0.25*cos(2*M_PI*X(2)));
+                  const real_t s = (1. + 0.25*cos(2*M_PI*X(2)));
                   rx *= s;
                   ry *= s;
                }
-               return ( erfc(w*(X(0)-cx-rx))*erfc(-w*(X(0)-cx+rx)) *
-                        erfc(w*(X(1)-cy-ry))*erfc(-w*(X(1)-cy+ry)) )/16;
+               return ( std::erfc(w*(X(0)-cx-rx))*std::erfc(-w*(X(0)-cx+rx)) *
+                        std::erfc(w*(X(1)-cy-ry))*std::erfc(-w*(X(1)-cy+ry)) )/16;
             }
          }
       }
       case 2:
       {
-         double x_ = X(0), y_ = X(1), rho, phi;
-         rho = hypot(x_, y_);
+         real_t x_ = X(0), y_ = X(1), rho, phi;
+         rho = std::hypot(x_, y_);
          phi = atan2(y_, x_);
          return pow(sin(M_PI*rho),2)*sin(3*phi);
       }
       case 3:
       {
-         const double f = M_PI;
+         const real_t f = M_PI;
          return sin(f*X(0))*sin(f*X(1));
       }
    }
@@ -608,7 +609,7 @@ double u0_function(const Vector &x)
 }
 
 // Inflow boundary condition (zero for the problems considered in this example)
-double inflow_function(const Vector &x)
+real_t inflow_function(const Vector &x)
 {
    switch (problem)
    {

examples/ex9p.cpp

@@ -59,10 +59,10 @@ int problem;
 void velocity_function(const Vector &x, Vector &v);
 
 // Initial condition
-double u0_function(const Vector &x);
+real_t u0_function(const Vector &x);
 
 // Inflow boundary condition
-double inflow_function(const Vector &x);
+real_t inflow_function(const Vector &x);
 
 // Mesh bounding box
 Vector bb_min, bb_max;
@@ -135,7 +135,7 @@ private:
    HypreParMatrix *A;
    GMRESSolver linear_solver;
    Solver *prec;
-   double dt;
+   real_t dt;
 public:
    DG_Solver(HypreParMatrix &M_, HypreParMatrix &K_, const FiniteElementSpace &fes,
              PrecType prec_type)
@@ -169,7 +169,7 @@ public:
       M.GetDiag(M_diag);
    }
 
-   void SetTimeStep(double dt_)
+   void SetTimeStep(real_t dt_)
    {
       if (dt_ != dt)
       {
@@ -224,7 +224,7 @@ public:
                 PrecType prec_type);
 
    virtual void Mult(const Vector &x, Vector &y) const;
-   virtual void ImplicitSolve(const double dt, const Vector &x, Vector &k);
+   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
 
    virtual ~FE_Evolution();
 };
@@ -249,8 +249,8 @@ int main(int argc, char *argv[])
    bool fa = false;
    const char *device_config = "cpu";
    int ode_solver_type = 4;
-   double t_final = 10.0;
-   double dt = 0.01;
+   real_t t_final = 10.0;
+   real_t dt = 0.01;
    bool visualization = true;
    bool visit = false;
    bool paraview = false;
@@ -425,7 +425,7 @@ int main(int argc, char *argv[])
    }
 
    m->AddDomainIntegrator(new MassIntegrator);
-   constexpr double alpha = -1.0;
+   constexpr real_t alpha = -1.0;
    k->AddDomainIntegrator(new ConvectionIntegrator(velocity, alpha));
    k->AddInteriorFaceIntegrator(
       new NonconservativeDGTraceIntegrator(velocity, alpha));
@@ -566,14 +566,14 @@ int main(int argc, char *argv[])
    //     iterations, ti, with a time-step dt).
    FE_Evolution adv(*m, *k, *B, prec_type);
 
-   double t = 0.0;
+   real_t t = 0.0;
    adv.SetTime(t);
    ode_solver->Init(adv);
 
    bool done = false;
    for (int ti = 0; !done; )
    {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);
       ode_solver->Step(*U, t, dt_real);
       ti++;
 
@@ -659,9 +659,9 @@ int main(int argc, char *argv[])
 // Implementation of class FE_Evolution
 FE_Evolution::FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
                            const Vector &b_, PrecType prec_type)
-   : TimeDependentOperator(M_.Height()), b(b_),
+   : TimeDependentOperator(M_.ParFESpace()->GetTrueVSize()), b(b_),
      M_solver(M_.ParFESpace()->GetComm()),
-     z(M_.Height())
+     z(height)
 {
    if (M_.GetAssemblyLevel()==AssemblyLevel::LEGACY)
    {
@@ -704,7 +704,7 @@ FE_Evolution::FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
 //    u_t = M^{-1}(Ku + b),
 // by solving associated linear system
 //    (M - dt*K) d = K*u + b
-void FE_Evolution::ImplicitSolve(const double dt, const Vector &x, Vector &k)
+void FE_Evolution::ImplicitSolve(const real_t dt, const Vector &x, Vector &k)
 {
    K->Mult(x, z);
    z += b;
@@ -736,7 +736,7 @@ void velocity_function(const Vector &x, Vector &v)
    Vector X(dim);
    for (int i = 0; i < dim; i++)
    {
-      double center = (bb_min[i] + bb_max[i]) * 0.5;
+      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
       X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
    }
 
@@ -758,7 +758,7 @@ void velocity_function(const Vector &x, Vector &v)
       case 2:
       {
          // Clockwise rotation in 2D around the origin
-         const double w = M_PI/2;
+         const real_t w = M_PI/2;
          switch (dim)
          {
             case 1: v(0) = 1.0; break;
@@ -770,8 +770,8 @@ void velocity_function(const Vector &x, Vector &v)
       case 3:
       {
          // Clockwise twisting rotation in 2D around the origin
-         const double w = M_PI/2;
-         double d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
+         const real_t w = M_PI/2;
+         real_t d = max((X(0)+1.)*(1.-X(0)),0.) * max((X(1)+1.)*(1.-X(1)),0.);
          d = d*d;
          switch (dim)
          {
@@ -785,7 +785,7 @@ void velocity_function(const Vector &x, Vector &v)
 }
 
 // Initial condition
-double u0_function(const Vector &x)
+real_t u0_function(const Vector &x)
 {
    int dim = x.Size();
 
@@ -793,7 +793,7 @@ double u0_function(const Vector &x)
    Vector X(dim);
    for (int i = 0; i < dim; i++)
    {
-      double center = (bb_min[i] + bb_max[i]) * 0.5;
+      real_t center = (bb_min[i] + bb_max[i]) * 0.5;
       X(i) = 2 * (x(i) - center) / (bb_max[i] - bb_min[i]);
    }
 
@@ -809,28 +809,28 @@ double u0_function(const Vector &x)
             case 2:
             case 3:
             {
-               double rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
+               real_t rx = 0.45, ry = 0.25, cx = 0., cy = -0.2, w = 10.;
                if (dim == 3)
                {
-                  const double s = (1. + 0.25*cos(2*M_PI*X(2)));
+                  const real_t s = (1. + 0.25*cos(2*M_PI*X(2)));
                   rx *= s;
                   ry *= s;
                }
-               return ( erfc(w*(X(0)-cx-rx))*erfc(-w*(X(0)-cx+rx)) *
-                        erfc(w*(X(1)-cy-ry))*erfc(-w*(X(1)-cy+ry)) )/16;
+               return ( std::erfc(w*(X(0)-cx-rx))*std::erfc(-w*(X(0)-cx+rx)) *
+                        std::erfc(w*(X(1)-cy-ry))*std::erfc(-w*(X(1)-cy+ry)) )/16;
             }
          }
       }
       case 2:
       {
-         double x_ = X(0), y_ = X(1), rho, phi;
-         rho = hypot(x_, y_);
+         real_t x_ = X(0), y_ = X(1), rho, phi;
+         rho = std::hypot(x_, y_);
          phi = atan2(y_, x_);
          return pow(sin(M_PI*rho),2)*sin(3*phi);
       }
       case 3:
       {
-         const double f = M_PI;
+         const real_t f = M_PI;
          return sin(f*X(0))*sin(f*X(1));
       }
    }
@@ -838,7 +838,7 @@ double u0_function(const Vector &x)
 }
 
 // Inflow boundary condition (zero for the problems considered in this example)
-double inflow_function(const Vector &x)
+real_t inflow_function(const Vector &x)
 {
    switch (problem)
    {

examples/ginkgo/ex1.cpp

@@ -3,28 +3,28 @@
 //
 // Compile with: make ex1
 //
-// Sample runs:  ex1 -m ../data/square-disc.mesh
-//               ex1 -m ../data/star.mesh
-//               ex1 -m ../data/star-mixed.mesh
-//               ex1 -m ../data/escher.mesh
-//               ex1 -m ../data/fichera.mesh
-//               ex1 -m ../data/fichera-mixed.mesh
-//               ex1 -m ../data/toroid-wedge.mesh
-//               ex1 -m ../data/square-disc-p2.vtk -o 2
-//               ex1 -m ../data/square-disc-p3.mesh -o 3
-//               ex1 -m ../data/square-disc-nurbs.mesh -o -1
-//               ex1 -m ../data/star-mixed-p2.mesh -o 2
-//               ex1 -m ../data/disc-nurbs.mesh -o -1
-//               ex1 -m ../data/pipe-nurbs.mesh -o -1
-//               ex1 -m ../data/fichera-mixed-p2.mesh -o 2
-//               ex1 -m ../data/star-surf.mesh
-//               ex1 -m ../data/square-disc-surf.mesh
-//               ex1 -m ../data/inline-segment.mesh
-//               ex1 -m ../data/amr-quad.mesh
-//               ex1 -m ../data/amr-hex.mesh
-//               ex1 -m ../data/fichera-amr.mesh
-//               ex1 -m ../data/mobius-strip.mesh
-//               ex1 -m ../data/mobius-strip.mesh -o -1 -sc
+// Sample runs:  ex1 -m ../../data/square-disc.mesh
+//               ex1 -m ../../data/star.mesh
+//               ex1 -m ../../data/star-mixed.mesh
+//               ex1 -m ../../data/escher.mesh
+//               ex1 -m ../../data/fichera.mesh
+//               ex1 -m ../../data/fichera-mixed.mesh
+//               ex1 -m ../../data/toroid-wedge.mesh
+//               ex1 -m ../../data/square-disc-p2.vtk -o 2
+//               ex1 -m ../../data/square-disc-p3.mesh -o 3
+//               ex1 -m ../../data/square-disc-nurbs.mesh -o -1
+//               ex1 -m ../../data/star-mixed-p2.mesh -o 2
+//               ex1 -m ../../data/disc-nurbs.mesh -o -1
+//               ex1 -m ../../data/pipe-nurbs.mesh -o -1
+//               ex1 -m ../../data/fichera-mixed-p2.mesh -o 2
+//               ex1 -m ../../data/star-surf.mesh
+//               ex1 -m ../../data/square-disc-surf.mesh
+//               ex1 -m ../../data/inline-segment.mesh
+//               ex1 -m ../../data/amr-quad.mesh
+//               ex1 -m ../../data/amr-hex.mesh
+//               ex1 -m ../../data/fichera-amr.mesh
+//               ex1 -m ../../data/mobius-strip.mesh
+//               ex1 -m ../../data/mobius-strip.mesh -o -1 -sc
 //
 // Device sample runs:
 //               ex1 -pa -d cuda
@@ -32,7 +32,7 @@
 //               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 -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/makefile

@@ -22,15 +22,19 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
-  ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
-  ex31 ex33 ex34 ex36 ex37
+   ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
+   ex31 ex33 ex34 ex36 ex37
 PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
-  ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
-  ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
-	ex37p
+   ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
+   ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
+   ex37p
 SEQ_DEVICE_EXAMPLES = ex1 ex3 ex4 ex5 ex6 ex9 ex22 ex24 ex25 ex26 ex34
 PAR_DEVICE_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex9p ex13p ex22p \
-  ex24p ex25p ex26p ex34p ex35p
+   ex24p ex25p ex26p ex34p ex35p
+
+ifeq ($(MFEM_USE_LAPACK),YES)
+   SEQ_EXAMPLES += ex38
+endif
 
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)

examples/petsc/ex11p.cpp

@@ -273,12 +273,13 @@ int main(int argc, char *argv[])
 #ifdef MFEM_USE_STRUMPACK
          if (sp_solver)
          {
-            STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+            STRUMPACKSolver * strumpack = new STRUMPACKSolver(MPI_COMM_WORLD, argc, argv);
             strumpack->SetPrintFactorStatistics(true);
             strumpack->SetPrintSolveStatistics(false);
             strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
             strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
-            strumpack->DisableMatching();
+            strumpack->SetMatching(strumpack::MatchingJob::NONE);
+            strumpack->SetCompression(strumpack::CompressionType::NONE);
             strumpack->SetOperator(*Arow);
             strumpack->SetFromCommandLine();
             precond = strumpack;

examples/petsc/ex5p.cpp

@@ -17,7 +17,7 @@
 //               finite elements (velocity u) and piecewise discontinuous
 //               polynomials (pressure p).
 //
-//               The example demonstrates the use of the BlockMatrix class, as
+//               The example demonstrates the use of the BlockOperator class, as
 //               well as the collective saving of several grid functions in a
 //               VisIt (visit.llnl.gov) visualization format.
 //

examples/petsc/ex9p.cpp

@@ -520,10 +520,10 @@ int main(int argc, char *argv[])
 // Implementation of class FE_Evolution
 FE_Evolution::FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
                            const Vector &b_,bool M_in_lhs)
-   : TimeDependentOperator(M_.Height(), 0.0,
+   : TimeDependentOperator(M_.ParFESpace()->GetTrueVSize(), 0.0,
                            M_in_lhs ? TimeDependentOperator::IMPLICIT
                            : TimeDependentOperator::EXPLICIT),
-     b(b_), comm(M_.ParFESpace()->GetComm()), M_solver(comm), z(M_.Height()),
+     b(b_), comm(M_.ParFESpace()->GetComm()), M_solver(comm), z(height),
      iJacobian(NULL), rJacobian(NULL)
 {
    MAlev = M_.GetAssemblyLevel();

examples/sundials/ex9.cpp

@@ -476,7 +476,8 @@ int main(int argc, char *argv[])
 
 // Implementation of class FE_Evolution
 FE_Evolution::FE_Evolution(BilinearForm &M_, BilinearForm &K_, const Vector &b_)
-   : TimeDependentOperator(M_.Height()), M(M_), K(K_), b(b_), z(M_.Height())
+   : TimeDependentOperator(M_.FESpace()->GetTrueVSize()),
+     M(M_), K(K_), b(b_), z(height)
 {
    Array<int> ess_tdof_list;
    if (M.GetAssemblyLevel() == AssemblyLevel::LEGACY)

examples/sundials/ex9p.cpp

@@ -679,10 +679,10 @@ int main(int argc, char *argv[])
 // Implementation of class FE_Evolution
 FE_Evolution::FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_,
                            const Vector &b_, PrecType prec_type)
-   : TimeDependentOperator(M_.Height()),
+   : TimeDependentOperator(M_.ParFESpace()->GetTrueVSize()),
      b(b_),
      M_solver(M_.ParFESpace()->GetComm()),
-     z(M_.Height())
+     z(height)
 {
    if (M_.GetAssemblyLevel()==AssemblyLevel::LEGACY)
    {

fem/CMakeLists.txt

@@ -25,6 +25,8 @@ set(SRCS
   integ/bilininteg_diffusion_ea.cpp
   integ/bilininteg_diffusion_patch.cpp
   integ/bilininteg_divdiv_pa.cpp
+  integ/bilininteg_elasticity_ea.cpp
+  integ/bilininteg_elasticity_pa.cpp
   integ/bilininteg_gradient_pa.cpp
   integ/bilininteg_interp_pa.cpp
   integ/bilininteg_mass_mf.cpp
@@ -41,6 +43,7 @@ set(SRCS
   integ/bilininteg_vectorfediv_pa.cpp
   integ/bilininteg_vectorfemass_pa.cpp
   integ/bilininteg_diffusion_kernels.cpp
+  integ/bilininteg_elasticity_kernels.cpp
   integ/bilininteg_hcurl_kernels.cpp
   integ/bilininteg_hdiv_kernels.cpp
   integ/bilininteg_hcurlhdiv_kernels.cpp
@@ -77,6 +80,7 @@ set(SRCS
   gridfunc.cpp
   hybridization.cpp
   intrules.cpp
+  intrules_cut.cpp
   ceed/interface/basis.cpp
   ceed/interface/restriction.cpp
   ceed/interface/operator.cpp
@@ -96,9 +100,6 @@ set(SRCS
   lor/lor_ads.cpp
   lor/lor_ams.cpp
   lor/lor_batched.cpp
-  lor/lor_h1.cpp
-  lor/lor_nd.cpp
-  lor/lor_rt.cpp
   multigrid.cpp
   nonlinearform.cpp
   nonlinearform_ext.cpp
@@ -155,6 +156,7 @@ set(HDRS
   bilinearform_ext.hpp
   bilininteg.hpp
   integ/bilininteg_diffusion_kernels.hpp
+  integ/bilininteg_elasticity_kernels.hpp
   integ/bilininteg_hcurl_kernels.hpp
   integ/bilininteg_hdiv_kernels.hpp
   integ/bilininteg_hcurlhdiv_kernels.hpp
@@ -186,6 +188,7 @@ set(HDRS
   gridfunc.hpp
   hybridization.hpp
   intrules.hpp
+  intrules_cut.hpp
   ceed/interface/basis.hpp
   ceed/interface/integrator.hpp
   ceed/interface/interface.hpp

fem/bilinearform.cpp

@@ -56,7 +56,7 @@ void BilinearForm::AllocMat()
 
    int *I = dof_dof.GetI();
    int *J = dof_dof.GetJ();
-   double *data = Memory<double>(I[height]);
+   real_t *data = Memory<real_t>(I[height]);
 
    mat = new SparseMatrix(I, J, data, height, height, true, true, true);
    *mat = 0.0;
@@ -101,6 +101,7 @@ BilinearForm::BilinearForm (FiniteElementSpace * f, BilinearForm * bf, int ps)
 
    // Copy the pointers to the integrators
    domain_integs = bf->domain_integs;
+   domain_integs_marker = bf->domain_integs_marker;
 
    boundary_integs = bf->boundary_integs;
    boundary_integs_marker = bf->boundary_integs_marker;
@@ -208,12 +209,12 @@ void BilinearForm::UseSparsity(SparseMatrix &A)
    UseSparsity(A.GetI(), A.GetJ(), A.ColumnsAreSorted());
 }
 
-double& BilinearForm::Elem (int i, int j)
+real_t& BilinearForm::Elem (int i, int j)
 {
    return mat -> Elem(i,j);
 }
 
-const double& BilinearForm::Elem (int i, int j) const
+const real_t& BilinearForm::Elem (int i, int j) const
 {
    return mat -> Elem(i,j);
 }
@@ -433,6 +434,9 @@ void BilinearForm::Assemble(int skip_zeros)
       // Element-wise integration
       for (int i = 0; i < fes -> GetNE(); i++)
       {
+         // Set both doftrans (potentially needed to assemble the element
+         // matrix) and vdofs, which is also needed when the element matrices
+         // are pre-assembled.
          doftrans = fes->GetElementVDofs(i, vdofs);
          if (element_matrices)
          {
@@ -441,6 +445,8 @@ void BilinearForm::Assemble(int skip_zeros)
          else
          {
             const int elem_attr = fes->GetMesh()->GetAttribute(i);
+            eltrans = fes->GetElementTransformation(i);
+
             elmat.SetSize(0);
             for (int k = 0; k < domain_integs.Size(); k++)
             {
@@ -448,9 +454,8 @@ void BilinearForm::Assemble(int skip_zeros)
                     (*(domain_integs_marker[k]))[elem_attr-1] == 1)
                    && !domain_integs[k]->Patchwise())
                {
-                  const FiniteElement &fe = *fes->GetFE(i);
-                  eltrans = fes->GetElementTransformation(i);
-                  domain_integs[k]->AssembleElementMatrix(fe, *eltrans, elemmat);
+                  domain_integs[k]->AssembleElementMatrix(*fes->GetFE(i),
+                                                          *eltrans, elemmat);
                   if (elmat.Size() == 0)
                   {
                      elmat = elemmat;
@@ -996,7 +1001,7 @@ void BilinearForm::EliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
 }
 
 void BilinearForm::EliminateEssentialBCDiag (const Array<int> &bdr_attr_is_ess,
-                                             double value)
+                                             real_t value)
 {
    Array<int> ess_dofs, conf_ess_dofs;
    fes->GetEssentialVDofs(bdr_attr_is_ess, ess_dofs);
@@ -1072,7 +1077,8 @@ void BilinearForm::EliminateEssentialBCFromDofs(
 void BilinearForm::EliminateEssentialBCFromDofs (const Array<int> &ess_dofs,
                                                  DiagonalPolicy dpolicy)
 {
-   MFEM_ASSERT(ess_dofs.Size() == height, "incorrect dof Array size");
+   MFEM_ASSERT(ess_dofs.Size() == height,
+               "incorrect dof Array size: " << ess_dofs.Size() << ' ' << height);
 
    for (int i = 0; i < ess_dofs.Size(); i++)
       if (ess_dofs[i] < 0)
@@ -1082,9 +1088,10 @@ void BilinearForm::EliminateEssentialBCFromDofs (const Array<int> &ess_dofs,
 }
 
 void BilinearForm::EliminateEssentialBCFromDofsDiag (const Array<int> &ess_dofs,
-                                                     double value)
+                                                     real_t value)
 {
-   MFEM_ASSERT(ess_dofs.Size() == height, "incorrect dof Array size");
+   MFEM_ASSERT(ess_dofs.Size() == height,
+               "incorrect dof Array size: " << ess_dofs.Size() << ' ' << height);
 
    for (int i = 0; i < ess_dofs.Size(); i++)
       if (ess_dofs[i] < 0)
@@ -1222,11 +1229,14 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
 
    // Copy the pointers to the integrators
    domain_integs = mbf->domain_integs;
-   boundary_integs = mbf->boundary_integs;
-   trace_face_integs = mbf->trace_face_integs;
-   boundary_trace_face_integs = mbf->boundary_trace_face_integs;
+   domain_integs_marker = mbf->domain_integs_marker;
 
+   boundary_integs = mbf->boundary_integs;
    boundary_integs_marker = mbf->boundary_integs_marker;
+
+   trace_face_integs = mbf->trace_face_integs;
+
+   boundary_trace_face_integs = mbf->boundary_trace_face_integs;
    boundary_trace_face_integs_marker = mbf->boundary_trace_face_integs_marker;
 
    assembly = AssemblyLevel::LEGACY;
@@ -1264,12 +1274,12 @@ void MixedBilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
    }
 }
 
-double & MixedBilinearForm::Elem (int i, int j)
+real_t & MixedBilinearForm::Elem (int i, int j)
 {
    return (*mat)(i, j);
 }
 
-const double & MixedBilinearForm::Elem (int i, int j) const
+const real_t & MixedBilinearForm::Elem (int i, int j) const
 {
    return (*mat)(i, j);
 }
@@ -1281,7 +1291,7 @@ void MixedBilinearForm::Mult(const Vector & x, Vector & y) const
 }
 
 void MixedBilinearForm::AddMult(const Vector & x, Vector & y,
-                                const double a) const
+                                const real_t a) const
 {
    if (ext)
    {
@@ -1300,7 +1310,7 @@ void MixedBilinearForm::MultTranspose(const Vector & x, Vector & y) const
 }
 
 void MixedBilinearForm::AddMultTranspose(const Vector & x, Vector & y,
-                                         const double a) const
+                                         const real_t a) const
 {
    if (ext)
    {
@@ -1349,6 +1359,14 @@ void MixedBilinearForm::GetBlocks(Array2D<SparseMatrix *> &blocks) const
 void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi)
 {
    domain_integs.Append (bfi);
+   domain_integs_marker.Append(NULL); // NULL marker means apply everywhere
+}
+
+void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi,
+                                             Array<int> &elem_marker)
+{
+   domain_integs.Append (bfi);
+   domain_integs_marker.Append(&elem_marker);
 }
 
 void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
@@ -1383,7 +1401,7 @@ void MixedBilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator *bfi,
    boundary_trace_face_integs_marker.Append(&bdr_marker);
 }
 
-void MixedBilinearForm::Assemble (int skip_zeros)
+void MixedBilinearForm::Assemble(int skip_zeros)
 {
    if (ext)
    {
@@ -1405,8 +1423,20 @@ void MixedBilinearForm::Assemble (int skip_zeros)
 
    if (domain_integs.Size())
    {
+      for (int k = 0; k < domain_integs.Size(); k++)
+      {
+         if (domain_integs_marker[k] != NULL)
+         {
+            MFEM_VERIFY(domain_integs_marker[k]->Size() ==
+                        (mesh->attributes.Size() ? mesh->attributes.Max() : 0),
+                        "invalid element marker for domain integrator #"
+                        << k << ", counting from zero");
+         }
+      }
+
       for (int i = 0; i < test_fes -> GetNE(); i++)
       {
+         const int elem_attr = mesh->GetAttribute(i);
          dom_dof_trans = trial_fes -> GetElementVDofs (i, trial_vdofs);
          ran_dof_trans = test_fes  -> GetElementVDofs (i, test_vdofs);
          eltrans = test_fes -> GetElementTransformation (i);
@@ -1415,10 +1445,14 @@ void MixedBilinearForm::Assemble (int skip_zeros)
          elmat = 0.0;
          for (int k = 0; k < domain_integs.Size(); k++)
          {
-            domain_integs[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
-                                                        *test_fes  -> GetFE(i),
-                                                        *eltrans, elemmat);
-            elmat += elemmat;
+            if (domain_integs_marker[k] == NULL ||
+                (*(domain_integs_marker[k]))[elem_attr-1] == 1)
+            {
+               domain_integs[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
+                                                           *test_fes  -> GetFE(i),
+                                                           *eltrans, elemmat);
+               elmat += elemmat;
+            }
          }
          if (ran_dof_trans || dom_dof_trans)
          {
@@ -1941,41 +1975,56 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
       return;
    }
 
-   Array<int> dom_vdofs, ran_vdofs;
-   ElementTransformation *T;
+   ElementTransformation *eltrans;
    DofTransformation * dom_dof_trans;
    DofTransformation * ran_dof_trans;
-   const FiniteElement *dom_fe, *ran_fe;
-   DenseMatrix totelmat, elmat;
+   DenseMatrix elmat;
+
+   Mesh *mesh = test_fes->GetMesh();
 
    if (mat == NULL)
    {
       mat = new SparseMatrix(height, width);
    }
 
-   if (domain_integs.Size() > 0)
+   if (domain_integs.Size())
    {
+      for (int k = 0; k < domain_integs.Size(); k++)
+      {
+         if (domain_integs_marker[k] != NULL)
+         {
+            MFEM_VERIFY(domain_integs_marker[k]->Size() ==
+                        (mesh->attributes.Size() ? mesh->attributes.Max() : 0),
+                        "invalid element marker for domain integrator #"
+                        << k << ", counting from zero");
+         }
+      }
+
       for (int i = 0; i < test_fes->GetNE(); i++)
       {
-         dom_dof_trans = trial_fes->GetElementVDofs(i, dom_vdofs);
-         ran_dof_trans = test_fes->GetElementVDofs(i, ran_vdofs);
-         T = test_fes->GetElementTransformation(i);
-         dom_fe = trial_fes->GetFE(i);
-         ran_fe = test_fes->GetFE(i);
+         const int elem_attr = mesh->GetAttribute(i);
+         dom_dof_trans = trial_fes->GetElementVDofs(i, trial_vdofs);
+         ran_dof_trans = test_fes->GetElementVDofs(i, test_vdofs);
+         eltrans = test_fes->GetElementTransformation(i);
 
-         domain_integs[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                  totelmat);
-         for (int j = 1; j < domain_integs.Size(); j++)
+         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+         elmat = 0.0;
+         for (int k = 0; k < domain_integs.Size(); k++)
          {
-            domain_integs[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                     elmat);
-            totelmat += elmat;
+            if (domain_integs_marker[k] == NULL ||
+                (*(domain_integs_marker[k]))[elem_attr-1] == 1)
+            {
+               domain_integs[k]->AssembleElementMatrix2(*trial_fes->GetFE(i),
+                                                        *test_fes->GetFE(i),
+                                                        *eltrans, elemmat);
+               elmat += elemmat;
+            }
          }
          if (ran_dof_trans || dom_dof_trans)
          {
-            TransformPrimal(ran_dof_trans, dom_dof_trans, totelmat);
+            TransformPrimal(ran_dof_trans, dom_dof_trans, elemmat);
          }
-         mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
+         mat->SetSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
       }
    }
 
@@ -1984,21 +2033,20 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
       const int nfaces = test_fes->GetMesh()->GetNumFaces();
       for (int i = 0; i < nfaces; i++)
       {
-         trial_fes->GetFaceVDofs(i, dom_vdofs);
-         test_fes->GetFaceVDofs(i, ran_vdofs);
-         T = test_fes->GetMesh()->GetFaceTransformation(i);
-         dom_fe = trial_fes->GetFaceElement(i);
-         ran_fe = test_fes->GetFaceElement(i);
+         trial_fes->GetFaceVDofs(i, trial_vdofs);
+         test_fes->GetFaceVDofs(i, test_vdofs);
+         eltrans = test_fes->GetMesh()->GetFaceTransformation(i);
 
-         trace_face_integs[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                      totelmat);
-         for (int j = 1; j < trace_face_integs.Size(); j++)
+         elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+         elmat = 0.0;
+         for (int k = 0; k < trace_face_integs.Size(); k++)
          {
-            trace_face_integs[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T,
-                                                         elmat);
-            totelmat += elmat;
+            trace_face_integs[k]->AssembleElementMatrix2(*trial_fes->GetFaceElement(i),
+                                                         *test_fes->GetFaceElement(i),
+                                                         *eltrans, elemmat);
+            elmat += elemmat;
          }
-         mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
+         mat->SetSubMatrix(test_vdofs, trial_vdofs, elmat, skip_zeros);
       }
    }
 }

fem/bilinearform.hpp

@@ -100,7 +100,7 @@ protected:
    /// Includes all by default.
    /// 0 - ignore attribute
    /// 1 - include attribute
-   Array<Array<int>*>             domain_integs_marker;
+   Array<Array<int>*> domain_integs_marker; ///< Entries are not owned.
 
    /// Set of Boundary Integrators to be applied.
    Array<BilinearFormIntegrator*> boundary_integs;
@@ -279,13 +279,13 @@ public:
    { return &boundary_face_integs_marker; }
 
    /// Returns a reference to: \f$ M_{ij} \f$
-   const double &operator()(int i, int j) { return (*mat)(i,j); }
+   const real_t &operator()(int i, int j) { return (*mat)(i,j); }
 
    /// Returns a reference to: \f$ M_{ij} \f$
-   virtual double &Elem(int i, int j);
+   virtual real_t &Elem(int i, int j);
 
    /// Returns constant reference to: \f$ M_{ij} \f$
-   virtual const double &Elem(int i, int j) const;
+   virtual const real_t &Elem(int i, int j) const;
 
    /// Matrix vector multiplication:  \f$ y = M x \f$
    virtual void Mult(const Vector &x, Vector &y) const;
@@ -297,7 +297,7 @@ public:
    { mat->Mult(x, y); mat_e->AddMult(x, y); }
 
    /// Add the matrix vector multiple to a vector:  \f$ y += a M x \f$
-   virtual void AddMult(const Vector &x, Vector &y, const double a = 1.0) const
+   virtual void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const
    { mat -> AddMult (x, y, a); }
 
    /** @brief Add the original uneliminated matrix vector multiple to a vector.
@@ -308,7 +308,7 @@ public:
 
    /// Add the matrix transpose vector multiplication:  \f$ y += a M^T x \f$
    virtual void AddMultTranspose(const Vector & x, Vector & y,
-                                 const double a = 1.0) const
+                                 const real_t a = 1.0) const
    { mat->AddMultTranspose(x, y, a); }
 
    /** @brief Add the original uneliminated matrix transpose vector
@@ -321,7 +321,7 @@ public:
    virtual void MultTranspose(const Vector & x, Vector & y) const;
 
    /// Compute \f$ y^T M x \f$
-   double InnerProduct(const Vector &x, const Vector &y) const
+   real_t InnerProduct(const Vector &x, const Vector &y) const
    { return mat->InnerProduct (x, y); }
 
    /// Returns a pointer to (approximation) of the matrix inverse:  \f$ M^{-1} \f$
@@ -423,7 +423,7 @@ public:
                              Array<int> &bdr_marker);
 
    /// Sets all sparse values of \f$ M \f$ and \f$ M_e \f$ to 'a'.
-   void operator=(const double a)
+   void operator=(const real_t a)
    {
       if (mat != NULL) { *mat = a; }
       if (mat_e != NULL) { *mat_e = a; }
@@ -614,7 +614,7 @@ public:
                              DiagonalPolicy dpolicy = DIAG_ONE);
    /// Perform elimination and set the diagonal entry to the given value
    void EliminateEssentialBCDiag(const Array<int> &bdr_attr_is_ess,
-                                 double value);
+                                 real_t value);
 
    /// Eliminate the given @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
    /** In this case the eliminations are applied to the internal \f$ M \f$
@@ -643,7 +643,7 @@ public:
                                      DiagonalPolicy dpolicy = DIAG_ONE);
    /// Perform elimination and set the diagonal entry to the given value
    void EliminateEssentialBCFromDofsDiag(const Array<int> &ess_dofs,
-                                         double value);
+                                         real_t value);
 
    /** @brief Use the stored eliminated part of the matrix (see
        EliminateVDofs(const Array<int> &, DiagonalPolicy)) to modify the r.h.s.
@@ -652,7 +652,7 @@ public:
                             Vector &b);
 
    /// Compute inner product for full uneliminated matrix \f$ y^T M x + y^T M_e x \f$
-   double FullInnerProduct(const Vector &x, const Vector &y) const
+   real_t FullInnerProduct(const Vector &x, const Vector &y) const
    { return mat->InnerProduct(x, y) + mat_e->InnerProduct(x, y); }
 
    /// Update the @a FiniteElementSpace and delete all data associated with the old one.
@@ -722,10 +722,13 @@ protected:
 
    /// Domain integrators.
    Array<BilinearFormIntegrator*> domain_integs;
+   /// Entries are not owned.
+   Array<Array<int>*> domain_integs_marker;
 
    /// Boundary integrators.
    Array<BilinearFormIntegrator*> boundary_integs;
-   Array<Array<int>*> boundary_integs_marker; ///< Entries are not owned.
+   /// Entries are not owned.
+   Array<Array<int>*> boundary_integs_marker;
 
    /// Trace face (skeleton) integrators.
    Array<BilinearFormIntegrator*> trace_face_integs;
@@ -767,20 +770,20 @@ public:
                      MixedBilinearForm *mbf);
 
    /// Returns a reference to: \f$ M_{ij} \f$
-   virtual double &Elem(int i, int j);
+   virtual real_t &Elem(int i, int j);
 
    /// Returns a reference to: \f$ M_{ij} \f$
-   virtual const double &Elem(int i, int j) const;
+   virtual const real_t &Elem(int i, int j) const;
 
    /// Matrix multiplication: \f$ y = M x \f$
    virtual void Mult(const Vector & x, Vector & y) const;
 
    virtual void AddMult(const Vector & x, Vector & y,
-                        const double a = 1.0) const;
+                        const real_t a = 1.0) const;
 
    virtual void MultTranspose(const Vector & x, Vector & y) const;
    virtual void AddMultTranspose(const Vector & x, Vector & y,
-                                 const double a = 1.0) const;
+                                 const real_t a = 1.0) const;
 
    virtual MatrixInverse *Inverse() const;
 
@@ -805,12 +808,16 @@ public:
    /// Adds a domain integrator. Assumes ownership of @a bfi.
    void AddDomainIntegrator(BilinearFormIntegrator *bfi);
 
+   /// Adds a domain integrator. Assumes ownership of @a bfi.
+   void AddDomainIntegrator(BilinearFormIntegrator *bfi,
+                            Array<int> &elem_marker);
+
    /// Adds a boundary integrator. Assumes ownership of @a bfi.
    void AddBoundaryIntegrator(BilinearFormIntegrator *bfi);
 
    /// Adds a boundary integrator. Assumes ownership of @a bfi.
-   void AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
-                               Array<int> &bdr_marker);
+   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi,
+                              Array<int> &bdr_marker);
 
    /** @brief Add a trace face integrator. Assumes ownership of @a bfi.
 
@@ -820,14 +827,18 @@ public:
    void AddTraceFaceIntegrator(BilinearFormIntegrator *bfi);
 
    /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
-   void AddBdrTraceFaceIntegrator (BilinearFormIntegrator * bfi);
+   void AddBdrTraceFaceIntegrator(BilinearFormIntegrator * bfi);
 
    /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
-   void AddBdrTraceFaceIntegrator (BilinearFormIntegrator * bfi,
-                                   Array<int> &bdr_marker);
+   void AddBdrTraceFaceIntegrator(BilinearFormIntegrator * bfi,
+                                  Array<int> &bdr_marker);
 
    /// Access all integrators added with AddDomainIntegrator().
    Array<BilinearFormIntegrator*> *GetDBFI() { return &domain_integs; }
+   /** @brief Access all domain markers added with AddDomainIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetDBFI_Marker() { return &domain_integs_marker; }
 
    /// Access all integrators added with AddBoundaryIntegrator().
    Array<BilinearFormIntegrator*> *GetBBFI() { return &boundary_integs; }
@@ -849,7 +860,7 @@ public:
    { return &boundary_trace_face_integs_marker; }
 
    /// Sets all sparse values of \f$ M \f$ to @a a.
-   void operator=(const double a) { *mat = a; }
+   void operator=(const real_t a) { *mat = a; }
 
    /// Set the desired assembly level. The default is AssemblyLevel::LEGACY.
    /** This method must be called before assembly. */
@@ -1065,6 +1076,9 @@ public:
    /// Adds a domain interpolator. Assumes ownership of @a di.
    void AddDomainInterpolator(DiscreteInterpolator *di)
    { AddDomainIntegrator(di); }
+   void AddDomainInterpolator(DiscreteInterpolator *di,
+                              Array<int> &elem_marker)
+   { AddDomainIntegrator(di, elem_marker); }
 
    /// Adds a trace face interpolator. Assumes ownership of @a di.
    void AddTraceFaceInterpolator(DiscreteInterpolator *di)
@@ -1072,6 +1086,7 @@ public:
 
    /// Access all interpolators added with AddDomainInterpolator().
    Array<BilinearFormIntegrator*> *GetDI() { return &domain_integs; }
+   Array<Array<int>*> *GetDI_Marker() { return &domain_integs_marker; }
 
    /// Set the desired assembly level. The default is AssemblyLevel::FULL.
    /** This method must be called before assembly. */

fem/bilinearform_ext.cpp

@@ -255,9 +255,7 @@ PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
 void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
 {
    if ( Device::Allows(Backend::CEED_MASK) ) { return; }
-   ElementDofOrdering ordering = UsesTensorBasis(*a->FESpace())?
-                                 ElementDofOrdering::LEXICOGRAPHIC:
-                                 ElementDofOrdering::NATIVE;
+   ElementDofOrdering ordering = GetEVectorOrdering(*a->FESpace());
    elem_restrict = trial_fes->GetElementRestriction(ordering);
    if (elem_restrict)
    {
@@ -303,7 +301,7 @@ void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
       std::unordered_map<int,int> f_to_be;
       for (int i = 0; i < mesh.GetNBE(); ++i)
       {
-         const int f = mesh.GetBdrElementEdgeIndex(i);
+         const int f = mesh.GetBdrElementFaceIndex(i);
          f_to_be[f] = i;
       }
       const int nf_bdr = trial_fes->GetNFbyType(FaceType::Boundary);
@@ -791,7 +789,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
       {
          const int e = glob_j/NDOFS;
          const int j = glob_j%NDOFS;
-         double res = 0.0;
+         real_t res = 0.0;
          for (int i = 0; i < NDOFS; i++)
          {
             res += A(i, j, e)*X(i, e);
@@ -826,7 +824,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
             {
                const int f = glob_j/NDOFS;
                const int j = glob_j%NDOFS;
-               double res = 0.0;
+               real_t res = 0.0;
                for (int i = 0; i < NDOFS; i++)
                {
                   res += A_int(i, j, 0, f)*X(i, 0, f);
@@ -845,7 +843,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
          {
             const int f = glob_j/NDOFS;
             const int j = glob_j%NDOFS;
-            double res = 0.0;
+            real_t res = 0.0;
             for (int i = 0; i < NDOFS; i++)
             {
                res += A_ext(i, j, 0, f)*X(i, 0, f);
@@ -882,7 +880,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
          {
             const int f = glob_j/NDOFS;
             const int j = glob_j%NDOFS;
-            double res = 0.0;
+            real_t res = 0.0;
             for (int i = 0; i < NDOFS; i++)
             {
                res += A(i, j, f)*X(i, f);
@@ -919,7 +917,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
       {
          const int e = glob_j/NDOFS;
          const int j = glob_j%NDOFS;
-         double res = 0.0;
+         real_t res = 0.0;
          for (int i = 0; i < NDOFS; i++)
          {
             res += A(j, i, e)*X(i, e);
@@ -954,7 +952,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
             {
                const int f = glob_j/NDOFS;
                const int j = glob_j%NDOFS;
-               double res = 0.0;
+               real_t res = 0.0;
                for (int i = 0; i < NDOFS; i++)
                {
                   res += A_int(j, i, 0, f)*X(i, 0, f);
@@ -973,7 +971,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
          {
             const int f = glob_j/NDOFS;
             const int j = glob_j%NDOFS;
-            double res = 0.0;
+            real_t res = 0.0;
             for (int i = 0; i < NDOFS; i++)
             {
                res += A_ext(j, i, 1, f)*X(i, 0, f);
@@ -1010,7 +1008,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
          {
             const int f = glob_j/NDOFS;
             const int j = glob_j%NDOFS;
-            double res = 0.0;
+            real_t res = 0.0;
             for (int i = 0; i < NDOFS; i++)
             {
                res += A(j, i, f)*X(i, f);
@@ -1438,7 +1436,7 @@ void PAMixedBilinearFormExtension::SetupMultInputs(
    const Operator *elem_restrict_y,
    Vector &y,
    Vector &localY,
-   const double c) const
+   const real_t c) const
 {
    // * G operation: localX = c*local(x)
    if (elem_restrict_x)
@@ -1478,7 +1476,7 @@ void PAMixedBilinearFormExtension::Mult(const Vector &x, Vector &y) const
 }
 
 void PAMixedBilinearFormExtension::AddMult(const Vector &x, Vector &y,
-                                           const double c) const
+                                           const real_t c) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
    const int iSz = integrators.Size();
@@ -1510,7 +1508,7 @@ void PAMixedBilinearFormExtension::MultTranspose(const Vector &x,
 }
 
 void PAMixedBilinearFormExtension::AddMultTranspose(const Vector &x, Vector &y,
-                                                    const double c) const
+                                                    const real_t c) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
    const int iSz = integrators.Size();
@@ -1644,7 +1642,7 @@ void PADiscreteLinearOperatorExtension::Assemble()
 }
 
 void PADiscreteLinearOperatorExtension::AddMult(
-   const Vector &x, Vector &y, const double c) const
+   const Vector &x, Vector &y, const real_t c) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
    const int iSz = integrators.Size();
@@ -1677,7 +1675,7 @@ void PADiscreteLinearOperatorExtension::AddMult(
 }
 
 void PADiscreteLinearOperatorExtension::AddMultTranspose(
-   const Vector &x, Vector &y, const double c) const
+   const Vector &x, Vector &y, const real_t c) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
    const int iSz = integrators.Size();

fem/bilinearform_ext.hpp

@@ -248,7 +248,7 @@ protected:
    void SetupMultInputs(const Operator *elem_restrict_x,
                         const Vector &x, Vector &localX,
                         const Operator *elem_restrict_y,
-                        Vector &y, Vector &localY, const double c) const;
+                        Vector &y, Vector &localY, const real_t c) const;
 
 public:
    PAMixedBilinearFormExtension(MixedBilinearForm *form);
@@ -277,11 +277,11 @@ public:
    /// y = A*x
    void Mult(const Vector &x, Vector &y) const;
    /// y += c*A*x
-   void AddMult(const Vector &x, Vector &y, const double c=1.0) const;
+   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const;
    /// y = A^T*x
    void MultTranspose(const Vector &x, Vector &y) const;
    /// y += c*A^T*x
-   void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;
+   void AddMultTranspose(const Vector &x, Vector &y, const real_t c=1.0) const;
    /// Assemble the diagonal of ADA^T for a diagonal vector D.
    void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
 
@@ -305,9 +305,9 @@ public:
    /// Partial assembly of all internal integrators
    void Assemble();
 
-   void AddMult(const Vector &x, Vector &y, const double c=1.0) const;
+   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const;
 
-   void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;
+   void AddMultTranspose(const Vector &x, Vector &y, const real_t c=1.0) const;
 
    void FormRectangularSystemOperator(const Array<int>&, const Array<int>&,
                                       OperatorHandle& A);

fem/bilininteg.cpp

@@ -14,6 +14,7 @@
 #include "fem.hpp"
 #include <cmath>
 #include <algorithm>
+#include <memory>
 
 using namespace std;
 
@@ -497,7 +498,7 @@ void MixedScalarIntegrator::AssembleElementMatrix2(
       this->CalcTestShape(test_fe, Trans, test_shape);
       this->CalcTrialShape(trial_fe, Trans, trial_shape);
 
-      double w = Trans.Weight() * ip.weight;
+      real_t w = Trans.Weight() * ip.weight;
 
       if (Q)
       {
@@ -591,7 +592,7 @@ void MixedVectorIntegrator::AssembleElementMatrix2(
          this->CalcTrialShape(trial_fe, Trans, trial_shape);
       }
 
-      double w = Trans.Weight() * ip.weight;
+      real_t w = Trans.Weight() * ip.weight;
 
       if (MQ)
       {
@@ -705,7 +706,7 @@ void MixedScalarVectorIntegrator::AssembleElementMatrix2(
    int sca_nd = sca_fe->GetDof();
    int vec_nd = vec_fe->GetDof();
    int vdim = GetVDim(*vec_fe);
-   double vtmp;
+   real_t vtmp;
 
    MFEM_VERIFY(VQ->GetVDim() == vdim, "MixedScalarVectorIntegrator: "
                "Dimensions of VectorCoefficient and Vector-valued basis "
@@ -744,7 +745,7 @@ void MixedScalarVectorIntegrator::AssembleElementMatrix2(
       this->CalcShape(*sca_fe, Trans, shape);
       this->CalcVShape(*vec_fe, Trans, vshape);
 
-      double w = Trans.Weight() * ip.weight;
+      real_t w = Trans.Weight() * ip.weight;
 
       VQ->Eval(V, Trans, ip);
       V *= w;
@@ -769,7 +770,7 @@ void GradientIntegrator::AssembleElementMatrix2(
    dim = test_fe.GetDim();
    int trial_dof = trial_fe.GetDof();
    int test_dof = test_fe.GetDof();
-   double c;
+   real_t c;
    Vector d_col;
 
    dshape.SetSize(trial_dof, dim);
@@ -787,13 +788,13 @@ void GradientIntegrator::AssembleElementMatrix2(
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
-
-      trial_fe.CalcDShape(ip, dshape);
-      test_fe.CalcShape(ip, shape);
-
       Trans.SetIntPoint(&ip);
+
       CalcAdjugate(Trans.Jacobian(), Jadj);
 
+      test_fe.CalcPhysShape(Trans, shape);
+      trial_fe.CalcDShape(ip, dshape);
+
       Mult(dshape, Jadj, gshape);
 
       c = ip.weight;
@@ -836,7 +837,7 @@ void DiffusionIntegrator::AssembleElementMatrix
    dim = el.GetDim();
    int spaceDim = Trans.GetSpaceDim();
    bool square = (dim == spaceDim);
-   double w;
+   real_t w;
 
    if (VQ)
    {
@@ -930,7 +931,7 @@ void DiffusionIntegrator::AssembleElementMatrix2(
    dim = trial_fe.GetDim();
    int spaceDim = Trans.GetSpaceDim();
    bool square = (dim == spaceDim);
-   double w;
+   real_t w;
 
    if (VQ)
    {
@@ -1012,7 +1013,7 @@ void DiffusionIntegrator::AssembleElementVector(
    int nd = el.GetDof();
    dim = el.GetDim();
    int spaceDim = Tr.GetSpaceDim();
-   double w;
+   real_t w;
 
    if (VQ)
    {
@@ -1186,7 +1187,7 @@ void DiffusionIntegrator::ComputeElementFlux
    }
 }
 
-double DiffusionIntegrator::ComputeFluxEnergy
+real_t DiffusionIntegrator::ComputeFluxEnergy
 ( const FiniteElement &fluxelem, ElementTransformation &Trans,
   Vector &flux, Vector* d_energy)
 {
@@ -1209,7 +1210,7 @@ double DiffusionIntegrator::ComputeFluxEnergy
    int order = 2 * fluxelem.GetOrder(); // <--
    const IntegrationRule *ir = &IntRules.Get(fluxelem.GetGeomType(), order);
 
-   double energy = 0.0;
+   real_t energy = 0.0;
    if (d_energy) { *d_energy = 0.0; }
 
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -1227,7 +1228,7 @@ double DiffusionIntegrator::ComputeFluxEnergy
       }
 
       Trans.SetIntPoint(&ip);
-      double w = Trans.Weight() * ip.weight;
+      real_t w = Trans.Weight() * ip.weight;
 
       if (MQ)
       {
@@ -1242,7 +1243,7 @@ double DiffusionIntegrator::ComputeFluxEnergy
       }
       else
       {
-         double e = (pointflux * pointflux);
+         real_t e = (pointflux * pointflux);
          if (Q) { e *= Q->Eval(Trans, ip); }
          energy += w * e;
       }
@@ -1290,7 +1291,7 @@ void MassIntegrator::AssembleElementMatrix
 {
    int nd = el.GetDof();
    // int dim = el.GetDim();
-   double w;
+   real_t w;
 
 #ifdef MFEM_THREAD_SAFE
    Vector shape;
@@ -1324,7 +1325,7 @@ void MassIntegrator::AssembleElementMatrix2(
 {
    int tr_nd = trial_fe.GetDof();
    int te_nd = test_fe.GetDof();
-   double w;
+   real_t w;
 
 #ifdef MFEM_THREAD_SAFE
    Vector shape, te_shape;
@@ -1340,10 +1341,11 @@ void MassIntegrator::AssembleElementMatrix2(
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
-      trial_fe.CalcShape(ip, shape);
-      test_fe.CalcShape(ip, te_shape);
-
       Trans.SetIntPoint (&ip);
+
+      trial_fe.CalcPhysShape(Trans, shape);
+      test_fe.CalcPhysShape(Trans, te_shape);
+
       w = Trans.Weight() * ip.weight;
       if (Q)
       {
@@ -1378,7 +1380,7 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
                "support for interior faces is not implemented");
 
    int nd1 = el1.GetDof();
-   double w;
+   real_t w;
 
 #ifdef MFEM_THREAD_SAFE
    Vector shape;
@@ -1497,15 +1499,15 @@ void GroupConvectionIntegrator::AssembleElementMatrix(
 
       Mult(dshape, adjJ, grad);
 
-      double w = alpha * ip.weight;
+      real_t w = alpha * ip.weight;
 
       // elmat(k,l) += \sum_s w*shape(k)*Q_nodal(s,k)*grad(l,s)
       for (int k = 0; k < nd; k++)
       {
-         double wsk = w*shape(k);
+         real_t wsk = w*shape(k);
          for (int l = 0; l < nd; l++)
          {
-            double a = 0.0;
+            real_t a = 0.0;
             for (int s = 0; s < dim; s++)
             {
                a += Q_nodal(s,k)*grad(l,s);
@@ -1538,7 +1540,7 @@ void VectorMassIntegrator::AssembleElementMatrix
    int nd = el.GetDof();
    int spaceDim = Trans.GetSpaceDim();
 
-   double norm;
+   real_t norm;
 
    // If vdim is not set, set it to the space dimension
    vdim = (vdim == -1) ? spaceDim : vdim;
@@ -1620,7 +1622,7 @@ void VectorMassIntegrator::AssembleElementMatrix2(
    int tr_nd = trial_fe.GetDof();
    int te_nd = test_fe.GetDof();
 
-   double norm;
+   real_t norm;
 
    // If vdim is not set, set it to the space dimension
    vdim = (vdim == -1) ? Trans.GetSpaceDim() : vdim;
@@ -1727,7 +1729,7 @@ void VectorFEDivergenceIntegrator::AssembleElementMatrix2(
       trial_fe.CalcDivShape(ip, divshape);
       Trans.SetIntPoint(&ip);
       test_fe.CalcPhysShape(Trans, shape);
-      double w = ip.weight;
+      real_t w = ip.weight;
       if (Q)
       {
          Trans.SetIntPoint(&ip);
@@ -1808,7 +1810,7 @@ void VectorFEWeakDivergenceIntegrator::AssembleElementMatrix2(
 
       trial_fe.CalcVShape(Trans, vshape);
 
-      double w = ip.weight;
+      real_t w = ip.weight;
 
       if (Q)
       {
@@ -1898,7 +1900,7 @@ void VectorFECurlIntegrator::AssembleElementMatrix2(
          }
       }
 
-      double w = ip.weight;
+      real_t w = ip.weight;
 
       if (Q)
       {
@@ -1929,7 +1931,7 @@ void DerivativeIntegrator::AssembleElementMatrix2 (
    int spaceDim = Trans.GetSpaceDim();
 
    int i, l;
-   double det;
+   real_t det;
 
    elmat.SetSize (test_nd,trial_nd);
    dshape.SetSize (trial_nd,dim);
@@ -1992,7 +1994,7 @@ void CurlCurlIntegrator::AssembleElementMatrix
    int nd = el.GetDof();
    dim = el.GetDim();
    int dimc = el.GetCurlDim();
-   double w;
+   real_t w;
 
 #ifdef MFEM_THREAD_SAFE
    Vector D;
@@ -2065,7 +2067,7 @@ void CurlCurlIntegrator::AssembleElementMatrix2(const FiniteElement &trial_fe,
    int te_nd = test_fe.GetDof();
    dim = trial_fe.GetDim();
    int dimc = trial_fe.GetCurlDim();
-   double w;
+   real_t w;
 
 #ifdef MFEM_THREAD_SAFE
    Vector D;
@@ -2152,7 +2154,7 @@ void CurlCurlIntegrator
    // TODO: Q, wcoef?
 }
 
-double CurlCurlIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
+real_t CurlCurlIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
                                              ElementTransformation &Trans,
                                              Vector &flux, Vector *d_energy)
 {
@@ -2169,7 +2171,7 @@ double CurlCurlIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
    int order = 2 * fluxelem.GetOrder(); // <--
    const IntegrationRule &ir = IntRules.Get(fluxelem.GetGeomType(), order);
 
-   double energy = 0.0;
+   real_t energy = 0.0;
    if (d_energy) { *d_energy = 0.0; }
 
    Vector* pfluxes = NULL;
@@ -2187,9 +2189,9 @@ double CurlCurlIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
       // fluxelem.CalcVShape(ip, vshape);
       vshape.MultTranspose(flux, pointflux);
 
-      double w = Trans.Weight() * ip.weight;
+      real_t w = Trans.Weight() * ip.weight;
 
-      double e = w * (pointflux * pointflux);
+      real_t e = w * (pointflux * pointflux);
 
       if (Q)
       {
@@ -2291,7 +2293,7 @@ void VectorCurlCurlIntegrator::AssembleElementMatrix(
 
       Trans.SetIntPoint(&ip);
       CalcAdjugate(Trans.Jacobian(), Jadj);
-      double w = ip.weight / Trans.Weight();
+      real_t w = ip.weight / Trans.Weight();
 
       Mult(dshape_hat, Jadj, dshape);
       dshape.GradToCurl(curlshape);
@@ -2305,7 +2307,7 @@ void VectorCurlCurlIntegrator::AssembleElementMatrix(
    }
 }
 
-double VectorCurlCurlIntegrator::GetElementEnergy(
+real_t VectorCurlCurlIntegrator::GetElementEnergy(
    const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun)
 {
    int dim = el.GetDim();
@@ -2330,7 +2332,7 @@ double VectorCurlCurlIntegrator::GetElementEnergy(
       ir = &IntRules.Get(el.GetGeomType(), order);
    }
 
-   double energy = 0.;
+   real_t energy = 0.;
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
@@ -2340,20 +2342,20 @@ double VectorCurlCurlIntegrator::GetElementEnergy(
 
       Tr.SetIntPoint(&ip);
       CalcAdjugate(Tr.Jacobian(), Jadj);
-      double w = ip.weight / Tr.Weight();
+      real_t w = ip.weight / Tr.Weight();
 
       Mult(grad_hat, Jadj, grad);
 
       if (dim == 2)
       {
-         double curl = grad(0,1) - grad(1,0);
+         real_t curl = grad(0,1) - grad(1,0);
          w *= curl * curl;
       }
       else
       {
-         double curl_x = grad(2,1) - grad(1,2);
-         double curl_y = grad(0,2) - grad(2,0);
-         double curl_z = grad(1,0) - grad(0,1);
+         real_t curl_x = grad(2,1) - grad(1,2);
+         real_t curl_y = grad(0,2) - grad(2,0);
+         real_t curl_z = grad(1,0) - grad(0,1);
          w *= curl_x * curl_x + curl_y * curl_y + curl_z * curl_z;
       }
 
@@ -2403,7 +2405,7 @@ void MixedCurlIntegrator::AssembleElementMatrix2(
    shape.SetSize(test_dof);
    elmat = 0.0;
 
-   double c;
+   real_t c;
    Vector d_col;
    const IntegrationRule *ir = IntRule;
 
@@ -2436,7 +2438,7 @@ void MixedCurlIntegrator::AssembleElementMatrix2(
 
       for (int d = 0; d < dimc; ++d)
       {
-         double * curldata = &(curlshape.GetData())[d*trial_dof];
+         real_t * curldata = &(curlshape.GetData())[d*trial_dof];
          for (int jj = 0; jj < trial_dof; ++jj)
          {
             for (int ii = 0; ii < test_dof; ++ii)
@@ -2458,7 +2460,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix(
    int spaceDim = Trans.GetSpaceDim();
    int vdim = std::max(spaceDim, el.GetRangeDim());
 
-   double w;
+   real_t w;
 
 #ifdef MFEM_THREAD_SAFE
    Vector D(DQ ? DQ->GetVDim() : 0);
@@ -2527,7 +2529,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix2(
       int vdim = std::max(spaceDim, trial_fe.GetRangeDim());
       int trial_dof = trial_fe.GetDof();
       int test_dof = test_fe.GetDof();
-      double w;
+      real_t w;
 
 #ifdef MFEM_THREAD_SAFE
       DenseMatrix trial_vshape(trial_dof, spaceDim);
@@ -2587,7 +2589,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix2(
                {
                   for (int k = 0; k < trial_dof; k++)
                   {
-                     double Kv = 0.0;
+                     real_t Kv = 0.0;
                      for (int vd = 0; vd < spaceDim; vd++)
                      {
                         Kv += K(d, vd) * trial_vshape(k, vd);
@@ -2626,7 +2628,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix2(
       int test_vdim = std::max(spaceDim, test_fe.GetRangeDim());
       int trial_dof = trial_fe.GetDof();
       int test_dof = test_fe.GetDof();
-      double w;
+      real_t w;
 
 #ifdef MFEM_THREAD_SAFE
       DenseMatrix trial_vshape(trial_dof,trial_vdim);
@@ -2700,7 +2702,7 @@ void VectorDivergenceIntegrator::AssembleElementMatrix2(
    dim  = trial_fe.GetDim();
    int trial_dof = trial_fe.GetDof();
    int test_dof = test_fe.GetDof();
-   double c;
+   real_t c;
 
    dshape.SetSize (trial_dof, dim);
    gshape.SetSize (trial_dof, dim);
@@ -2757,7 +2759,7 @@ void DivDivIntegrator::AssembleElementMatrix(
    DenseMatrix &elmat)
 {
    int dof = el.GetDof();
-   double c;
+   real_t c;
 
 #ifdef MFEM_THREAD_SAFE
    Vector divshape(dof);
@@ -2802,7 +2804,7 @@ void DivDivIntegrator::AssembleElementMatrix2(
 {
    int tr_nd = trial_fe.GetDof();
    int te_nd = test_fe.GetDof();
-   double c;
+   real_t c;
 
 #ifdef MFEM_THREAD_SAFE
    Vector divshape(tr_nd);
@@ -2886,7 +2888,7 @@ void VectorDiffusionIntegrator::AssembleElementMatrix(
       el.CalcDShape(ip, dshape);
 
       Trans.SetIntPoint(&ip);
-      double w = Trans.Weight();
+      real_t w = Trans.Weight();
       w = ip.weight / (square ? w : w*w*w);
       // AdjugateJacobian = / adj(J),         if J is square
       //                    \ adj(J^t.J).J^t, otherwise
@@ -2971,7 +2973,7 @@ void VectorDiffusionIntegrator::AssembleElementVector(
       el.CalcDShape(ip, dshape);
 
       Tr.SetIntPoint(&ip);
-      double w = Tr.Weight();
+      real_t w = Tr.Weight();
       w = ip.weight / (square ? w : w*w*w);
       Mult(dshape, Tr.AdjugateJacobian(), dshapedxt);
       MultAAt(dshapedxt, pelmat);
@@ -3015,13 +3017,19 @@ void VectorDiffusionIntegrator::AssembleElementVector(
    }
 }
 
+ElasticityComponentIntegrator::ElasticityComponentIntegrator(
+   ElasticityIntegrator &parent_, int i_, int j_)
+   : parent(parent_),
+     i_block(i_),
+     j_block(j_)
+{ }
 
 void ElasticityIntegrator::AssembleElementMatrix(
    const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 {
    int dof = el.GetDof();
    int dim = el.GetDim();
-   double w, L, M;
+   real_t w, L, M;
 
    MFEM_ASSERT(dim == Trans.GetSpaceDim(), "");
 
@@ -3106,7 +3114,7 @@ void ElasticityIntegrator::ComputeElementFlux(
    const int dof = el.GetDof();
    const int dim = el.GetDim();
    const int tdim = dim*(dim+1)/2; // num. entries in a symmetric tensor
-   double L, M;
+   real_t L, M;
 
    MFEM_ASSERT(dim == 2 || dim == 3,
                "dimension is not supported: dim = " << dim);
@@ -3120,7 +3128,7 @@ void ElasticityIntegrator::ComputeElementFlux(
    dshape.SetSize(dof, dim);
 #endif
 
-   double gh_data[9], grad_data[9];
+   real_t gh_data[9], grad_data[9];
    DenseMatrix gh(gh_data, dim, dim);
    DenseMatrix grad(grad_data, dim, dim);
 
@@ -3154,7 +3162,7 @@ void ElasticityIntegrator::ComputeElementFlux(
 
       // stress = 2*M*e(u) + L*tr(e(u))*I, where
       //   e(u) = (1/2)*(grad(u) + grad(u)^T)
-      const double M2 = 2.0*M;
+      const real_t M2 = 2.0*M;
       if (dim == 2)
       {
          L *= (grad(0,0) + grad(1,1));
@@ -3177,14 +3185,14 @@ void ElasticityIntegrator::ComputeElementFlux(
    }
 }
 
-double ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
+real_t ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
                                                ElementTransformation &Trans,
                                                Vector &flux, Vector *d_energy)
 {
    const int dof = fluxelem.GetDof();
    const int dim = fluxelem.GetDim();
    const int tdim = dim*(dim+1)/2; // num. entries in a symmetric tensor
-   double L, M;
+   real_t L, M;
 
    // The MFEM_ASSERT constraints in ElasticityIntegrator::ComputeElementFlux
    // are assumed here too.
@@ -3196,7 +3204,7 @@ double ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
 #else
    Vector shape(dof);
 #endif
-   double pointstress_data[6];
+   real_t pointstress_data[6];
    Vector pointstress(pointstress_data, tdim);
 
    // View of the 'flux' vector as a (dof x tdim) matrix
@@ -3212,7 +3220,7 @@ double ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
       ir = &IntRules.Get(fluxelem.GetGeomType(), order);
    }
 
-   double energy = 0.0;
+   real_t energy = 0.0;
 
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
@@ -3222,7 +3230,7 @@ double ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
       flux_mat.MultTranspose(shape, pointstress);
 
       Trans.SetIntPoint(&ip);
-      double w = Trans.Weight() * ip.weight;
+      real_t w = Trans.Weight() * ip.weight;
 
       M = mu->Eval(Trans, ip);
       if (lambda)
@@ -3246,19 +3254,19 @@ double ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
       // Then from the first identity above we can find the strain:
       //    e = (1/(2*mu))*(s - lambda*tr(e)*I)
 
-      double pt_e; // point strain energy density
-      const double *s = pointstress_data;
+      real_t pt_e; // point strain energy density
+      const real_t *s = pointstress_data;
       if (dim == 2)
       {
          // s entries: s_xx, s_yy, s_xy
-         const double tr_e = (s[0] + s[1])/(2*(M + L));
+         const real_t tr_e = (s[0] + s[1])/(2*(M + L));
          L *= tr_e;
          pt_e = (0.25/M)*(s[0]*(s[0] - L) + s[1]*(s[1] - L) + 2*s[2]*s[2]);
       }
       else // (dim == 3)
       {
          // s entries: s_xx, s_yy, s_zz, s_xy, s_xz, s_yz
-         const double tr_e = (s[0] + s[1] + s[2])/(2*M + 3*L);
+         const real_t tr_e = (s[0] + s[1] + s[2])/(2*M + 3*L);
          L *= tr_e;
          pt_e = (0.25/M)*(s[0]*(s[0] - L) + s[1]*(s[1] - L) + s[2]*(s[2] - L) +
                           2*(s[3]*s[3] + s[4]*s[4] + s[5]*s[5]));
@@ -3277,7 +3285,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
 {
    int ndof1, ndof2;
 
-   double un, a, b, w;
+   real_t un, a, b, w;
 
    dim = el1.GetDim();
    ndof1 = el1.GetDof();
@@ -3350,7 +3358,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
 
       if (rho)
       {
-         double rho_p;
+         real_t rho_p;
          if (un >= 0.0 && ndof2)
          {
             rho_p = rho->Eval(*Trans.Elem2, eip2);
@@ -3417,7 +3425,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
 {
    int dim, ndof1, ndof2, ndofs;
    bool kappa_is_nonzero = (kappa != 0.);
-   double w, wq = 0.0;
+   real_t w, wq = 0.0;
 
    dim = el1.GetDim();
    ndof1 = el1.GetDof();
@@ -3592,7 +3600,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
          wq *= kappa;
          for (int i = 0; i < ndof1; i++)
          {
-            const double wsi = wq*shape1(i);
+            const real_t wsi = wq*shape1(i);
             for (int j = 0; j <= i; j++)
             {
                jmat(i, j) += wsi * shape1(j);
@@ -3603,7 +3611,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
             for (int i = 0; i < ndof2; i++)
             {
                const int i2 = ndof1 + i;
-               const double wsi = wq*shape2(i);
+               const real_t wsi = wq*shape2(i);
                for (int j = 0; j < ndof1; j++)
                {
                   jmat(i2, j) -= wsi * shape1(j);
@@ -3624,7 +3632,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
       {
          for (int j = 0; j < i; j++)
          {
-            double aij = elmat(i,j), aji = elmat(j,i), mij = jmat(i,j);
+            real_t aij = elmat(i,j), aji = elmat(j,i), mij = jmat(i,j);
             elmat(i,j) = sigma*aji - aij + mij;
             elmat(j,i) = sigma*aij - aji + mij;
          }
@@ -3637,7 +3645,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
       {
          for (int j = 0; j < i; j++)
          {
-            double aij = elmat(i,j), aji = elmat(j,i);
+            real_t aij = elmat(i,j), aji = elmat(j,i);
             elmat(i,j) = sigma*aji - aij;
             elmat(j,i) = sigma*aij - aji;
          }
@@ -3651,7 +3659,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
 void DGElasticityIntegrator::AssembleBlock(
    const int dim, const int row_ndofs, const int col_ndofs,
    const int row_offset, const int col_offset,
-   const double jmatcoef, const Vector &col_nL, const Vector &col_nM,
+   const real_t jmatcoef, const Vector &col_nL, const Vector &col_nM,
    const Vector &row_shape, const Vector &col_shape,
    const Vector &col_dshape_dnM, const DenseMatrix &col_dshape,
    DenseMatrix &elmat, DenseMatrix &jmat)
@@ -3660,12 +3668,12 @@ void DGElasticityIntegrator::AssembleBlock(
    {
       for (int jdof = 0; jdof < col_ndofs; ++jdof, ++j)
       {
-         const double t2 = col_dshape_dnM(jdof);
+         const real_t t2 = col_dshape_dnM(jdof);
          for (int im = 0, i = row_offset; im < dim; ++im)
          {
-            const double t1 = col_dshape(jdof, jm) * col_nL(im);
-            const double t3 = col_dshape(jdof, im) * col_nM(jm);
-            const double tt = t1 + ((im == jm) ? t2 : 0.0) + t3;
+            const real_t t1 = col_dshape(jdof, jm) * col_nL(im);
+            const real_t t3 = col_dshape(jdof, im) * col_nM(jm);
+            const real_t tt = t1 + ((im == jm) ? t2 : 0.0) + t3;
             for (int idof = 0; idof < row_ndofs; ++idof, ++i)
             {
                elmat(i, j) += row_shape(idof) * tt;
@@ -3682,7 +3690,7 @@ void DGElasticityIntegrator::AssembleBlock(
       const int io = row_offset + d*row_ndofs;
       for (int jdof = 0, j = jo; jdof < col_ndofs; ++jdof, ++j)
       {
-         const double sj = jmatcoef * col_shape(jdof);
+         const real_t sj = jmatcoef * col_shape(jdof);
          for (int i = max(io,j), idof = i - io; idof < row_ndofs; ++idof, ++i)
          {
             jmat(i, j) += row_shape(idof) * sj;
@@ -3782,7 +3790,7 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
          CalcOrtho(Trans.Jacobian(), nor);
       }
 
-      double w, wLM;
+      real_t w, wLM;
       if (ndofs2)
       {
          el2.CalcShape(eip2, shape2);
@@ -3791,9 +3799,9 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
          Mult(dshape2, adjJ, dshape2_ps);
 
          w = ip.weight/2;
-         const double w2 = w / Trans.Elem2->Weight();
-         const double wL2 = w2 * lambda->Eval(*Trans.Elem2, eip2);
-         const double wM2 = w2 * mu->Eval(*Trans.Elem2, eip2);
+         const real_t w2 = w / Trans.Elem2->Weight();
+         const real_t wL2 = w2 * lambda->Eval(*Trans.Elem2, eip2);
+         const real_t wM2 = w2 * mu->Eval(*Trans.Elem2, eip2);
          nL2.Set(wL2, nor);
          nM2.Set(wM2, nor);
          wLM = (wL2 + 2.0*wM2);
@@ -3806,16 +3814,16 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
       }
 
       {
-         const double w1 = w / Trans.Elem1->Weight();
-         const double wL1 = w1 * lambda->Eval(*Trans.Elem1, eip1);
-         const double wM1 = w1 * mu->Eval(*Trans.Elem1, eip1);
+         const real_t w1 = w / Trans.Elem1->Weight();
+         const real_t wL1 = w1 * lambda->Eval(*Trans.Elem1, eip1);
+         const real_t wM1 = w1 * mu->Eval(*Trans.Elem1, eip1);
          nL1.Set(wL1, nor);
          nM1.Set(wM1, nor);
          wLM += (wL1 + 2.0*wM1);
          dshape1_ps.Mult(nM1, dshape1_dnM);
       }
 
-      const double jmatcoef = kappa * (nor*nor) * wLM;
+      const real_t jmatcoef = kappa * (nor*nor) * wLM;
 
       // (1,1) block
       AssembleBlock(
@@ -3848,7 +3856,7 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
       {
          for (int j = 0; j < i; ++j)
          {
-            double aij = elmat(i,j), aji = elmat(j,i), mij = jmat(i,j);
+            real_t aij = elmat(i,j), aji = elmat(j,i), mij = jmat(i,j);
             elmat(i,j) = alpha*aji - aij + mij;
             elmat(j,i) = alpha*aij - aji + mij;
          }
@@ -3861,7 +3869,7 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
       {
          for (int j = 0; j < i; ++j)
          {
-            double aij = elmat(i,j), aji = elmat(j,i);
+            real_t aij = elmat(i,j), aji = elmat(j,i);
             elmat(i,j) = alpha*aji - aij;
             elmat(j,i) = alpha*aij - aji;
          }
@@ -3879,7 +3887,7 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
    int i, j, face_ndof, ndof1, ndof2;
    int order;
 
-   double w;
+   real_t w;
 
    face_ndof = trial_face_fe.GetDof();
    ndof1 = test_fe1.GetDof();
@@ -4087,7 +4095,7 @@ void TraceIntegrator::AssembleTraceFaceMatrix(int elem,
       MFEM_VERIFY(elem == Trans.Elem2->ElementNo, "Elem != Trans.Elem2->ElementNo");
    }
 
-   double scale = 1.0;
+   real_t scale = 1.0;
    if (iel != elem) { scale = -1.; }
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
@@ -4153,7 +4161,7 @@ void NormalTraceIntegrator::AssembleTraceFaceMatrix(int elem,
       MFEM_VERIFY(elem == Trans.Elem2->ElementNo, "Elem != Trans.Elem2->ElementNo");
    }
 
-   double scale = 1.0;
+   real_t scale = 1.0;
    if (iel != elem) { scale = -1.; }
 
    for (int p = 0; p < ir->GetNPoints(); p++)
@@ -4232,7 +4240,7 @@ void TangentTraceIntegrator::AssembleTraceFaceMatrix(int elem,
       MFEM_VERIFY(elem == Trans.Elem2->ElementNo, "Elem != Trans.Elem2->ElementNo");
    }
 
-   double scale = 1.0;
+   real_t scale = 1.0;
    if (iel != elem) { scale = -1.; }
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
@@ -4256,7 +4264,7 @@ void TangentTraceIntegrator::AssembleTraceFaceMatrix(int elem,
       // rotate
       cross_product(normal, shape, shape_n);
 
-      const double w = scale*ip.weight;
+      const real_t w = scale*ip.weight;
       AddMult_a_ABt(w,shape_n, face_shape, elmat);
    }
 }