The full text of the GNU Lesser General Public version 2.1 is quoted
below.
-The subdirectory "bundled/" is not licensed by the deal.II authors. PLEASE
-NOTE THAT THE SOFTWARE THERE IS COPYRIGHTED BY OTHERS THAN THE deal.II
-AUTHORS, but is included by permission. For details, consult the stated
-licenses there.
+The subdirectories "bundled/" and "contrib/" contain third party software.
+PLEASE NOTE THAT THE SOFTWARE THERE IS COPYRIGHTED BY OTHERS THAN THE
+deal.II AUTHORS, but is included by permission. For details, consult the
+stated licenses there.
----------------------------------------------------------------------
$ cd build
$ cmake -DCMAKE_INSTALL_PREFIX=/path/where/deal.II/should/be/intalled/to ..
$ make install (alternatively $ make -j<N> install)
+ $ make test
A detailed ReadME can be found at ./doc/readme.html and
./doc/users/cmake.html or at http://www.dealii.org/.
"
DEAL_II_ICC_NUMERICLIMITS_BUG)
-IF(DEAL_II_ICC_NUMERICLIMITS_BUG)
+#
+# icc-14.0.0 has an astonishing bug [1] where it hits an internal compiler
+# error when run in C++11 mode with libstdc++-4.7 (from gcc).
+#
+# We just disable C++11 mode in this case
+#
+# [1] http://software.intel.com/en-us/forums/topic/472385
+#
+# - Matthias Maier, 2013
+#
+CHECK_CXX_COMPILER_BUG(
+ "
+ #include <vector>
+ template<typename T> void foo()
+ {
+ std::vector<double> data(100);
+ }
+ int main()
+ {
+ foo<int>();
+ }
+ "
+ DEAL_II_ICC_LIBSTDCPP47CXX11_BUG)
+
+
+IF( DEAL_II_ICC_NUMERICLIMITS_BUG OR
+ DEAL_II_ICC_LIBSTDCPP47CXX11_BUG )
MESSAGE(STATUS
- "DEAL_II_ICC_NUMERICLIMITS_BUG found, disabling c++11 support"
+ "Intel C++11 bug found, disabling C++11 support"
)
STRIP_FLAG(CMAKE_CXX_FLAGS "${DEAL_II_CXX11_FLAG}")
SET(DEAL_II_CAN_USE_CXX1X FALSE)
SET(DEAL_II_USE_CXX11 FALSE)
ENDIF()
+
#
# gcc-4.8.1 has some problems with the constexpr "vertices_per_cell" in the
# definition of alternating_form_at_vertices.
${CMAKE_CURRENT_BINARY_DIR}/${DEAL_II_PROJECT_CONFIG_NAME}ConfigVersion.cmake
@ONLY
)
-
INSTALL(FILES
${CMAKE_CURRENT_BINARY_DIR}/${DEAL_II_PROJECT_CONFIG_NAME}Config.cmake
${CMAKE_CURRENT_BINARY_DIR}/${DEAL_II_PROJECT_CONFIG_NAME}ConfigVersion.cmake
#
FOREACH(build ${DEAL_II_BUILD_TYPES})
+
TO_STRING_AND_ADD_PREFIX(MAKEFILE_DEFINITIONS_${build}
"-D"
${DEAL_II_USER_DEFINITIONS}
#
# Ideally, DEAL_II_EXTERNAL_LIBRARIES should just contain a list of
# full library paths. Nevertheless, filter out all elements that are
- # not a full path starting with "/".
+ # not a full path starting with "/" or that happen to be a "framework"
+ # - we won't deal with that in Make.global_options.
#
+
SET(_libs)
FOREACH(_lib
${DEAL_II_EXTERNAL_LIBRARIES_${build}}
${DEAL_II_EXTERNAL_LIBRARIES}
)
- IF(_lib MATCHES "^\\s*/")
+ IF(_lib MATCHES "^\\s*\\/" AND NOT _lib MATCHES "\\.framework$")
LIST(APPEND _libs "${_lib}")
ENDIF()
ENDFOREACH()
${_libs}
)
- MESSAGE("\n\nDEBUG:")
-
SET(_paths)
FOREACH(_lib
$(D)/${DEAL_II_LIBRARY_RELDIR}/${CONFIG_LIBRARY_${build}}
#
# Strip leading and trailing whitespace
#
- MESSAGE("--> \"${_lib}\"")
STRING(STRIP "${_lib}" _lib)
- MESSAGE(" stripped: \"${_lib}\"")
- IF(_lib MATCHES "^(/|\\$\\(D\\))")
- # Full path: /path/to/libfoo.so:
+ IF(_lib MATCHES "^\\/.*\\.framework$")
+ #
+ # We have a MacOSX framework
+ #
+ # TODO: What do?
+ #
+
+ ELSEIF(_lib MATCHES "^(\\/|\\$\\(D\\))")
+ #
+ # Full path: /path/to/libfoo.(so|dylib|etc):
+ #
# Extract library paths:
GET_FILENAME_COMPONENT(_path ${_lib} PATH)
LIST(APPEND _paths ${_path})
- MESSAGE(" appended: \"${_lib}\"")
LIST(APPEND MAKEFILE_LIBS_${build} ${_lib})
- ELSEIF(_lib MATCHES "^-")
- # Library is of the form "-lflag", don't touch it:
- MESSAGE(" appended: \"${_lib}\"")
+ ELSEIF(_lib MATCHES "^-l")
+ #
+ # Library is of the form "-lfoo":
+ #
LIST(APPEND MAKEFILE_LIBS_${build} ${_lib})
- ELSEIF(NOT "${_lib}" STREQUAL "")
- # Well in this case we just assume that we have to append an "-l"
- # Note: This won't cover case where a relative library name, such as
- # libfoo.so, libfoo.dylib, etc. is specified...
- MESSAGE(" appended: \"-l${_lib}\"")
+ ELSEIF(NOT _lib MATCHES "^\\s*$" AND NOT _lib MATCHES "\\.so(\\.[0-9]+)*$")
+ #
+ # Well in this case we just assume that we have to append a "-l"
+ #
+
LIST(APPEND MAKEFILE_LIBS_${build} "-l${_lib}")
+ ELSE()
+ #
+ # For now, ignore the rest.
+ #
+ # TODO: What do?
+ #
ENDIF()
- ENDFOREACH()
-# MESSAGE(FATAL_ERROR "bailout")
+ ENDFOREACH()
#
# And build up an rpath:
ENDMACRO()
-
MACRO(FEATURE_LAPACK_CONFIGURE_EXTERNAL)
-
- ADD_FLAGS(DEAL_II_LINKER_FLAGS "${LAPACK_LINKER_FLAGS}")
- DEAL_II_APPEND_LIBRARIES(${LAPACK_LIBRARIES})
-
+ REGISTER_FEATURE(LAPACK)
CHECK_FOR_LAPACK_FUNCTIONS()
ENDMACRO()
MACRO(FEATURE_MPI_CONFIGURE_EXTERNAL)
- ADD_FLAGS(CMAKE_CXX_FLAGS "${MPI_CXX_COMPILE_FLAGS}")
- ADD_FLAGS(DEAL_II_LINKER_FLAGS "${MPI_CXX_LINK_FLAGS}")
-
- DEAL_II_APPEND_LIBRARIES(${MPI_CXX_LIBRARIES})
- INCLUDE_DIRECTORIES(${MPI_CXX_INCLUDE_PATH})
-
+ #
# The user has to know the location of the mpi headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${MPI_CXX_INCLUDE_PATH})
+ #
+ SET(MPI_CXX_ADD_TO_USER_INCLUDE_DIRS TRUE)
+
+ REGISTER_FEATURE(MPI_CXX)
ENDMACRO()
MACRO(FEATURE_THREADS_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES(${TBB_INCLUDE_DIR})
- DEAL_II_APPEND_LIBRARIES(${TBB_LIBRARIES})
+ REGISTER_FEATURE(TBB)
IF(CMAKE_BUILD_TYPE MATCHES "Debug")
IF(TBB_WITH_DEBUG_LIB)
"TBB_USE_DEBUG=1" "TBB_DO_ASSERT=1"
)
ENDIF()
-
ENDIF()
#
FIND_LIBRARY(dl_LIBRARY NAMES dl)
MARK_AS_ADVANCED(dl_LIBRARY)
IF(NOT dl_LIBRARY MATCHES "-NOTFOUND")
- DEAL_II_APPEND_LIBRARIES(${dl_LIBRARY})
+ LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES ${dl_LIBRARY})
ENDIF()
INCLUDE_DIRECTORIES(${TBB_FOLDER}/include)
MACRO(FEATURE_TRILINOS_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES(${TRILINOS_INCLUDE_DIRS})
-
- # The user has to know the location of the trilinos headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${TRILINOS_INCLUDE_DIRS})
-
- DEAL_II_APPEND_LIBRARIES(${TRILINOS_LIBRARIES})
+ SET(TRILINOS_ADD_TO_USER_INCLUDE_DIRS TRUE)
+ REGISTER_FEATURE(TRILINOS)
SET(DEAL_II_EXPAND_TRILINOS_VECTOR "TrilinosWrappers::Vector")
SET(DEAL_II_EXPAND_TRILINOS_BLOCKVECTOR "TrilinosWrappers::BlockVector")
MACRO(FEATURE_PETSC_CONFIGURE_EXTERNAL)
INCLUDE_DIRECTORIES(${PETSC_INCLUDE_DIRS})
- # The user has to know the location of the petsc headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${PETSC_INCLUDE_DIRS})
-
- DEAL_II_APPEND_LIBRARIES(${PETSC_LIBRARIES})
+ SET(PETSC_ADD_TO_USER_INCLUDE_DIRS TRUE)
+ REGISTER_FEATURE(PETSC)
#
# Disable a bunch of warnings when compiling with petsc:
MARK_AS_ADVANCED(Boost_DIR)
- SET(BOOST_VERSION_MAJOR "${Boost_MAJOR_VERSION}")
- SET(BOOST_VERSION_MINOR "${Boost_MINOR_VERSION}")
- SET(BOOST_VERSION_SUBMINOR "${Boost_SUBMINOR_VERSION}")
- SET(BOOST_VERSION
- "${BOOST_VERSION_MAJOR}.${BOOST_VERSION_MINOR}.${BOOST_VERSION_SUBMINOR}"
- )
-
IF( Boost_SERIALIZATION_FOUND AND
Boost_SYSTEM_FOUND AND
- (NOT DEAL_II_WITH_THREADS OR Boost_THREAD_FOUND)
- )
+ (NOT DEAL_II_WITH_THREADS OR Boost_THREAD_FOUND) )
+
+ SET(BOOST_VERSION_MAJOR "${Boost_MAJOR_VERSION}")
+ SET(BOOST_VERSION_MINOR "${Boost_MINOR_VERSION}")
+ SET(BOOST_VERSION_SUBMINOR "${Boost_SUBMINOR_VERSION}")
+ SET(BOOST_VERSION
+ "${BOOST_VERSION_MAJOR}.${BOOST_VERSION_MINOR}.${BOOST_VERSION_SUBMINOR}"
+ )
+
+ #
+ # Remove "pthread" from Boost_LIBRARIES. Threading, if necessary, is
+ # already set up via configure_1_threads.cmake.
+ #
+ LIST(REMOVE_ITEM Boost_LIBRARIES "pthread")
+
+ SET(BOOST_INCLUDE_DIRS ${Boost_INCLUDE_DIRS})
+ SET(BOOST_LIBRARIES ${Boost_LIBRARIES})
+
MARK_AS_ADVANCED(BOOST_DIR)
+
SET(${var} TRUE)
+
ELSE()
+
SET(BOOST_DIR "" CACHE PATH
"An optional hint to a boost directory"
)
ENDMACRO()
-MACRO(FEATURE_BOOST_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES (${Boost_INCLUDE_DIRS})
-
- # The user has to know the location of the boost headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${Boost_INCLUDE_DIRS})
-
- #
- # Remove "pthread" from Boost_LIBRARIES. Threading, if necessary, is
- # already set up via configure_1_threads.cmake.
- #
- LIST(REMOVE_ITEM Boost_LIBRARIES "pthread")
-
- DEAL_II_APPEND_LIBRARIES(${Boost_LIBRARIES})
-
-ENDMACRO()
+#
+# The user has to know the location of the boost headers as well:
+#
+SET(BOOST_ADD_TO_USER_INCLUDE_DIRS TRUE)
MACRO(FEATURE_BOOST_CONFIGURE_BUNDLED)
ENDMACRO()
-MACRO(FEATURE_HDF5_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES(${HDF5_INCLUDE_DIRS})
-
- # The user has to know the location of the HDF5 headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${HDF5_INCLUDE_DIRS})
-
- DEAL_II_APPEND_LIBRARIES(${HDF5_LIBRARIES})
-ENDMACRO()
+#
+# The user has to know the location of the hdf5 headers as well:
+#
+SET(HDF5_ADD_TO_USER_INCLUDE_DIRS TRUE)
CONFIGURE_FEATURE(HDF5)
SET(FEATURE_MUMPS_DEPENDS DEAL_II_WITH_MPI DEAL_II_WITH_LAPACK)
-MACRO(FEATURE_MUMPS_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES(${MUMPS_INCLUDE_DIRS})
- # The user has to know the location of the MUMPS headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${MUMPS_INCLUDE_DIRS})
+#
+# The user has to know the location of the MUMPS headers as well:
+#
+SET(MUMPS_ADD_TO_USER_INCLUDE_DIRS TRUE)
- DEAL_II_APPEND_LIBRARIES(${MUMPS_LIBRARIES})
-ENDMACRO()
CONFIGURE_FEATURE(MUMPS)
ENDMACRO()
-MACRO(FEATURE_P4EST_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES(${P4EST_INCLUDE_DIRS})
-
- # The user has to know the location of the P4EST headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${P4EST_INCLUDE_DIRS})
+#
+# The user has to know the location of the P4est headers as well:
+#
+SET(P4EST_ADD_TO_USER_INCLUDE_DIRS TRUE)
- DEAL_II_APPEND_LIBRARIES(${P4EST_LIBRARIES})
-ENDMACRO()
CONFIGURE_FEATURE(P4EST)
ENDIF()
ENDMACRO()
-MACRO(FEATURE_SLEPC_CONFIGURE_EXTERNAL)
- INCLUDE_DIRECTORIES(${SLEPC_INCLUDE_DIRS})
- # The user has to know the location of the SLEPC headers as well:
- LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${SLEPC_INCLUDE_DIRS})
-
- DEAL_II_APPEND_LIBRARIES(${SLEPC_LIBRARIES})
-ENDMACRO()
+#
+# The user has to know the location of the SLEPC headers as well:
+#
+SET(SLEPC_ADD_TO_USER_INCLUDE_DIRS TRUE)
MACRO(FEATURE_SLEPC_ERROR_MESSAGE)
ENDMACRO()
-#
-# Default macro for basic external setup:
-#
-MACRO(FEATURE_CONFIGURE_EXTERNAL _feature)
- IF(DEFINED ${_feature}_INCLUDE_DIRS)
- INCLUDE_DIRECTORIES(${${_feature}_INCLUDE_DIRS})
- ENDIF()
- IF(DEFINED ${_feature}_LIBRARIES)
- DEAL_II_APPEND_LIBRARIES(${${_feature}_LIBRARIES})
- ENDIF()
- IF(DEFINED ${_feature}_LINKER_FLAGS)
- ADD_FLAGS(DEAL_II_LINKER_FLAGS "${${_feature}_LINKER_FLAGS}")
- ENDIF()
-ENDMACRO()
-
-
########################################################################
# #
# CONFIGURE_FEATURE: #
IF(COMMAND FEATURE_${_feature}_CONFIGURE_EXTERNAL)
RUN_COMMAND("FEATURE_${_feature}_CONFIGURE_EXTERNAL()")
ELSE()
- FEATURE_CONFIGURE_EXTERNAL(${_feature})
+ REGISTER_FEATURE(${_feature})
ENDIF()
MESSAGE(STATUS "DEAL_II_WITH_${_feature} successfully set up with external dependencies.")
+++ /dev/null
-## ---------------------------------------------------------------------
-## $Id$
-##
-## Copyright (C) 2013 by the deal.II authors
-##
-## This file is part of the deal.II library.
-##
-## The deal.II library is free software; you can use it, redistribute
-## it, and/or modify it under the terms of the GNU Lesser General
-## Public License as published by the Free Software Foundation; either
-## version 2.1 of the License, or (at your option) any later version.
-## The full text of the license can be found in the file LICENSE at
-## the top level of the deal.II distribution.
-##
-## ---------------------------------------------------------------------
-
-#
-# A small macro to add libraries to
-# DEAL_II_EXTERNAL_LIBRARIES
-# DEAL_II_EXTERNAL_LIBRARIES_DEBUG
-# DEAL_II_EXTERNAL_LIBRARIES_RELEASE
-# depending on the "optmized", "debug" or "general" keyword
-#
-# Usage:
-# DEAL_II_APPEND_LIBRARIES(<list of libraries>)
-#
-
-MACRO(DEAL_II_APPEND_LIBRARIES)
-
- SET(_toggle "general")
- FOREACH(_tmp ${ARGN})
- IF( "${_tmp}" STREQUAL "debug" OR
- "${_tmp}" STREQUAL "optimized" OR
- "${_tmp}" STREQUAL "general" )
- SET(_toggle "${_tmp}")
- ELSE()
- IF("${_toggle}" STREQUAL "general")
- LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES ${_tmp})
- ELSEIF("${_toggle}" STREQUAL "debug")
- LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES_DEBUG ${_tmp})
- ELSEIF("${_toggle}" STREQUAL "optimized")
- LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES_RELEASE ${_tmp})
- ENDIF()
- ENDIF()
- ENDFOREACH()
-
-ENDMACRO()
# $ make edit_cache - to change (cached) configuration variables
# and rerun the configure and generate phases of CMake
#
-# $ make strip_comments - strip the source files in this
+# $ make strip_comments - to strip the source files in this
# directory off the documentation comments
# $ make clean - to remove the generated executable as well as
# all intermediate compilation files
SET(_define_test FALSE)
ENDIF()
ELSE()
- MESSAGE(WARNING "
+ MESSAGE(FATAL_ERROR "
Invalid feature constraint \"${_match}\" in file
\"${_comparison}\":
-The feature \"DEAL_II_${_feature}\" does not exist. Test dropped.\n"
+The feature \"DEAL_II_${_feature}\" does not exist.\n"
)
- SET(_define_test FALSE)
+ #SET(_define_test FALSE)
ENDIF()
ENDFOREACH()
--- /dev/null
+## ---------------------------------------------------------------------
+## $Id$
+##
+## Copyright (C) 2013 by the deal.II authors
+##
+## This file is part of the deal.II library.
+##
+## The deal.II library is free software; you can use it, redistribute
+## it, and/or modify it under the terms of the GNU Lesser General
+## Public License as published by the Free Software Foundation; either
+## version 2.1 of the License, or (at your option) any later version.
+## The full text of the license can be found in the file LICENSE at
+## the top level of the deal.II distribution.
+##
+## ---------------------------------------------------------------------
+
+#
+# This macro is used for the feature configuration in deal.II
+#
+# Usage:
+# REGISTER_FEATURE(feature)
+#
+# This macro will
+#
+# - add ${feature}_INCLUDE_DIRS and ${feature}_INCLUDE_PATH
+# to the list of (internal) include
+# directories
+# - and if ${feature}_ADD_TO_USER_INCLUDE_DIRS is defined also to
+# DEAL_II_USER_INCLUDE_DIRS
+#
+# - add ${feature}_LINKER_FLAGS and ${feature}_LINK_FLAGS to
+# DEAL_II_LINKER_FLAGS
+#
+# - add ${feature}_CXX_FLAGS and ${feature}_COMPILE_FLAGS to
+# CMAKE_CXX_FLAGS
+#
+# - add ${feature}_LIBRARIES to the list of deal.II libraries depending
+# on general, optimized or debug keyword
+#
+
+
+MACRO(REGISTER_FEATURE _feature)
+ MESSAGE(STATUS "Register enabled external feature ${_feature}:")
+
+ # variables for include directories:
+ FOREACH(_var ${_feature}_INCLUDE_DIRS ${_feature}_INCLUDE_PATH)
+ IF(DEFINED ${_var})
+ MESSAGE(STATUS " ${_var}")
+ INCLUDE_DIRECTORIES(${${_var}})
+ IF(${_feature}_ADD_TO_USER_INCLUDE_DIRS)
+ LIST(APPEND DEAL_II_USER_INCLUDE_DIRS ${${_var}})
+ ENDIF()
+ ENDIF()
+ ENDFOREACH()
+
+ # variables for linker flags:
+ FOREACH(_var ${_feature}_LINKER_FLAGS ${_feature}_LINK_FLAGS)
+ IF(DEFINED ${_var})
+ MESSAGE(STATUS " ${_var}")
+ ADD_FLAGS(DEAL_II_LINKER_FLAGS "${${_var}}")
+ ENDIF()
+ ENDFOREACH()
+
+ # variables for compiler flags:
+ FOREACH(_var ${_feature}_CXX_FLAGS ${_feature}_COMPILE_FLAGS)
+ IF(DEFINED ${_var})
+ MESSAGE(STATUS " ${_var}")
+ ADD_FLAGS(CMAKE_CXX_FLAGS "${${_var}}")
+ ENDIF()
+ ENDFOREACH()
+
+ IF(DEFINED ${_feature}_LIBRARIES)
+ MESSAGE(STATUS " ${_feature}_LIBRARIES")
+ #
+ # Add ${_feature}_LIBRARIES to
+ # DEAL_II_EXTERNAL_LIBRARIES
+ # DEAL_II_EXTERNAL_LIBRARIES_DEBUG
+ # DEAL_II_EXTERNAL_LIBRARIES_RELEASE
+ # depending on the "optmized", "debug" or "general" keyword
+ #
+ SET(_toggle "general")
+ FOREACH(_tmp ${${_feature}_LIBRARIES})
+ IF( "${_tmp}" STREQUAL "debug" OR
+ "${_tmp}" STREQUAL "optimized" OR
+ "${_tmp}" STREQUAL "general" )
+ SET(_toggle "${_tmp}")
+ ELSE()
+ IF("${_toggle}" STREQUAL "general")
+ LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES ${_tmp})
+ ELSEIF("${_toggle}" STREQUAL "debug")
+ LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES_DEBUG ${_tmp})
+ ELSEIF("${_toggle}" STREQUAL "optimized")
+ LIST(APPEND DEAL_II_EXTERNAL_LIBRARIES_RELEASE ${_tmp})
+ ENDIF()
+ ENDIF()
+ ENDFOREACH()
+ ENDIF()
+
+ENDMACRO()
ENDFOREACH()
SWITCH_LIBRARY_PREFERENCE()
+ #
+ # Filter out spurious "FALSE" in the library lists:
+ #
+ IF(DEFINED BLAS_LIBRARIES)
+ LIST(REMOVE_ITEM BLAS_LIBRARIES "FALSE")
+ ENDIF()
+ LIST(REMOVE_ITEM LAPACK_LIBRARIES "FALSE")
+
MARK_AS_ADVANCED(
BLAS_DIR
LAPACK_DIR
)
#
- # If we couldn't find LAPACK, clean up the library variables:
+ # Clean up the library variables in case we couldn't find the libraries
+ # to avoid spurious inclusions of "-NOTFOUND" or "FALSE":
#
-
- IF("${BLAS_LIBRARIES}" STREQUAL "FALSE")
- SET(BLAS_LIBRARIES "")
- ENDIF()
- IF("${LAPACK_LIBRARIES}" STREQUAL "FALSE")
- SET(LAPACK_LIBRARIES "")
- ENDIF()
+ SET(BLAS_LIBRARIES)
+ SET(LAPACK_LIBRARIES)
ENDIF()
lib${LIB_SUFFIX} lib64 lib
)
-FIND_FILE(HDF5_PUBCONF H5pubconf.h
+FIND_FILE(HDF5_PUBCONF NAMES H5pubconf.h H5pubconf-64.h
HINTS
${HDF5_INCLUDE_DIR}
${HDF5_DIR}
# PETSC_VERSION_PATCH
# PETSC_WITH_MPIUNI
# PETSC_WITH_64BIT_INDICES
+# PETSC_WITH_COMPLEX
#
INCLUDE(FindPackageHandleStandardArgs)
SET(PETSC_WITH_64BIT_INDICES TRUE)
ENDIF()
+ #
+ # Is petsc compiled with support for COMPLEX numbers?
+ #
+ FILE(STRINGS "${PETSC_PETSCCONF_H}" PETSC_COMPLEX_STRING
+ REGEX "#define.*PETSC_USE_COMPLEX 1")
+ IF("${PETSC_COMPLEX_STRING}" STREQUAL "")
+ SET(PETSC_WITH_COMPLEX FALSE)
+ ELSE()
+ SET(PETSC_WITH_COMPLEX TRUE)
+ ENDIF()
+
FILE(STRINGS "${PETSC_PETSCVERSION_H}" PETSC_VERSION_MAJOR_STRING
REGEX "#define.*PETSC_VERSION_MAJOR")
STRING(REGEX REPLACE "^.*PETSC_VERSION_MAJOR.*([0-9]+).*" "\\1"
# ${CMAKE_CXX_COMPILER}
"
)
-_detailed(
-"# CMAKE_GENERATOR: ${CMAKE_GENERATOR}
-"
- )
+
+IF(CMAKE_C_COMPILER_WORKS)
+ _detailed("# CMAKE_C_COMPILER: ${CMAKE_C_COMPILER}\n")
+ENDIF()
+IF(CMAKE_Fortran_COMPILER_WORKS)
+ _detailed("# CMAKE_Fortran_COMPILER: ${CMAKE_Fortran_COMPILER}\n")
+ENDIF()
+_detailed("# CMAKE_GENERATOR: ${CMAKE_GENERATOR}\n")
+
IF(CMAKE_CROSSCOMPILING)
_both(
"#\n# CROSSCOMPILING!\n"
IF( # MPI:
_var2 MATCHES "^${_feature}_CXX_(COMPILER|COMPILE_FLAGS|LINK_FLAGS|LIBRARIES|INCLUDE_PATH)$" OR
# Boost:
- ( _feature MATCHES "BOOST" AND _var2 MATCHES "^Boost_(LIBRARIES|INCLUDE_DIRS)$" ) OR
+ ( _feature MATCHES "BOOST" AND _var2 MATCHES "^BOOST_(LIBRARIES|INCLUDE_DIRS)$" ) OR
# TBB:
( _feature MATCHES "THREADS" AND _var2 MATCHES "^TBB_(LIBRARIES|INCLUDE_DIRS)$" ) OR
# Generic:
----------
This program is distributed under the GNU GPL v2.0 copyright. Details can be found at:
http://www.gnu.org/licenses/gpl-2.0.html
+
+This copyright is extended to the example mesh files distributed with this program, namely
+./mesh/2d/2d_test.*
+./mesh/2d/quad.*
+./mesh/3d/CC.*
+./mesh/3d/CC_cubit_new.*
+./mesh/3d/CC_cubit_old.*
+./mesh/3d/test_cube_1.*
+./mesh/3d/test_cube_pave_1.*
+./mesh/3d/test_cube_two_materials.*
\ No newline at end of file
This folder contains the html documentation of deal.II
-With the exception of the content under publications/* and reports/* the
-documentation is covered by the same license as the deal.II library itself,
-namely LGPL-2.1+.
+The documentation is generally covered by the same license as the deal.II
+library itself, namely LGPL-2.1+.
-Unclear license status:
+Exceptions:
- external-libraries/p4est-setup.sh
- doxygen/doxygen.sty
- doxygen/options.dox.in
- reports/*
+ external-libraries/p4est-setup.sh - coming from the p4est project, GPL-2+
+++ /dev/null
-\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{doxygen}
-\RequirePackage{calc}
-\RequirePackage{array}
-\pagestyle{fancyplain}
-\newcommand{\clearemptydoublepage}{\newpage{\pagestyle{empty}\cleardoublepage}}
-\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
-\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
-\lhead[\fancyplain{}{\bfseries\thepage}]
- {\fancyplain{}{\bfseries\rightmark}}
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-\rfoot[\fancyplain{}{\bfseries\scriptsize Generated on Wed Jan 11 21:30:49 2006 by doxygen\lfoot[]{\fancyplain{}{\bfseries\scriptsize Generated on Wed Jan 11 21:30:49 2006 by doxygen}}
-\cfoot{}
-\newenvironment{CompactList}
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- \setlength{\itemsep}{-3pt}
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-{\end{itemize}}
-\newcommand{\PBS}[1]{\let\temp=\\#1\let\\=\temp}
-\newlength{\tmplength}
-\newenvironment{TabularC}[1]
-{
-\setlength{\tmplength}
- {\linewidth/(#1)-\tabcolsep*2-\arrayrulewidth*(#1+1)/(#1)}
- \par\begin{tabular*}{\linewidth}
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-{\end{tabular*}\par}
-\newcommand{\entrylabel}[1]{
- {\parbox[b]{\labelwidth-4pt}{\makebox[0pt][l]{\textbf{#1}}\\}}}
-\newenvironment{Desc}
-{\begin{list}{}
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- \renewcommand{\makelabel}{\entrylabel}
- }
-}
-{\end{list}}
-\newenvironment{Indent}
- {\begin{list}{}{\setlength{\leftmargin}{0.5cm}}
- \item[]\ignorespaces}
- {\unskip\end{list}}
-\setlength{\parindent}{0cm}
-\setlength{\parskip}{0.2cm}
-\addtocounter{secnumdepth}{1}
-\sloppy
-\usepackage[T1]{fontenc}
-# Doxyfile 1.3.6
-
-# This file describes the settings to be used by the documentation system
-# doxygen (www.doxygen.org) for a project
-#
-# All text after a hash (#) is considered a comment and will be ignored
-# The format is:
-# TAG = value [value, ...]
-# For lists items can also be appended using:
-# TAG += value [value, ...]
-# Values that contain spaces should be placed between quotes (" ")
-
-#---------------------------------------------------------------------------
-# Project related configuration options
-#---------------------------------------------------------------------------
-
-# The PROJECT_NAME tag is a single word (or a sequence of words surrounded
-# by quotes) that should identify the project.
+# This file contains project-specific configurations for the
+# deal.II documentation.
PROJECT_NAME = "The deal.II library"
-
-# The PROJECT_NUMBER tag can be used to enter a project or revision number.
-# This could be handy for archiving the generated documentation or
-# if some version control system is used.
-
PROJECT_NUMBER = "Reference documentation for deal.II version @DEAL_II_PACKAGE_VERSION@"
-
-# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute)
-# base path where the generated documentation will be put.
-# If a relative path is entered, it will be relative to the location
-# where doxygen was started. If left blank the current directory will be used.
-
OUTPUT_DIRECTORY = .
-# If the CREATE_SUBDIRS tag is set to YES, then doxygen will create
-# 4096 sub-directories (in 2 levels) under the output directory of each output
-# format and will distribute the generated files over these directories.
-# Enabling this option can be useful when feeding doxygen a huge amount of
-# source files, where putting all generated files in the same directory would
-# otherwise cause performance problems for the file system.
-
+# The doxygen documentation says this about the following flag:
+# If the CREATE_SUBDIRS tag is set to YES, then doxygen will create
+# 4096 sub-directories (in 2 levels) under the output directory of each output
+# format and will distribute the generated files over these directories.
+# Enabling this option can be useful when feeding doxygen a huge amount of
+# source files, where putting all generated files in the same directory would
+# otherwise cause performance problems for the file system.
+# We set the flag to NO since we occasionally need to reference individual
+# doxygen-generated files from other parts of the documentation and need
+# to have predictable file paths.
+#
+# The same is true for SHORT_NAMES, which compresses file names, and
+# CASE_SENSE_NAMES which allows file names to contain upper case letters.
CREATE_SUBDIRS = NO
+SHORT_NAMES = NO
+CASE_SENSE_NAMES = YES
-# The OUTPUT_LANGUAGE tag is used to specify the language in which all
-# documentation generated by doxygen is written. Doxygen will use this
-# information to generate all constant output in the proper language.
-# The default language is English, other supported languages are:
-# Afrikaans, Arabic, Brazilian, Catalan, Chinese, Chinese-Traditional,
-# Croatian, Czech, Danish, Dutch, Finnish, French, German, Greek, Hungarian,
-# Italian, Japanese, Japanese-en (Japanese with English messages), Korean,
-# Korean-en, Lithuanian, Norwegian, Polish, Portuguese, Romanian, Russian,
-# Serbian, Slovak, Slovene, Spanish, Swedish, and Ukrainian.
-
-OUTPUT_LANGUAGE = English
-
-# If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will
-# include brief member descriptions after the members that are listed in
-# the file and class documentation (similar to JavaDoc).
-# Set to NO to disable this.
-
-BRIEF_MEMBER_DESC = YES
-
-# If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend
-# the brief description of a member or function before the detailed description.
-# Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the
-# brief descriptions will be completely suppressed.
-
-REPEAT_BRIEF = YES
-
-# This tag implements a quasi-intelligent brief description abbreviator
-# that is used to form the text in various listings. Each string
-# in this list, if found as the leading text of the brief description, will be
-# stripped from the text and the result after processing the whole list, is
-# used as the annotated text. Otherwise, the brief description is used as-is.
-# If left blank, the following values are used ("$name" is automatically
-# replaced with the name of the entity): "The $name class" "The $name widget"
-# "The $name file" "is" "provides" "specifies" "contains"
-# "represents" "a" "an" "the"
-
-ABBREVIATE_BRIEF =
-
-# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then
-# Doxygen will generate a detailed section even if there is only a brief
-# description.
-
-ALWAYS_DETAILED_SEC = NO
-
-# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all
-# inherited members of a class in the documentation of that class as if those
-# members were ordinary class members. Constructors, destructors and assignment
-# operators of the base classes will not be shown.
INLINE_INHERITED_MEMB = NO
-
-# If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full
-# path before files name in the file list and in the header files. If set
-# to NO the shortest path that makes the file name unique will be used.
-
-FULL_PATH_NAMES = YES
-
-# If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag
-# can be used to strip a user-defined part of the path. Stripping is
-# only done if one of the specified strings matches the left-hand part of
-# the path. The tag can be used to show relative paths in the file list.
-# If left blank the directory from which doxygen is run is used as the
-# path to strip.
-
STRIP_FROM_PATH = @CMAKE_SOURCE_DIR@ @CMAKE_BINARY_DIR@
-
-# The STRIP_FROM_INC_PATH tag can be used to strip a user-defined part of
-# the path mentioned in the documentation of a class, which tells
-# the reader which header file to include in order to use a class.
-# If left blank only the name of the header file containing the class
-# definition is used. Otherwise one should specify the include paths that
-# are normally passed to the compiler using the -I flag.
-
-STRIP_FROM_INC_PATH =
-
-# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter
-# (but less readable) file names. This can be useful is your file systems
-# doesn't support long names like on DOS, Mac, or CD-ROM.
-
-SHORT_NAMES = NO
-
-# If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen
-# will interpret the first line (until the first dot) of a JavaDoc-style
-# comment as the brief description. If set to NO, the JavaDoc
-# comments will behave just like regular Qt-style comments
-# (thus requiring an explicit @brief command for a brief description.)
-
JAVADOC_AUTOBRIEF = NO
-
-# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen
-# treat a multi-line C++ special comment block (i.e. a block of //! or ///
-# comments) as a brief description. This used to be the default behaviour.
-# The new default is to treat a multi-line C++ comment block as a detailed
-# description. Set this tag to YES if you prefer the old behaviour instead.
-
-MULTILINE_CPP_IS_BRIEF = NO
-
-# If the INHERIT_DOCS tag is set to YES (the default) then an undocumented
-# member inherits the documentation from any documented member that it
-# re-implements.
-
INHERIT_DOCS = YES
-
-# If the SEPARATE_MEMBER_PAGES tag is set to YES, then doxygen will produce
-# a new page for each member. If set to NO, the documentation of a member will
-# be part of the file/class/namespace that contains it.
-
-SEPARATE_MEMBER_PAGES = NO
-
-# The TAB_SIZE tag can be used to set the number of spaces in a tab.
-# Doxygen uses this value to replace tabs by spaces in code fragments.
-
TAB_SIZE = 8
-# This tag can be used to specify a number of aliases that acts
-# as commands in the documentation. An alias has the form "name=value".
-# For example adding "sideeffect=\par Side Effects:\n" will allow you to
-# put the command \sideeffect (or @sideeffect) in the documentation, which
-# will result in a user-defined paragraph with heading "Side Effects:".
-# You can put \n's in the value part of an alias to insert newlines.
-
-ALIASES =
-
-# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C
-# sources only. Doxygen will then generate output that is more tailored for C.
-# For instance, some of the names that are used will be different. The list
-# of all members will be omitted, etc.
-
-OPTIMIZE_OUTPUT_FOR_C = NO
-
-# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java
-# sources only. Doxygen will then generate output that is more tailored for Java.
-# For instance, namespaces will be presented as packages, qualified scopes
-# will look different, etc.
-
-OPTIMIZE_OUTPUT_JAVA = NO
-
-# If you use STL classes (i.e. std::string, std::vector, etc.) but do not want to
-# include (a tag file for) the STL sources as input, then you should
-# set this tag to YES in order to let doxygen match functions declarations and
-# definitions whose arguments contain STL classes (e.g. func(std::string); v.s.
-# func(std::string) {}). This also make the inheritance and collaboration
-# diagrams that involve STL classes more complete and accurate.
-
-BUILTIN_STL_SUPPORT = NO
-
-# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC
-# tag is set to YES, then doxygen will reuse the documentation of the first
-# member in the group (if any) for the other members of the group. By default
-# all members of a group must be documented explicitly.
-
-DISTRIBUTE_GROUP_DOC = NO
-
-# Set the SUBGROUPING tag to YES (the default) to allow class member groups of
-# the same type (for instance a group of public functions) to be put as a
-# subgroup of that type (e.g. under the Public Functions section). Set it to
-# NO to prevent subgrouping. Alternatively, this can be done per class using
-# the \nosubgrouping command.
+BUILTIN_STL_SUPPORT = YES
-SUBGROUPING = YES
#---------------------------------------------------------------------------
# Build related configuration options
#---------------------------------------------------------------------------
-# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in
-# documentation are documented, even if no documentation was available.
-# Private class members and static file members will be hidden unless
-# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES
-
EXTRACT_ALL = NO
-
-# If the EXTRACT_PRIVATE tag is set to YES all private members of a class
-# will be included in the documentation.
-
EXTRACT_PRIVATE = YES
-
-# If the EXTRACT_STATIC tag is set to YES all static members of a file
-# will be included in the documentation.
-
EXTRACT_STATIC = YES
-
-# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs)
-# defined locally in source files will be included in the documentation.
-# If set to NO only classes defined in header files are included.
-
EXTRACT_LOCAL_CLASSES = YES
-
-# This flag is only useful for Objective-C code. When set to YES local
-# methods, which are defined in the implementation section but not in
-# the interface are included in the documentation.
-# If set to NO (the default) only methods in the interface are included.
-
-EXTRACT_LOCAL_METHODS = NO
-
-# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all
-# undocumented members of documented classes, files or namespaces.
-# If set to NO (the default) these members will be included in the
-# various overviews, but no documentation section is generated.
-# This option has no effect if EXTRACT_ALL is enabled.
-
-HIDE_UNDOC_MEMBERS = YES
-
-# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all
-# undocumented classes that are normally visible in the class hierarchy.
-# If set to NO (the default) these classes will be included in the various
-# overviews. This option has no effect if EXTRACT_ALL is enabled.
-
-HIDE_UNDOC_CLASSES = YES
-
-# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all
-# friend (class|struct|union) declarations.
-# If set to NO (the default) these declarations will be included in the
-# documentation.
-
-HIDE_FRIEND_COMPOUNDS = NO
-
-# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any
-# documentation blocks found inside the body of a function.
-# If set to NO (the default) these blocks will be appended to the
-# function's detailed documentation block.
-
-HIDE_IN_BODY_DOCS = NO
-
-# The INTERNAL_DOCS tag determines if documentation
-# that is typed after a \internal command is included. If the tag is set
-# to NO (the default) then the documentation will be excluded.
-# Set it to YES to include the internal documentation.
-
-INTERNAL_DOCS = NO
-
-# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate
-# file names in lower-case letters. If set to YES upper-case letters are also
-# allowed. This is useful if you have classes or files whose names only differ
-# in case and if your file system supports case sensitive file names. Windows
-# and Mac users are advised to set this option to NO.
-
-CASE_SENSE_NAMES = YES
-
-# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen
-# will show members with their full class and namespace scopes in the
-# documentation. If set to YES the scope will be hidden.
-
-HIDE_SCOPE_NAMES = NO
-
-# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen
-# will put a list of the files that are included by a file in the documentation
-# of that file.
-
-SHOW_INCLUDE_FILES = NO
-
-# If the INLINE_INFO tag is set to YES (the default) then a tag [inline]
-# is inserted in the documentation for inline members.
-
-INLINE_INFO = YES
-
-# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen
-# will sort the (detailed) documentation of file and class members
-# alphabetically by member name. If set to NO the members will appear in
-# declaration order.
-
+HIDE_UNDOC_MEMBERS = NO
+HIDE_UNDOC_CLASSES = NO
SORT_MEMBER_DOCS = NO
-
-# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the
-# brief documentation of file, namespace and class members alphabetically
-# by member name. If set to NO (the default) the members will appear in
-# declaration order.
-
SORT_BRIEF_DOCS = NO
-
-# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be
-# sorted by fully-qualified names, including namespaces. If set to
-# NO (the default), the class list will be sorted only by class name,
-# not including the namespace part.
-# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.
-# Note: This option applies only to the class list, not to the
-# alphabetical list.
-
SORT_BY_SCOPE_NAME = NO
-
-# The GENERATE_TODOLIST tag can be used to enable (YES) or
-# disable (NO) the todo list. This list is created by putting \todo
-# commands in the documentation.
-
GENERATE_TODOLIST = YES
-
-# The GENERATE_TESTLIST tag can be used to enable (YES) or
-# disable (NO) the test list. This list is created by putting \test
-# commands in the documentation.
-
-GENERATE_TESTLIST = YES
-
-# The GENERATE_BUGLIST tag can be used to enable (YES) or
-# disable (NO) the bug list. This list is created by putting \bug
-# commands in the documentation.
-
-GENERATE_BUGLIST = YES
-
-# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or
-# disable (NO) the deprecated list. This list is created by putting
-# \deprecated commands in the documentation.
-
GENERATE_DEPRECATEDLIST= YES
-
-# The ENABLED_SECTIONS tag can be used to enable conditional
-# documentation sections, marked by \if sectionname ... \endif.
-
-ENABLED_SECTIONS = YES
-
-# The MAX_INITIALIZER_LINES tag determines the maximum number of lines
-# the initial value of a variable or define consists of for it to appear in
-# the documentation. If the initializer consists of more lines than specified
-# here it will be hidden. Use a value of 0 to hide initializers completely.
-# The appearance of the initializer of individual variables and defines in the
-# documentation can be controlled using \showinitializer or \hideinitializer
-# command in the documentation regardless of this setting.
-
-MAX_INITIALIZER_LINES = 30
-
-# Set the SHOW_USED_FILES tag to NO to disable the list of files generated
-# at the bottom of the documentation of classes and structs. If set to YES the
-# list will mention the files that were used to generate the documentation.
-
SHOW_USED_FILES = YES
-# The FILE_VERSION_FILTER tag can be used to specify a program or script that
-# doxygen should invoke to get the current version for each file (typically from the
-# version control system). Doxygen will invoke the program by executing (via
-# popen()) the command <command> <input-file>, where <command> is the value of
-# the FILE_VERSION_FILTER tag, and <input-file> is the name of an input file
-# provided by doxygen. Whatever the program writes to standard output
-# is used as the file version. See the manual for examples.
-
-FILE_VERSION_FILTER =
-
#---------------------------------------------------------------------------
# configuration options related to warning and progress messages
#---------------------------------------------------------------------------
-# The QUIET tag can be used to turn on/off the messages that are generated
-# by doxygen. Possible values are YES and NO. If left blank NO is used.
-
QUIET = YES
-
-# The WARNINGS tag can be used to turn on/off the warning messages that are
-# generated by doxygen. Possible values are YES and NO. If left blank
-# NO is used.
-
WARNINGS = YES
-
-# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings
-# for undocumented members. If EXTRACT_ALL is set to YES then this flag will
-# automatically be disabled.
-
WARN_IF_UNDOCUMENTED = YES
-
-# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for
-# potential errors in the documentation, such as not documenting some
-# parameters in a documented function, or documenting parameters that
-# don't exist or using markup commands wrongly.
-
WARN_IF_DOC_ERROR = YES
-# This WARN_NO_PARAMDOC option can be abled to get warnings for
-# functions that are documented, but have no documentation for their parameters
-# or return value. If set to NO (the default) doxygen will only warn about
-# wrong or incomplete parameter documentation, but not about the absence of
-# documentation.
-
-WARN_NO_PARAMDOC = NO
-
-# The WARN_FORMAT tag determines the format of the warning messages that
-# doxygen can produce. The string should contain the $file, $line, and $text
-# tags, which will be replaced by the file and line number from which the
-# warning originated and the warning text. Optionally the format may contain
-# $version, which will be replaced by the version of the file (if it could
-# be obtained via FILE_VERSION_FILTER)
-
-WARN_FORMAT = "$file:$line: $text "
-
-# The WARN_LOGFILE tag can be used to specify a file to which warning
-# and error messages should be written. If left blank the output is written
-# to stderr.
-
-WARN_LOGFILE =
-
#---------------------------------------------------------------------------
# configuration options related to the input files
#---------------------------------------------------------------------------
-# The INPUT tag can be used to specify the files and/or directories that contain
-# documented source files. You may enter file names like "myfile.cpp" or
-# directories like "/usr/src/myproject". Separate the files or directories
-# with spaces.
-
INPUT =
-
-# If the value of the INPUT tag contains directories, you can use the
-# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
-# and *.h) to filter out the source-files in the directories. If left
-# blank the following patterns are tested:
-# *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh *.hxx
-# *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.py
-
-FILE_PATTERNS =
-
-# The RECURSIVE tag can be used to turn specify whether or not subdirectories
-# should be searched for input files as well. Possible values are YES and NO.
-# If left blank NO is used.
-
-RECURSIVE = NO
-
-# The EXCLUDE tag can be used to specify files and/or directories that should
-# excluded from the INPUT source files. This way you can easily exclude a
-# subdirectory from a directory tree whose root is specified with the INPUT tag.
-
-EXCLUDE =
-
-# The EXCLUDE_SYMLINKS tag can be used select whether or not files or
-# directories that are symbolic links (a Unix filesystem feature) are excluded
-# from the input.
-
-EXCLUDE_SYMLINKS = NO
-
-# If the value of the INPUT tag contains directories, you can use the
-# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude
-# certain files from those directories. Note that the wildcards are matched
-# against the file with absolute path, so to exclude all test directories
-# for example use the pattern */test/*
-
EXCLUDE_PATTERNS = *.templates.h
-
-# The EXAMPLE_PATH tag can be used to specify one or more files or
-# directories that contain example code fragments that are included (see
-# the \include command).
-
EXAMPLE_PATH = @CMAKE_BINARY_DIR@/doc/doxygen/tutorial \
@CMAKE_SOURCE_DIR@/examples/doxygen
-
-# If the value of the EXAMPLE_PATH tag contains directories, you can use the
-# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
-# and *.h) to filter out the source-files in the directories. If left
-# blank all files are included.
-
-EXAMPLE_PATTERNS =
-
-# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be
-# searched for input files to be used with the \include or \dontinclude
-# commands irrespective of the value of the RECURSIVE tag.
-# Possible values are YES and NO. If left blank NO is used.
-
EXAMPLE_RECURSIVE = NO
-
-# The IMAGE_PATH tag can be used to specify one or more files or
-# directories that contain image that are included in the documentation (see
-# the \image command). This is overwritten in deal.dox
-
IMAGE_PATH =
-
-# The INPUT_FILTER tag can be used to specify a program that doxygen should
-# invoke to filter for each input file. Doxygen will invoke the filter program
-# by executing (via popen()) the command <filter> <input-file>, where <filter>
-# is the value of the INPUT_FILTER tag, and <input-file> is the name of an
-# input file. Doxygen will then use the output that the filter program writes
-# to standard output. If FILTER_PATTERNS is specified, this tag will be
-# ignored.
-
INPUT_FILTER = ${CMAKE_SOURCE_DIR}/doc/doxygen/scripts/filter
-
-# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern
-# basis. Doxygen will compare the file name with each pattern and apply the
-# filter if there is a match. The filters are a list of the form:
-# pattern=filter (like *.cpp=my_cpp_filter). See INPUT_FILTER for further
-# info on how filters are used. If FILTER_PATTERNS is empty, INPUT_FILTER
-# is applied to all files.
-
-FILTER_PATTERNS =
-
-# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
-# INPUT_FILTER) will be used to filter the input files when producing source
-# files to browse (i.e. when SOURCE_BROWSER is set to YES).
-
FILTER_SOURCE_FILES = YES
#---------------------------------------------------------------------------
# configuration options related to source browsing
#---------------------------------------------------------------------------
-# If the SOURCE_BROWSER tag is set to YES then a list of source files will
-# be generated. Documented entities will be cross-referenced with these sources.
-# Note: To get rid of all source code in the generated output, make sure also
-# VERBATIM_HEADERS is set to NO. If you have enabled CALL_GRAPH or CALLER_GRAPH
-# then you must also enable this option. If you don't then doxygen will produce
-# a warning and turn it on anyway
-
SOURCE_BROWSER = YES
-
-# Setting the INLINE_SOURCES tag to YES will include the body
-# of functions and classes directly in the documentation.
-
INLINE_SOURCES = NO
-
-# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct
-# doxygen to hide any special comment blocks from generated source code
-# fragments. Normal C and C++ comments will always remain visible.
-
STRIP_CODE_COMMENTS = YES
-
-# If the REFERENCED_BY_RELATION tag is set to YES (the default)
-# then for each documented function all documented
-# functions referencing it will be listed.
-
-REFERENCED_BY_RELATION = YES
-
-# If the REFERENCES_RELATION tag is set to YES (the default)
-# then for each documented function all documented entities
-# called/used by that function will be listed.
-
-REFERENCES_RELATION = YES
-
-# If the REFERENCES_LINK_SOURCE tag is set to YES (the default)
-# and SOURCE_BROWSER tag is set to YES, then the hyperlinks from
-# functions in REFERENCES_RELATION and REFERENCED_BY_RELATION lists will
-# link to the source code. Otherwise they will link to the documentstion.
-
-REFERENCES_LINK_SOURCE = YES
-
-# If the USE_HTAGS tag is set to YES then the references to source code
-# will point to the HTML generated by the htags(1) tool instead of doxygen
-# built-in source browser. The htags tool is part of GNU's global source
-# tagging system (see http://www.gnu.org/software/global/global.html). You
-# will need version 4.8.6 or higher.
-
USE_HTAGS = NO
-
-# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen
-# will generate a verbatim copy of the header file for each class for
-# which an include is specified. Set to NO to disable this.
-
VERBATIM_HEADERS = NO
#---------------------------------------------------------------------------
# configuration options related to the alphabetical class index
#---------------------------------------------------------------------------
-# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index
-# of all compounds will be generated. Enable this if the project
-# contains a lot of classes, structs, unions or interfaces.
-
ALPHABETICAL_INDEX = YES
-
-# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then
-# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns
-# in which this list will be split (can be a number in the range [1..20])
-
COLS_IN_ALPHA_INDEX = 3
-# In case all classes in a project start with a common prefix, all
-# classes will be put under the same header in the alphabetical index.
-# The IGNORE_PREFIX tag can be used to specify one or more prefixes that
-# should be ignored while generating the index headers.
-
-IGNORE_PREFIX =
-
#---------------------------------------------------------------------------
# configuration options related to the HTML output
#---------------------------------------------------------------------------
-# If the GENERATE_HTML tag is set to YES (the default) Doxygen will
-# generate HTML output.
-
GENERATE_HTML = YES
-
-# The HTML_OUTPUT tag is used to specify where the HTML docs will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `html' will be used as the default path.
-
HTML_OUTPUT = deal.II
-
-# The HTML_FILE_EXTENSION tag can be used to specify the file extension for
-# each generated HTML page (for example: .htm,.php,.asp). If it is left blank
-# doxygen will generate files with .html extension.
-
HTML_FILE_EXTENSION = .html
-
-# The HTML_HEADER tag can be used to specify a personal HTML header for
-# each generated HTML page. If it is left blank doxygen will generate a
-# standard header.
-
HTML_HEADER = header.html
-
-# The HTML_FOOTER tag can be used to specify a personal HTML footer for
-# each generated HTML page. If it is left blank doxygen will generate a
-# standard footer.
-
HTML_FOOTER = footer.html
-# The HTML_STYLESHEET tag can be used to specify a user-defined cascading
-# style sheet that is used by each HTML page. It can be used to
-# fine-tune the look of the HTML output. If the tag is left blank doxygen
-# will generate a default style sheet. Note that doxygen will try to copy
-# the style sheet file to the HTML output directory, so don't put your own
-# stylesheet in the HTML output directory as well, or it will be erased!
-
-HTML_STYLESHEET =
-
-# If the GENERATE_HTMLHELP tag is set to YES, additional index files
-# will be generated that can be used as input for tools like the
-# Microsoft HTML help workshop to generate a compressed HTML help file (.chm)
-# of the generated HTML documentation.
-
-GENERATE_HTMLHELP = NO
-
-# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can
-# be used to specify the file name of the resulting .chm file. You
-# can add a path in front of the file if the result should not be
-# written to the html output directory.
-
-CHM_FILE =
-
-# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can
-# be used to specify the location (absolute path including file name) of
-# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run
-# the HTML help compiler on the generated index.hhp.
-
-HHC_LOCATION =
-
-# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag
-# controls if a separate .chi index file is generated (YES) or that
-# it should be included in the master .chm file (NO).
-
-GENERATE_CHI = NO
-
-# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag
-# controls whether a binary table of contents is generated (YES) or a
-# normal table of contents (NO) in the .chm file.
-
-BINARY_TOC = NO
-
-# The TOC_EXPAND flag can be set to YES to add extra items for group members
-# to the contents of the HTML help documentation and to the tree view.
-
-TOC_EXPAND = NO
-
-# The DISABLE_INDEX tag can be used to turn on/off the condensed index at
-# top of each HTML page. The value NO (the default) enables the index and
-# the value YES disables it.
-
-DISABLE_INDEX = NO
-
-# This tag can be used to set the number of enum values (range [1..20])
-# that doxygen will group on one line in the generated HTML documentation.
-
-ENUM_VALUES_PER_LINE = 4
-
-# If the GENERATE_TREEVIEW tag is set to YES, a side panel will be
-# generated containing a tree-like index structure (just like the one that
-# is generated for HTML Help). For this to work a browser that supports
-# JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+,
-# Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are
-# probably better off using the HTML help feature.
-
-GENERATE_TREEVIEW = NO
-
-# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be
-# used to set the initial width (in pixels) of the frame in which the tree
-# is shown.
-
-TREEVIEW_WIDTH = 250
-
#---------------------------------------------------------------------------
# configuration options related to the LaTeX output
#---------------------------------------------------------------------------
-# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will
-# generate Latex output.
-
+# don't generate latex output -- it's simply too big!
GENERATE_LATEX = NO
-# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `latex' will be used as the default path.
-
-LATEX_OUTPUT = LaTeX/deal.II
-
-# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be
-# invoked. If left blank `latex' will be used as the default command name.
-
-LATEX_CMD_NAME = latex
-
-# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to
-# generate index for LaTeX. If left blank `makeindex' will be used as the
-# default command name.
-
-MAKEINDEX_CMD_NAME = makeindex
-
-# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact
-# LaTeX documents. This may be useful for small projects and may help to
-# save some trees in general.
-
-COMPACT_LATEX = NO
-
-# The PAPER_TYPE tag can be used to set the paper type that is used
-# by the printer. Possible values are: a4, a4wide, letter, legal and
-# executive. If left blank a4wide will be used.
-
+# but set a few flags for when processing formulas embedded
+# in the documentation.
PAPER_TYPE = a4wide
-
-# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX
-# packages that should be included in the LaTeX output.
-
EXTRA_PACKAGES = amsmath amsfonts
-
-# The LATEX_HEADER tag can be used to specify a personal LaTeX header for
-# the generated latex document. The header should contain everything until
-# the first chapter. If it is left blank doxygen will generate a
-# standard header. Notice: only use this tag if you know what you are doing!
-
-LATEX_HEADER =
-
-# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated
-# is prepared for conversion to pdf (using ps2pdf). The pdf file will
-# contain links (just like the HTML output) instead of page references
-# This makes the output suitable for online browsing using a pdf viewer.
-
-PDF_HYPERLINKS = NO
-
-# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of
-# plain latex in the generated Makefile. Set this option to YES to get a
-# higher quality PDF documentation.
-
-USE_PDFLATEX = NO
-
-# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode.
-# command to the generated LaTeX files. This will instruct LaTeX to keep
-# running if errors occur, instead of asking the user for help.
-# This option is also used when generating formulas in HTML.
-
LATEX_BATCHMODE = YES
-# If LATEX_HIDE_INDICES is set to YES then doxygen will not
-# include the index chapters (such as File Index, Compound Index, etc.)
-# in the output.
-
-LATEX_HIDE_INDICES = NO
-
#---------------------------------------------------------------------------
-# configuration options related to the RTF output
+# Other output formats
#---------------------------------------------------------------------------
-# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output
-# The RTF output is optimized for Word 97 and may not look very pretty with
-# other RTF readers or editors.
-
GENERATE_RTF = NO
-
-# The RTF_OUTPUT tag is used to specify where the RTF docs will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `rtf' will be used as the default path.
-
-RTF_OUTPUT = rtf
-
-# If the COMPACT_RTF tag is set to YES Doxygen generates more compact
-# RTF documents. This may be useful for small projects and may help to
-# save some trees in general.
-
-COMPACT_RTF = NO
-
-# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated
-# will contain hyperlink fields. The RTF file will
-# contain links (just like the HTML output) instead of page references.
-# This makes the output suitable for online browsing using WORD or other
-# programs which support those fields.
-# Note: wordpad (write) and others do not support links.
-
-RTF_HYPERLINKS = NO
-
-# Load stylesheet definitions from file. Syntax is similar to doxygen's
-# config file, i.e. a series of assignments. You only have to provide
-# replacements, missing definitions are set to their default value.
-
-RTF_STYLESHEET_FILE =
-
-# Set optional variables used in the generation of an rtf document.
-# Syntax is similar to doxygen's config file.
-
-RTF_EXTENSIONS_FILE =
-
-#---------------------------------------------------------------------------
-# configuration options related to the man page output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_MAN tag is set to YES (the default) Doxygen will
-# generate man pages
-
GENERATE_MAN = NO
-
-# The MAN_OUTPUT tag is used to specify where the man pages will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `man' will be used as the default path.
-
-MAN_OUTPUT = man
-
-# The MAN_EXTENSION tag determines the extension that is added to
-# the generated man pages (default is the subroutine's section .3)
-
-MAN_EXTENSION = .3
-
-# If the MAN_LINKS tag is set to YES and Doxygen generates man output,
-# then it will generate one additional man file for each entity
-# documented in the real man page(s). These additional files
-# only source the real man page, but without them the man command
-# would be unable to find the correct page. The default is NO.
-
-MAN_LINKS = NO
-
-#---------------------------------------------------------------------------
-# configuration options related to the XML output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_XML tag is set to YES Doxygen will
-# generate an XML file that captures the structure of
-# the code including all documentation.
-
GENERATE_XML = NO
-
-# The XML_OUTPUT tag is used to specify where the XML pages will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `xml' will be used as the default path.
-
-XML_OUTPUT = xml
-
-# The XML_SCHEMA tag can be used to specify an XML schema,
-# which can be used by a validating XML parser to check the
-# syntax of the XML files.
-
-XML_SCHEMA =
-
-# The XML_DTD tag can be used to specify an XML DTD,
-# which can be used by a validating XML parser to check the
-# syntax of the XML files.
-
-XML_DTD =
-
-# If the XML_PROGRAMLISTING tag is set to YES Doxygen will
-# dump the program listings (including syntax highlighting
-# and cross-referencing information) to the XML output. Note that
-# enabling this will significantly increase the size of the XML output.
-
-XML_PROGRAMLISTING = YES
-
-#---------------------------------------------------------------------------
-# configuration options for the AutoGen Definitions output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will
-# generate an AutoGen Definitions (see autogen.sf.net) file
-# that captures the structure of the code including all
-# documentation. Note that this feature is still experimental
-# and incomplete at the moment.
-
GENERATE_AUTOGEN_DEF = NO
-
-#---------------------------------------------------------------------------
-# configuration options related to the Perl module output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_PERLMOD tag is set to YES Doxygen will
-# generate a Perl module file that captures the structure of
-# the code including all documentation. Note that this
-# feature is still experimental and incomplete at the
-# moment.
-
GENERATE_PERLMOD = NO
-# If the PERLMOD_LATEX tag is set to YES Doxygen will generate
-# the necessary Makefile rules, Perl scripts and LaTeX code to be able
-# to generate PDF and DVI output from the Perl module output.
-
-PERLMOD_LATEX = NO
-
-# If the PERLMOD_PRETTY tag is set to YES the Perl module output will be
-# nicely formatted so it can be parsed by a human reader. This is useful
-# if you want to understand what is going on. On the other hand, if this
-# tag is set to NO the size of the Perl module output will be much smaller
-# and Perl will parse it just the same.
-
-PERLMOD_PRETTY = YES
-
-# The names of the make variables in the generated doxyrules.make file
-# are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX.
-# This is useful so different doxyrules.make files included by the same
-# Makefile don't overwrite each other's variables.
-
-PERLMOD_MAKEVAR_PREFIX =
-
#---------------------------------------------------------------------------
# Configuration options related to the preprocessor
#---------------------------------------------------------------------------
-# If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will
-# evaluate all C-preprocessor directives found in the sources and include
-# files.
-
ENABLE_PREPROCESSING = YES
-
-# If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro
-# names in the source code. If set to NO (the default) only conditional
-# compilation will be performed. Macro expansion can be done in a controlled
-# way by setting EXPAND_ONLY_PREDEF to YES.
-
MACRO_EXPANSION = YES
-
-# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES
-# then the macro expansion is limited to the macros specified with the
-# PREDEFINED and EXPAND_AS_DEFINED tags.
-
EXPAND_ONLY_PREDEF = YES
-
-# If the SEARCH_INCLUDES tag is set to YES (the default) the includes files
-# in the INCLUDE_PATH (see below) will be search if a #include is found.
-
SEARCH_INCLUDES = YES
-
-# The INCLUDE_PATH tag can be used to specify one or more directories that
-# contain include files that are not input files but should be processed by
-# the preprocessor.
-
INCLUDE_PATH = @CMAKE_SOURCE_DIR@/include/deal.II
-
-# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
-# patterns (like *.h and *.hpp) to filter out the header-files in the
-# directories. If left blank, the patterns specified with FILE_PATTERNS will
-# be used.
-
INCLUDE_FILE_PATTERNS =
-# The PREDEFINED tag can be used to specify one or more macro names that
-# are defined before the preprocessor is started (similar to the -D option of
-# gcc). The argument of the tag is a list of macros of the form: name
-# or name=definition (no spaces). If the definition and the = are
-# omitted =1 is assumed. To prevent a macro definition from being
-# undefined via #undef or recursively expanded use the := operator
-# instead of the = operator.
-
-# [deal.II] Set MT flags so that the corresponding documentation will always
-# be visible, irrespective of whether MT is actually switched on or not. Do
-# the same for a bunch of other external packages as well. Also, define a
-# variable DOXYGEN in order to mask out inline functions
-
+# set a few variables that help us generate documentation for
+# things like the PETSc and Trilinos wrappers, even if they were
+# not configured
PREDEFINED = DOXYGEN=1 \
DEBUG=1 \
DEAL_II_WITH_PETSC=1 \
DEAL_II_WITH_P4EST=1 \
DEAL_II_WITH_MPI=1
-# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then
-# this tag can be used to specify a list of macro names that should be expanded.
-# The macro definition that is found in the sources will be used.
-# Use the PREDEFINED tag if you want to use a different macro definition.
-
+# do not expand exception declarations
EXPAND_AS_DEFINED = DeclException0 \
DeclException1 \
DeclException2 \
DeclException3 \
DeclException4 \
DeclException5
-
-# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then
-# doxygen's preprocessor will remove all function-like macros that are alone
-# on a line, have an all uppercase name, and do not end with a semicolon. Such
-# function macros are typically used for boiler-plate code, and will confuse
-# the parser if not removed.
-
SKIP_FUNCTION_MACROS = YES
#---------------------------------------------------------------------------
# Configuration::additions related to external references
#---------------------------------------------------------------------------
-# The TAGFILES option can be used to specify one or more tagfiles.
-# Optionally an initial location of the external documentation
-# can be added for each tagfile. The format of a tag file without
-# this location is as follows:
-# TAGFILES = file1 file2 ...
-# Adding location for the tag files is done as follows:
-# TAGFILES = file1=loc1 "file2 = loc2" ...
-# where "loc1" and "loc2" can be relative or absolute paths or
-# URLs. If a location is present for each tag, the installdox tool
-# does not have to be run to correct the links.
-# Note that each tag file must have a unique name
-# (where the name does NOT include the path)
-# If a tag file is not located in the directory in which doxygen
-# is run, you must also specify the path to the tagfile here.
-
-TAGFILES =
-
-# When a file name is specified after GENERATE_TAGFILE, doxygen will create
-# a tag file that is based on the input files it reads.
-
GENERATE_TAGFILE = deal.tag
-
-# If the ALLEXTERNALS tag is set to YES all external classes will be listed
-# in the class index. If set to NO only the inherited external classes
-# will be listed.
-
ALLEXTERNALS = NO
-
-# If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed
-# in the modules index. If set to NO, only the current project's groups will
-# be listed.
-
EXTERNAL_GROUPS = YES
-
-# The PERL_PATH should be the absolute path and name of the perl script
-# interpreter (i.e. the result of `which perl').
-
PERL_PATH = /usr/bin/perl
#---------------------------------------------------------------------------
# Configuration options related to the dot tool
#---------------------------------------------------------------------------
-# If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will
-# generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base
-# or super classes. Setting the tag to NO turns the diagrams off. Note that
-# this option is superseded by the HAVE_DOT option below. This is only a
-# fallback. It is recommended to install and use dot, since it yields more
-# powerful graphs.
-
CLASS_DIAGRAMS = YES
-
-# If set to YES, the inheritance and collaboration graphs will hide
-# inheritance and usage relations if the target is undocumented
-# or is not a class.
-
HIDE_UNDOC_RELATIONS = NO
-
-# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is
-# available from the path. This tool is part of Graphviz, a graph visualization
-# toolkit from AT&T and Lucent Bell Labs. The other options in this section
-# have no effect if this option is set to NO (the default)
-
HAVE_DOT = YES
-
-# If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen
-# will generate a graph for each documented class showing the direct and
-# indirect inheritance relations. Setting this tag to YES will force the
-# the CLASS_DIAGRAMS tag to NO.
-
CLASS_GRAPH = YES
-
-# If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen
-# will generate a graph for each documented class showing the direct and
-# indirect implementation dependencies (inheritance, containment, and
-# class references variables) of the class with other documented classes.
-
COLLABORATION_GRAPH = NO
-
-# If the GROUP_GRAPHS and HAVE_DOT tags are set to YES then doxygen
-# will generate a graph for groups, showing the direct groups dependencies
-
GROUP_GRAPHS = YES
-
-# If the UML_LOOK tag is set to YES doxygen will generate inheritance and
-# collaboration diagrams in a style similar to the OMG's Unified Modeling
-# Language.
-
UML_LOOK = NO
-
-# If set to YES, the inheritance and collaboration graphs will show the
-# relations between templates and their instances.
-
TEMPLATE_RELATIONS = YES
-
-# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT
-# tags are set to YES then doxygen will generate a graph for each documented
-# file showing the direct and indirect include dependencies of the file with
-# other documented files.
-
INCLUDE_GRAPH = YES
-
-# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and
-# HAVE_DOT tags are set to YES then doxygen will generate a graph for each
-# documented header file showing the documented files that directly or
-# indirectly include this file.
-
INCLUDED_BY_GRAPH = YES
-
-# If the CALL_GRAPH, SOURCE_BROWSER and HAVE_DOT tags are set to YES then doxygen will
-# generate a call dependency graph for every global function or class method.
-# Note that enabling this option will significantly increase the time of a run.
-# So in most cases it will be better to enable call graphs for selected
-# functions only using the \callgraph command.
-
CALL_GRAPH = NO
-
-# If the CALLER_GRAPH, SOURCE_BROWSER and HAVE_DOT tags are set to YES then doxygen will
-# generate a caller dependency graph for every global function or class method.
-# Note that enabling this option will significantly increase the time of a run.
-# So in most cases it will be better to enable caller graphs for selected
-# functions only using the \callergraph command.
-
CALLER_GRAPH = NO
-
-# If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen
-# will graphical hierarchy of all classes instead of a textual one.
-
GRAPHICAL_HIERARCHY = NO
-
-# If the DIRECTORY_GRAPH, SHOW_DIRECTORIES and HAVE_DOT tags are set to YES
-# then doxygen will show the dependencies a directory has on other directories
-# in a graphical way. The dependency relations are determined by the #include
-# relations between the files in the directories.
-
DIRECTORY_GRAPH = YES
-
-# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images
-# generated by dot. Possible values are png, jpg, or gif
-# If left blank png will be used.
-
DOT_IMAGE_FORMAT = png
-
-# The tag DOT_PATH can be used to specify the path where the dot tool can be
-# found. If left blank, it is assumed the dot tool can be found in the path.
-
-DOT_PATH =
-
-# The DOTFILE_DIRS tag can be used to specify one or more directories that
-# contain dot files that are included in the documentation (see the
-# \dotfile command).
-
-DOTFILE_DIRS =
-
-# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the
-# graphs generated by dot. A depth value of 3 means that only nodes reachable
-# from the root by following a path via at most 3 edges will be shown. Nodes
-# that lay further from the root node will be omitted. Note that setting this
-# option to 1 or 2 may greatly reduce the computation time needed for large
-# code bases. Also note that the size of a graph can be further restricted by
-# DOT_GRAPH_MAX_NODES. Using a depth of 0 means no depth restriction.
-
-MAX_DOT_GRAPH_DEPTH = 2
-
-# Set the DOT_TRANSPARENT tag to YES to generate images with a transparent
-# background. This is disabled by default, which results in a white background.
-# Warning: Depending on the platform used, enabling this option may lead to
-# badly anti-aliased labels on the edges of a graph (i.e. they become hard to
-# read).
-
+MAX_DOT_GRAPH_DEPTH = 3
DOT_TRANSPARENT = NO
-
-# Set the DOT_MULTI_TARGETS tag to YES allow dot to generate multiple output
-# files in one run (i.e. multiple -o and -T options on the command line). This
-# makes dot run faster, but since only newer versions of dot (>1.8.10)
-# support this, this feature is disabled by default.
-
-DOT_MULTI_TARGETS = NO
-
-# If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will
-# generate a legend page explaining the meaning of the various boxes and
-# arrows in the dot generated graphs.
-
GENERATE_LEGEND = YES
-# If the DOT_CLEANUP tag is set to YES (the default) Doxygen will
-# remove the intermediate dot files that are used to generate
-# the various graphs.
-
DOT_CLEANUP = YES
#---------------------------------------------------------------------------
# Configuration::additions related to the search engine
#---------------------------------------------------------------------------
-# The SEARCHENGINE tag specifies whether or not a search engine should be
-# used. If set to NO the values of all tags below this one will be ignored.
-
SEARCHENGINE = YES
SERVER_BASED_SEARCH = NO
<ol>
+ <li> New: introduced "make test" that runs a minimal set of tests. We
+ encourage every user to run this, especially if they run in to problems.
+ The tests are automatically picked depending on the configuration and
+ will be shipped with every release.
+ <br>
+ (Timo Heister, Matthias Maier, 2013/11/08)
+ </li>
+
<li> Changed: It is now possible to restore a parallel Triangulation
(and solutions) with a different number of processors it was saved with
using Triangulation::save() and Triangulation::load().
<h3>Specific improvements</h3>
<ol>
+ <li> Fixed: The CellData class now has a default constructor that
+ sets the material and boundary indicators to zero. This fixes certain
+ internal errors with the Intel ICC compiler.
+ <br>
+ (Wolfgang Bangerth, 2013/11/13)
+ </li>
+
+ <li> New: There is now a framework for coloring graphs, with functions
+ in namespace GraphColoring.
+ <br>
+ (Bruno Turcksin, Martin Kronbichler, 2013/11/06)
+ </li>
+
<li>
Fixed: the DerivativeApproximation class was not working correctly when
used with parallel vectors.
</p>
<dl>
+ <dt>
+ <strong>2013/11/01: step-42 solves an elasto-plastic contact problem </strong>
+ </dt>
+ <dd>
+ step-42, written by Jörg Frohne, Timo Heister and Wolfgang
+ Bangerth, shows how to solve an elasto-plastic contact problem.
+ The program is an extension of step-41 to a much more complex
+ equation (nonlinear elasto-plasticity) and also demonstrates
+ how to compute solutions for such problems in parallel.
+ </dd>
+
<dt>
<strong>2013/10/01: step-51 implements an HDG method </strong>
</dt>
cd build
cmake -DCMAKE_INSTALL_PREFIX=/path/to/install/dir ../deal.II
make install
+ make test
</pre>
<p>
- These steps compile, link and install the deal.II library. The
- whole process should take between a few minutes and an hour, depending
- on your machine.
+ These steps compile, link, install the deal.II library, and run a few
+ consistency checks. The whole process should take between a few minutes
+ and an hour, depending on your machine.
</p>
<p>
paths.</b>
However, this behavior can be changed using command line switches to
the initial call to <code>cmake</code>. A detailed description
- can be found here: <a href="development/cmake.html">Detailed build system description</a>.
+ can be found here: <a href="users/cmake.html">Detailed build system description</a>.
</p>
<p>
for <acronym>deal.II</acronym> being able to use them).
For details on how to set up <acronym>deal.II</acronym> with a
non standard BLAS/LAPACK implementation, see the
- <a href="development/cmake.html#advanced">advanced
+ <a href="users/cmake.html#advanced">advanced
setup</a> section in the CMake ReadME.
</p>
</dd>
The <acronym>deal.II</acronym> <code>cmake</code> system allows far
greater control over what exactly is configured or built than just the
outline above. If you want to learn more about this, take a look
- <a href="development/cmake.html">here</a>.
+ <a href="users/cmake.html">here</a>. You might also be interested in
+ <a href="users/cmakelists.html">CMake for user projects</a> or
+ <a href="developers/cmake-internals.html">build system internals</a>.
</p>
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-%%EndFont
-%%BeginFont: CMBX12
-%!PS-AdobeFont-1.1: CMBX12 1.0
-%%CreationDate: 1991 Aug 20 16:34:54
-
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMBX12) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Bold) readonly def
-/ItalicAngle 0 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMBX12 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 12 /fi put
-dup 45 /hyphen put
-dup 46 /period put
-dup 49 /one put
-dup 50 /two put
-dup 51 /three put
-dup 52 /four put
-dup 53 /five put
-dup 54 /six put
-dup 55 /seven put
-dup 58 /colon put
-dup 65 /A put
-dup 67 /C put
-dup 73 /I put
-dup 76 /L put
-dup 83 /S put
-dup 84 /T put
-dup 86 /V put
-dup 97 /a put
-dup 98 /b put
-dup 99 /c put
-dup 100 /d put
-dup 101 /e put
-dup 102 /f put
-dup 103 /g put
-dup 104 /h put
-dup 105 /i put
-dup 107 /k put
-dup 108 /l put
-dup 109 /m put
-dup 110 /n put
-dup 111 /o put
-dup 112 /p put
-dup 113 /q put
-dup 114 /r put
-dup 115 /s put
-dup 116 /t put
-dup 117 /u put
-dup 118 /v put
-dup 121 /y put
-readonly def
-/FontBBox{-53 -251 1139 750}readonly def
-/UniqueXX 5000769 def
-currentdict end
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-% Math Symbol fonts were designed by the American Mathematical Society.
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-% Math Symbol fonts were designed by the American Mathematical Society.
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-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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-%%CreationDate: 1996 Jul 23 07:53:53
-
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
-11 dict begin
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-/version (1.100) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMMI7) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
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-%%BeginFont: CMSY10
-%!PS-AdobeFont-1.1: CMSY10 1.0
-%%CreationDate: 1991 Aug 15 07:20:57
-
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.0) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMSY10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.035 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMSY10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 0 /minus put
-dup 1 /periodcentered put
-dup 2 /multiply put
-dup 15 /bullet put
-dup 17 /equivalence put
-dup 20 /lessequal put
-dup 25 /approxequal put
-dup 32 /arrowleft put
-dup 33 /arrowright put
-dup 50 /element put
-dup 54 /negationslash put
-dup 56 /universal put
-dup 102 /braceleft put
-dup 103 /braceright put
-dup 106 /bar put
-dup 114 /nabla put
-readonly def
-/FontBBox{-29 -960 1116 775}readonly def
-/UniqueXX 5000820 def
-currentdict end
-currentfile eexec
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-
-%%EndFont
-%%BeginFont: CMMI10
-%!PS-AdobeFont-1.1: CMMI10 1.100
-%%CreationDate: 1996 Jul 23 07:53:57
-
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.100) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMMI10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMMI10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 12 /beta put
-dup 14 /delta put
-dup 21 /lambda put
-dup 22 /mu put
-dup 23 /nu put
-dup 32 /psi put
-dup 39 /phi1 put
-dup 58 /period put
-dup 59 /comma put
-dup 60 /less put
-dup 61 /slash put
-dup 64 /partialdiff put
-dup 65 /A put
-dup 70 /F put
-dup 73 /I put
-dup 74 /J put
-dup 75 /K put
-dup 78 /N put
-dup 81 /Q put
-dup 85 /U put
-dup 86 /V put
-dup 97 /a put
-dup 98 /b put
-dup 99 /c put
-dup 100 /d put
-dup 102 /f put
-dup 103 /g put
-dup 105 /i put
-dup 106 /j put
-dup 108 /l put
-dup 111 /o put
-dup 112 /p put
-dup 113 /q put
-dup 117 /u put
-dup 118 /v put
-dup 119 /w put
-dup 120 /x put
-readonly def
-/FontBBox{-32 -250 1048 750}readonly def
-/UniqueXX 5087385 def
-currentdict end
-currentfile eexec
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-%%EndFont
-%%BeginFont: CMTI10
-%!PS-AdobeFont-1.1: CMTI10 1.00B
-%%CreationDate: 1992 Feb 19 19:56:16
-
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.00B) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMTI10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle -14.04 def
-/isFixedPitch false def
-end readonly def
-/FontName /CMTI10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 12 /fi put
-dup 45 /hyphen put
-dup 58 /colon put
-dup 68 /D put
-dup 71 /G put
-dup 97 /a put
-dup 99 /c put
-dup 100 /d put
-dup 101 /e put
-dup 102 /f put
-dup 103 /g put
-dup 104 /h put
-dup 105 /i put
-dup 108 /l put
-dup 109 /m put
-dup 110 /n put
-dup 111 /o put
-dup 112 /p put
-dup 114 /r put
-dup 115 /s put
-dup 116 /t put
-dup 117 /u put
-dup 118 /v put
-dup 119 /w put
-dup 122 /z put
-readonly def
-/FontBBox{-163 -250 1146 969}readonly def
-/UniqueXX 5000828 def
-currentdict end
-currentfile eexec
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-%%EndFont
-%%BeginFont: CMTT10
-%!PS-AdobeFont-1.1: CMTT10 1.00B
-%%CreationDate: 1992 Apr 26 10:42:42
-
-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
-11 dict begin
-/FontInfo 7 dict dup begin
-/version (1.00B) readonly def
-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
-/FullName (CMTT10) readonly def
-/FamilyName (Computer Modern) readonly def
-/Weight (Medium) readonly def
-/ItalicAngle 0 def
-/isFixedPitch true def
-end readonly def
-/FontName /CMTT10 def
-/PaintType 0 def
-/FontType 1 def
-/FontMatrix [0.001 0 0 0.001 0 0] readonly def
-/Encoding 256 array
-0 1 255 {1 index exch /.notdef put} for
-dup 33 /exclam put
-dup 38 /ampersand put
-dup 40 /parenleft put
-dup 41 /parenright put
-dup 42 /asterisk put
-dup 43 /plus put
-dup 44 /comma put
-dup 45 /hyphen put
-dup 46 /period put
-dup 47 /slash put
-dup 48 /zero put
-dup 49 /one put
-dup 50 /two put
-dup 58 /colon put
-dup 59 /semicolon put
-dup 60 /less put
-dup 61 /equal put
-dup 62 /greater put
-dup 63 /question put
-dup 68 /D put
-dup 69 /E put
-dup 70 /F put
-dup 71 /G put
-dup 72 /H put
-dup 73 /I put
-dup 74 /J put
-dup 77 /M put
-dup 81 /Q put
-dup 84 /T put
-dup 85 /U put
-dup 86 /V put
-dup 87 /W put
-dup 91 /bracketleft put
-dup 93 /bracketright put
-dup 95 /underscore put
-dup 97 /a put
-dup 98 /b put
-dup 99 /c put
-dup 100 /d put
-dup 101 /e put
-dup 102 /f put
-dup 103 /g put
-dup 104 /h put
-dup 105 /i put
-dup 106 /j put
-dup 107 /k put
-dup 108 /l put
-dup 109 /m put
-dup 110 /n put
-dup 111 /o put
-dup 112 /p put
-dup 113 /q put
-dup 114 /r put
-dup 115 /s put
-dup 116 /t put
-dup 117 /u put
-dup 118 /v put
-dup 119 /w put
-dup 120 /x put
-dup 121 /y put
-dup 122 /z put
-dup 123 /braceleft put
-dup 124 /bar put
-dup 125 /braceright put
-readonly def
-/FontBBox{-4 -235 731 800}readonly def
-/UniqueXX 5000832 def
-currentdict end
-currentfile eexec
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-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
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-%%CreationDate: 1991 Aug 20 16:38:05
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-% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
-
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-/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
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-dup 104 /h put
-dup 105 /i put
-dup 108 /l put
-dup 110 /n put
-dup 111 /o put
-dup 114 /r put
-dup 116 /t put
-dup 117 /u put
-dup 119 /w put
-dup 121 /y put
-dup 122 /z put
-dup 127 /dieresis put
-readonly def
-/FontBBox{-34 -251 988 750}readonly def
-/UniqueXX 5000794 def
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-\documentclass{article}
-\usepackage{times}
-\usepackage{amsmath}
-\usepackage{amsfonts}
-\usepackage{a4}
-\newcommand{\leftpartial}{\overleftarrow \partial}
-\newcommand{\rightpartial}{\overrightarrow \partial}
-\renewcommand{\div}{\nabla\cdot}
-\renewcommand{\vec}[1]{{\mathbf #1}}
-\begin{document}
-
-
-\begin{center}
- \begin{huge}
- Assembling matrices in \texttt{deal.II}
- \end{huge}
-
- \vspace*{0.5cm}
-
- \begin{large}
- Wolfgang Bangerth\\
- ETH Z\"urich, Switzerland\\[12pt]
- May 2002
- \end{large}
-\end{center}
-
-
-\section{Introduction}
-
-Assembling the system matrix for finite element discretizations is standard,
-at least as far as scalar problems are concerned. However, things become a
-little more complicated in implementations once problems are vector-valued,
-and in particular if finite elements are used in which different components of
-vector-valued shape functions are coupled, such as for example for
-divergence-free elements.
-
-It is this case that we are interested in in this report, and we will discuss
-the implementational details user programs must follow if they want to use
-such elements with \texttt{deal.II}. In order to explain the problem in a
-simple way, we start by reviewing the algorithms that are used, first for the
-scalar case, then for the case of ``simple'' vector-valued finite elements,
-and finally for the most general case. However, we do not intend to give an
-introduction into the derivation of finite element methods, or of posing a
-partial differential equation in weak form.
-
-The interface for vector-valued finite element shape functions with more than
-one non-zero component that is described in this report is presently being
-implemented, and will be merged with the library after version 3.4 is
-released. Thus, it will be part of version 3.5 or 4.0 of the library,
-depending on which version number we will assign to the successor of 3.4. By
-then, the library will also contain an implementation of Nedelec elements, for
-which these techniques are necessary. The interface for primitive
-vector-valued shape functions, for which only one vector component is
-non-zero, has been part of the library since its publication with version 3.0.
-
-
-
-
-\section{Linear systems for finite element methods}
-
-We start by briefly introducing the way finite element matrices are assembled
-``on paper''. As usual in finite elements, we take the weak form of the partial
-differential equation. In the most general case, it reads: \textit{find $u\in
- V$ such that}
-\begin{gather*}
- a(u, v) = (f,v)_\Omega \qquad \forall v\in V,
-\end{gather*}
-where $a(\cdot,\cdot)$ is the bilinear form associated with the partial
-differential equations, and $V$ is the space of test functions. For
-simplicity, we have here assumed that the problem is linear and that then
-$a(\cdot,\cdot)$ is a bilinear form; if the problem is nonlinear, it is
-usually solved using a sequence of linear problems, so this is no restriction.
-
-In finite elements, we define an approximation of the solution $u$ by choosing
-a finite dimensional subspace $V_h$ spanned by the basis functions
-$\{\varphi_i\}$, and searching $u_h\in V_h$ by testing the weak form by the
-test functions from $V_h$. The problem then reads: \textit{find $u_h\in V_h$
-such that}
-\begin{gather*}
- a(u_h, v_h) = (f,v_h)_\Omega \qquad \forall v_h\in V_h.
-\end{gather*}
-
-Now, $\{\varphi_i\}$ is a basis of $V_h$. We denote the dimension of $V_h$ by
-$N$, and will henceforth let all sums be over the range $0\ldots N-1$, to keep
-with the standard notation of the C/C++ programming languages. With this, we
-can expand the solution $u_h=\sum_{j=0}^{N-1} U_j \varphi_j$, and by
-bilinearity of the form $a(\cdot,\cdot)$, the problem above is equivalent to
-\begin{gather}
- \label{eq:lin-1}
- \sum_{j=0}^{N-1} U_j a(\varphi_j,\varphi_i) = (f, \varphi_i)
- \qquad
- \forall i=0\ldots N-1.
-\end{gather}
-Denoting
-\begin{gather*}
- A_{ij} = a(\varphi_j,\varphi_i),
- \qquad
- \qquad
- F_j = (f, \varphi_j),
-\end{gather*}
-the equations determining the expansion coefficients $U_i$ are therefore:
-\begin{gather}
- \label{eq:lin-2}
- A U = F.
-\end{gather}
-
-Note that we have taken a reverted order of indices in the definition of $A$,
-since we want the linear system \eqref{eq:lin-2} with the solution to the
-right of the matrix, to keep with standard notation, instead of to the left as
-in \eqref{eq:lin-1}. For symmetric problems, there is no difference, but for
-non-symmetric ones this is a common source for problems and a rather common
-trap.
-
-For partial differential equations, the bilinear form used in \eqref{eq:lin-1}
-involves an integral over the domain $\Omega$ on which the problem is
-posed. For example, for the Laplace equation we have
-\begin{gather*}
- A_{ij}
- =
- a(\varphi_j, \varphi_i)
- =
- (\nabla \varphi_j, \nabla \varphi_i)_\Omega
- =
- \int_\Omega \nabla \varphi_j \cdot \nabla \varphi_i \; dx.
-\end{gather*}
-For practical purposes, we split this equation into integrals over the
-individual cells $K$ of the triangulation $\mathbb T$ we use for the
-discretization. In \texttt{deal.II}, these cells are always lines,
-quadrilaterals, or hexahedra. With this, we have that
-\begin{gather*}
- A = \sum_{K \in {\mathbb T}} A^K,
- \qquad\qquad
- A^K_{ij} = a_K(\varphi_j, \varphi_i)
- \qquad
- 0\le i,j\le N-1,
-\end{gather*}
-where the bilinear form $a_K(\cdot,\cdot)$ only involves an integral over the
-cell $K$. The important point is that we do so since for the localized basis
-functions used in finite elements, $A^K$ is a matrix with almost only zeros.
-The only elements which are not zero are those corresponding to indices $i,j$
-indicating those shape functions that have support also on the element $K$.
-For example, in 2d and using the usual bilinear shape functions for a scalar
-problem, only the four shape functions associated with the vertices of the
-cell $K$ are nonzero on $K$, and thus only the entries in $A^K$ are nonzero
-where the four rows corresponding to these indices and the respective four
-columns intersect.
-
-In general, assume that there are $N_K$ shape functions with support on cell
-$K$, and let the set of their indices be denoted by $I_K$. Then we can define
-a matrix $\hat A^K$ of (small dimension) $N_K\times N_K$ holding these nonzero
-entries, and we can obtain back the original contribution $A_K$ to $A$ by the
-transformation
-\begin{gather*}
- A^K_{ij} =
- \left\{
- \begin{array}{ll}
- 0 & \text{if $i\not\in I_K$ or $j\not\in I_K$,} \\
- \hat A^K_{local(i),local(j)} & \text{otherwise},
- \end{array}
- \right.
- \qquad 0\le i,j\le N-1.
-\end{gather*}
-Here, $local(i)$ gives the number of the global degree of freedom $i$ on the
-cell $K$, i.e. the position of $i$ in the index set $I_K$. One could call
-$\hat A^K$ the \texttt{reduced} form of $A^K$, since the many zero rows and
-column have been stripped.
-
-In general, when assembling the global matrix, the reverse way is used: when
-adding up $A^K$ to $A$, we do so only with $\hat A^K$ by
-\begin{gather*}
- A_{global(i),global(j)}
- +\!\!=
- \hat A^K_{ij}
- \qquad
- \qquad
- 0\le i,j\le N_K-1.
-\end{gather*}
-Thus, indices only run over the (small) range $0\ldots N_K-1$ instead of
-$0\ldots N-1$. Here, $global(i)$ denotes the global number of the degree of
-freedom with number $i$ on this cell $K$, i.e. $global(i)=I_K[i]$, where the
-bracket operator returns the $i$th element of the set $I_K$.
-
-The main part of assembling finite element matrices is therefore to assemble
-the local matrix $\hat A^K$. Before we go on with discussing how this is done
-in \texttt{deal.II}, we would like to comment on the evaluation of the
-integrals involved. Since the integrals are usually too complex to be
-evaluated exactly (they may depend on coefficients appearing in the equation,
-or the solution of previous steps in nonlinear or time-dependent problems),
-they are approximated by quadrature. Assume we have a quadrature formula with
-$N_q$ points $x_q$ defined on cell in real space (as opposed to the unit cell)
-and weights $w_q$. Then, for example for the Laplace equation, we approximate
-\begin{gather}
- \hat A^K_{ij}
- \equiv
- \int_K \nabla\varphi_i \cdot \nabla \varphi_j \; dx
- \approx
- \sum_{q=0}^{N_q-1}
- \nabla\varphi_i(x_q) \cdot \nabla \varphi_j(x_q)
- \ w_q |\text{det} \ J(\hat x_q)|.
-\end{gather}
-For other problems, the integrand is different, but the principle remains the
-same. $\text{det}\ J(\hat x_q)$ denotes the determinant of the Jacobian of the
-transformation between the unit cell on which the quadrature weights are
-defined, and the real cell, and $\hat x_q$ is the point on the unit cell
-corresponding to the quadrature point $x_q$ in real space.
-
-Since all matrices and right hand side vectors only require knowledge of the
-values and gradients of shape functions at quadrature points, this is all that
-\texttt{deal.II} usually provides. One can see this as a kind of \textit{view}
-on a finite element, as it only provides a certain perspective on the actual
-definition of a shape function. Nevertheless, this is entirely sufficient for
-all purposes of programming finite element programs.
-
-In \texttt{deal.II} the \texttt{FEValues} class does this: you give it a
-finite element definition, a quadrature formula object, and an object defining
-the transformation between unit and real cell, and it provides you with the
-values, gradient, and second derivatives of shape functions at the quadrature
-points. It also gives access to the determinant of the Jacobian, although only
-multiplied with $w_q$ as these two are always used in conjunction. It also
-provides you with many other fields, such as normal vectors to the outer
-boundary. In practice you do not need them all computed on each cell; thus,
-you have to specify explicitly in which data you are interested when
-constructing \texttt{FEValues} objects.
-
-In the following, we provide a list of connections between the symbols introduced
-above, and the respective functions and variable names used in typical
-\texttt{deal.II} programs. With this, we will subsequently show the basic
-structure of an assembly routine. If you have already taken a look at the
-example programs provided with \texttt{deal.II}, you will recognize all these
-names. If you haven't, this would be a good time to look at the first
-three of them.
-
-
-\begin{center}
- \begin{tabular}{|ll|}
- \hline
- $A$ & \texttt{system\_matrix} \\
- $\hat A^K$ & \texttt{cell\_matrix} \\
- $K$ & \texttt{cell} \\
- $N$ & \texttt{dof\_handler.n\_dofs()} \\
- $N_K$ & \texttt{fe.dofs\_per\_cell} \\
- $I_K$ & \texttt{local\_dof\_indices} \\
- $N_q$ & \texttt{quadrature\_formula.n\_quadrature\_points} \\
- $\varphi_i(x_q)$ & \texttt{fe\_values.shape\_value(i,q)} \\
- $\nabla\varphi_i(x_q)$ & \texttt{fe\_values.shape\_grad(i,q)} \\
- $x_q$ & \texttt{fe\_values.quadrature\_point(q)} \\
- $|\text{det} J(\hat x_q)| w_q$ & \texttt{fe\_values.JxW(q)} \\
- \hline
- \end{tabular}
-\end{center}
-
-With this vocabulary, the typical matrix assembly loop in \texttt{deal.II} has
-the following form: first declare a quadrature object and use it for the
-initialization of a \texttt{FEValues} object as discussed above:
-\begin{verbatim}
- QGauss2<2> quadrature_formula;
- FEValues<2> fe_values (fe, quadrature_formula,
- UpdateFlags(update_values |
- update_gradients |
- update_JxW_values));
-\end{verbatim}
-In practice, you may want to use a different set of fields to be updated on
-each cell. For example if you do not need the values of shape functions on a
-cell, you may omit \texttt{update\_values} from the list. Also note that by
-default a bi- or tri-linear (depending on space dimension) mapping between
-unit and real cell is used. Other mappings are possible, for example quadratic
-ones, or a mapping that makes use of the fact that in many cases cells are
-actually rectangular, rather than arbitrary quadrilaterals; in order to use
-them, another constructor of the \texttt{FEValues} class can be used, which
-takes a mapping object as first argument, before the other arguments listed
-above.
-
-Next we define abbreviations for the values of $N_K$ and $N_q$:
-\begin{verbatim}
- const unsigned int
- dofs_per_cell = fe.dofs_per_cell,
- n_q_points = quadrature_formula.n_quadrature_points;
-\end{verbatim}
-Then have an object to store the matrix $\hat A^K$, which is of size
-$N_K\times N_K$:
-\begin{verbatim}
- FullMatrix<double> cell_matrix (dofs_per_cell, dofs_per_cell);
-\end{verbatim}
-And an object representing the set of global indices of degrees of freedom,
-previously denoted by $I_K$, that have support on the present cell, i.e. those
-degrees of freedom local to the present cell:
-\begin{verbatim}
- std::vector<unsigned int> local_dof_indices (dofs_per_cell);
-\end{verbatim}
-The next step is then to loop over all cells:
-\begin{verbatim}
- typename DoFHandler<dim>::active_cell_iterator
- cell = dof_handler.begin_active(),
- endc = dof_handler.end();
- for (; cell!=endc; ++cell)
- {
-\end{verbatim}
-On each cell, first tell the \texttt{FEValues} object to compute the values of
-the various fields for this particular cell, and do not forget to reset the
-local matrix $\hat A^K$ to zero before adding it up:
-\begin{verbatim}
- fe_values.reinit (cell);
- cell_matrix.clear ();
-\end{verbatim}
-Now comes the main part, assembling the local matrix $\hat A^K$. It consists
-of a loop over all indices $0\le i,j \le N_K$ and all quadrature points $0\le
-q\le N_q$, and summing up the contributions. As this is what we will discuss
-in detail later on, we only denote it here by an ellipse:
-\begin{verbatim}
- for (unsigned int i=0; i<dofs_per_cell; ++i)
- for (unsigned int j=0; j<dofs_per_cell; ++j)
- for (unsigned int q=0; q<n_q_points; ++q)
- cell_matrix(i,j) += ...;
-
-\end{verbatim}
-After we have $\hat A^K$, we still have to sum it into the global matrix
-$A$. This is done by first getting the set $I_K$ of the global indices of the
-shape functions that were active on this cell, and then distributing $\hat
-A^K$:
-\begin{verbatim}
- cell->get_dof_indices (local_dof_indices);
-
- for (unsigned int i=0; i<dofs_per_cell; ++i)
- for (unsigned int j=0; j<dofs_per_cell; ++j)
- system_matrix.add (local_dof_indices[i],
- local_dof_indices[j],
- cell_matrix(i,j));
- };
-\end{verbatim}
-When this is done, we go on to the next cell.
-
-Within this framework, the only open point is assembling $\hat A^K$ on one
-quadrature point. This will be subject of the rest of this report.
-
-
-\section{Assembling scalar problems}
-
-For scalar problems, assembling $\hat A^K$ is relatively simple. With the
-terms introduced above, and for the Laplace equation, this looks as follows:
-\begin{verbatim}
- local_matrix(i,j) += (fe_values.shape_grad(i,q_point) *
- fe_values.shape_grad(j,q_point) *
- fe_values.JxW (q_point));
-\end{verbatim}
-This term is placed in the innermost loop, i.e. is performed for all indices
-$i,j$, and all quadrature points \texttt{q\_point}.
-
-For nonsymmetric problems, the order of terms has to be considered, as
-mentioned above. For example, for the advection equation
-\begin{gather*}
- \beta \cdot \nabla u = f,
-\end{gather*}
-with which the bilinear form
-\begin{gather*}
- a(u,v) = (\beta \cdot \nabla u, v)_\Omega
-\end{gather*}
-is associated, the local matrix is assembled as
-\begin{verbatim}
- local_matrix(i,j) += (fe_values.shape_values(i,q_point) *
- ( beta * fe_values.shape_grad(j,q_point) ) *
- fe_values.JxW (q_point));
-\end{verbatim}
-Here, \texttt{beta} is an object of type \texttt{Tensor<1,dim>}, which
-represents a tensor of rank 1 in \texttt{dim} space dimensions.
-
-Assembling matrices for scalar problems is also shown from a practical
-perspective in many of the example programs of \texttt{deal.II}, where it is
-also demonstrated how to do this for the right hand side vectors. Thus, scalar
-problems are not too interesting, and we now turn to vector-valued problems.
-
-
-
-\section{Vector-valued problems}
-
-Since we need some problems at which we will explain assembling the matrix for
-the vector-valued case, we now briefly introduce two simple equations. The
-first are the Lam\'e equations of elasticity, which are taken for the symmetric
-case, then we briefly introduce the Stokes equations as a nonsymmetric problem.
-
-\subsection{The elastic equations}
-\label{sec:elastic}
-
-As first example for the methods we are going to discuss for vector-valued
-problems, we consider the elastic Lam\'e equations for isotropic materials,
-which read in strong form:
-$$
- -
- \nabla (\lambda+\mu) (\div \vec u)
- -
- (\nabla \cdot \mu \nabla) \vec u
- =
- \vec f.
-$$
-These equations describe the three-dimensional deformation $\vec u$ of an
-elastic body under a body force $\vec f$. The respective bilinear form
-associated with this operator is then
-$$
- a(\vec u, \vec v) =
- \left(
- (\lambda+\mu) \div \vec u, \div \vec v
- \right)_\Omega
- +
- \sum_k
- \left(
- \mu \nabla u_k, \nabla v_k
- \right)_\Omega,
-$$
-or as a sum over components:
-$$
- a(\vec u, \vec v) =
- \sum_{k,l}
- \left(
- (\lambda+\mu) \partial_l u_l, \partial_k v_k
- \right)_\Omega
- +
- \sum_{k,l}
- \left(
- \mu \partial_l u_k, \partial_l v_k
- \right)_\Omega.
-$$
-
-When assembling matrices, it is advantageous to write the weak form
-(i.e. after integration by parts) as a kind of operator. This is since matrix
-elements after discretization are defined as
-\begin{gather*}
- A_{ij} = a(\varphi_j,\varphi_i)_\Omega,
-\end{gather*}
-where $\varphi_i,\varphi_j$ are two vector-valued trial functions, and it
-would be nice if we could write the bilinear form $a(\cdot,\cdot)$ as a kind
-of scalar product $(\varphi_i, Q \varphi_j)$, where $Q$ is a differential
-operator. This is trivial if we take $Q$ as the operator of the strong form,
-$Q=-\nabla (\lambda+\mu) \div - (\nabla \cdot \mu \nabla)$, but we wanted to
-do this for the weak form. For this, we introduce some notation that is used
-in quantum field theory: for differential operators, we indicate by an arrow
-placed atop of it whether it shall act on the object to the left or to the
-right of it. Thus,
-$\varphi \overleftarrow\nabla \cdot \overrightarrow\nabla \psi
-=(\nabla\varphi)\cdot(\nabla\psi)$. With this, a simple computation shows
-that
-\begin{multline*}
- a(\vec u,\vec v)
- =
- (\lambda+\mu)
- \left(
- \begin{pmatrix}
- u_1 \\ u_2
- \end{pmatrix}
- \mid
- \begin{pmatrix}
- \leftpartial_1 \rightpartial_1 &
- \leftpartial_1 \rightpartial_2 \\
- \leftpartial_2 \rightpartial_1 &
- \leftpartial_2 \rightpartial_2
- \end{pmatrix}
- \mid
- \begin{pmatrix}
- v_1 \\ v_2
- \end{pmatrix}
- \right)_\Omega
- \\
- +
- \mu
- \left(
- \begin{pmatrix}
- u_1 \\ u_2
- \end{pmatrix}
- \mid
- \left(
- \leftpartial_1 \rightpartial_1 +
- \leftpartial_2 \rightpartial_2
- \right)
- \begin{pmatrix}
- 1 & 0 \\
- 0 & 1
- \end{pmatrix}
- \mid
- \begin{pmatrix}
- v_1 \\ v_2
- \end{pmatrix}
- \right)_\Omega.
-\end{multline*}
-The sought operator $Q$ is then
-\begin{gather*}
- Q
- =
- (\lambda+\mu)
- \begin{pmatrix}
- \leftpartial_1 \rightpartial_1 &
- \leftpartial_1 \rightpartial_2 \\
- \leftpartial_2 \rightpartial_1 &
- \leftpartial_2 \rightpartial_2
- \end{pmatrix}
- +
- \mu
- \begin{pmatrix}
- \leftpartial_1 \rightpartial_1 +
- \leftpartial_2 \rightpartial_2 & 0 \\
- 0 & \leftpartial_1 \rightpartial_1 +
- \leftpartial_2 \rightpartial_2
- \end{pmatrix},
-\end{gather*}
-and $a(\vec u,\vec v)=(\vec u | Q | \vec v)$. We demonstrate the fact that $Q$
-acts to both sides by placing it in the middle of the scalar product, just as
-in the bra-ket notation of quantum physics.
-
-The advantages of this formulation will become clear when discussing
-assembling matrices below. For now, we remark that the symmetry of the weak
-form is equally apparent from the form of $Q$ as well as from the initial
-definition of $a(\cdot,\cdot)$.
-
-
-
-\subsection{The Stokes equations}
-\label{sec:stokes}
-
-For a nonsymmetric problem, we take the Stokes equations:
-\begin{align*}
- -\Delta \vec u + \nabla p &= 0,
- \\
- \text{div } \vec u &= 0.
-\end{align*}
-We denote by $\vec w=\{\vec u,p\}$ the entire solution vector. In the weak
-form, the above equations read
-\begin{gather*}
- a(\vec u,p; \vec v, q)
- =
- \nu(\nabla \vec u_1, \nabla \vec v_1)
- +\nu(\nabla \vec u_2, \nabla \vec v_2)
- - (p, \nabla\cdot \vec v)
- + (\nabla\cdot\vec u, q).
-\end{gather*}
-Since we integrated the gradient term in the first equation by parts, but not
-the divergence term in the second equation, the problem is now
-nonsymmetric. If we would have liked, we could have made the problem symmetric
-again by multiplying the entire second equation by $-1$, but we don't want to
-do that for now for illustrational purposes.
-
-Again, we introduce the operator $Q$ for this problem, which after some
-computations turns out to be
-\begin{gather*}
- Q
- =
- \begin{pmatrix}
- \nu(\leftpartial_1 \rightpartial_1 +
- \leftpartial_2 \rightpartial_2) & 0 & -\leftpartial_1 \\
- 0 & \nu(\leftpartial_1 \rightpartial_1 +
- \leftpartial_2 \rightpartial_2) & -\leftpartial_2 \\
- \rightpartial_1 & \rightpartial_2 & 0
- \end{pmatrix}.
-\end{gather*}
-Again, it is clear from this form that we could have made the operator
-symmetric by multiplying the last row by $-1$. Note when checking the symmetry
-of $Q$ that taking the transpose of such an operator means reverting the
-directions of the arrows over the operators, and exchanging their order.
-For example, using the first term, these two steps are
-$\leftpartial_1 \rightpartial_1 \rightarrow \rightpartial_1 \leftpartial_1
-\rightarrow \leftpartial_1 \rightpartial_1$.
-
-
-\section{Assembling vector-valued problems: The simple case}
-
-The simple case in assembling vector-valued problems is when the (also
-vector-valued) shape functions are chosen such that only one component in the
-vector is nonzero. This is usually the case, if we choose the shape functions
-to be the outer product of scalar shape functions, such as independent
-bilinear ansatz spaces for each component of a finite element space.
-
-In this case, each shape function $\Phi_i$ has the representation
-\begin{gather*}
- \Phi_i(\vec x) =
- \left( 0, \dots, 0, \varphi_i(\vec x), 0, \ldots, 0\right)^T,
-\end{gather*}
-where $\Phi_i$ is the vector-valued shape function, and $\varphi_i$ its
-only non-zero component. Let us denote by $c(i)$ the index of this non-zero
-component, then $\Phi_i$ can also be written as
-\begin{gather*}
- \left(\Phi_i(\vec x)\right)_l
- =
- \varphi_i(\vec x) \delta_{c(i),l},
-\end{gather*}
-with the Kronecker delta function $\delta_{jk}$.
-
-With this simple form, the cell matrix on cell $K$ has a simple form:
-\begin{gather*}
- A^K_{ij}
- =
- a_K(\Phi_i,\Phi_j)
- =
- \left(\Phi_i \mid Q \mid \Phi_j \right)_K
- =
- \left(\varphi_i \mid Q_{c(i),c(j)} \mid \varphi_j \right)_K.
-\end{gather*}
-Thus, in assembling the local cell matrices, we only have to determine the
-single components in which the two shape functions are non-zero, and
-pick one element from the matrix $Q$ to assemble each entry of the cell
-matrix with the help of the values of the functions $\varphi_i$ at the
-quadrature points. Here, it comes handy that we have written the operator as a
-matrix operator $Q$, since this makes it very clear how shape functions $i$
-and $j$ couple: if $Q_{c(i),c(j)}$ is zero, then they do not couple at all for
-this operator. Otherwise, it is easily visible which derivative acts on which
-shape function for this combination of shape functions.
-
-In \texttt{deal.II}, these two actions mentioned above (getting the non-zero
-component of a shape function, and the value of this component at a given
-quadrature point) are done as follows:
-\begin{itemize}
-\item \textit{Determining the non-zero component:} Given the shape function
- with number $i$ (i.e. its index local to the degrees of freedom on the
- present cell), its only non-zero component is obtained by the function call
-\begin{verbatim}
- const unsigned int nonzero_component_i
- = fe.system_to_component_index(i).first;
-\end{verbatim}
- The \texttt{FiniteElement::system\_to\_component\_index} returns a pair of
- numbers for each index $0\le i < N_K$, the first of which denotes the only
- non-zero component of the shape function $i$. Since for the case described
- in this section, the individual components of the vector-valued finite
- element are independent, we consider each component as a set of scalar shape
- functions; the second number of the pair returned by the function then
- denotes the index of the shape function $\varphi_i$ within the shape
- functions corresponding to this component.
-
- If, for example, our finite element in use is a $Q^2/Q^2/Q^1$ combination
- (for example for 2d flow computations: bi-quadratic ansatz functions for the
- velocities, bi-linear for the pressure), then we have a total of 22 shape
- functions (9+9+4). For each $0\le i < 22$, the first part of the pair
- returned by the function described above, $c(i)$, may then either be 0, 1,
- or 2, denoting the three possible components of the finite element. If
- $c(i)$ is either 0 or 1, then the component to which the shape function $i$
- belongs is a bi-quadratic one, and the second index is between $0$ and $8$
- (inclusive) as the $Q^2$ element has 9 shape functions. If $c(i)==2$, then
- the second part is between 0 and 3 (inclusive).
-
-\item \textit{Getting the value of $\varphi_i(\vec x_q)$:} Since only one
- component of $\Phi_i$ is non-zero, we can use the same function as before,
- i.e. \texttt{FEValues::shape\_value(i,q)}, which in the scalar case returned
- the value of shape function $i$ at quadrature point $q$. Likewise, the
- \texttt{FEValues::shape\_grad(i,q)} function returns the gradient of this
- particular component.
-
- In other words, whether the finite element is scalar or not, the two
- indicated functions return value and gradient of the only non-zero component
- of a shape function. If the finite element is scalar, then it is of course
- clear which component this is (since there $c(i)==0$ for all valid indices
- $i$), in the vector-valued case, it is component $c(i)$.
-\end{itemize}
-
-
-\subsection{The elastic equations}
-\label{sec:elastic-simple}
-
-With this, and the definition of the ``bi-directional'' operator $Q$ in
-Section~\ref{sec:elastic}, the local matrix assembly function for the elastic
-equations would then read as follows:
-\begin{verbatim}
- for (unsigned int i=0; i<fe.dofs_per_cell; ++i)
- for (unsigned int j=0; j<fe.dofs_per_cell; ++j)
- for (unsigned int q=0; q<n_q_points; ++q)
- {
- const unsigned int
- comp_i = fe.system_to_component_index(i).first,
- comp_j = fe.system_to_component_index(j).first;
-
- // first assemble part with lambda+mu
- cell_matrix(i,j) += ((lambda+mu) *
- fe_values.shape_grad(i,q)[comp_i] *
- fe_values.shape_grad(j,q)[comp_j] *
- fe_values.JxW(q));
-
- // then part with mu only
- if (comp_i == comp_j)
- cell_matrix(i,j) += (mu *
- (fe_values.shape_grad(i,q) *
- fe_values.shape_grad(j,q) )*
- fe_values.JxW(q));
- };
-\end{verbatim}
-Note that this code works in any space dimension, not only for
-\texttt{dim==2}. Optimization of this is possible by hoisting the computation
-of \texttt{comp\_i} and \texttt{comp\_j}, denoting $c(i)$ and $c(j)$,
-respectively, out of the inner loops. Also, if the coefficients are
-non-constant, they need to be computed at each quadrature point; this may be
-done using this fragment in the innermost loop:
-\begin{verbatim}
- const double
- lambda_value = lambda.value(fe_values.quadrature_point(q)),
- mu_value = mu.value(fe_values.quadrature_point(q));
-\end{verbatim}
-assuming that \texttt{lambda,mu} are variables of classes describing space
-dependent functions, and which are derived
-from the \texttt{Function<dim>} class.
-
-
-\subsection{The Stokes equations}
-\label{sec:stokes-simple}
-
-For the Stokes equation, things are slightly more complicated since the three
-components denote different quantities, and the operator $Q$ does not have
-such a simple form, but the case is still simple enough. We present its
-generalization to an arbitrary number of space dimensions, i.e. assume that
-there are \texttt{dim} velocity variables and one scalar pressure:
-\begin{verbatim}
- for (unsigned int i=0; i<fe.dofs_per_cell; ++i)
- for (unsigned int j=0; j<fe.dofs_per_cell; ++j)
- for (unsigned int q=0; q<n_q_points; ++q)
- {
- const unsigned int
- comp_i = fe.system_to_component_index(i).first,
- comp_j = fe.system_to_component_index(j).first;
-
- // velocity-velocity coupling?
- if ((comp_i<dim) && (comp_j<dim))
- if (comp_i == comp_j)
- cell_matrix(i,j) += (nu *
- (fe_values.shape_grad(i,q) *
- fe_values.shape_grad(j,q) ) *
- fe_values.JxW(q));
-
- // velocity-pressure coupling
- if ((comp_i<dim) && (comp_j==dim))
- cell_matrix(i,j) += (-fe_values.shape_grad(i,q)[comp_i] *
- fe_values.shape_value(j,q) *
- fe_values.JxW(q));
-
- // pressure-velocity coupling
- if ((comp_i==dim) && (comp_j<dim))
- cell_matrix(i,j) += (fe_values.shape_value(i,q) *
- fe_values.shape_grad(j,q)[comp_j] *
- fe_values.JxW(q));
- };
-\end{verbatim}
-Again, optimization is possible by observing that only one of the outer
-\texttt{if}s in the body can be true, for example using \texttt{else} clauses,
-or \texttt{break} statements.
-
-
-\section{Assembling vector-valued problems: The complicated case}
-
-The more complicated case is when more than one component of a vector-valued
-shape function is non-zero, i.e. the representation
-\begin{gather*}
- \Phi_i(\vec x) =
- \left( 0, \dots, 0, \varphi_i(\vec x), 0, \ldots, 0\right)^T,
-\end{gather*}
-does not hold any more. The usual case where this happens is when shape
-functions have to satisfy certain constraints, such as that they should have
-zero divergence or curl, or when the normal fluxes at some points, e.g. the
-face centers, are the degrees of freedom:
-$\vec n\cdot \Phi_i(x_a) = \delta_{ia}$. In this case, the individual
-components of a shape function are no more independent, and thus cannot be
-chosen such that only one component is non-zero.
-
-What happens in this case? First, the function
-\texttt{FiniteElement::system\_\-to\_\-component\_\-index} does not make much sense
-any more, since a shape function $\Phi_i$ cannot be associated with only one
-vector component any more. Calling this function for basis functions $\Phi_i$
-that are not restricted to only one non-zero component will thus yield an
-exception being thrown.
-
-Second, the functions \texttt{FEValues::shape\_value} and
-\texttt{FEValues::shape\_grad} returning the values and gradients of the only
-non-zero component of a shape function at a quadrature point cannot work any
-more, since there are now more than only one non-zero components for some or
-all values of $i$. For those shape function for which this holds, you will
-again get an exception upon calling these functions.
-
-
-\subsubsection*{Getting information about shape functions}
-
-So how do you find out whether calling these functions is ok or not? In other
-words, how do you know whether shape function $\Phi_i$ has only one non-zero
-component, or more? For this, there are two functions:
-\texttt{FiniteElement::is\_primitive(i)} returns as a \texttt{bool} whether
-the shape function has only one non-zero component. For example, for a
-$Q^2/Q^2/Q^1$ element, this would be \texttt{true} for all 22 shape functions.
-For a finite element for which every shape function is non-zero in more than
-one component, it would be \texttt{false} for all indices $i$. It might also
-be \texttt{true} for only some shape functions, for example if the velocity
-components of the Stokes discretization are done using some more complicated
-element, but the pressure component with a $Q^1$, then it would be
-\texttt{true} for the pressure shape functions, but \texttt{false} otherwise.
-
-Second, the \texttt{FiniteElement::n\_nonzero\_components(i)} function returns
-in how many components the $i$th shape function is non-zero. Again, for the
-$Q^2/Q^2/Q^1$ combination, this would yield the value 1 for all allowed
-indices $i$. For coupled elements, it would be greater than 1.
-
-Third, you may sometimes want to know in which components a certain shape
-function is non-zero. For this, the
-\texttt{FiniteElement::get\_nonzero\_components(i)} function is the right thing: it
-returns a reference to a vector of boolean values, one for each component of
-the vector-valued finite element, and the values indicate whether the shape
-function is non-zero for each of them.
-
-Note that if you have the result of
-\texttt{FiniteElement::get\_\-nonzero\_\-components(i)}, then the result of
-\texttt{FiniteElement::n\_nonzero\_components(i)} is simply the number of
-\texttt{true} values in the array returned by the first function. In the same
-way,
-\texttt{FiniteElement::\-is\_primitive(i)} is simply whether
-\texttt{FiniteElement::\-n\_nonzero\_\-components(i)} returned a value other than
-1. The functions are thus redundant in some way, but useful nevertheless. Of
-course, the values of the \texttt{FiniteElement::\-is\_primitive(i)}
-and \texttt{FiniteElement::n\_nonzero\_components(i)} functions are not
-recomputed every time based on the result of some other function, but are
-cached once at the time of construction of a finite element object.
-
-
-\subsubsection*{Evaluating shape functions}
-
-Now, we have seen which functions cannot be called for non-primitive shape
-functions, and also how to find out about shape functions and whether they are
-primitive and the like. Yet, we don't have replacements for the functions that
-cannot be called, so here they are: instead of \texttt{FEValues::shape\_value}
-and \texttt{FEValues::shape\_grad}, call
-\texttt{FEValues::shape\_value\_component} and
-\texttt{FEValues::shape\_grad\_component}. These functions take as arguments
-first the number of the shape function, and second the number of the
-quadrature point (these are also the arguments of the original functions), but
-now as additional third argument the vector component.
-
-Of course, these functions can be called on primitive shape functions as
-well. In that case, the following holds:
-\begin{itemize}
-\item The value of \texttt{FEValues::shape\_value\_component(i,q,c)} is equal
- to \texttt{FEValues::\-shape\_value(i,q)} if and only if the component
- \texttt{c} is equal to \texttt{fe.system\_to\_\-component\_\-index(i).first},
- i.e. if \texttt{c} is the only non-zero component of the shape function
- \texttt{i}.
-\item For all other components \texttt{c}, the returned value of
- \texttt{FEValues::shape\_\-value\_\-component(i,q,c)} is zero.
-\end{itemize}
-The same of course also holds for
-\texttt{FEValues::shape\_grad\_component(i,q,c)} and
-\texttt{FEValues::shape\_2nd\_derivative\_component(i,q,c)}.
-
-
-\subsection{The elastic equations}
-
-With the above, we can now assemble the matrix for the elastic equation in
-mostly the same way as before. The difference is that for each shape function,
-we have to loop over all components. The code then looks like this (compare
-this with the one in Section~\ref{sec:elastic-simple}):
-\begin{verbatim}
- for (unsigned int i=0; i<fe.dofs_per_cell; ++i)
- for (unsigned int comp_i=0; comp_i<fe.n_components(); ++comp_i)
- for (unsigned int j=0; j<fe.dofs_per_cell; ++j)
- for (unsigned int comp_j=0; comp_j<fe.n_components(); ++comp_j)
- for (unsigned int q=0; q<n_q_points; ++q)
- {
- // first assemble part with lambda+mu
- cell_matrix(i,j)
- += ((lambda+mu) *
- fe_values.shape_grad_component(i,q,comp_i)[comp_i] *
- fe_values.shape_grad_component(j,q,comp_j)[comp_j] *
- fe_values.JxW(q));
-
- // then part with mu only
- if (comp_i == comp_j)
- cell_matrix(i,j)
- += (mu *
- (fe_values.shape_grad_component(i,q,comp_i) *
- fe_values.shape_grad_component(j,q,comp_j) )*
- fe_values.JxW(q));
- };
-\end{verbatim}
-If you dislike this particular order of the loops, you can reorder them as you
-like, as they are independent.
-
-The code as shown above can be optimized. For example, instead of
-unconditionally performing the loop over all components of shape functions $i$
-of $j$, we might first ask whether these shape functions are primitive, using
-\texttt{fe.is\_primitive(i)}, and use the loop only if the result is false;
-if, on the other hand, the result is true, we only need to set
-\texttt{comp\_i} to the fixed value
-\texttt{fe.system\_to\_component\_index(i).first}, and likewise for shape
-function $j$.
-
-Another possibility for optimization would be to ask whether a certain
-component over which we loop is actually non-zero, or if the shape function is
-a non-primitive one but happens to be zero in the present component
-nevertheless. For this, we could replace the loop over \texttt{comp\_i} by
-this:
-\begin{verbatim}
- for (unsigned int comp_i=0; comp_i<fe.n_components(); ++comp_i)
- if (fe.get_nonzero_components(i)[comp_i] == true)
-\end{verbatim}
-If the if-clause does not succeed then this component of the shape function is
-definitely zero, and there will not be a contribution to the matrix anyway, so
-we can also skip the computations.
-
-
-\subsection{The Stokes equations}
-
-Likewise, this is now the code for the Stokes equations:
-\begin{verbatim}
- for (unsigned int i=0; i<fe.dofs_per_cell; ++i)
- for (unsigned int comp_i=0; comp_i<fe.n_components(); ++comp_i)
- for (unsigned int j=0; j<fe.dofs_per_cell; ++j)
- for (unsigned int comp_j=0; comp_j<fe.n_components(); ++comp_j)
- for (unsigned int q=0; q<n_q_points; ++q)
- {
- // velocity-velocity coupling?
- if ((comp_i<dim) && (comp_j<dim))
- if (comp_i == comp_j)
- cell_matrix(i,j)
- += (nu *
- (fe_values.shape_grad_component(i,q,comp_i) *
- fe_values.shape_grad_component(j,q,comp_j) ) *
- fe_values.JxW(q));
-
- // velocity-pressure coupling
- if ((comp_i<dim) && (comp_j==dim))
- cell_matrix(i,j)
- += (-fe_values.shape_grad_component(i,q,comp_i)[comp_i] *
- fe_values.shape_value_component(j,q,comp_j) *
- fe_values.JxW(q));
-
- // pressure-velocity coupling
- if ((comp_i==dim) && (comp_j<dim))
- cell_matrix(i,j)
- += (fe_values.shape_value_component(i,q,comp_i) *
- fe_values.shape_grad_component(j,q,comp_j)[comp_j] *
- fe_values.JxW(q));
- };
-\end{verbatim}
-Again, the same optimizations as above are possible. Here, they even seem
-worthwhile, since it is often the case that the velocity variables are
-discretized using a non-primitive finite element, while the pressure uses a
-primitive element. In that case, some shape functions are primitive (namely
-those discretizing the pressure), and of the non-primitive shape functions
-(those for the velocity variables) some vector components (the pressure
-components) are always zero. Thus, both optimizations described above would be
-useful. We leave the implementation of this to the reader.
-
-
-\section{Conclusions}
-
-We have shown how finite element matrices are assembled using the
-functionality of the \texttt{deal.II} library. For the scalar case, and, in
-the vector-valued case, if the
-finite element shape functions are such that only one vector component of each
-shape function is non-zero, assembling is relatively simple. In the other
-case, when there are shape functions with more than one non-zero component,
-some more care is necessary, but assembling is still straightforward and
-follows the same pattern as before.
-
-\end{document}
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-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Frameset//EN"
- "http://www.w3.org/TR/REC-html40/frameset.dtd">
-<html>
- <head>
- <link href="../../screen.css" rel="StyleSheet" media="screen">
- <title>The deal.II Homepage</title>
- <meta name="author" content="the deal.II authors <authors@dealii.org>">
- <meta name="keywords" content="deal.II"></head>
-
- </head>
-<BODY LINK="#0000ff" VLINK="#800080">
-
-<H1 ALIGN="CENTER">
-Description of the C++ class hierarchy for the
-accessor classes
-</H1>
-
-
-<p ALIGN="CENTER">
- <strong> Wolfgang Bangerth, 1998, 1999, 2000</strong>
-</p>
-
-
-<p>
-The class hierarchy of the accessor classes used to retrieve and store
-data in the triangulation and degree of freedom handler objects is one
-of the more complicated parts of the library. It makes heavy use of
-class templates with integers as template parameters as well as of
-explicit specialization of classes and member functions. Therefore,
-it is not so easy to see the connections and inheritance relations
-within this part of the class tree; this document tries to shed a bit
-of light onto this.
-</p>
-
-<p>
-Furthermore, it lists the member functions that can be queried to
-obtain information from an iterator.
-</p>
-
-
-<strong>Table of contents</strong>
-<ul>
- <li> <a href="#intro" target="body">What iterators and accessors
- are</a>
- <li> <a href="#tria-accessors" target="body">The triangulation
- accessor hierarchy</a>
- <li> <a href="#tria-typedefs" target="body">Typedefs of the
- Triangulation class to iterators and accessors</a>
- <li> <a href="#tria-functions" target="body">Functions offered by
- triangulation accessors</a>
- <li> <a href="#dof-accessors" target="body">The degree of freedom
- accessor hierarchy</a>
- <li> <a href="#dof-typedefs" target="body">Typedefs of the
- DoFHandler class to iterators and accessors</a>
- <li> <a href="#dof-functions" target="body">Functions offered by
- degree of freedom accessors</a>
-</ul>
-
-
-<a name="intro"></a>
-<H3>
-What iterators and accessors are
-</H3>
-
-<p>
-When using adative finite elements, the data structures often are
-extremely complex, requiring multiply indirected access and complex
-relationships between the different places where data is stored. The
-traditional way to handle this is to put all data which belongs
-together somehow into a structure or object; however, sometimes this
-can not be done efficiently, leading to either higher memory
-consumption (when you have to store many small data pieces and because
-you have to store a lot of pointers to other objects) or higher coding
-requirements (when you want to follow all those pointers to the object
-you desire).
-</p>
-
-<p>
-Therefore, we took over a concept which was already used in the C++
-standard template library, namely iterators and accessors. An accessor
-is an object that looks like if it had all the information stored but
-really only delegates the access to the right places; in fact, within
-this library, accessor store almost no information but know where to
-get everything from the complex and nested data structures the
-triangulation object offers. They have a simple interface which allows
-to extract any desired information from the triangulation and
-therefore makes access much easier and safer in three ways: first it
-performs range and parameter checking when in debugging mode; second,
-it encapsulates the access to the real data from the user, hiding the
-true data structures and thus allowing them without changing the user
-programs as well as those parts of the library which only act through
-accessors; and third by reducing the coding errors because of reduced
-complexity, since the chains of indirect access are replaces by simple
-commands.
-</p>
-
-<p>
-Iterators are a related concept: while accessors act as if they were
-structures with data contained in them, iterators act as if they were
-pointers pointing to accessors. You can dereference them using the
--> and * operators as with any other pointer, but they have more
-functionality. Essentially, they have overloaded ++ and -- operators,
-which allow the next or previous object pointed to to be just about
-anywhere in memory. A good introductory example are the iterators of
-the STL <CODE>list<T></CODE> class, which act on a linked list
-as if it were a contiguous array. The iterators in this library go
-even a step further: they do not point to different objects but rather
-tell the associated accessor object which data to look at
-next.
-</p>
-
-<p>
-Additionally, there are different versions of the iterators which
-behave differently when being incremented or decremented: while
-<I>raw</I> iterators let the associated accessor point to any of the
-objects it is made for, <I>normal</I> iterators always point to
-objects which are in use. Usually, you will not want to see cells or
-lines which are there but are unused by the triangulation (these cells
-are somewhat like holes in the arrays of the triangulation; such
-things happen when unrefining a cell, the freed memory is then kept
-for a while because of better efficiency), so you will almost never
-want to use raw iterators; they are mostly there for internal use in
-the library. Normal iterators are almost like raw iterators, but
-whenever you call the ++ or -- operator, the look at what they are
-pointing at and skip all unused elements by increasing or decreasing
-the pointer as often as necessary to reach the next used object.
-</p>
-
-<p>
-Finally, there are <I>active</I> iterators, which are the most
-important ones. They are like normal iterators but only point to
-active cells or lines. By active we mean that they have no children;
-in the context in which this library is used, this is equivalent to
-the fact that we do computations on these cells, lines or
-whatever. Active iterators are normal iterators which skip over all
-non-active cells, lines, etc when being incremented or decremented.
-</p>
-
-
-
-<a name="tria-accessors"></a>
-<H3>
-The triangulation accessor hierarchy
-</H3>
-
-<p>
-The triangulation accessors are used to retrieve and store data in the
-triangulation. There exist accessors for lines in one and higher
-dimensions, accessors for quads in two and higher dimensions, and so
-on. The general naming scheme is as follows:
-<ul>
-<li> <code>TriaAccessor<dim></code> is a general base class
- which is of not much interest.
-<li> <code>TriaObjectAccessor<objectdim,spacedim></code> denotes
- an accessor for an object with dimension
- <code>objectdim</code> in a <code>spacedim</code> dimensional
- space. It is derived from <code>TriaAccessor<spacedim></code>.
-<li> <code>CellAccessor<dim></code> presents the special
- properties that a cell has. It is therefore derived from
- <code>TriaObjectAccessor<spacedimdim,spacedim></code>.
-</ul>
-</p>
-
-<p>
-Their inheritance trees in the different space dimensions therefore
-look like this:
-</p>
-
-<hr>
-
-<CENTER>
-<IMG SRC="1d-tria.jpg" ALIGN="CENTER" WIDTH="80%">
-</CENTER>
-<p>
-
-<hr>
-
-<CENTER>
-<IMG SRC="2d-tria.jpg" ALIGN="CENTER" WIDTH="80%">
-</CENTER>
-<p>
-
-<hr>
-
-<CENTER>
-<IMG SRC="3d-tria.jpg" ALIGN="CENTER" WIDTH="80%">
-</CENTER>
-<p>
-
-<hr>
-
-<p>
-Some of the data is only useful if an object is a cell. For example,
-neighborship is only accessible for cells, while faces (e.g. lines in
-2D) can't access their neighbors (neither the adjacent cells, nor the
-other faces it touches). Therefore, the CellAccessor classes are
-derived from whatever object a cell is in the respective dimension,
-i.e. from lines in 1D, from quads in 2D, and so on.
-</p>
-
-
-
-<a name="tria-typedefs"></a>
-<H4>
-Typedefs of the Triangulation class to iterators and accessors
-</H4>
-
-<p>
-The <CODE>Triangulation<1></CODE> class declares the following data
-types which involve accessors:
-<PRE>
- typedef TriaRawIterator <1,CellAccessor<1> > raw_line_iterator;
- typedef TriaIterator <1,CellAccessor<1> > line_iterator;
- typedef TriaActiveIterator<1,CellAccessor<1> > active_line_iterator;
-
- typedef raw_line_iterator raw_cell_iterator;
- typedef line_iterator cell_iterator;
- typedef active_line_iterator active_cell_iterator;
-</PRE>
-Since lines are cells in one space dimension, all line iterators are
-cell iterators as well.
-</p>
-
-<p>
-In two space dimensions, the following types are declared by the
-<CODE>Triangulation<2></CODE> class:
-<PRE>
- typedef TriaRawIterator <2,TriaObjectAccessor<1, 2> > raw_line_iterator;
- typedef TriaIterator <2,TriaObjectAccessor<1, 2> > line_iterator;
- typedef TriaActiveIterator<2,TriaObjectAccessor<1, 2> > active_line_iterator;
-
- typedef TriaRawIterator <2,CellAccessor<2> > raw_quad_iterator;
- typedef TriaIterator <2,CellAccessor<2> > quad_iterator;
- typedef TriaActiveIterator<2,CellAccessor<2> > active_quad_iterator;
-
- typedef raw_quad_iterator raw_cell_iterator;
- typedef quad_iterator cell_iterator;
- typedef active_quad_iterator active_cell_iterator;
-
- typedef raw_line_iterator raw_face_iterator;
- typedef line_iterator face_iterator;
- typedef active_line_iterator active_face_iterator;
-</PRE>
-Since in this space dimension, quads are cells and lines are the faces
-of cells, the appropriate face and cell iterators are declared in
-terms of the underlying accessor types.
-</p>
-
-
-<p>
-In three space dimensions, the following types are declared by the
-<CODE>Triangulation<3></CODE> class:
-<PRE>
- typedef TriaRawIterator <3,TriaObjectAccessor<1, 3> > raw_line_iterator;
- typedef TriaIterator <3,TriaObjectAccessor<1, 3> > line_iterator;
- typedef TriaActiveIterator<3,TriaObjectAccessor<1, 3> > active_line_iterator;
-
- typedef TriaRawIterator <3,TriaObjectAccessor<2, 3> > raw_quad_iterator;
- typedef TriaIterator <3,TriaObjectAccessor<2, 3> > quad_iterator;
- typedef TriaActiveIterator<3,TriaObjectAccessor<2, 3> > active_quad_iterator;
-
- typedef TriaRawIterator <3,CellAccessor<3> > raw_hex_iterator;
- typedef TriaIterator <3,CellAccessor<3> > hex_iterator;
- typedef TriaActiveIterator<3,CellAccessor<3> > active_hex_iterator;
-
- typedef raw_hex_iterator raw_cell_iterator;
- typedef hex_iterator cell_iterator;
- typedef active_hex_iterator active_cell_iterator;
-
- typedef raw_quad_iterator raw_face_iterator;
- typedef quad_iterator face_iterator;
- typedef active_quad_iterator active_face_iterator;
-</PRE>
-Since in this space dimension, hexes are cells and quads are the faces
-of cells, the appropriate face and cell iterators are declared in
-terms of the underlying accessor types.
-</p>
-
-
-
-<a name="tria-functions"></a>
-<h4>Functions offered by triangulation accessors</h4>
-
-<p>
-We briefly state a short list of the functions offered by the
-triangulation accessors. For a more complete discussion of these
-functions, please refer to the online
-<a href="../../documentation.html" target="body">API
-documentation of the `grid' classes</a>. These functions can be
-accessed by <code>iterator->function()</code> if <code>iterator</code>
-is a cell-, face-, hex-, quad-, or line-iterator. Some functions are
-not available for all iterator types, which is noted for the
-individual entries.
-</p>
-
-<dl>
- <dt><em>
- level ()
- </em></dt>
-
- <dd>
- Return the hierarchical refinement level on
- which this object lives.
- </dd>
-
-
- <dt><em>
- index ()
- </em></dt>
-
- <dd>
- Return the index within the hierarchical refinement level on
- which this object lives.
- </dd>
-
-
- <dt><em>
- get_triangulation ()
- </em></dt>
-
- <dd>
- Return a reference to the triangulation to which this object belongs.
- </dd>
-
-
- <dt><em>
- vertex_index (vertex_number)
- </em></dt>
-
- <dd>
- Return the global index of one of the vertices of this object.
- </dd>
-
-
- <dt><em>
- vertex (vertex_number)
- </em></dt>
-
- <dd>
- Return the position of the respective vertex in space.
- </dd>
-
-
- <dt><em>
- used ()
- </em></dt>
-
- <dd>
- Return whether the object is used. The return value is
- <code>true</code> for all iterators that are either normal iterators
- or active iterators, only raw iterators can return
- <code>false</code>. Since raw iterators are only used in the
- interiors of the library, you will not usually need this function.
- </dd>
-
-
- <dt><em>
- set_used () / clear_used ()
- </em></dt>
-
- <dd>
- Set or clear the flag that describes whether the object is used by
- the triangulation. Only for internal use.
- </dd>
-
-
- <dt><em>
- user_flag_set ()
- </em></dt>
-
- <dd>
- Return whether the user flag is set.
- </dd>
-
-
- <dt><em>
- set_user_flag () / clear_user_flag ()
- </em></dt>
-
- <dd>
- Set or clear the flag that might be used by a user to indicate that
- something should happen with this object.
- </dd>
-
-
- <dt><em>
- recursively_set_user_flag () / recursively_clear_user_flag ()
- </em></dt>
-
- <dd>
- Set or clear the user flag for this cell and all its descendants.
- </dd>
-
-
- <dt><em>
- user_pointer ()
- </em></dt>
-
- <dd>
- Query the pointer belonging to this object which may be used by
- the user to store additional information with this object.
- </dd>
-
-
- <dt><em>
- set_user_pointer () / clear_user_pointer ()
- </em></dt>
-
- <dd>
- Set or clear a pointer belonging to this object which may be used by
- the user to store additional information with this object.
- </dd>
-
-
- <dt><em>
- child (child_number)
- </em></dt>
-
- <dd>
- Return an iterator to one of the children of this object.
- </dd>
-
-
- <dt><em>
- child_index (child_number)
- </em></dt>
-
- <dd>
- Return the index of the child within the next finer level of the
- triangulation.
- </dd>
-
-
- <dt><em>
- set_children (index), clear_children ()
- </em></dt>
-
- <dd>
- Only for internal use.
- </dd>
-
-
- <dt><em>
- has_children ()
- </em></dt>
-
- <dd>
- Return whether an object has children, i.e. whether it is further
- refined. If it has children, then it is not active.
- </dd>
-
-
- <dt><em>
- max_refinement_depth ()
- </em></dt>
-
- <dd>
- Return how often this cell or one of its children is refined.
- </dd>
-
-
- <dt><em>
- boundary_indicator
- </em></dt>
-
- <dd>
- Return the number of the boundary at which this object lies, if the
- object has a dimension less than the space dimension.
- </dd>
-
-
- <dt><em>
- set_boundary_indicator (boundary_id)
- </em></dt>
-
- <dd>
- Set the number of the boundary to which this object belongs.
- </dd>
-
-
- <dt><em>
- at_boundary ()
- </em></dt>
-
- <dd>
- Return whether this object is at the boundary (if the dimension of
- the object is less than the space dimension), or one of its faces is
- at the boundary for cells.
- </dd>
-
-
- <dt><em>
- has_boundary_lines ()
- </em></dt>
-
- <dd>
- Return whether one of the lines bounding this cell is at the
- boundary. For 1d and 2d this is equivalent to <em>at_boundary</em>,
- in 3d, there are cases where bounding lines of a hex are at the
- boundary, while the faces are in the interior. (Only for cell
- iterators.)
- </dd>
-
-
- <dt><em>
- diameter ()
- </em></dt>
-
- <dd>
- Return the diameter of the object.
- </dd>
-
-
- <dt><em>
- center ()
- </em></dt>
-
- <dd>
- Return the coordinates of the center of the object.
- </dd>
-
-
- <dt><em>
- barycenter ()
- </em></dt>
-
- <dd>
- Return the coordinates of the barycenter of the object.
- </dd>
-
-
- <dt><em>
- measure ()
- </em></dt>
-
- <dd>
- Return the length, area, or volume of an object, depending on the
- dimension of the object.
- </dd>
-
-
- <dt><em>
- point_inside (point)
- </em></dt>
-
- <dd>
- Return whether the given point is inside this cell, or rather the
- (bi-, tri-)linearly mapped image of the unit cell with the vertices
- of this cell. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- number_of_children ()
- </em></dt>
-
- <dd>
- Accumulated number of children and their children.
- </dd>
-
-
- <dt><em>
- line (line_number)
- </em></dt>
-
- <dd>
- Return an iterator to one of the bounding lines of this object. (Only
- for iterators to quadrilaterals and hexahedra.)
- </dd>
-
-
- <dt><em>
- line_index (line_number)
- </em></dt>
-
- <dd>
- Return the index of one of the bounding lines of this object. The
- level index is the same as that of the present object. (Only
- for iterators to quadrilaterals and hexahedra.)
- </dd>
-
-
- <dt><em>
- quad (quad_number)
- </em></dt>
-
- <dd>
- Return an iterator to one of the bounding quadrilaterals of this
- object. (Only for iterators to hexahedra.)
- </dd>
-
-
- <dt><em>
- line_index (line_number)
- </em></dt>
-
- <dd>
- Return the index of one of the bounding quadrilaterals of this
- object. The level index is the same as that of the present
- object. (Only for iterators to hexahedra.)
- </dd>
-
-
- <dt><em>
- neighbor (neighbor_number)
- </em></dt>
-
- <dd>
- Return iterator to one of the neighbors. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- neighbor_index (neighbor_number) / neighbor_level (neighbor_number)
- </em></dt>
-
- <dd>
- Return number and level of one of the neighbors. (Only for cell
- iterators.)
- </dd>
-
-
- <dt><em>
- set_neighbor ()
- </em></dt>
-
- <dd>
- Set a neighbor. Only for internal use. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- neighbor_of_neighbor (neighbor_number)
- </em></dt>
-
- <dd>
- Return the how-manyth neighbor the present cell is of the neighbor
- specified by the argument. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- at_boundary (face_number)
- </em></dt>
-
- <dd>
- Return whether this cell's given face is at the boundary. (Only for
- cell iterators.)
- </dd>
-
-
- <dt><em>
- refine_flag_set ()
- </em></dt>
-
- <dd>
- Return whether the refinement flag is set or not for the present
- cell. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- set_refine_flag () / clear_refine_flag ()
- </em></dt>
-
- <dd>
- Set/clear the flag indicating refinement. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- coarsen_flag_set ()
- </em></dt>
-
- <dd>
- Query whether the flag indicating coarsening is set for this
- object. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- set_coarsen_flag () / claer_coarsen_flag ()
- </em></dt>
-
- <dd>
- Set/clear the flag indicating coarsening. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- face (face_number)
- </em></dt>
-
- <dd>
- Return an iterator to one of the faces of this cell, if dimension is
- greater than one. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- material_id ()
- </em></dt>
-
- <dd>
- Return the material number of this cell. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- set_material_id (id)
- </em></dt>
-
- <dd>
- Set the material number of this cell. (Only for cell iterators.)
- </dd>
-
-
- <dt><em>
- active ()
- </em></dt>
-
- <dd>
- Return whether this cell is active, i.e. has no children. (Only for
- cell iterators.)
- </dd>
-</dl>
-
-
-
-<a name="dof-accessors"></a>
-<H3>
-The degree of freedom accessor hierarchy
-</H3>
-
-<p>
-The DoFAccessor classes provide access to the degree of freedom
-information associated with cells, lines, etc. The inheritance
-relationship is much the same as for the triangulation accessor
-classes, as can be seen from the following pictures.
-
-<hr>
-
-<CENTER>
-<IMG SRC="1d-dof.jpg" ALIGN="CENTER" WIDTH="80%">
-</CENTER>
-<p>
-
-
-<hr>
-
-<CENTER>
-<IMG SRC="2d-dof.jpg" ALIGN="CENTER" WIDTH="80%">
-</CENTER>
-<p>
-
-
-<hr>
-
-<CENTER>
-<IMG SRC="3d-dof.jpg" ALIGN="CENTER" WIDTH="80%">
-</CENTER>
-<p>
-
-<hr>
-
-<p>
-The main difference to the triangulation accessor hierarchy is that we
-want the DoF accessors to provide the information about the degrees of
-freedom, but for convenience also that of the triangulation. This way,
-we can get all the information from one object rather than needing two
-which work in parallel, and the class hierarchy shown above does
-exactly this.
-</p>
-
-<p>
-For the named reason, it is necessary to derive the
-<code>DoFObjectAccessor<1,dim></code> from the
-<code>TriaObjectAccessor<1,dim></code> class of the
-triangulation accessor hierarchy, as well as the
-<code>DoFObjectAccessor<2,dim></code> from the
-<code>TriaObjectAccessor<2,dim></code>. However, we would also
-like to include the functionality added by the CellAccessor class;
-this is done through some template magic: when in one space dimension,
-the <code>DoFObjectAccessor<1,1></code> is derived from
-CellAccessor<1>, while when in higher dimensions, it is derived
-from <code>DoFObjectAccessor<1,dim></code>; the same applies for
-the <code>DoFObjectAccessor<2,dim></code> class. Note that this
-way, CellAccessor is always a base class to DoFCellAccessor and the
-inheritance lattice is dimension dependant; the exact way of achieving
-this is complicated but not of interest here.
-</p>
-
-
-<a name="dof-typedefs"></a>
-<H4>
-Typedefs of the DoFHandler class to iterators and accessors
-</H4>
-
-<p>
-The typedefs done by the DoFHandler class are much alike those done by
-the Triangulation class. They could be summarized as follows:
-</p>
-
-<p>
-For one space dimension:
-<PRE>
- typedef TriaRawIterator <1,DoFCellAccessor<1> > raw_line_iterator;
- typedef TriaIterator <1,DoFCellAccessor<1> > line_iterator;
- typedef TriaActiveIterator<1,DoFCellAccessor<1> > active_line_iterator;
-
- typedef raw_line_iterator raw_cell_iterator;
- typedef line_iterator cell_iterator;
- typedef active_line_iterator active_cell_iterator;
-</PRE>
-Since lines are cells in one space dimension, all line iterators are
-cell iterators as well.
-</p>
-
-<p>
-For two space dimensions:
-<PRE>
- typedef TriaRawIterator <2,DoFObjectAccessor<1, 2> > raw_line_iterator;
- typedef TriaIterator <2,DoFObjectAccessor<1, 2> > line_iterator;
- typedef TriaActiveIterator<2,DoFObjectAccessor<1, 2> > active_line_iterator;
-
- typedef TriaRawIterator <2,DoFCellAccessor<2> > raw_quad_iterator;
- typedef TriaIterator <2,DoFCellAccessor<2> > quad_iterator;
- typedef TriaActiveIterator<2,DoFCellAccessor<2> > active_quad_iterator;
-
- typedef raw_quad_iterator raw_cell_iterator;
- typedef quad_iterator cell_iterator;
- typedef active_quad_iterator active_cell_iterator;
-
- typedef raw_line_iterator raw_face_iterator;
- typedef line_iterator face_iterator;
- typedef active_line_iterator active_face_iterator;
-</PRE>
-</p>
-
-<p>
-For three space dimensions:
-<PRE>
- typedef TriaRawIterator <3,DoFObjectAccessor<1, 3> > raw_line_iterator;
- typedef TriaIterator <3,DoFObjectAccessor<1, 3> > line_iterator;
- typedef TriaActiveIterator<3,DoFObjectAccessor<1, 3> > active_line_iterator;
-
- typedef TriaRawIterator <3,DoFObjectAccessor<2, 3> > raw_quad_iterator;
- typedef TriaIterator <3,DoFObjectAccessor<2, 3> > quad_iterator;
- typedef TriaActiveIterator<3,DoFObjectAccessor<2, 3> > active_quad_iterator;
-
- typedef TriaRawIterator <3,DoFCellAccessor<3> > raw_hex_iterator;
- typedef TriaIterator <3,DoFCellAccessor<3> > hex_iterator;
- typedef TriaActiveIterator<3,DoFCellAccessor<3> > active_hex_iterator;
-
- typedef raw_hex_iterator raw_cell_iterator;
- typedef hex_iterator cell_iterator;
- typedef active_hex_iterator active_cell_iterator;
-
- typedef raw_quad_iterator raw_face_iterator;
- typedef quad_iterator face_iterator;
- typedef active_quad_iterator active_face_iterator;
-</PRE>
-</p>
-
-
-
-<a name="dof-functions"></a>
-<h4>Functions offered by degree of freedom accessors</h4>
-
-<p>
-Since degree of freedom accessors are derived from triangulation
-accessors, they inherit the functionality of these accessors, but add
-some of their own. We only list the additional functionality
-below. For a full reference, including data types of parameters and
-return values, please refer to the general
-<a href="../../documentation.html" target="body">API
-documentation of the `DoF' classes</a>.
-</p>
-
-
-<dl>
- <dt><em>
- dof_index (dof_number)
- </em></dt>
-
- <dd>
- Return the global index of one of the DoFs on this object.
- </dd>
-
-
- <dt><em>
- set_dof_index (dof_number, index)
- </em></dt>
-
- <dd>
- Set the index of a DoF. Only for internal use.
- </dd>
-
-
- <dt><em>
- vertex_dof_index (vertex_number, dof_number)
- </em></dt>
-
- <dd>
- Return the index of one of the DoFs on one of the vertices of this
- object.
- </dd>
-
-
- <dt><em>
- set_vertex_dof_index (...)
- </em></dt>
-
- <dd>
- Set the vertex DoF index. Only for internal use.
- </dd>
-
-
- <dt><em>
- get_dof_indices (vector_of_indices)
- </em></dt>
-
- <dd>
- Return a vector of the indices of the DoFs on this object.
- </dd>
-
-
- <dt><em>
- get_dof_values (global_values, local_values)
- </em></dt>
-
- <dd>
- Extract and return the values of the DoFs on this object from a data
- vector defined on all DoFs.
- </dd>
-
-
- <dt><em>
- set_dof_values (local_values, global_values)
- </em></dt>
-
- <dd>
- Reverse operation: take values of DoFs on this object, and set them
- into a global data vector.
- </dd>
-
-
- <dt><em>
- distribute_local_to_global (local_source, global_destination)
- </em></dt>
-
- <dd>
- Add the elements of local_source, defining values of the degrees of
- freedom on this object, to the elements of the global data
- vector. The two parameters may be either vectors or matrices.
- </dd>
-
-
- <dt><em>
- get_interpolated_dof_values (global_values, local_interpolation)
- </em></dt>
-
- <dd>
- Interpolate the global field to this cell. If this cell is active,
- then this is the restriction of the global field to this cell,
- but when this cell is not active then it is the interpolation of the
- restriction of the field to the child cells and the interpolation to
- the present one. (For cell iterators only.)
- </dd>
-
-
- <dt><em>
- set_dof_values_by_interpolation (local_values, global_interpolation)
- </em></dt>
-
- <dd>
- Inverse operation: interpolate the local values to the children (if
- this cell is not active) and set the respective values in the global
- vector. (For cell iterators only.)
- </dd>
-</dl>
-
-
-<HR>
-
-<div ALIGN="RIGHT">
-Wolfgang Bangerth, 1998, 1999, 2000
-</div>
-<p> </P></BODY>
-</HTML>
-
-
-
-</BODY>
-</HTML>
-
<ul>
<li>
A brief report about the classes involved in the
- <a href="class-hierarchies/index.html"
+ <a href="http://www.dealii.org/reports/class-hierarchies/index.html"
target="body">iterators and accessors</a>
used to access cells in the triangulations and the data
thereon, such as their geometry, the number of the
</li>
<li>
- A brief report on <a href="mapping_q/index.html"
+ A brief report on <a href="http://www.dealii.org/reports/mapping_q/index.html"
target="body">mapping</a> functions of higher polynomial
degrees (by Ralf Hartmann). These allow the realisation
of higher order boundary approximations. This report
<li>
A report on
- <a href="assemble/assemble.pdf"
+ <a href="http://www.dealii.org/reports/assemble/assemble.pdf"
target="body">assembling matrices</a> (by Wolfgang
Bangerth). This report looks in particular at how
matrices are assembled for vector-valued problems, and
how things change if vector-valued finite elements are
used for which the shape functions have more than one
non-zero vector component, such as Nedelec or
- Raviart-Thomas elements. There are printable
- versions of the report
- <a href="assemble/assemble.ps"
- target="body">in postscript</a> and
- <a href="assemble/assemble.pdf"
- target="body">PDF format</a>.
+ Raviart-Thomas elements.
</li>
<li>
A very detailed report on
- <a href="nedelec/nedelec.pdf"
+ <a href="http://www.dealii.org/reports/nedelec/nedelec.pdf"
target="body">Nedelec elements</a> (by Anna
Schneebeli, University of Basel, Switzerland). It
explains the construction and application of Nedelec
edge elements for H-curl spaces, as used, for example,
in the numerical solution of the Maxwell equations. It
also gives numerical results obtained with deal.II.
- There is also a <a href="nedelec/nedelec.ps"
- target="body">postscript version of the report</a>.
</li>
<li>
A report on the
- <a href="codimension-one/desimone-heltai-manigrasso.pdf"
+ <a href="http://www.dealii.org/reports/codimension-one/desimone-heltai-manigrasso.pdf"
target="body">codimension one</a> capabilities of the library
(by Antonio DeSimone, Luca Heltai and Cataldo Manigrasso,
SISSA, Trieste, Italy). It explains in detail how to use the
+++ /dev/null
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
-<!--Converted with LaTeX2HTML 98.1p1 release (March 2nd, 1998)
-originally by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds
-* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
-* with significant contributions from:
- Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
-<HTML>
-<HEAD>
-<TITLE>No Title</TITLE>
-<META NAME="description" CONTENT="No Title">
-<META NAME="keywords" CONTENT="mapping">
-<META NAME="resource-type" CONTENT="document">
-<META NAME="distribution" CONTENT="global">
-<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
-<LINK REL="STYLESHEET" HREF="../../screen.css">
-<LINK REL="next" HREF="node1.html">
-</HEAD>
-<BODY >
-<p>
-In modified form taken from
-<br>
-<br>
-<a href="http://ganymed.iwr.uni-heidelberg.de/~hartmann/" target="_top">Ralf Hartmann</a>
-<br>
-Adaptive Finite Element Methods for the Compressible Euler Equations
-<br>
-PhD thesis, University of Heidelberg, 2002.
-</p>
-
-
-<P>
-<DIV ALIGN="CENTER">
-<FONT SIZE="+4"><B>Higher order Boundary approximation</B></FONT>
-
-</DIV>
-<P>
-<B>Introduction:</B> In many numerical applications the domain
-
-<!-- MATH: $\Omega\subset\mathbb R^d$ -->
-<IMG
- WIDTH="61" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img6.gif"
- ALT="$\Omega\subset\mathbb R^d$">,
-<IMG
- WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img7.gif"
- ALT="$d\geq 2$">
-is not a polygonal domain but includes
-curved boundaries. For these cases the boundary cannot be represented
-exactly by the discretised boundary. Approximating the boundary by a
-piecewise linear boundary interpolation, i.e. by a polygonal boundary,
-may in some applications not be sufficient. In these cases a higher
-order boundary approximation, for example by piecewise quadratic or
-cubic boundary interpolation, must be employed. In the finite element
-framework this higher order boundary approximation is realized by
-mapping the reference element <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">
-to the element
-
-<!-- MATH: $K=\sigma_K(\hat K)$ -->
-<IMG
- WIDTH="96" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
- SRC="img9.gif"
- ALT="$K=\sigma_K(\hat K)$">
-in real space, whereas on cells <I>K</I> at the
-boundary, i.e.
-<!-- MATH: $\partial K\cap\Gamma=\emptyset$ -->
-<IMG
- WIDTH="93" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
- SRC="img10.gif"
- ALT="$\partial K\cap\Gamma=\emptyset$">,
-the mappings
-<IMG
- WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img11.gif"
- ALT="$\sigma_K$">
-are given by polynomial functions of higher degree.
-
-<P>
-<B>Elements with general mapping functions <IMG
- WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img11.gif"
- ALT="$\sigma_K$">.</B> We begin
-by first introducing some notation. Let <IMG
- WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img12.gif"
- ALT="$K\in T_h$">
-be a cell of the
-triangulation <I>T</I><SUB><I>h</I></SUB> with
-<!-- MATH: $K=\sigma_K(\hat K)$ -->
-<IMG
- WIDTH="96" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
- SRC="img9.gif"
- ALT="$K=\sigma_K(\hat K)$">,
-where <IMG
- WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img11.gif"
- ALT="$\sigma_K$">is a smooth bijective mapping of the reference element (unit square)
-<IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">
-to the element <I>K</I> in real space, see Figure
-<A HREF="index.html#fig:mapping">1</A>.
-<BR>
-<DIV ALIGN="CENTER"><A NAME="fig:mapping"> </A><A NAME="183"> </A>
-<TABLE WIDTH="50%">
-<CAPTION><STRONG>Figure:</STRONG>
-Mapping <IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">
-of reference element <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">
-to the element <I>K</I> in real space.</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: $\includegraphics[scale=0.3]{figures/m1.ps}$ -->
-<IMG
- WIDTH="660" ALIGN="BOTTOM" BORDER="0"
- SRC="img13.gif"
- ALT="\includegraphics[scale=0.3]{figures/m1.ps}"></DIV></TD></TR>
-</TABLE>
-</DIV>
-<BR>
-<P>
-In the following and for the sake of simplicity we suppress the letter
-<I>K</I> in the subscript and write <IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">
-instead of <IMG
- WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img11.gif"
- ALT="$\sigma_K$">.
-
-<P>
-<B>Mapping functions of higher polynomial degree.</B> A mapping
-function <IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">,
-that maps the reference element <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">
-to an
-arbitrary quadrilateral cell <I>K</I> with straight boundaries, can in
-general be represented by a bilinear function, i.e. by a
-<I>Q</I><SUB>1</SUB>-mapping. For the case that the cell <I>K</I> includes curved
-boundaries it might be necessary to employ polynomial mapping
-functions of higher degree.
-
-<P>
-Given a degree <I>p</I>>0, a cell <IMG
- WIDTH="61" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img12.gif"
- ALT="$K\in T_h$">,
-and (<I>p</I>+1)<SUP><I>d</I></SUP> mapping
-support points <IMG
- WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img14.gif"
- ALT="$p_i\in K$">,
-
-<!-- MATH: $i=0,\ldots,(p+1)^d-1$ -->
-<IMG
- WIDTH="174" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img15.gif"
- ALT="$i=0,\ldots,(p+1)^d-1$">,
-we define a
-<I>Q</I><SUB><I>p</I></SUB>-mapping
-<!-- MATH: $\sigma\in [Q_p]^d$ -->
-<IMG
- WIDTH="75" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img16.gif"
- ALT="$\sigma\in [Q_p]^d$">
-as follows
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-\sigma(\hat x)=\sum_{i=0}^{(p+1)^d-1}p_i\phi_i(\hat x).
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:def-mapping-q"> </A><IMG
- WIDTH="176" HEIGHT="66"
- SRC="img17.gif"
- ALT="\begin{displaymath}
-\sigma(\hat x)=\sum_{i=0}^{(p+1)^d-1}p_i\phi_i(\hat x).
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(1)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-Here, <IMG
- WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img18.gif"
- ALT="$\phi_i$">,
-
-<!-- MATH: $i=0,\ldots,(p+1)^d-1$ -->
-<IMG
- WIDTH="174" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img15.gif"
- ALT="$i=0,\ldots,(p+1)^d-1$">
-denote the Lagrange interpolation
-basis functions, that satisfy
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-\phi_i(\hat p_j)=\delta_{ij}, \quad i,j=0,\ldots,(p+1)^d-1,
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="302" HEIGHT="32"
- SRC="img19.gif"
- ALT="\begin{displaymath}\phi_i(\hat p_j)=\delta_{ij}, \quad i,j=0,\ldots,(p+1)^d-1,
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-where <IMG
- WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img20.gif"
- ALT="$\hat p_i$">,
-
-<!-- MATH: $i=0,\ldots,(p+1)^d-1$ -->
-<IMG
- WIDTH="174" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img15.gif"
- ALT="$i=0,\ldots,(p+1)^d-1$">
-denote the Lagrange support
-points on the unit cell <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">.
-The definition of <IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">(<A HREF="index.html#eq:def-mapping-q">1</A>) ensures that each of the unit support points
-<IMG
- WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img20.gif"
- ALT="$\hat p_i$">
-is mapped onto the corresponding mapping support points
-<I>p</I><SUB><I>i</I></SUB>, i.e.
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-\sigma(\hat p_i)=p_i, \quad i=0,\ldots,(p+1)^d-1
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:point-mappings"> </A><IMG
- WIDTH="270" HEIGHT="31"
- SRC="img21.gif"
- ALT="\begin{displaymath}
-\sigma(\hat p_i)=p_i, \quad i=0,\ldots,(p+1)^d-1
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(2)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-Analogous to Lagrange finite elements the unit Lagrange support points
-<IMG
- WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img20.gif"
- ALT="$\hat p_i$">
-are equidistantly distributed on <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">
-based on a tensor
-product mesh. In the following we only consider the two-dimensional
-case, <I>d</I>=2. For that case, Figure <A HREF="index.html#fig:unit-mapping-points">2</A>
-shows the distributions of the unit support points <IMG
- WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img20.gif"
- ALT="$\hat p_i$">,
-
-<!-- MATH: $i=0,\ldots,(p+1)^2-1$ -->
-<IMG
- WIDTH="174" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
- SRC="img22.gif"
- ALT="$i=0,\ldots,(p+1)^2-1$">
-for degrees
-<!-- MATH: $p=1,\ldots,4$ -->
-<IMG
- WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img5.gif"
- ALT="$p=1,\ldots ,4$">.
-<BR>
-<DIV ALIGN="CENTER"><A NAME="fig:unit-mapping-points"> </A><A NAME="184"> </A>
-<TABLE WIDTH="50%">
-<CAPTION><STRONG>Figure:</STRONG>
-Unit support points <IMG
- WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img20.gif"
- ALT="$\hat p_i$">,
-
-<!-- MATH: $0\leq i<(p+1)^2$ -->
-<IMG
- WIDTH="126" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
- SRC="img4.gif"
- ALT="$0\leq i<(p+1)^2$">,
-for degrees
-<!-- MATH: $p=1,\ldots,4$ -->
-<IMG
- WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img5.gif"
- ALT="$p=1,\ldots ,4$">.</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: $\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q1_n.eps}$ -->
-<IMG
- WIDTH="180" ALIGN="BOTTOM" BORDER="0"
- SRC="img23.gif"
- ALT="\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q1_n.eps}">
-
-<!-- MATH: $\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q2_n.eps}$ -->
-<IMG
- WIDTH="180" ALIGN="BOTTOM" BORDER="0"
- SRC="img24.gif"
- ALT="\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q2_n.eps}">
-
-<!-- MATH: $\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q3_n.eps}$ -->
-<IMG
- WIDTH="180" ALIGN="BOTTOM" BORDER="0"
- SRC="img25.gif"
- ALT="\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q3_n.eps}">
-
-<!-- MATH: $\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q4_n.eps}$ -->
-<IMG
- WIDTH="180" ALIGN="BOTTOM" BORDER="0"
- SRC="img26.gif"
- ALT="\includegraphics*[width=2.750cm]{../../../phd/figures/boundary_approximation/mapping/unit_points_q4_n.eps}"></DIV></TD></TR>
-</TABLE>
-</DIV>
-<BR>
-Let the ordering and numbering of the unit support points be as
-follows: first the corners, then the points on the edges and finally
-the inner support points, see also Figure
-<A HREF="index.html#fig:unit-mapping-points">2</A>. Thus the first 4<I>p</I> points are placed
-on the boundary
-<!-- MATH: $\partial\hat K$ -->
-<IMG
- WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img27.gif"
- ALT="$\partial\hat K$">
-of the reference cell, i.e.
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-\hat p_k\in\partial\hat K, \quad k=0,\ldots,4p-1.
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="225" HEIGHT="30"
- SRC="img28.gif"
- ALT="\begin{displaymath}\hat p_k\in\partial\hat K, \quad k=0,\ldots,4p-1.
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-According to (<A HREF="index.html#eq:point-mappings">2</A>) these points are mapped to the
-mapping support points <I>p</I><SUB><I>k</I></SUB>,
-<!-- MATH: $k=0,\ldots,4p-1$ -->
-<IMG
- WIDTH="135" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img29.gif"
- ALT="$k=0,\ldots,4p-1$">
-that are chosen to be
-placed on the boundary of the real cell in approximatively equal
-distances, i.e.
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-p_k\in\partial K, \quad k=0,\ldots,4p-1.
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="224" HEIGHT="30"
- SRC="img30.gif"
- ALT="\begin{displaymath}p_k\in\partial K, \quad k=0,\ldots,4p-1.
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-While the support points <I>p</I><SUB><I>k</I></SUB>,
-<!-- MATH: $k=0,\ldots,4p-1$ -->
-<IMG
- WIDTH="135" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img29.gif"
- ALT="$k=0,\ldots,4p-1$">
-on the boundary are
-given by the boundary description of the real cell <I>K</I>, the <EM>inner
- mapping support points</EM>
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-p_i\in K\setminus\partial K, \quad i=4p,\ldots,(p+1)^2-1
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="297" HEIGHT="31"
- SRC="img31.gif"
- ALT="\begin{displaymath}p_i\in K\setminus\partial K, \quad i=4p,\ldots,(p+1)^2-1
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-are not uniquely determined. Numerical tests show that it is not a
-trivial task to define the positions of the inner mapping support
-points appropriately. If they are not chosen appropriately the
-resulting mapping <IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">
-for a cell <I>K</I> may degenerate, i.e. the
-mapping <IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">
-for some cell <I>K</I> may not be bijective.
-
-<P>
-<B>Computation of inner support points by smooth transformation.</B>
-In the following we will define the positions of the inner mapping
-support points so that the mapping does - in all practical cases - <I>not</I>
-degenerate. To this end, we employ an approach for the mapping of the
-support points, that is in the style of the smooth transformations
-that is used to transform structured triangulations to match complex
-boundary discriptions. In the following, again for notational
-convenience, we consider only the two-dimensional case.
-
-<P>
-The smooth transformation mentioned above is based on solutions to the
-Laplace equation that is solved on the reference cell <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">.
-Discrete boundary conditions are imposed that are given by the
-coordinates of the mapping support points <I>p</I><SUB><I>k</I></SUB>,
-<!-- MATH: $k=0,\ldots,4p-1$ -->
-<IMG
- WIDTH="135" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img29.gif"
- ALT="$k=0,\ldots,4p-1$">,
-on
-the boundary of the cell <I>K</I> in real space.
-
-<P>
-To be more explicite we define a Laplace problem on the unit
-cell <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-\begin{array}{rcll}
--\hat\Delta \sigma_l(\hat x)&=&0, \quad &\hat x\in \hat K,\\
- \sigma_l(\hat x)&=&{g_l}|_{\partial \hat K}(\hat x), \quad &\hat x\in \partial\hat K,
-\end{array}
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:local-laplace-problem"> </A><IMG
- WIDTH="273" HEIGHT="53"
- SRC="img32.gif"
- ALT="\begin{displaymath}
-\begin{array}{rcll}
--\hat\Delta \sigma_l(\hat x)&=&0, \quad...
-...l \hat K}(\hat x), \quad &\hat x\in \partial\hat K,
-\end{array}\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(3)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-for each component <IMG
- WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
- SRC="img33.gif"
- ALT="$\sigma_l$">,
-<I>l</I>=1,2, of the <I>Q</I><SUB><I>p</I></SUB> mapping
-<IMG
- WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
- SRC="img1.gif"
- ALT="$\sigma $">.
-Here, the discrete boundary function
-<!-- MATH: $g\in [Q_p]^2$ -->
-<IMG
- WIDTH="73" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
- SRC="img34.gif"
- ALT="$g\in [Q_p]^2$">
-is
-given by
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-g_l(\hat x)=\sum_{i=0}^{4p-1}(p_i)_l\phi_i(\hat x), \quad l=1,\ldots,d
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:discrete-boundary-function"> </A><IMG
- WIDTH="277" HEIGHT="62"
- SRC="img35.gif"
- ALT="\begin{displaymath}
-g_l(\hat x)=\sum_{i=0}^{4p-1}(p_i)_l\phi_i(\hat x), \quad l=1,\ldots,d
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(4)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-where (<I>p</I><SUB><I>i</I></SUB>)<SUB><I>l</I></SUB> denotes the <I>l</I>th component of the support point <I>p</I><SUB><I>i</I></SUB>,
-and <IMG
- WIDTH="20" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img18.gif"
- ALT="$\phi_i$">
-the corresponding Lagrangian interpolation basis
-function. We recall that the numbering of the mapping support points
-involves
-<!-- MATH: $p_k\in\partial K$ -->
-<IMG
- WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img36.gif"
- ALT="$p_k\in\partial K$">
-for
-<!-- MATH: $k=0,\ldots, 4p-1$ -->
-<IMG
- WIDTH="135" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img29.gif"
- ALT="$k=0,\ldots,4p-1$">.
-Substituting
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-\tilde \sigma_l:=\sigma_l-g_l, \quad l=1,2,
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:def-tilde-sigma"> </A><IMG
- WIDTH="176" HEIGHT="30"
- SRC="img37.gif"
- ALT="\begin{displaymath}
-\tilde \sigma_l:=\sigma_l-g_l, \quad l=1,2,
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(5)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-into the Laplace problem (<A HREF="index.html#eq:local-laplace-problem">3</A>) yields the
-zero boundary value problem,
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-\begin{array}{rcll}
--\hat\Delta \tilde\sigma_l(\hat x)&=&\hat\Delta g_l(\hat x), \quad &\hat x\in \hat K,\\
- \tilde\sigma_l(\hat x)&=&0, \quad &\hat x\in \partial\hat K,
-\end{array}
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:transformed-local-laplace-problem"> </A><IMG
- WIDTH="262" HEIGHT="53"
- SRC="img38.gif"
- ALT="\begin{displaymath}
-\begin{array}{rcll}
--\hat\Delta \tilde\sigma_l(\hat x)&=&\h...
-...gma_l(\hat x)&=&0, \quad &\hat x\in \partial\hat K,
-\end{array}\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(6)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-that is equivalent to the following variational formulation
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-\tilde\sigma_l\in H^1_0(\hat K):\qquad
-(\hat\nabla \tilde\sigma_l, \hat\nabla \phi)_{\hat K}
- = -(\hat\nabla g_l, \hat\nabla \phi)_{\hat K} \quad \forall \phi\in H^1_0(\hat K).
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="467" HEIGHT="33"
- SRC="img39.gif"
- ALT="\begin{displaymath}\tilde\sigma_l\in H^1_0(\hat K):\qquad
-(\hat\nabla \tilde\si...
-...\hat\nabla \phi)_{\hat K} \quad \forall \phi\in H^1_0(\hat K). \end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-Discretisation of this problem
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-\tilde\sigma_l\in Q_p(\hat K):\qquad
-(\hat\nabla \tilde\sigma_l, \hat\nabla \phi_{4p+i})_{\hat K}
- = -(\hat\nabla g_l, \hat\nabla \phi_{4p+i})_{\hat K} \quad \forall i=0,\ldots, (p-1)^2-1,
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="609" HEIGHT="33"
- SRC="img40.gif"
- ALT="\begin{displaymath}\tilde\sigma_l\in Q_p(\hat K):\qquad
-(\hat\nabla \tilde\sigm...
-...bla \phi_{4p+i})_{\hat K} \quad \forall i=0,\ldots, (p-1)^2-1, \end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-and recalling definitions (<A HREF="index.html#eq:def-mapping-q">1</A>), (<A HREF="index.html#eq:def-tilde-sigma">5</A>) and (<A HREF="index.html#eq:discrete-boundary-function">4</A>) gives
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-\sum_{j=1}^{(p-1)^2}S_{ij}(p_{4p+j})_l=-\sum_{k=0}^{4p-1}T_{ik}(p_k)_l, \quad i=0, \ldots, (p-1)^2-1,
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:discrete-local-laplace"> </A><IMG
- WIDTH="455" HEIGHT="68"
- SRC="img41.gif"
- ALT="\begin{displaymath}
-\sum_{j=1}^{(p-1)^2}S_{ij}(p_{4p+j})_l=-\sum_{k=0}^{4p-1}T_{ik}(p_k)_l, \quad i=0, \ldots, (p-1)^2-1,
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(7)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-with the matrices
-<!-- MATH: $S_{ij}\in\mathbb R^{(p-1)^2\times(p-1)^2}$ -->
-<IMG
- WIDTH="155" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
- SRC="img42.gif"
- ALT="$S_{ij}\in\mathbb R^{(p-1)^2\times(p-1)^2}$">
-and
-<!-- MATH: $T_{ik}\in\mathbb R^{(p-1)^2\times 4p}$ -->
-<IMG
- WIDTH="128" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
- SRC="img43.gif"
- ALT="$T_{ik}\in\mathbb R^{(p-1)^2\times 4p}$">
-given by
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-S_{ij}=(\hat\nabla \phi_{4p+i}, \hat\nabla \phi_{4p+j})_{\hat K}, \quad i,j=0,\ldots,(p-1)^2-1,
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="404" HEIGHT="33"
- SRC="img44.gif"
- ALT="\begin{displaymath}S_{ij}=(\hat\nabla \phi_{4p+i}, \hat\nabla \phi_{4p+j})_{\hat K}, \quad i,j=0,\ldots,(p-1)^2-1,
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-and
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-T_{ik}=(\hat\nabla \phi_{4p+i}, \hat\nabla \phi_k)_{\hat K}, \quad i=0,\ldots,(p-1)^2-1,\quad k=0,\ldots,4p-1.
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="522" HEIGHT="33"
- SRC="img45.gif"
- ALT="\begin{displaymath}T_{ik}=(\hat\nabla \phi_{4p+i}, \hat\nabla \phi_k)_{\hat K}, \quad i=0,\ldots,(p-1)^2-1,\quad k=0,\ldots,4p-1.
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-The solutions to problem (<A HREF="index.html#eq:discrete-local-laplace">7</A>) for <I>l</I>=1,2 are
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-(p_{4p+j})_l=-\sum_{i=0}^{(p-1)^2-1}\sum_{k=0}^{4p-1}S^{-1}_{ji}T_{ik}(p_k)_l, \quad j=0,\ldots,(p-1)^2-1,
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="481" HEIGHT="66"
- SRC="img46.gif"
- ALT="\begin{displaymath}(p_{4p+j})_l=-\sum_{i=0}^{(p-1)^2-1}\sum_{k=0}^{4p-1}S^{-1}_{ji}T_{ik}(p_k)_l, \quad j=0,\ldots,(p-1)^2-1,
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-that may be written in compact form:
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-p_{4p+j}=\sum_{k=0}^{4p-1}c_{jk}p_k, \quad j=0,\ldots,(p-1)^2-1,
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:linear-combination-laplace"> </A><IMG
- WIDTH="337" HEIGHT="62"
- SRC="img47.gif"
- ALT="\begin{displaymath}
-p_{4p+j}=\sum_{k=0}^{4p-1}c_{jk}p_k, \quad j=0,\ldots,(p-1)^2-1,
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(8)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-where <I>c</I><SUB><I>jk</I></SUB> represents the coefficient
-<BR><P></P>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: \begin{equation}
-c_{jk}=-\sum_{i=0}^{(p-1)^2-1}S^{-1}_{ji}T_{ik}.
-\end{equation} -->
-
-<TABLE WIDTH="100%" ALIGN="CENTER">
-<TR VALIGN="MIDDLE"><TD ALIGN="CENTER" NOWRAP><A NAME="eq:coefficients"> </A><IMG
- WIDTH="180" HEIGHT="65"
- SRC="img48.gif"
- ALT="\begin{displaymath}
-c_{jk}=-\sum_{i=0}^{(p-1)^2-1}S^{-1}_{ji}T_{ik}.
-\end{displaymath}"></TD>
-<TD WIDTH=10 ALIGN="RIGHT">
-(9)</TD></TR>
-</TABLE>
-</DIV>
-<BR CLEAR="ALL"><P></P>
-of the linear combination (<A HREF="index.html#eq:linear-combination-laplace">8</A>), that
-represents the dependency of the <I>j</I>th inner mapping support point
-<I>p</I><SUB>4<I>p</I>+<I>j</I></SUB> on the support points <I>p</I><SUB><I>k</I></SUB>,
-<!-- MATH: $k=0,\ldots,4p-1$ -->
-<IMG
- WIDTH="135" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
- SRC="img29.gif"
- ALT="$k=0,\ldots,4p-1$">,
-that are
-placed on the boundary of the cell <I>K</I>. For a fixed degree <I>p</I>, these
-coefficients <I>c</I><SUB><I>jk</I></SUB> are the same for the mapping of <EM>all</EM> cells
-<I>K</I> in real space because the <I>c</I><SUB><I>jk</I></SUB> depend only on the reference
-element <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">.
-Therefore the coefficients <I>c</I><SUB><I>jk</I></SUB> can be
-precomputed and result in following linear combinations:
-
-<P>
-For <I>p</I>=2 the linear combination turns out to be
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-p_8=\tfrac{1}{16}\sum_{k=0}^3p_k+\tfrac{3}{16}\sum_{k=4}^7p_k,
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="196" HEIGHT="61"
- SRC="img49.gif"
- ALT="\begin{displaymath}p_8=\tfrac{1}{16}\sum_{k=0}^3p_k+\tfrac{3}{16}\sum_{k=4}^7p_k,
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-see also Figure <A HREF="index.html#fig:coefficients-q2-q3">3</A>, left.
-<BR>
-<DIV ALIGN="CENTER"><A NAME="fig:coefficients-q2-q3"> </A><A NAME="185"> </A>
-<TABLE WIDTH="50%">
-<CAPTION><STRONG>Figure 3:</STRONG>
-Left: Coefficients <I>c</I><SUB>8,<I>k</I></SUB> for <I>Q</I><SUB>2</SUB> mapping. Right: Coefficients <I>c</I><SUB>12,<I>k</I></SUB> for <I>Q</I><SUB>3</SUB> mapping.</CAPTION>
-<TR><TD>
-<DIV ALIGN="CENTER">
-
-<!-- MATH: $\includegraphics*[scale=0.4]{figures/m2.ps}$ -->
-<IMG
- WIDTH="700" ALIGN="BOTTOM" BORDER="0"
- SRC="img50.gif"
- ALT="\includegraphics*[scale=0.4]{figures/m2.ps}"></DIV></TD></TR>
-</TABLE>
-</DIV>
-<BR>
-For the case that <I>p</I>=3, Figure <A HREF="index.html#fig:coefficients-q2-q3">3</A>, right, shows the coefficients <I>c</I><SUB>12,<I>k</I></SUB> of the linear combination for the inner mapping support point <I>p</I><SUB>12</SUB>. The coefficents for the points <I>p</I><SUB>13</SUB>, <I>p</I><SUB>14</SUB> and <I>p</I><SUB>15</SUB> can be obtain by rotation of the coefficients.
-
-<P>
-<B>Implementation in deal.II.</B> The coefficients <I>c</I><SUB><I>jk</I></SUB>, see
-(<A HREF="index.html#eq:coefficients">9</A>), are represented in the <I>MappingQ</I>
-class by the <I>laplace_on_quad_vector</I> as follows
-<BR><P></P>
-<DIV ALIGN="CENTER">
-<!-- MATH: \begin{displaymath}
-\mbox{\textit{laplace\_on\_quad\_vector}[j][k]}=c_{jk}
-\end{displaymath} -->
-
-
-<IMG
- WIDTH="247" HEIGHT="32"
- SRC="img51.gif"
- ALT="\begin{displaymath}\mbox{\textit{laplace\_on\_quad\_vector}[j][k]}=c_{jk}
-\end{displaymath}">
-</DIV>
-<BR CLEAR="ALL">
-<P></P>
-These coefficients are the same for the mapping of <EM>all</EM> cells
-<I>K</I> in real space because the <I>c</I><SUB><I>jk</I></SUB> depend only on the reference
-element <IMG
- WIDTH="21" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
- SRC="img8.gif"
- ALT="$\hat K$">.
-Hence for a given degree <I>p</I> the
-<I>laplace_on_quad_vector</I> can be filled by the constructor of
-the <I>MappingQ</I> class. This is done by calling the
-<I>MappingQ::set_laplace_on_quad_vector</I> function that
-includes the coefficients hardcoded for <I>p</I>=2 and <I>p</I>=3 in <I>d</I>=2 dimensions, and a routine for computing the coefficients according to
-(<A HREF="index.html#eq:coefficients">9</A>) for all other cases. The mapping support
-points <IMG
- WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
- SRC="img14.gif"
- ALT="$p_i\in K$">,
-
-<!-- MATH: $i=0,\ldots,(p+1)^d-1$ -->
-<IMG
- WIDTH="174" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
- SRC="img15.gif"
- ALT="$i=0,\ldots,(p+1)^d-1$">
-are computed once for each
-MappingQ object by the
-<I>MappingQ::compute_support_points_laplace</I> that is invoked
-by the virtual <I>compute_mapping_support_points</I> function of
-the base <I>Mapping</I> class. In
-<I>MappingQ::compute_support_points_laplace</I>, first the 4<I>p</I> points on the boundary of the cell are computed (by calling
-<I>MappingQ::add_line_support_points</I>), then by calling
-<I>MappingQ::apply_laplace_vector</I> the remaining (<I>p</I>-1)<SUP>2</SUP> inner mapping supports points are computed, where
-<I>MappingQ::apply_laplace_vector</I> just performs the linear
-combination given in (<A HREF="index.html#eq:linear-combination-laplace">8</A>).
-<BR><HR>
-</FONT>
-<ADDRESS>
-<I>Ralf Hartmann</I>
-<BR><I>2001-09-03</I>
-</ADDRESS>
-</BODY>
-</HTML>
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-5321 389 mt 5321 415 L
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-5321 389 mt 5321 389 L
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-5544 4614 mt 5544 4587 L
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-DO
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-SO
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-SO
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-DO
-6173 4614 mt 6173 389 L
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-SO
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-6255 389 mt 6255 415 L
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-SO
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- 899 2706 mt 6255 2706 L
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-SO
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-67 -114 1817 1294 2 MP stroke
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-0 -143 2123 3909 2 MP stroke
-72 -136 2123 3708 2 MP stroke
-124 -142 2123 3507 2 MP stroke
-175 -137 2123 3306 2 MP stroke
-214 -137 2123 3105 2 MP stroke
-237 -137 2123 2903 2 MP stroke
-254 -137 2123 2702 2 MP stroke
-257 -137 2123 2501 2 MP stroke
-250 -138 2123 2300 2 MP stroke
-236 -138 2123 2099 2 MP stroke
-210 -138 2123 1897 2 MP stroke
-173 -138 2123 1696 2 MP stroke
-125 -137 2123 1495 2 MP stroke
-69 -139 2123 1294 2 MP stroke
-0 -136 2123 1093 2 MP stroke
-0 -156 2429 3909 2 MP stroke
-63 -156 2429 3708 2 MP stroke
-125 -156 2429 3507 2 MP stroke
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-208 -156 2429 3105 2 MP stroke
-237 -152 2429 2903 2 MP stroke
-250 -155 2429 2702 2 MP stroke
-257 -154 2429 2501 2 MP stroke
-252 -156 2429 2300 2 MP stroke
-236 -156 2429 2099 2 MP stroke
-209 -155 2429 1897 2 MP stroke
-171 -155 2429 1696 2 MP stroke
-125 -155 2429 1495 2 MP stroke
-65 -155 2429 1294 2 MP stroke
-0 -155 2429 1093 2 MP stroke
-0 -169 2735 3909 2 MP stroke
-71 -163 2735 3708 2 MP stroke
-125 -168 2735 3507 2 MP stroke
-175 -164 2735 3306 2 MP stroke
-208 -168 2735 3105 2 MP stroke
-236 -164 2735 2903 2 MP stroke
-251 -166 2735 2702 2 MP stroke
-257 -165 2735 2501 2 MP stroke
-252 -166 2735 2300 2 MP stroke
-236 -166 2735 2099 2 MP stroke
-209 -164 2735 1897 2 MP stroke
-174 -166 2735 1696 2 MP stroke
-125 -164 2735 1495 2 MP stroke
-70 -167 2735 1294 2 MP stroke
-0 -163 2735 1093 2 MP stroke
-0 -169 3041 3909 2 MP stroke
-64 -169 3041 3708 2 MP stroke
-125 -169 3041 3507 2 MP stroke
-170 -169 3041 3306 2 MP stroke
-209 -169 3041 3105 2 MP stroke
-234 -169 3041 2903 2 MP stroke
-251 -169 3041 2702 2 MP stroke
-257 -169 3041 2501 2 MP stroke
-251 -169 3041 2300 2 MP stroke
-234 -169 3041 2099 2 MP stroke
-209 -169 3041 1897 2 MP stroke
-170 -169 3041 1696 2 MP stroke
-125 -169 3041 1495 2 MP stroke
-64 -169 3041 1294 2 MP stroke
-0 -169 3041 1093 2 MP stroke
-0 -163 3347 3909 2 MP stroke
-71 -167 3347 3708 2 MP stroke
-125 -164 3347 3507 2 MP stroke
-174 -167 3347 3306 2 MP stroke
-209 -165 3347 3105 2 MP stroke
-236 -166 3347 2903 2 MP stroke
-252 -165 3347 2702 2 MP stroke
-257 -165 3347 2501 2 MP stroke
-251 -167 3347 2300 2 MP stroke
-237 -165 3347 2099 2 MP stroke
-209 -167 3347 1897 2 MP stroke
-175 -164 3347 1696 2 MP stroke
-125 -168 3347 1495 2 MP stroke
-72 -163 3347 1294 2 MP stroke
-0 -169 3347 1093 2 MP stroke
-0 -154 3653 3909 2 MP stroke
-66 -155 3653 3708 2 MP stroke
-125 -155 3653 3507 2 MP stroke
-172 -155 3653 3306 2 MP stroke
-210 -156 3653 3105 2 MP stroke
-236 -155 3653 2903 2 MP stroke
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-250 -156 3653 2300 2 MP stroke
-237 -153 3653 2099 2 MP stroke
-208 -155 3653 1897 2 MP stroke
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-125 -156 3653 1495 2 MP stroke
-63 -156 3653 1294 2 MP stroke
-0 -157 3653 1093 2 MP stroke
-0 -136 3959 3909 2 MP stroke
-70 -138 3959 3708 2 MP stroke
-126 -137 3959 3507 2 MP stroke
-174 -138 3959 3306 2 MP stroke
-210 -138 3959 3105 2 MP stroke
-236 -137 3959 2903 2 MP stroke
-251 -137 3959 2702 2 MP stroke
-257 -137 3959 2501 2 MP stroke
-255 -137 3959 2300 2 MP stroke
-237 -137 3959 2099 2 MP stroke
-215 -136 3959 1897 2 MP stroke
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-125 -142 3959 1495 2 MP stroke
-73 -136 3959 1294 2 MP stroke
-0 -144 3959 1093 2 MP stroke
-0 -113 4265 3909 2 MP stroke
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-208 -115 4265 1897 2 MP stroke
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-0 -81 4571 3909 2 MP stroke
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-0 -91 4571 1093 2 MP stroke
-0 -44 4877 3909 2 MP stroke
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-238 -42 4877 2099 2 MP stroke
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-177 -40 4877 1696 2 MP stroke
-124 -48 4877 1495 2 MP stroke
-74 -40 4877 1294 2 MP stroke
-0 -49 4877 1093 2 MP stroke
-5183 3909 PD
-68 0 5183 3708 2 MP stroke
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-172 0 5183 3306 2 MP stroke
-207 0 5183 3105 2 MP stroke
-236 0 5183 2903 2 MP stroke
-248 0 5183 2702 2 MP stroke
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-218 0 5183 1897 2 MP stroke
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-75 0 5183 1294 2 MP stroke
-5183 1093 PD
--5 1 5 1 909 3908 3 MP stroke
--25 5 25 5 948 3703 3 MP stroke
--45 10 45 10 991 3497 3 MP stroke
--58 12 58 13 1017 3293 3 MP stroke
--71 15 71 16 1045 3089 3 MP stroke
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--85 19 85 18 1071 2684 3 MP stroke
--85 18 85 18 1071 2483 3 MP stroke
--81 18 81 18 1065 2282 3 MP stroke
--78 16 78 17 1056 2082 3 MP stroke
--68 15 68 14 1037 1883 3 MP stroke
--57 13 57 12 1014 1684 3 MP stroke
--40 9 40 9 982 1486 3 MP stroke
--22 5 22 5 944 1289 3 MP stroke
-899 1093 PD
-8 17 9 -17 1196 3877 3 MP stroke
--18 19 31 -8 1248 3676 3 MP stroke
--33 24 49 -7 1280 3466 3 MP stroke
--52 26 65 -1 1316 3266 3 MP stroke
--60 30 76 -1 1335 3058 3 MP stroke
--71 31 85 3 1357 2859 3 MP stroke
--74 33 90 2 1363 2653 3 MP stroke
--78 32 92 5 1370 2454 3 MP stroke
--76 34 92 3 1367 2250 3 MP stroke
--71 31 85 3 1355 2053 3 MP stroke
--62 30 77 0 1338 1852 3 MP stroke
--50 27 64 -2 1313 1654 3 MP stroke
--34 24 49 -6 1282 1456 3 MP stroke
--15 20 30 -10 1243 1259 3 MP stroke
-7 15 8 -15 1197 1063 3 MP stroke
-15 30 15 -30 1496 3849 3 MP stroke
--11 32 38 -21 1546 3648 3 MP stroke
--26 38 56 -20 1579 3438 3 MP stroke
--45 40 72 -14 1615 3238 3 MP stroke
--58 42 85 -11 1642 3034 3 MP stroke
--65 44 92 -10 1656 2831 3 MP stroke
--70 45 98 -9 1668 2629 3 MP stroke
--71 45 99 -8 1669 2427 3 MP stroke
--69 45 96 -10 1664 2227 3 MP stroke
--64 44 91 -10 1655 2026 3 MP stroke
--55 42 83 -12 1636 1827 3 MP stroke
--43 39 70 -14 1613 1628 3 MP stroke
--28 37 56 -19 1581 1431 3 MP stroke
--9 32 36 -22 1543 1233 3 MP stroke
-13 27 14 -27 1497 1038 3 MP stroke
-19 38 20 -38 1797 3831 3 MP stroke
--1 43 39 -34 1839 3626 3 MP stroke
--22 47 60 -29 1881 3420 3 MP stroke
--36 50 74 -26 1909 3216 3 MP stroke
--49 53 87 -23 1937 3012 3 MP stroke
--60 53 97 -19 1957 2812 3 MP stroke
--63 56 101 -20 1965 2607 3 MP stroke
--67 56 104 -19 1970 2408 3 MP stroke
--65 56 103 -20 1967 2205 3 MP stroke
--59 54 96 -20 1956 2006 3 MP stroke
--51 53 88 -23 1939 1806 3 MP stroke
--38 50 76 -26 1914 1608 3 MP stroke
--22 47 60 -29 1882 1410 3 MP stroke
--4 43 41 -33 1843 1213 3 MP stroke
-18 38 19 -38 1798 1017 3 MP stroke
-23 47 24 -47 2099 3813 3 MP stroke
--1 50 46 -40 2149 3612 3 MP stroke
--17 56 64 -38 2183 3403 3 MP stroke
--35 58 80 -33 2218 3202 3 MP stroke
--48 60 93 -30 2244 2998 3 MP stroke
--56 63 101 -29 2259 2795 3 MP stroke
--61 64 106 -27 2271 2592 3 MP stroke
--62 63 108 -27 2272 2391 3 MP stroke
--60 64 105 -28 2268 2190 3 MP stroke
--55 62 101 -28 2258 1989 3 MP stroke
--47 61 93 -31 2240 1790 3 MP stroke
--34 58 80 -33 2216 1591 3 MP stroke
--18 54 64 -36 2184 1394 3 MP stroke
-0 51 46 -41 2146 1196 3 MP stroke
-22 45 23 -45 2100 1002 3 MP stroke
-26 52 26 -52 2403 3805 3 MP stroke
-5 56 47 -47 2445 3599 3 MP stroke
--16 60 67 -43 2487 3394 3 MP stroke
--30 63 81 -39 2516 3189 3 MP stroke
--43 66 95 -36 2542 2985 3 MP stroke
--53 67 104 -33 2562 2784 3 MP stroke
--57 69 108 -33 2571 2580 3 MP stroke
--59 69 110 -32 2576 2379 3 MP stroke
--57 70 109 -34 2572 2178 3 MP stroke
--52 69 104 -35 2561 1978 3 MP stroke
--43 66 94 -36 2544 1778 3 MP stroke
--31 64 82 -39 2518 1580 3 MP stroke
--15 60 67 -42 2487 1382 3 MP stroke
-4 56 47 -46 2447 1185 3 MP stroke
-25 51 26 -51 2403 989 3 MP stroke
-28 56 28 -56 2707 3796 3 MP stroke
-4 59 50 -49 2756 3594 3 MP stroke
--14 64 69 -46 2791 3385 3 MP stroke
--31 66 85 -41 2825 3183 3 MP stroke
--41 70 96 -41 2847 2978 3 MP stroke
--50 71 105 -37 2866 2776 3 MP stroke
--55 73 111 -37 2875 2573 3 MP stroke
--57 73 112 -36 2880 2372 3 MP stroke
--56 73 111 -37 2876 2171 3 MP stroke
--50 71 105 -38 2866 1971 3 MP stroke
--42 69 96 -39 2848 1772 3 MP stroke
--30 67 85 -42 2824 1572 3 MP stroke
--14 63 68 -45 2792 1376 3 MP stroke
-5 60 51 -50 2754 1177 3 MP stroke
-27 53 27 -53 2708 983 3 MP stroke
-28 56 28 -56 3013 3796 3 MP stroke
-7 60 49 -51 3056 3590 3 MP stroke
--13 65 69 -47 3097 3385 3 MP stroke
--28 68 84 -43 3127 3180 3 MP stroke
--41 70 97 -40 3153 2976 3 MP stroke
--49 73 105 -39 3170 2773 3 MP stroke
--55 74 111 -38 3181 2571 3 MP stroke
--57 74 113 -37 3185 2369 3 MP stroke
--55 74 111 -38 3181 2169 3 MP stroke
--49 72 105 -39 3170 1969 3 MP stroke
--41 71 97 -41 3153 1769 3 MP stroke
--28 68 84 -44 3127 1571 3 MP stroke
--13 65 69 -47 3097 1373 3 MP stroke
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-28 55 28 -55 3013 979 3 MP stroke
-27 54 27 -54 3320 3800 3 MP stroke
-4 60 51 -50 3367 3591 3 MP stroke
--14 63 68 -45 3404 3388 3 MP stroke
--30 68 85 -43 3436 3182 3 MP stroke
--42 69 96 -39 3460 2979 3 MP stroke
--50 72 105 -38 3478 2775 3 MP stroke
--56 72 111 -36 3488 2573 3 MP stroke
--57 73 112 -36 3492 2372 3 MP stroke
--55 73 111 -37 3487 2170 3 MP stroke
--51 71 106 -37 3478 1971 3 MP stroke
--42 70 97 -40 3459 1770 3 MP stroke
--31 67 85 -42 3437 1574 3 MP stroke
--13 64 69 -46 3403 1373 3 MP stroke
-3 59 51 -48 3368 1179 3 MP stroke
-28 55 28 -55 3319 979 3 MP stroke
-26 51 26 -51 3627 3806 3 MP stroke
-4 56 48 -47 3671 3600 3 MP stroke
--15 60 67 -42 3711 3394 3 MP stroke
--31 63 83 -39 3742 3190 3 MP stroke
--44 67 95 -37 3768 2986 3 MP stroke
--52 68 103 -34 3786 2782 3 MP stroke
--57 69 109 -33 3796 2580 3 MP stroke
--59 69 110 -32 3800 2379 3 MP stroke
--56 70 108 -34 3795 2178 3 MP stroke
--53 67 104 -33 3786 1979 3 MP stroke
--43 66 94 -36 3767 1778 3 MP stroke
--29 64 81 -40 3740 1580 3 MP stroke
--16 60 67 -43 3711 1382 3 MP stroke
-5 56 47 -47 3669 1185 3 MP stroke
-26 52 26 -52 3627 988 3 MP stroke
-23 45 22 -45 3937 3818 3 MP stroke
-0 50 46 -40 3983 3610 3 MP stroke
--19 54 64 -36 4021 3406 3 MP stroke
--35 58 81 -33 4052 3201 3 MP stroke
--46 60 92 -30 4077 2997 3 MP stroke
--55 62 101 -28 4094 2794 3 MP stroke
--60 63 106 -27 4104 2592 3 MP stroke
--62 63 107 -27 4109 2391 3 MP stroke
--62 63 107 -27 4107 2190 3 MP stroke
--55 62 101 -28 4095 1990 3 MP stroke
--48 60 94 -29 4080 1790 3 MP stroke
--36 57 81 -32 4054 1592 3 MP stroke
--18 56 65 -38 4019 1391 3 MP stroke
--2 50 47 -40 3985 1198 3 MP stroke
-24 48 24 -48 3935 997 3 MP stroke
-19 37 19 -37 4246 3833 3 MP stroke
--3 42 41 -32 4291 3627 3 MP stroke
--23 47 60 -29 4331 3422 3 MP stroke
--38 50 76 -25 4362 3217 3 MP stroke
--50 52 88 -22 4387 3013 3 MP stroke
--59 54 97 -20 4404 2811 3 MP stroke
--64 56 102 -19 4416 2607 3 MP stroke
--66 56 103 -19 4419 2408 3 MP stroke
--64 56 102 -20 4413 2205 3 MP stroke
--60 54 96 -20 4406 2008 3 MP stroke
--50 53 88 -23 4385 1805 3 MP stroke
--36 50 74 -26 4358 1607 3 MP stroke
--22 47 61 -30 4329 1409 3 MP stroke
--1 43 40 -34 4287 1212 3 MP stroke
-19 39 19 -39 4246 1015 3 MP stroke
-14 27 13 -27 4558 3855 3 MP stroke
--9 33 37 -23 4603 3648 3 MP stroke
--28 37 55 -18 4642 3442 3 MP stroke
--43 40 71 -15 4673 3238 3 MP stroke
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--64 44 92 -10 4715 2831 3 MP stroke
--68 45 95 -9 4725 2629 3 MP stroke
--71 45 98 -8 4730 2427 3 MP stroke
--71 45 98 -8 4729 2226 3 MP stroke
--64 44 91 -10 4717 2027 3 MP stroke
--58 43 85 -12 4703 1827 3 MP stroke
--44 40 71 -15 4676 1629 3 MP stroke
--26 38 55 -20 4640 1426 3 MP stroke
--11 32 38 -22 4607 1234 3 MP stroke
-15 30 15 -30 4556 1032 3 MP stroke
-8 15 7 -15 4870 3880 3 MP stroke
--15 20 30 -10 4915 3673 3 MP stroke
--34 24 49 -6 4954 3468 3 MP stroke
--50 27 64 -2 4986 3264 3 MP stroke
--62 30 77 0 5011 3059 3 MP stroke
--71 31 85 2 5028 2858 3 MP stroke
--77 33 92 3 5040 2653 3 MP stroke
--77 32 91 5 5043 2454 3 MP stroke
--75 33 90 3 5036 2250 3 MP stroke
--72 31 86 3 5029 2054 3 MP stroke
--60 30 76 -1 5008 1851 3 MP stroke
--52 26 65 0 4989 1656 3 MP stroke
--33 25 49 -7 4952 1454 3 MP stroke
--18 19 31 -8 4920 1262 3 MP stroke
-8 16 8 -16 4869 1060 3 MP stroke
-5183 3909 PD
--22 5 22 5 5229 3703 3 MP stroke
--41 9 41 9 5266 3498 3 MP stroke
--56 12 56 13 5299 3293 3 MP stroke
--68 14 68 15 5322 3090 3 MP stroke
--78 17 78 16 5341 2887 3 MP stroke
--82 18 82 18 5349 2684 3 MP stroke
--84 18 84 18 5356 2483 3 MP stroke
--84 18 84 19 5356 2281 3 MP stroke
--79 17 79 17 5342 2082 3 MP stroke
--72 16 72 15 5329 1882 3 MP stroke
--58 13 58 12 5302 1684 3 MP stroke
--46 10 46 10 5275 1485 3 MP stroke
--25 5 25 5 5233 1289 3 MP stroke
-5183 1093 PD
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- @endspecial 758 2326 a Fk(Figure)30 b(4:)41 b(V)-8 b(ector-\014eld)32
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-c0
-1 j
-1 sg
- 0 0 6913 5185 PR
-6 w
-0 4225 5356 0 0 -4225 899 4614 4 MP
-PP
--5356 0 0 4225 5356 0 0 -4225 899 4614 5 MP stroke
-4 w
-DO
-SO
-6 w
-0 sg
- 899 4614 mt 6255 4614 L
- 899 389 mt 6255 389 L
- 899 4614 mt 899 389 L
-6255 4614 mt 6255 389 L
- 899 4614 mt 6255 4614 L
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- 746 4759 mt
-(-1.5) s
-1791 4614 mt 1791 4560 L
-1791 389 mt 1791 442 L
-1688 4759 mt
-(-1) s
-2684 4614 mt 2684 4560 L
-2684 389 mt 2684 442 L
-2531 4759 mt
-(-0.5) s
-3577 4614 mt 3577 4560 L
-3577 389 mt 3577 442 L
-3544 4759 mt
-(0) s
-4469 4614 mt 4469 4560 L
-4469 389 mt 4469 442 L
-4386 4759 mt
-(0.5) s
-5362 4614 mt 5362 4560 L
-5362 389 mt 5362 442 L
-5329 4759 mt
-(1) s
-6255 4614 mt 6255 4560 L
-6255 389 mt 6255 442 L
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-(1.5) s
- 899 4614 mt 952 4614 L
-6255 4614 mt 6201 4614 L
- 628 4658 mt
-(-1.5) s
- 899 3909 mt 952 3909 L
-6255 3909 mt 6201 3909 L
- 728 3953 mt
-(-1) s
- 899 3205 mt 952 3205 L
-6255 3205 mt 6201 3205 L
- 628 3249 mt
-(-0.5) s
- 899 2501 mt 952 2501 L
-6255 2501 mt 6201 2501 L
- 798 2545 mt
-(0) s
- 899 1797 mt 952 1797 L
-6255 1797 mt 6201 1797 L
- 698 1841 mt
-(0.5) s
- 899 1093 mt 952 1093 L
-6255 1093 mt 6201 1093 L
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-(1) s
- 899 389 mt 952 389 L
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- 899 4614 mt 6255 4614 L
- 899 389 mt 6255 389 L
- 899 4614 mt 899 389 L
-6255 4614 mt 6255 389 L
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-1791 3909 PD
-135 0 1791 3708 2 MP stroke
-243 0 1791 3507 2 MP stroke
-303 0 1791 3306 2 MP stroke
-303 0 1791 3105 2 MP stroke
-243 0 1791 2903 2 MP stroke
-135 0 1791 2702 2 MP stroke
-1791 2501 PD
--135 0 1791 2300 2 MP stroke
--243 0 1791 2099 2 MP stroke
--303 0 1791 1897 2 MP stroke
--303 0 1791 1696 2 MP stroke
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--135 0 1791 1294 2 MP stroke
-1791 1093 PD
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-274 -26 2046 3105 2 MP stroke
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-122 -96 2046 2702 2 MP stroke
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--122 -96 2046 2300 2 MP stroke
--220 -64 2046 2099 2 MP stroke
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--122 96 2046 1294 2 MP stroke
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-0 -192 2301 2501 2 MP stroke
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--180 47 2301 1696 2 MP stroke
--145 114 2301 1495 2 MP stroke
--80 173 2301 1294 2 MP stroke
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-74 -59 2556 3105 2 MP stroke
-59 -142 2556 2903 2 MP stroke
-33 -216 2556 2702 2 MP stroke
-0 -239 2556 2501 2 MP stroke
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--59 -143 2556 2099 2 MP stroke
--73 -58 2556 1897 2 MP stroke
--73 58 2556 1696 2 MP stroke
--59 142 2556 1495 2 MP stroke
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--73 -59 2811 3105 2 MP stroke
--59 -142 2811 2903 2 MP stroke
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-74 -58 2811 1897 2 MP stroke
-74 58 2811 1696 2 MP stroke
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-33 216 2811 1294 2 MP stroke
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--80 174 3066 3708 2 MP stroke
--144 114 3066 3507 2 MP stroke
--180 46 3066 3306 2 MP stroke
--180 -47 3066 3105 2 MP stroke
--144 -114 3066 2903 2 MP stroke
--80 -173 3066 2702 2 MP stroke
-0 -192 3066 2501 2 MP stroke
-81 -174 3066 2300 2 MP stroke
-145 -115 3066 2099 2 MP stroke
-181 -46 3066 1897 2 MP stroke
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-81 173 3066 1294 2 MP stroke
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--274 -26 3321 3105 2 MP stroke
--219 -63 3321 2903 2 MP stroke
--121 -96 3321 2702 2 MP stroke
-0 -106 3321 2501 2 MP stroke
-122 -96 3321 2300 2 MP stroke
-220 -64 3321 2099 2 MP stroke
-274 -25 3321 1897 2 MP stroke
-274 26 3321 1696 2 MP stroke
-220 64 3321 1495 2 MP stroke
-122 96 3321 1294 2 MP stroke
-0 106 3321 1093 2 MP stroke
-3577 3909 PD
--135 0 3577 3708 2 MP stroke
--243 0 3577 3507 2 MP stroke
--303 0 3577 3306 2 MP stroke
--303 0 3577 3105 2 MP stroke
--244 0 3577 2903 2 MP stroke
--135 0 3577 2702 2 MP stroke
-3577 2501 PD
-134 0 3577 2300 2 MP stroke
-243 0 3577 2099 2 MP stroke
-302 0 3577 1897 2 MP stroke
-302 0 3577 1696 2 MP stroke
-242 0 3577 1495 2 MP stroke
-134 0 3577 1294 2 MP stroke
-3577 1093 PD
-0 -106 3832 3909 2 MP stroke
--122 -96 3832 3708 2 MP stroke
--220 -64 3832 3507 2 MP stroke
--274 -26 3832 3306 2 MP stroke
--274 25 3832 3105 2 MP stroke
--220 64 3832 2903 2 MP stroke
--122 96 3832 2702 2 MP stroke
-0 106 3832 2501 2 MP stroke
-121 96 3832 2300 2 MP stroke
-219 63 3832 2099 2 MP stroke
-274 26 3832 1897 2 MP stroke
-274 -26 3832 1696 2 MP stroke
-219 -64 3832 1495 2 MP stroke
-122 -96 3832 1294 2 MP stroke
-0 -107 3832 1093 2 MP stroke
-0 -191 4087 3909 2 MP stroke
--81 -173 4087 3708 2 MP stroke
--145 -114 4087 3507 2 MP stroke
--181 -47 4087 3306 2 MP stroke
--181 46 4087 3105 2 MP stroke
--145 115 4087 2903 2 MP stroke
--81 174 4087 2702 2 MP stroke
-0 192 4087 2501 2 MP stroke
-80 173 4087 2300 2 MP stroke
-144 114 4087 2099 2 MP stroke
-180 47 4087 1897 2 MP stroke
-180 -46 4087 1696 2 MP stroke
-144 -114 4087 1495 2 MP stroke
-80 -174 4087 1294 2 MP stroke
-0 -192 4087 1093 2 MP stroke
-0 -239 4342 3909 2 MP stroke
--33 -216 4342 3708 2 MP stroke
--59 -143 4342 3507 2 MP stroke
--74 -58 4342 3306 2 MP stroke
--74 58 4342 3105 2 MP stroke
--59 143 4342 2903 2 MP stroke
--33 216 4342 2702 2 MP stroke
-0 239 4342 2501 2 MP stroke
-32 216 4342 2300 2 MP stroke
-59 142 4342 2099 2 MP stroke
-73 59 4342 1897 2 MP stroke
-73 -58 4342 1696 2 MP stroke
-59 -143 4342 1495 2 MP stroke
-33 -216 4342 1294 2 MP stroke
-0 -239 4342 1093 2 MP stroke
-0 -239 4597 3909 2 MP stroke
-32 -216 4597 3708 2 MP stroke
-59 -142 4597 3507 2 MP stroke
-73 -58 4597 3306 2 MP stroke
-73 58 4597 3105 2 MP stroke
-59 143 4597 2903 2 MP stroke
-33 216 4597 2702 2 MP stroke
-0 239 4597 2501 2 MP stroke
--33 216 4597 2300 2 MP stroke
--59 142 4597 2099 2 MP stroke
--74 59 4597 1897 2 MP stroke
--74 -58 4597 1696 2 MP stroke
--59 -142 4597 1495 2 MP stroke
--33 -216 4597 1294 2 MP stroke
-0 -239 4597 1093 2 MP stroke
-0 -191 4852 3909 2 MP stroke
-80 -173 4852 3708 2 MP stroke
-145 -114 4852 3507 2 MP stroke
-180 -47 4852 3306 2 MP stroke
-181 46 4852 3105 2 MP stroke
-145 115 4852 2903 2 MP stroke
-80 174 4852 2702 2 MP stroke
-0 192 4852 2501 2 MP stroke
--81 173 4852 2300 2 MP stroke
--145 114 4852 2099 2 MP stroke
--181 47 4852 1897 2 MP stroke
--181 -46 4852 1696 2 MP stroke
--145 -114 4852 1495 2 MP stroke
--80 -174 4852 1294 2 MP stroke
-0 -192 4852 1093 2 MP stroke
-0 -106 5107 3909 2 MP stroke
-122 -96 5107 3708 2 MP stroke
-220 -63 5107 3507 2 MP stroke
-274 -26 5107 3306 2 MP stroke
-274 26 5107 3105 2 MP stroke
-220 64 5107 2903 2 MP stroke
-122 96 5107 2702 2 MP stroke
-0 106 5107 2501 2 MP stroke
--122 96 5107 2300 2 MP stroke
--220 63 5107 2099 2 MP stroke
--274 26 5107 1897 2 MP stroke
--274 -25 5107 1696 2 MP stroke
--220 -63 5107 1495 2 MP stroke
--122 -96 5107 1294 2 MP stroke
-0 -107 5107 1093 2 MP stroke
-5362 3909 PD
-135 0 5362 3708 2 MP stroke
-243 0 5362 3507 2 MP stroke
-303 0 5362 3306 2 MP stroke
-303 0 5362 3105 2 MP stroke
-243 0 5362 2903 2 MP stroke
-135 0 5362 2702 2 MP stroke
-5362 2501 PD
--135 0 5362 2300 2 MP stroke
--243 0 5362 2099 2 MP stroke
--303 0 5362 1897 2 MP stroke
--303 0 5362 1696 2 MP stroke
--243 0 5362 1495 2 MP stroke
--135 0 5362 1294 2 MP stroke
-5362 1093 PD
-1791 3909 PD
--45 12 45 11 1881 3697 3 MP stroke
--80 21 80 21 1954 3486 3 MP stroke
--100 26 100 26 1994 3280 3 MP stroke
--100 26 100 26 1994 3079 3 MP stroke
--80 21 80 20 1954 2883 3 MP stroke
--45 12 45 11 1881 2691 3 MP stroke
-1791 2501 PD
-45 -12 -45 -11 1701 2311 3 MP stroke
-80 -21 -80 -20 1628 2119 3 MP stroke
-100 -26 -100 -26 1588 1923 3 MP stroke
-100 -26 -100 -26 1588 1722 3 MP stroke
-80 -21 -80 -21 1628 1516 3 MP stroke
-45 -12 -45 -11 1701 1305 3 MP stroke
-1791 1093 PD
--14 -35 -15 35 2061 3981 3 MP stroke
--53 -21 27 42 2141 3762 3 MP stroke
--81 -2 64 40 2202 3530 3 MP stroke
--94 15 87 32 2233 3299 3 MP stroke
--87 32 94 15 2226 3064 3 MP stroke
--64 40 81 -2 2185 2842 3 MP stroke
--27 42 53 -21 2115 2627 3 MP stroke
-15 35 14 -35 2032 2430 3 MP stroke
-54 21 -27 -42 1951 2246 3 MP stroke
-82 2 -64 -40 1890 2075 3 MP stroke
-94 -15 -87 -33 1859 1904 3 MP stroke
-87 -32 -94 -15 1866 1737 3 MP stroke
-64 -39 -82 2 1908 1556 3 MP stroke
-27 -42 -54 21 1978 1369 3 MP stroke
--14 -35 -15 35 2061 1164 3 MP stroke
--26 -63 -27 63 2328 4038 3 MP stroke
--50 -51 2 65 2379 3817 3 MP stroke
--63 -25 32 50 2414 3571 3 MP stroke
--66 0 53 31 2429 3321 3 MP stroke
--53 31 66 0 2416 3058 3 MP stroke
--32 50 63 -25 2383 2814 3 MP stroke
--3 64 51 -50 2331 2579 3 MP stroke
-27 64 26 -64 2275 2373 3 MP stroke
-50 51 -2 -65 2223 2191 3 MP stroke
-64 26 -32 -50 2188 2034 3 MP stroke
-67 0 -54 -31 2174 1882 3 MP stroke
-53 -31 -66 0 2187 1743 3 MP stroke
-32 -50 -64 25 2220 1584 3 MP stroke
-3 -64 -50 50 2271 1417 3 MP stroke
--26 -63 -27 63 2328 1221 3 MP stroke
--33 -79 -33 79 2589 4069 3 MP stroke
--41 -68 -19 74 2608 3850 3 MP stroke
--39 -42 -1 52 2616 3597 3 MP stroke
--32 -13 16 26 2614 3338 3 MP stroke
--16 26 32 -13 2598 3059 3 MP stroke
-1 52 39 -42 2576 2803 3 MP stroke
-19 74 40 -69 2549 2555 3 MP stroke
-33 79 33 -79 2523 2341 3 MP stroke
-41 68 19 -74 2504 2158 3 MP stroke
-39 42 0 -52 2497 2008 3 MP stroke
-32 13 -16 -26 2499 1865 3 MP stroke
-16 -25 -32 13 2515 1741 3 MP stroke
-0 -52 -39 41 2536 1596 3 MP stroke
--19 -74 -40 69 2564 1441 3 MP stroke
--33 -79 -33 79 2589 1253 3 MP stroke
--33 -79 -33 79 2844 4069 3 MP stroke
--19 -74 -41 68 2819 3856 3 MP stroke
-0 -53 -39 42 2791 3608 3 MP stroke
-16 -26 -32 13 2770 3351 3 MP stroke
-32 13 -16 -26 2754 3072 3 MP stroke
-39 42 0 -52 2752 2813 3 MP stroke
-40 69 19 -74 2760 2560 3 MP stroke
-33 79 33 -79 2778 2341 3 MP stroke
-19 74 41 -68 2803 2152 3 MP stroke
-1 52 39 -42 2831 1998 3 MP stroke
--16 26 32 -13 2853 1852 3 MP stroke
--32 -12 16 25 2869 1729 3 MP stroke
--39 -42 -1 52 2871 1586 3 MP stroke
--40 -68 -19 74 2863 1436 3 MP stroke
--33 -79 -33 79 2844 1253 3 MP stroke
--26 -63 -27 63 3093 4038 3 MP stroke
-2 -65 -50 51 3036 3831 3 MP stroke
-32 -50 -63 25 2985 3596 3 MP stroke
-53 -31 -66 -1 2952 3353 3 MP stroke
-66 0 -53 -31 2939 3089 3 MP stroke
-63 25 -32 -50 2954 2839 3 MP stroke
-51 50 -3 -64 2989 2593 3 MP stroke
-27 64 26 -64 3040 2373 3 MP stroke
--3 65 51 -51 3096 2177 3 MP stroke
--32 51 63 -26 3148 2010 3 MP stroke
--53 31 66 0 3181 1851 3 MP stroke
--66 0 53 31 3194 1712 3 MP stroke
--63 -25 32 50 3179 1559 3 MP stroke
--51 -50 3 64 3144 1403 3 MP stroke
--26 -63 -27 63 3093 1221 3 MP stroke
--14 -35 -15 35 3336 3981 3 MP stroke
-27 -42 -54 21 3253 3783 3 MP stroke
-63 -40 -81 3 3183 3568 3 MP stroke
-87 -32 -94 -15 3141 3347 3 MP stroke
-94 -15 -87 -32 3134 3111 3 MP stroke
-81 2 -63 -40 3165 2880 3 MP stroke
-53 21 -27 -42 3227 2648 3 MP stroke
-15 35 14 -35 3307 2430 3 MP stroke
--27 42 53 -21 3390 2225 3 MP stroke
--64 40 81 -2 3460 2037 3 MP stroke
--86 32 93 15 3502 1857 3 MP stroke
--94 15 86 32 3509 1690 3 MP stroke
--81 -2 64 40 3477 1519 3 MP stroke
--53 -21 26 42 3417 1348 3 MP stroke
--14 -35 -15 35 3336 1164 3 MP stroke
-1 0 3576 3909 2 MP stroke
-44 -11 -44 -12 3486 3720 3 MP stroke
-80 -21 -80 -21 3414 3528 3 MP stroke
-100 -26 -100 -26 3374 3332 3 MP stroke
-100 -26 -100 -26 3374 3131 3 MP stroke
-81 -21 -81 -21 3414 2924 3 MP stroke
-44 -11 -44 -12 3486 2714 3 MP stroke
-3577 2501 PD
--44 11 44 12 3667 2288 3 MP stroke
--81 21 81 21 3739 2078 3 MP stroke
--100 26 100 26 3779 1871 3 MP stroke
--100 26 100 26 3779 1670 3 MP stroke
--80 21 80 21 3739 1474 3 MP stroke
--44 11 44 12 3667 1282 3 MP stroke
--1 0 3577 1093 2 MP stroke
-14 35 15 -35 3817 3838 3 MP stroke
-53 21 -26 -42 3736 3654 3 MP stroke
-81 2 -64 -40 3676 3483 3 MP stroke
-94 -15 -86 -32 3644 3312 3 MP stroke
-86 -32 -93 -15 3651 3145 3 MP stroke
-64 -40 -81 2 3693 2965 3 MP stroke
-27 -42 -53 21 3763 2777 3 MP stroke
--15 -35 -14 35 3846 2572 3 MP stroke
--53 -21 27 42 3926 2354 3 MP stroke
--81 -2 63 40 3988 2122 3 MP stroke
--94 15 87 32 4019 1891 3 MP stroke
--87 32 94 15 4012 1655 3 MP stroke
--63 40 81 -3 3970 1434 3 MP stroke
--27 42 54 -21 3900 1219 3 MP stroke
-14 35 15 -35 3817 1021 3 MP stroke
-26 63 27 -63 4060 3781 3 MP stroke
-51 50 -3 -64 4009 3599 3 MP stroke
-63 25 -32 -50 3974 3443 3 MP stroke
-66 0 -53 -31 3959 3290 3 MP stroke
-53 -31 -66 0 3972 3151 3 MP stroke
-32 -51 -63 26 4005 2992 3 MP stroke
-3 -65 -51 51 4057 2825 3 MP stroke
--27 -64 -26 64 4113 2629 3 MP stroke
--51 -50 3 64 4164 2409 3 MP stroke
--63 -25 32 50 4199 2163 3 MP stroke
--66 0 53 31 4214 1913 3 MP stroke
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-26 63 27 -63 4060 964 3 MP stroke
-33 79 33 -79 4309 3749 3 MP stroke
-40 68 19 -74 4290 3566 3 MP stroke
-39 42 1 -52 4282 3416 3 MP stroke
-32 12 -16 -25 4284 3273 3 MP stroke
-16 -26 -32 13 4300 3150 3 MP stroke
--1 -52 -39 42 4322 3004 3 MP stroke
--19 -74 -41 68 4350 2850 3 MP stroke
--33 -79 -33 79 4375 2661 3 MP stroke
--40 -69 -19 74 4393 2442 3 MP stroke
--39 -42 0 52 4401 2189 3 MP stroke
--32 -13 16 26 4399 1930 3 MP stroke
--16 26 32 -13 4383 1651 3 MP stroke
-0 53 39 -42 4362 1394 3 MP stroke
-19 74 41 -68 4334 1146 3 MP stroke
-33 79 33 -79 4309 933 3 MP stroke
-33 79 33 -79 4564 3749 3 MP stroke
-19 74 40 -69 4589 3561 3 MP stroke
-0 52 39 -41 4617 3406 3 MP stroke
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--39 -42 0 52 4656 2994 3 MP stroke
--41 -68 -19 74 4649 2844 3 MP stroke
--33 -79 -33 79 4630 2661 3 MP stroke
--19 -74 -40 69 4604 2447 3 MP stroke
--1 -52 -39 42 4577 2199 3 MP stroke
-16 -26 -32 13 4555 1943 3 MP stroke
-32 13 -16 -26 4539 1664 3 MP stroke
-39 42 1 -52 4537 1405 3 MP stroke
-41 68 19 -74 4545 1152 3 MP stroke
-33 79 33 -79 4564 933 3 MP stroke
-26 63 27 -63 4825 3781 3 MP stroke
--3 64 50 -50 4882 3585 3 MP stroke
--32 50 64 -25 4933 3418 3 MP stroke
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--67 0 54 31 4979 3120 3 MP stroke
--64 -26 32 50 4965 2968 3 MP stroke
--50 -51 2 65 4930 2811 3 MP stroke
--27 -64 -26 64 4878 2629 3 MP stroke
-3 -64 -51 50 4822 2423 3 MP stroke
-32 -50 -63 25 4770 2188 3 MP stroke
-53 -31 -66 0 4737 1944 3 MP stroke
-66 0 -53 -31 4724 1681 3 MP stroke
-63 25 -32 -50 4739 1431 3 MP stroke
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-26 63 27 -63 4825 964 3 MP stroke
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--27 42 54 -21 5175 3633 3 MP stroke
--64 39 82 -2 5245 3446 3 MP stroke
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--94 15 87 33 5294 3098 3 MP stroke
--82 -2 64 40 5263 2927 3 MP stroke
--54 -21 27 42 5202 2756 3 MP stroke
--15 -35 -14 35 5121 2572 3 MP stroke
-27 -42 -53 21 5038 2375 3 MP stroke
-64 -40 -81 2 4968 2160 3 MP stroke
-87 -32 -94 -15 4927 1938 3 MP stroke
-94 -15 -87 -32 4920 1703 3 MP stroke
-81 2 -64 -40 4951 1472 3 MP stroke
-53 21 -27 -42 5012 1240 3 MP stroke
-14 35 15 -35 5092 1021 3 MP stroke
-5362 3909 PD
--45 12 45 11 5452 3697 3 MP stroke
--80 21 80 21 5525 3486 3 MP stroke
--100 26 100 26 5565 3280 3 MP stroke
--100 26 100 26 5565 3079 3 MP stroke
--80 21 80 20 5525 2883 3 MP stroke
--45 12 45 11 5452 2691 3 MP stroke
-5362 2501 PD
-45 -12 -45 -11 5272 2311 3 MP stroke
-80 -21 -80 -20 5199 2119 3 MP stroke
-100 -26 -100 -26 5159 1923 3 MP stroke
-100 -26 -100 -26 5159 1722 3 MP stroke
-80 -21 -80 -21 5199 1516 3 MP stroke
-45 -12 -45 -11 5272 1305 3 MP stroke
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-1949 5719 y Fk(23)p eop
-%%Trailer
-end
-userdict /end-hook known{end-hook}if
-%%EOF
+++ /dev/null
-
-<H1 ALIGN="CENTER">
-A short description of the new threading scheme
-</H1>
-
-
-<p ALIGN="CENTER">
- <strong> Wolfgang Bangerth, May 2003</strong>
-</p>
-
-
-<p>
-Since the first deal.II report on
-multithreading was written in 2000 (see the list of deal.II
-publications),
-we have put in place a new
-implementation of the threading scheme (the first release to contain it is
-4.0). The new scheme can do all that you could do before, so the report is in a
-sense still valid, but it describes a syntax that is no more used. We will here
-briefly describe this syntax as well as some considerations that guided us
-while implementing it. For general questions on multithreading, how programs
-that use it must look like, and for pitfalls to watch out for, please still
-refer to the report mentioned above.
-</p>
-
-<p>
-We note that since this report was written, there has been another
-incarnation of support for multicore machines, namely by using the
-Threading Building Blocks and tasks. The documentation module on
-parallel computing, available through the modules page of the deal.II
-manual, explains this new direction in more detail.
-</p>
-
-
-<h3>1. Rationale and Introduction</h3>
-
-
-<p>
-POSIX and other thread libraries only allow functions as thread entry
-points that satisfy the signature
-<code><pre>
- void * (*) (void *)
-</pre></code>
-and starting threads involves a clumsy syntax. Thread entry points
-with another signature need to be "wrapped", i.e. their arguments need
-to be stored in a structure, and we need a function with above
-signature that can be used to "unpack" the arguments and call the
-desired function. This basically forces us to have one such structure
-and entry function for each function signature that we want to start a
-thread with.
-</p>
-
-<p>
-The first incarnations of the threading scheme in deal.II already got a long
-way towards making this simpler, by hiding the thread entry points, the packing
-and unpacking behind a layer of carefully crafted templates. It allowed you to
-call (almost) any function with arbitrary argument lists on a new thread,
-except that functions that returned values were not allowed. Implementing such
-a template scheme is not simple, since, besides simplicity to use, it has to
-take care of the lifetimes of objects that need to be synchronised across
-threads, and in particular since templates do not allow for functions with
-arbitrary numbers of arguments - they need to be repeated for every number of
-arguments, which makes implementation tedious. Nevertheless, the old scheme was
-very much usable.
-</p>
-
-<p>
-However, the old scheme had a number of shortcomings:
-<ul>
-<li>The implementation did not allow for functions returning
- anything but <code>void</code>. We want to be able to call everything
- on a new thread that can also be called on the present one.</li>
-<li>Thread objects could not be copied. Rather, thread ids were put into a
-thread manager object that took care of it, but handling single, or even
-detached threads was not too convenient.</li>
-<li>The general syntax for calling a function on a new thread was a
- little clumsy and not intuitive.</li>
-</ul>
-</p>
-
-<p>
-Regarding the last point, note that any other function is called by
-<code><pre>
- f(arg1, arg2);
- obj.f(arg1, arg2);
-</pre></code>
-Ideally, the following syntax for starting any function on a new
-thread would be nice:
-<code><pre>
- spawn f(arg1, arg2);
- spawn obj.f(arg1,arg2);
-</pre></code>
-This syntax is not possible in C++, but the following syntax is,
-making it relatively clear what the intent of the statement is:
-<code><pre>
- spawn (f)(arg1, arg2);
- spawn (obj, &Class::f)(arg1,arg2);
-</pre></code>
-This is the syntax we will want to achieve (except for the fact that the
-<code>spawn</code> function is in a namespace <code>Threads</code>, just like
-all other entities described here).
-</p>
-
-<p>
-This text will discuss the details that are needed to implement
-this syntax, as well as the following points:
-<ul>
-<li>Overloading <code>spawn(</code>) so as to take unbound functions and member
-functions, whether virtual or static. Of course, every call needs to be type
-safe, i.e. the exact
- same conversions of arguments need to be performed as in a usual call (except
- for two additional copies that are necessary).</li>
-<li><code>spawn()</code> needs to return a value that allows us to identify,
-and join a thread. The syntax for this will be
-<code><pre>
- Thread<> t = spawn(f)(arg1, arg2);
- t.join ();
-</pre></code>
- If we don't save the return value of <code>spawn()</code>, as in the examples
- above, then we have just created a detached thread.</li>
-<li>Return values: if <code>f()</code> returns a value, say, an integer, then
-we want to be able to retrieve it once the thread has finished:
-<code><pre>
- Thread<int> t = spawn (f)(1., 1.);
- t.join ();
- int i = t.return_value ();
-</pre></code>
- This requires some care when functions return references, but some
- template magic will save us. Another special case are functions that
- return <code>void</code>.</li>
-<li>Thread groups: if threads are created inside a loop, we will want to
- put all of them into a <code>ThreadGroup</code> object, and wait for them
- collectively, rather than one-by-one.</li>
-</ul>
-</p>
-
-<p>
-Basically, the syntax above is all you need to know. It is as simple as
-that. The rest of this text, in comparison is very much of technical nature. I
-took most of it from a technical discussion I had with the author of the
-threading scheme in boost, William Kempf. It describes the way the threading
-scheme is implemented, the meaning of the various classes, etc. It probably
-doesn't give you much insight how to <em>use</em> it, but should explain in
-reasonable detail how it <em>works</em>. For more examples of use, take a look
-at a number of the example programs in deal.II, or at some places in the
-library itself.
-</p>
-
-
-<p>
-This paper is divided into the following parts:
-<ol>
-<li>This introduction</li>
-<li>Entities (functions, classes) that are used by both and that
- describe the newly created thread</li>
-<li>Entities that are used on the calling thread</li>
-<li>Entities that are used to create a thread</li>
-<li>Tool classes</li>
-<li>Open problems</li>
-<li>Further suggestions</li>
-</ol>
-We will present the main parts of the code in the text. The implementation is
-in the library; all entities that
-are not to be used by the user are placed into a namespace
-<code>internal</code>, those to be used are in a namespace
-<code>Threads</code>. The implementation uses Boost's shared_ptr. Some parts of
-the implementation parallel the
-boost::function library, but they are small and taylored to the
-particular purpose at hand; in particular, they make heavy use of the
-boost::tuple library. We note that the code has in some places already evolved
-a little bit beyond the state of this paper, but the main ideas are all to be
-found still.
-</p>
-
-
-
-<h3>2. Entities that describe threads</h3>
-
-
-<p>
-Each thread that has been created is described by exactly one object
-of type <code>thread_description<RT></code>, where <code>RT</code> here and in the
-sequel will always denote the return type of the function being called
-on a new thread. The <code>thread_description</code> class is split into an
-operating system dependent base class, and an independent derived
-class. The base class is responsible for abstracting the OS
-interface to the functions creating, joining, killing, and signalling
-threads. For POSIX threads, this class looks as follows:
-</p>
-
-<code><pre>
- struct thread_description_base {
- private:
- pthread_t pt;
- mutable volatile bool was_joined;
- mutable boost::mutex join_mutex;
- mutable boost::condition join_condition;
-
- public:
- thread_description_base () : was_joined (false) {};
- virtual ~thread_description_base () { /* ... */ };
-
- void create (void * (*p) (void *), void *d) {
- pthread_create (&pt, 0, p, d);
- };
-
- void join () const {
- if (was_joined)
- return;
- boost::mutex::scoped_lock lock(join_mutex);
- if (!was_joined)
- pthread_join (pt, 0);
- was_joined = true;
- };
- };
-</pre></code>
-
-<p>
-<code>join()</code> can be called more than once and uses Schmidt's thread-safe
-double-checking pattern for speed. There could be additional functions
-<code>kill()</code> or <code>send_signal()</code>, but these are not presently
-implemented.
-</p>
-
-<p>
-In the destructor, we need to make sure that a thread is joined at
-least once in its lifetime, or if not that it is being detached
-(otherwise, we create the thread equivalent of a zombie process, which
-will lead to a resource leak in the operating system). This is a
-little tricky, since the destructor might be called while the thread
-is still running; comments in the code explain how we work around
-this.
-</p>
-
-<p>
-The <code>thread_description<RT></code> class is derived from this base
-class:
-<code><pre>
- template <typename RT>
- struct thread_description : public thread_description_base
- {
- return_value<RT> ret_val;
- };
-</pre></code>
-</p>
-
-<p>
-Its only purpose is to provide a place of storage for the return
-value of the function being called on the new thread. Since functions
-might return references or just nothing at all, the <code>return_value</code>
-template is used. It is described below in the section on Tool
-Classes. The return value will be set on exit of the function being
-called.
-</p>
-
-<p>
-As mentioned, there is exactly one <code>thread_description<RT></code>
-object per created thread. It is accessed using <code>boost::shared_ptr</code>
-objects, and references are held from each <code>Thread<RT></code> object
-for this thread as
-well as from a wrapper function on the new thread. The object is thus
-deleted, when all <code>Thread<RT></code> objects for this thread have gone out of
-scope (or point to different threads) and the thread itself has
-finished; this is the appropriate time.
-</p>
-
-
-
-<h3>3. Entities that are used on the calling thread</h3>
-
-
-<p>
-On the calling thread, we basically use the <code>Thread<RT></code>
-class, <code>ThreadGroup<RT></code> class, and <code>spawn</code>
-function. The <code>Thread<RT></code> class has the following
-implementation:
-</p>
-
-<code><pre>
- template <typename RT = void>
- class Thread {
- public:
- Thread () {};
- Thread (const boost::shared_ptr<thread_description<RT> > &td)
- : thread_description (td) {};
-
- void join () const { thread_description->join (); };
-
- RT return_value () {
- join ();
- return thread_description->ret_val.get();
- };
-
- bool operator == (const thread &t) {
- return thread_description == t.thread_description;
- };
-
- private:
- boost::shared_ptr<thread_description<RT> > thread_description;
- };
-</pre></code>
-
-<p>
-Copy constructor and <code>operator=</code> are generated automatically by the
-compiler. Note that asking for the <code>return_value</code> automatically waits
-for the thread to finish, and that for this it is helpful that we can
-call <code>join()</code> more than once on the thread description object. The
-<code>return_value()</code> function also makes use of the fact that if <code>RT=void</code>,
-then the return construct is still valid. Furthermore, since this is
-the most common case, the template argument of the thread class has a
-default of <code>void</code>.
-</p>
-
-<p>
-The <code>ThreadGroup</code> class is a container distributing calls to its
-member functions to all its elements. Elements are added using
-<code>operator+=</code>, and they are stored using a
-<code>std::vector</code>. (A <code>std::set</code> would be more appropriate,
-but then we would have to have <code>operator<</code> for
-<code>Thread<RT></code> objects.) It has the same default value for the
-template argument:
-</p>
-
-<code><pre>
- template <typename RT = void>
- class ThreadGroup
- {
- public:
- ThreadGroup & operator += (const Thread<RT> &t) {
- threads.push_back (t);
- return *this;
- };
-
- void join_all () const {
- for (typename std::vector<Thread<RT> >::const_iterator
- t=threads.begin(); t!=threads.end(); ++t)
- t->join ();
- };
-
- private:
- std::vector<Thread<RT> > threads;
- };
-</pre></code>
-
-<p>
-Since objects of type <code>Thread<RT></code> are freely copyable, there
-is no need
-to provide an index operator for <code>ThreadGroup</code>; if you need to index
-its elements (for example to get at the return value), use
-<code>std::vector<Thread<RT> ></code>.
-</p>
-
-<p>
-Finally, there are overloads of the <code>spawn</code> template, for unbound
-functions, as well as <code>const</code> and non-<code>const</code> member
-functions. We only show them for unary member functions:
-<code><pre>
- template <typename RT, typename C, typename Arg1>
- mem_fun_encapsulator<RT,C,boost::tuple<Arg1> >
- spawn (C &c, RT (C::*fun_ptr)(Arg1)) {
- return mem_fun_encapsulator<RT, C, boost::tuple<Arg1> > (c,fun_ptr);
- }
-
- template <typename RT, typename C, typename Arg1>
- mem_fun_encapsulator<RT,const C,boost::tuple<Arg1> >
- spawn (const C &c, RT (C::*fun_ptr)(Arg1) const) {
- return mem_fun_encapsulator<RT, const C, boost::tuple<Arg1> > (c,fun_ptr);
- }
-</pre></code>
-</p>
-
-<p>
-Note that we need two overloaded versions, for <code>const</code> and
-non-<code>const</code>
-member functions. Both create an intermediate object (in the
-<code>internal</code>
-namespace) that will accept arguments in place of the function being
-called on the new thread, make sure a new thread is created, copy the
-arguments to the new thread's stack, and only then return. The exact
-mechanism is described in the next section.
-</p>
-
-<p>
-In the implementation, we have to repeat the functions above for
-binary, ternary, ... member functions, and also for unbound member
-functions. One would really like to have something also for objects other than
-pointers to (member-)functions that provide an
-<code>operator()</code>. However, this doesn't seem to be possible if
-<code>operator()</code> returns something other than <code>void</code> or takes
-arguments. This
-would need some kind of typeof-operator which is not standard C++. See the
-discussion in the Open Problems section.
-</p>
-
-
-<h3>4. Entities that are used to create a thread</h3>
-
-
-<p>
-In this section, we describe the gory details of copying arguments
-from the stack of the old thread to the stack of the new one. These
-details are not necessary to <em>use</em> the <code>spawn()</code> functions,
-so are probably boring and may be skipped.
-</p>
-
-<p>
-The basic idea is the following: <code>spawn()</code> returns an object and provides
-it with the address of the function to be called, and in the case of a
-member function with the address of an object. <code>mem_fun_encapsulator</code>
-looks like this:
-</p>
-
-<code><pre>
- template <typename RT, typename C, typename ArgList,
- int length = boost::tuples::length<ArgList>::value>
- class mem_fun_encapsulator;
-
- template <typename RT, typename C, typename ArgList>
- class mem_fun_encapsulator<RT,C,ArgList,1> {
- typedef typename mem_fun_ptr<RT,C,ArgList>::type MemFunPtr;
-
- public:
- mem_fun_encapsulator (C &c, MemFunPtr mem_fun_ptr)
- : c (c), mem_fun_ptr(mem_fun_ptr) {};
-
- Thread<RT>
- operator() (typename boost::tuples::element<0,ArgList>::type arg1) {
- return mem_fun_wrapper<RT,C,ArgList> (mem_fun_ptr, c,
- boost::tie(arg1)).fire_up ();
- };
-
- private:
- C &c;
- MemFunPtr mem_fun_ptr;
- };
-</pre></code>
-
-<p>
-(Note how the default value specification of the last template
-argument automatically redirects uses with three template parameters
-to the correct four-parameter specialization, even though the general
-template is never used.)
-</p>
-
-<p>
-The constructor stores the two addresses. If one calls
-<code><pre>
- spawn(obj, &C::f) (42);
-</pre></code>
-the next thing that is invoked is the <code>operator()</code> of this class. It
-takes the argument(s), creates a temporary with the two addresses and
-a reference to the argument (that's what <code>boost::tie</code>) does, and calls
-<code>fire_up()</code> on this temporary. <code>fire_up</code> has all the information, and does
-the work. Note that we will not pass references to the individual
-arguments, but bind them all together with <code>boost::tie</code>, so that we need
-not have different versions of the <code>mem_fun_wrapper</code> class for different
-numbers of arguments. (However, we need a separate partial
-specialization of the <code>mem_fun_encapsulator</code> class for each number of
-function arguments.) The <code>tie_args</code> template is used to make a version
-of the <code>ArgList</code> type with all reference types; it is described below.
-</p>
-
-<p>
-The next question, of course, is how <code>mem_fun_wrapper</code> looks like. Let
-us first consider the base class that it has in common with
-<code>fun_wrapper</code>, the wrapping class for non-member function objects:
-<code><pre>
- template <typename RT, typename EntryPointClass>
- struct wrapper_base {
- Thread<RT> fire_up () {
- thread_descriptor
- = DescriptionPointer(new typename thread_description<RT>());
-
- boost::mutex::scoped_lock lock (mutex);
- thread_descriptor->create (&EntryPointClass::entry_point,
- (void *)this);
- condition.wait (lock);
-
- return thread_descriptor;
- }
-
- protected:
- typedef boost::shared_ptr<thread_description<RT> >
- DescriptionPointer;
-
- DescriptionPointer thread_descriptor;
-
- mutable boost::mutex mutex;
- mutable boost::condition condition;
- };
-</pre></code>
-<p>
-<code>fire_up</code> is the only real function; it creates a thread descriptor
-object, and calls it with a pointer to the present object, and the address of
-the starting point is <code>EntryPointClass::entry_point</code>, where
-<code>EntryPoint</code> is the name of a class that implements this thread
-starting function and is passed as a template argument to
-<code>wrapper_base</code>.
-Before it starts the new thread, it acquires a mutex and
-afterwards wait until a condition is signalled before it finishes by
-using the thread descriptor object to generate a <code>Thread<RT></code>
-object.
-</p>
-
-<p>
-The magic happens in the derived class:
-<code><pre>
- template <typename RT, class C, typename ArgList>
- struct mem_fun_wrapper
- : public wrapper_base<RT, mem_fun_wrapper<RT,C,ArgList> >
- {
- typedef typename mem_fun_ptr<RT,C,ArgList>::type MemFunPtr;
- typedef typename tie_args<ArgList>::type ArgReferences;
- mem_fun_wrapper (MemFunPtr mem_fun_ptr,
- C &c,
- const ArgReferences &args)
- : c (c),
- mem_fun_ptr (mem_fun_ptr),
- args (args) {};
- private:
- mem_fun_wrapper ();
- mem_fun_wrapper (const mem_fun_wrapper &);
-
- C &c;
- MemFunPtr mem_fun_ptr;
- ArgReferences args;
-
- static void * entry_point (void *arg)
- {
- const wrapper_base<RT> *w
- = reinterpret_cast<const wrapper_base<RT>*> (arg);
- const mem_fun_wrapper *wrapper
- = static_cast<const mem_fun_wrapper*> (w);
- MemFunPtr mem_fun_ptr = wrapper->mem_fun_ptr;
- C &c = wrapper->c;
- ArgList args = wrapper->args;
-
- boost::shared_ptr<thread_description<RT> >
- thread_descriptor = wrapper->thread_descriptor;
-
- {
- boost::mutex::scoped_lock lock (wrapper->mutex);
- wrapper->condition.notify_one ();
- }
-
- call (mem_fun_ptr, c, args, thread_descriptor->ret_val);
-
- return 0;
- };
- };
-</pre></code>
-</p>
-
-<p>
-Note in particular, how this class passes itself as second template parameter
-to the base class, enabling the latter to call the
-<code>mem_fun_wrapper::entry_point</code> function as entry point to the new
-thread. When the fire_up function in the base
-class is called, it creates a new thread that starts inside this
-function, and the argument given to it is the address of the
-<code>wrapper_base</code> object. The first thing the <code>entry_point</code> function does, is
-to cast back this address to the real object's type (it knows the real
-type of the object, since the address of this function has been handed
-down through the template magic), then copies the address of
-the object to work with and the address of the member function to be
-called from the stack of the old thread to the stack of this new
-thread. It then also copies the arguments, which so far have been held
-only as references, but copies them by value. Next, it gets the
-address of the return thread descriptor, and with it the address of
-the return value (the <code>shared_ptr</code> will also make sure that the object
-lives long enough). The part in braces signals the condition to the
-old thread, which hangs in the <code>fire_up</code> function: the arguments have
-been copied, and the old thread can go on, eventually also destroying
-objects that have been copied by value. Finally, it calls the
-requested function with the proper arguments through a generic
-interface (described in the section on tools) and sets the return
-value of the thread.
-</p>
-
-
-<h3>5. Tool classes</h3>
-
-
-<p>
-In the implementation above, some tool classes have been used. These
-are briefly described here.
-</p>
-
-<h4>a) The <code>return_value<T></code> class template</h4>
-
-<p>
-This class stores a value of type <code>T</code> if <code>T</code> is not a
-reference or <code>void</code>. It offers <code>get()</code> and
-<code>set()</code> functions that get and set the value. If <code>T</code> is a
-reference type, then <code>set()</code> is obviously not possible since
-references cannot be rebound after construction time. The class therefore
-stores a pointer, and <code>set()</code> sets the pointer to the object the
-reference references. <code>get()</code> then returns the reference again. If
-<code>T</code> is <code>void</code>, then the class is empty and there is only
-a <code>get()<code> function that returns <code>void</code>.
-</p>
-
-<code><pre>
- template <typename RT> struct return_value
- {
- private:
- RT value;
- public:
- RT get () const { return value; }
- void set (RT v) { value = v; }
- };
-
- template <typename RT> struct return_value<RT &>
- {
- private:
- RT * value;
- public:
- RT & get () const { return *value; }
- void set (RT & v) { value = &v; }
- };
-
- template <> struct return_value<void> {
- static void get () {};
- };
-</pre></code>
-
-
-<h4>b) The <code>call</code> function templates</h4>
-
-<p>
-The <code>call</code> function templates take a function pointer, an argument list
-tuple, and the address of the return value object, and call the
-function with these arguments. Since we have to unpack the argument
-list, we have to dispatch to different functions, depending on the
-number of arguments, in the usual way:
-</p>
-
-<code><pre>
- template <int> struct int2type;
-
- template <typename RT, typename PFun, typename ArgList>
- static void call (PFun fun_ptr,
- ArgList &arg_list,
- return_value<RT> &ret_val)
- {
- Caller<RT>::do_call (fun_ptr, arg_list, ret_val,
- int2type<boost::tuples::length<ArgList>::value>());
- };
-</pre></code>
-
-<p>
-The <code>Caller</code> class has the following member functions:
-
-<code><pre>
- template <typename RT> struct Caller
- {
- template <typename PFun, typename ArgList>
- static void do_call (PFun fun_ptr,
- ArgList &arg_list,
- return_value<RT> &ret_val,
- const int2type<1> &)
- { ret_val.set ((*fun_ptr) (arg_list.template get<0>())); };
-
- // likewise for int2type<0>, int2type<2>, ...
- };
-</pre></code>
-</p>
-
-
-<p>
-There is a specialization <code>Caller<void></code> that does not set a return
-value, and for each call and <code>do_call</code> function there is a second
-function for member function pointers that takes an object as
-additional argument.
-</p>
-
-
-<h4>c) <code>mem_fun_ptr</code></h4>
-
-<p>
-In order to form a pointer to member function for both cases of <code>const</code>
-and non-<code>const</code> member functions, we need a simple tool:
-<code><pre>
- template <typename RT, class C, typename ArgList,
- int length = boost::tuples::length<ArgList>::value>
- struct mem_fun_ptr_helper;
-
- template <typename RT, class C, typename ArgList>
- struct mem_fun_ptr_helper<RT, C, ArgList, 1>
- {
- typedef RT (C::*type) (typename boost::tuples::element<0,ArgList>::type);
- };
-
- template <typename RT, class C, typename ArgList>
- struct mem_fun_ptr_helper<RT, const C, ArgList, 1>
- {
- typedef RT (C::*type) (typename boost::tuples::element<0,ArgList>::type) const;
- };
-
- template <typename RT, class C, typename ArgList>
- struct mem_fun_ptr
- {
- typedef typename mem_fun_ptr_helper<RT,C,ArgList>::type type;
- };
-</pre></code>
-</p>
-
-<p>
-Note that if the second template argument is a <code>const C</code>, then we mark
-the member function <code>const</code>. The two templates for <code>mem_fun_ptr_helper</code>
-have to be repeated for every number of arguments that we have in
-mind. Note also that the specification of the default argument in the
-declaration of the general template of <code>mem_fun_ptr_helper</code> saves us
-from recomputing it in <code>mem_fun_ptr</code>.
-</p>
-
-
-
-<h4>d) <code>add_reference</code> for tuples</h4>
-
-<p>
-The following classes add references to the elements of a tuple, thus
-providing the type equivalent of the return value of the <code>boost::tie</code>
-functions. There are probably ways inside boost's tuples library to do
-this, but I couldn't locate this.
-<code><pre>
- template <int N, typename Tuple>
- struct add_reference_to_Nth
- {
- typedef typename boost::tuples::element<N,Tuple>::type ArgType;
- typedef typename boost::add_reference<ArgType>::type type;
- };
-
- template <typename Tuple, int = boost::tuples::length<Tuple>::value>
- struct tie_args_helper;
-
- template <typename Tuple>
- struct tie_args_helper<Tuple,1>
- {
- typedef
- boost::tuple<typename add_reference_to_Nth<0,Tuple>::type>
- type;
- };
-
- template <typename Tuple>
- struct tie_args
- {
- typedef typename tie_args_helper<Tuple>::type type;
- };
-</pre></code>
-</p>
-<p>
-The <code>tie_args_helper</code> class is repeated for every number of elements we
-want to use.
-</p>
-
-
-
-<h3>6. Open Problems</h3>
-
-
-<h4>a) A variable lifetime problem</h4>
-<p>
-The only unsolved semantic problem I am aware of at present is the
-following: if we have a function
-<code><pre>
- void f(const int &i);
-</pre></code>
-then this function can be called as
-<code><pre>
- f(1);
-</pre></code>
-i.e. the compiler creates a temporary and passes its address to
-<code>f()</code>. When invoking <code>f()</code> on a new thread, however, as in
-<code><pre>
- spawn (f)(1);
-</pre></code>
-then it is only guaranteed that the call to <code>spawn()</code> does not return
-before the new thread is started and has copied the arguments to
-<code>f()</code>. However, the argument is only the reference to the temporary, not
-its value. <code>f()</code> will thus likely observe corrupted values for its
-argument. On the other hand, copying the value is no option either, of
-course. Since to the author's best knowledge the language does not
-provide means to avoid taking the address of a temporary, there is
-presently no way to avoid this problem. Suggestions for healing it are
-very welcome.
-</p>
-
-
-<h4>b) Forwarding of <code>operator()</code></h4>
-<p>
-Above, we have not defined an overload of <code>spawn</code> for functor-like
-objects, even though that would be desirable. One way to do so would be
-<code><pre>
- template <typename C>
- mem_fun_encapsulator<void,C,boost::tuple<> >
- spawn (C &c) {
- return spawn (c, &C::operator());
- }
-</pre></code>
-This only works if <code>operator()</code> satisfies the signature
-<code><pre>
- struct C { void operator() (); };
-</pre></code>
-</p>
-<p>
-We could add another overload if <code>operator()</code> is
-<code>const</code>. However, what one
-would like is an overload for more general signatures. Unfortunately,
-this requires that we can infer type and number of arguments and
-return type of <code>operator()</code> at the time we declare the return type of
-above overload of <code>spawn()</code>. I have not found a way to infer this
-information just by using the template parameter <code>C</code> -- it just seems
-not possible. What would work if it were supported by compilers is a
-kind of <code>typeof</code>-operator:
-<code><pre>
- template <typename C>
- typeof(spawn(c,&C::operator())) // **
- spawn (C &c) {
- return spawn (c, &C::operator());
- }
-</pre></code>
-</p>
-<p>
-When seeing the declaration, the compiler would automatically check
-which version of the overloaded <code>spawn()</code> function it would call, and
-correspondingly take the return type. gcc does support the <code>typeof</code>
-keyword, but even present CVS snapshots generate an internal compiler
-error on this construct.
-</p>
-
-<h4>c) Using a memory based scheme rather than condition variables</h4>
-<p>
-The scheme using mutices and condition variables to synchronise
-calling and called thread seems expensive. A simpler approach would be
-to replace it by letting the creating thread generate an object on the
-heap that holds copies of the arguments (instead of references as
-presently), spawn the new thread and just go on without any
-synchronisation.
-</p>
-
-<p>
-The calling thread would then not have to copy the arguments onto its
-local stack and signal to the calling thread. It would only have to
-delete the memory after the call to the user-supplied function
-returns. Apart from replacing <code>ArgReferences</code> by
-<code>ArgList</code> in some places,
-the scheme would basically just replace <code>*_encapsulator::operator()</code>,
-<code>fire_up</code>, and <code>thread_entry_point</code>:
-</p>
-
-<code><pre>
- thread<RT>
- operator() (typename boost::tuples::element<0,ArgList>::type arg1) {
- return (new mem_fun_wrapper<RT,C,ArgList> (mem_fun_ptr, c,
- boost::tie(arg1)))->fire_up ();
- };
-
- thread<RT> fire_up () {
- thread_descriptor
- = DescriptionPointer(new typename detail::thread_description<RT>());
-
- thread_descriptor->create (entry_point, (void *)this);
- // no synchronisation here
- return thread_descriptor;
- }
-
- static void * entry_point (void *arg) {
- wrapper_base<RT> *w = reinterpret_cast<wrapper_base<RT>*> (arg);
- fun_wrapper *wrapper = static_cast<fun_wrapper*> (w);
- // no copying here; no synchronisation necessary
- detail::call (wrapper->fun_ptr, wrapper->args,
- wrapper->thread_descriptor->ret_val);
- // delete memory
- delete wrapper;
- return 0;
- }
-</pre></code>
-
-<p>
-The perceived simplicity without using mutices and condition variable
-might be deceptive, however, since memory allocation and deallocation
-requires locking and unlocking mutices as well, and is generally not a
-cheap operation.
-</p>
-
-<p>
-However, the main problem is that I get spurious segmentation faults
-with this on my Linux box. These always happen inside the memory
-allocation and deallocation functions in the C++ and C language
-support libraries. I believe that these are not bugs in the
-application, but in the language runtime. However, my motivation to
-debug multithreading problems in the libc is very limited; for
-reference, valgrind 1.94 does not show accesses to uninitialized or
-already freed memory portions, even for runs that eventually crash
-later on.
-</p>
-
-
-<h3>7. Alternative Suggestions</h3>
-
-
-<p>
-Here are some additional suggestions for discussion:
-</p>
-
-<h4>a) Conversions between return values</h4>
-
-<p>
-If <code>f()</code> is a function returning an integer, then the following is
-legal:
-<code><pre>
- double d = f(arg1, arg2);
-</pre></code>
-The question, then, would be: do we want to allow conversions between
-<code>Thread<double></code> and <code>Thread<int></code> objects?
-And do we want to allow a
-conversion from <code>Thread<T></code> to <code>Thread<void></code>
-(i.e.: casting away the return value)?
-</p>
-
-<p>
-Since one can still assign the return value of the thread to a double,
-<code><pre>
- double d = thread.return_value();
-</pre></code>
-the only real merit in allowing conversions is in putting threads with
-different return value types into a <code>ThreadGroup</code>:
-<code><pre>
- double f1 ();
- int f2 ();
-
- ThreadTroup<double> tg;
- tg += spawn(f1)();
- tg += spawn(f2)(); // convert Thread<int> to Thread<double>
- tg.join_all ();
-</pre></code>
-</p>
-<p>
-Being able to do this is probably only syntactic sugar, except for the
-case where we are not interested in the return values of all threads,
-i.e. the conversion <code>Thread<T> -> Thread<void></code> seems
-like the only one that is really worth it.
-</p>
-
-<p>
-I have made some initial experiments with implementing general
-conversions. The main problem is that we need to allow conversion
-chains:
-<code><pre>
- thread<double> t1 = spawn (f)(arg1, arg2);
- thread<int> t2 = t1;
- thread<double> t3 = t2;
-</pre></code>
-</p>
-<p>
-If <code>f()</code> returns 1.5, then <code>t3.return_value()</code> needs to
-return 1.0. I believe that such conversions could be implemented, by adding the
-types in the chain into a <code>boost::tuple</code> of growing length, and writing
-a function that converts a value of the first type of this tuple to
-the second, to the third, ..., to the last type in the tuple. However,
-a plethora of internal compiler errors has scared me off doing more
-experiments in this direction.
-</p>
-
-
-<h4>b) Conversions between class types I</h4>
-
-<p>
-When you have a class hierarchy like
-<code><pre>
- struct B { void f(); };
- struct D : public B {};
-</pre></code>
-then calling
-<code><pre>
- spawn (D(), &B::f);
-</pre></code>
-fails for gcc (but succeeds with Intel's icc). Presumably, gcc is
-right: template arguments must match exactly, and <code>D()</code> is of type
-<code>D</code>, while <code>&B::f</code> leads to a class type of
-<code>B</code>. There is no function template for spawn for which this call can
-match without a derived-to-base conversion. We could now change the template
-<code><pre>
- template <typename RT, typename C, typename Arg1>
- mem_fun_encapsulator<RT,C,boost::tuple<Arg1> >
- spawn (C &c, RT (C::*fun_ptr)(Arg1)) {
- return mem_fun_encapsulator<RT, C, boost::tuple<Arg1> > (c,fun_ptr);
- }
-</pre></code>
-into
-<code><pre>
- template <typename RT, typename A, typename C, typename Arg1>
- mem_fun_encapsulator<RT,C,boost::tuple<Arg1> >
- spawn (A &a, RT (C::*fun_ptr)(Arg1)) {
- return mem_fun_encapsulator<RT, C, boost::tuple<Arg1> > (a,fun_ptr);
- }
-</pre></code>
-i.e. introduce another class template <code>A</code> for the type of the
-object. Since the arguments of the constructor to the
-<code>mem_fun_encapsulator</code> object are known, the compiler would perform a
-derived-to-base conversion for object <code>a</code> if necessary. I don't know
-whether this is desirable, in particular since also other conversions
-could happen here that one would not want (in the extreme case
-generating a temporary)..
-</p>
-
-
-<h4>c) Conversions between class types II</h4>
-
-<p>
-When one writes
-<code><pre>
- spawn (this, &X::f)
-</pre></code>
-one gets an error that "'this' is not convertible to type X&". One has
-to write <code>*this<code> instead. It would be simple to have another set of
-overloads of <code>spawn()</code> that accepts a pointer instead of a reference,
-and simply forwards to the existing function. This is just for the
-lazy people, probably, but it is a common case.
-</p>
-
-
-<h4>d) Catching exceptions</h4>
-
-<p>
-When a function on a new thread throws an exception, it only
-propagates up to one of the two <code>entry_point()</code> functions, then vanishes
-into the run-time system and kills the program. Ideally, we would have
-a way to pass it over to the main thread. This, however, would need
-some support from the language. Basically, we would need two
-operations:
-<ul>
-<li>clone an exception without knowing its type; we could then in the
- <code>entry_point</code> function catch it and stack it somewhere, just like we
- do for the return value</li>
-<li>back on the main thread, the <code>Thread::join()</code> function must raise this
- stored exception if there was one, again without knowing its type.</li>
-</ul>
-Given how exceptions are implemented usually, the machinery for these
-operations is probably there, but is not exported to the user through
-the run-time environment. Thus, an implementation of such ideas has to
-wait for changes in the language specification.
-</p>
-
-
-<HR>
-
-<div ALIGN="RIGHT">
-Wolfgang Bangerth, 2003
-</div>
-<p> </P></BODY>
-</HTML>
-
-
-
-</BODY>
-</HTML>
-
--- /dev/null
+This folder contains example programs for deal.II
+
+They are distributed under the same license as the deal.II library itself,
+namely LGPL-2.1+.
#!/bin/sh
+## ---------------------------------------------------------------------
+## $Id$
+##
+## Copyright (C) 2006 - 2013 by the deal.II authors
+##
+## This file is part of the deal.II library.
+##
+## The deal.II library is free software; you can use it, redistribute
+## it, and/or modify it under the terms of the GNU Lesser General
+## Public License as published by the Free Software Foundation; either
+## version 2.1 of the License, or (at your option) any later version.
+## The full text of the license can be found in the file LICENSE at
+## the top level of the deal.II distribution.
+##
+## ---------------------------------------------------------------------
+
+#
+# Author: Ivan Christov, Wolfgang Bangerth, Texas A&M University, 2006
+#
+
dim=1
tstep=0
tstepinc=20
gnuplot -persist $batchfile
# use ImageMagick to create an animated gif from the PNG files
-convert -delay 0 -loop 0 "solution-"$dim"d-*.png" "solution-"$dim"d.gif"
\ No newline at end of file
+convert -delay 0 -loop 0 "solution-"$dim"d-*.png" "solution-"$dim"d.gif"
break;
}
- old_solution = solution;
solution = tmp_vector;
+ old_solution = solution;
}
old_active_set = active_set;
#include <deal.II/base/config.h>
+#include <deal.II/base/thread_management.h>
#include <deal.II/base/std_cxx1x/function.h>
#include <deal.II/dofs/dof_handler.h>
#include <boost/unordered_map.hpp>
DEAL_II_NAMESPACE_OPEN
-/// This namespace contains the functions necessary to color a graph.
-namespace graph_coloring {
-
- /**
- * Create the partitioning using a simplified version of the Cuthill-McKee
- * algorithm (Breadth First Search algorithm).
- */
- template <typename Iterator>
- std::vector<std::vector<Iterator> > create_partitioning(Iterator const &begin,
- typename identity<Iterator>::type const &end,
- std_cxx1x::function<std::vector<types::global_dof_index> (Iterator const &)>
- const &get_conflict_indices)
+/**
+ * A namespace containing functions that can color graphs.
+ */
+namespace GraphColoring
+{
+ namespace internal
{
- std::vector<std::vector<Iterator> > partitioning(1,std::vector<Iterator> (1,begin));
- // Number of iterators.
- unsigned int n_iterators(0);
- // Create a map from conflict indices to iterators
- boost::unordered_map<types::global_dof_index,std::vector<Iterator> > indices_to_iterators;
- for (Iterator it=begin; it!=end; ++it)
+ /**
+ * Create a partitioning of the given range of iterators using a simplified
+ * version of the Cuthill-McKee algorithm (Breadth First Search algorithm).
+ * The function creates partitions that contain "zones" of iterators
+ * where the first partition contains the first iterator, the second
+ * zone contains all those iterators that have conflicts with the single
+ * element in the first zone, the third zone contains those iterators that
+ * have conflicts with the iterators of the second zone and have not previously
+ * been assigned to a zone, etc. If the iterators represent cells, then this
+ * generates partitions that are like onion shells around the very first
+ * cell. Note that elements in each zone may conflict with other elements in
+ * the same zone.
+ *
+ * The question whether two iterators conflict is determined by a user-provided
+ * function. The meaning of this function is discussed in the documentation of
+ * the GraphColoring::make_graph_coloring() function.
+ *
+ * @param[in] begin The first element of a range of iterators for which a
+ * partitioning is sought.
+ * @param[in] end The element past the end of the range of iterators.
+ * @param[in] get_conflict_indices A user defined function object returning
+ * a set of indicators that are descriptive of what represents a
+ * conflict. See above for a more thorough discussion.
+ * @return A set of sets of iterators (where sets are represented by
+ * std::vector for efficiency). Each element of the outermost set
+ * corresponds to the iterators pointing to objects that are in the
+ * same partition (i.e., the same zone).
+ *
+ * @author Martin Kronbichler, Bruno Turcksin
+ */
+ template <typename Iterator>
+ std::vector<std::vector<Iterator> >
+ create_partitioning(const Iterator &begin,
+ const typename identity<Iterator>::type &end,
+ const std_cxx1x::function<std::vector<types::global_dof_index> (const Iterator &)> &get_conflict_indices)
{
- std::vector<types::global_dof_index> conflict_indices = get_conflict_indices(it);
- const unsigned int n_conflict_indices(conflict_indices.size());
- for (unsigned int i=0; i<n_conflict_indices; ++i)
- indices_to_iterators[conflict_indices[i]].push_back(it);
- ++n_iterators;
- }
+ // Number of iterators.
+ unsigned int n_iterators = 0;
- // Create the partitioning.
- std::set<Iterator> used_it;
- used_it.insert(begin);
- while (used_it.size()!=n_iterators)
- {
- typename std::vector<Iterator>::iterator vector_it(partitioning.back().begin());
- typename std::vector<Iterator>::iterator vector_end(partitioning.back().end());
- std::vector<Iterator> new_zone;
- for (; vector_it!=vector_end; ++vector_it)
- {
- std::vector<types::global_dof_index> conflict_indices = get_conflict_indices(*vector_it);
- const unsigned int n_conflict_indices(conflict_indices.size());
- for (unsigned int i=0; i<n_conflict_indices; ++i)
+ // Create a map from conflict indices to iterators
+ boost::unordered_map<types::global_dof_index,std::vector<Iterator> > indices_to_iterators;
+ for (Iterator it=begin; it!=end; ++it)
{
- std::vector<Iterator> iterator_vector(indices_to_iterators[conflict_indices[i]]);
- for (unsigned int j=0; j<iterator_vector.size(); ++j)
- {
- // Check that the iterator is not associated to a zone yet.
- if (used_it.count(iterator_vector[j])==0)
+ const std::vector<types::global_dof_index> conflict_indices = get_conflict_indices(it);
+ const unsigned int n_conflict_indices = conflict_indices.size();
+ for (unsigned int i=0; i<n_conflict_indices; ++i)
+ indices_to_iterators[conflict_indices[i]].push_back(it);
+ ++n_iterators;
+ }
+
+ // create the very first zone which contains only the first
+ // iterator. then create the other zones. keep track of all the
+ // iterators that have already been assigned to a zone
+ std::vector<std::vector<Iterator> > zones(1,std::vector<Iterator> (1,begin));
+ std::set<Iterator> used_it;
+ used_it.insert(begin);
+ while (used_it.size()!=n_iterators)
+ {
+ // loop over the elements of the previous zone. for each element of
+ // the previous zone, get the conflict indices and from there get
+ // those iterators that are conflicting with the current element
+ typename std::vector<Iterator>::iterator previous_zone_it(zones.back().begin());
+ typename std::vector<Iterator>::iterator previous_zone_end(zones.back().end());
+ std::vector<Iterator> new_zone;
+ for (; previous_zone_it!=previous_zone_end; ++previous_zone_it)
{
- new_zone.push_back(iterator_vector[j]);
- used_it.insert(iterator_vector[j]);
+ std::vector<types::global_dof_index> conflict_indices = get_conflict_indices(*previous_zone_it);
+ const unsigned int n_conflict_indices(conflict_indices.size());
+ for (unsigned int i=0; i<n_conflict_indices; ++i)
+ {
+ const std::vector<Iterator> &conflicting_elements
+ = indices_to_iterators[conflict_indices[i]];
+ for (unsigned int j=0; j<conflicting_elements.size(); ++j)
+ {
+ // check that the iterator conflicting with the current one is not
+ // associated to a zone yet and if so, assign it to the current
+ // zone. mark it as used
+ //
+ // we can shortcut this test if the conflicting iterator is the
+ // current iterator
+ if ((conflicting_elements[j] != *previous_zone_it)
+ &&
+ (used_it.count(conflicting_elements[j])==0))
+ {
+ new_zone.push_back(conflicting_elements[j]);
+ used_it.insert(conflicting_elements[j]);
+ }
+ }
+ }
}
- }
+
+ // If there are iterators in the new zone, then the zone is added to the
+ // partition. Otherwise, the graph is disconnected and we need to find
+ // an iterator on the other part of the graph. start the whole process again
+ // with the first iterator that hasn't been assigned to a zone yet
+ if (new_zone.size()!=0)
+ zones.push_back(new_zone);
+ else
+ for (Iterator it=begin; it!=end; ++it)
+ if (used_it.count(it)==0)
+ {
+ zones.push_back(std::vector<Iterator> (1,it));
+ used_it.insert(it);
+ break;
+ }
}
- }
- // If there are iterators in the new zone, then the zone is added to the
- // partition. Otherwise, the graph is disconnected and we need to find
- // an iterator on the other part of the graph.
- if (new_zone.size()!=0)
- partitioning.push_back(new_zone);
- else
- for (Iterator it=begin; it!=end; ++it)
- if (used_it.count(it)==0)
- {
- partitioning.push_back(std::vector<Iterator> (1,it));
- break;
- }
- }
- return partitioning;
- }
+ return zones;
+ }
- /**
- * This function uses DSATUR (Degree SATURation) to color one zone of the
- * partition. DSATUR works as follows:
- * -# Arrange the vertices by decreasing order of degrees.
- * -# Color a vertex of maximal degree with color 1.
- * -# Choose a vertex with a maximal saturation degree. If there is equality,
- * choose any vertex of maximal degree in the uncolored subgraph.
- * -# Color the chosen vertex with the least possible (lowest numbered) color.
- * -# If all the vertices are colored, stop. Otherwise, return to 3.
- */
- template <typename Iterator>
- std::vector<std::vector<Iterator> > make_dsatur_coloring(std::vector<Iterator> &partition,
- std_cxx1x::function<std::vector<types::global_dof_index> (Iterator const &)>
- const &get_conflict_indices)
- {
- std::vector<std::vector<Iterator> > partition_coloring;
- // Number of zones composing the partitioning.
- const unsigned int partition_size(partition.size());
- std::vector<unsigned int> sorted_vertices(partition_size);
- std::vector<int> degrees(partition_size);
- std::vector<std::vector<types::global_dof_index> > conflict_indices(partition_size);
- std::vector<std::vector<unsigned int> > graph(partition_size);
-
- // Get the conflict indices associated to each iterator. The conflict_indices have to be sorted so
- // set_intersection can be used later.
- for (unsigned int i=0; i<partition_size; ++i)
+ /**
+ * This function uses DSATUR (Degree SATURation) to color the elements of
+ * a set. DSATUR works as follows:
+ * -# Arrange the vertices by decreasing order of degrees.
+ * -# Color a vertex of maximal degree with color 1.
+ * -# Choose a vertex with a maximal saturation degree. If there is equality,
+ * choose any vertex of maximal degree in the uncolored subgraph.
+ * -# Color the chosen vertex with the least possible (lowest numbered) color.
+ * -# If all the vertices are colored, stop. Otherwise, return to 3.
+ *
+ * @param[in] partition The set of iterators that should be colored.
+ * @param[in] get_conflict_indices A user defined function object returning
+ * a set of indicators that are descriptive of what represents a
+ * conflict. See above for a more thorough discussion.
+ * @param[out] partition_coloring A set of sets of iterators (where sets are represented by
+ * std::vector for efficiency). Each element of the outermost set
+ * corresponds to the iterators pointing to objects that are in the
+ * same partition (have the same color) and consequently do not
+ * conflict. The elements of different sets may conflict.
+ */
+ template <typename Iterator>
+ void
+ make_dsatur_coloring(std::vector<Iterator> &partition,
+ const std_cxx1x::function<std::vector<types::global_dof_index> (const Iterator &)> &get_conflict_indices,
+ std::vector<std::vector<Iterator> > &partition_coloring)
{
- conflict_indices[i] = get_conflict_indices(partition[i]);
- std::sort(conflict_indices[i].begin(),conflict_indices[i].end());
- }
-
- // Compute the degree of each vertex of the graph using the
- // intersection of the conflict indices.
- std::vector<types::global_dof_index> conflict_indices_intersection;
- std::vector<types::global_dof_index>::iterator intersection_it;
- for (unsigned int i=0; i<partition_size; ++i)
- for (unsigned int j=i+1; j<partition_size; ++j)
- {
- conflict_indices_intersection.resize(std::max(conflict_indices[i].size(),
- conflict_indices[j].size()));
- intersection_it = std::set_intersection(conflict_indices[i].begin(),
- conflict_indices[i].end(),conflict_indices[j].begin(),
- conflict_indices[j].end(),conflict_indices_intersection.begin());
- // If the two iterators share indices then we increase the degree of the
- // vertices and create an ''edge'' in the graph.
- if (intersection_it!=conflict_indices_intersection.begin())
+ partition_coloring.clear ();
+
+ // Number of zones composing the partitioning.
+ const unsigned int partition_size(partition.size());
+ std::vector<unsigned int> sorted_vertices(partition_size);
+ std::vector<int> degrees(partition_size);
+ std::vector<std::vector<types::global_dof_index> > conflict_indices(partition_size);
+ std::vector<std::vector<unsigned int> > graph(partition_size);
+
+ // Get the conflict indices associated to each iterator. The conflict_indices have to be sorted so
+ // set_intersection can be used later.
+ for (unsigned int i=0; i<partition_size; ++i)
{
- ++degrees[i];
- ++degrees[j];
- graph[i].push_back(j);
- graph[j].push_back(i);
+ conflict_indices[i] = get_conflict_indices(partition[i]);
+ std::sort(conflict_indices[i].begin(),conflict_indices[i].end());
}
- }
-
- // Sort the vertices by decreasing degree.
- std::vector<int>::iterator degrees_it;
- for (unsigned int i=0; i<partition_size; ++i)
- {
- // Find the largest element.
- degrees_it = std::max_element(degrees.begin(),degrees.end());
- sorted_vertices[i] = degrees_it-degrees.begin();
- // Put the largest element to -1 so it cannot be chosen again.
- *degrees_it = -1;
- }
- // Color the graph.
- std::vector<boost::unordered_set<unsigned int> > colors_used;
- for (unsigned int i=0; i<partition_size; ++i)
- {
- const unsigned int current_vertex(sorted_vertices[i]);
- bool new_color(true);
- // Try to use an existing color, i.e., try to find a color which is not
- // associated to one of the vertices linked to current_vertex.
- // Loop over the color.
- for (unsigned int j=0; j<partition_coloring.size(); ++j)
- {
- // Loop on the vertices linked to current_vertex. If one vertex linked
- // to current_vertex is already using the color j, this color cannot
- // be used anymore.
- bool unused_color(true);
- for (unsigned int k=0; k<graph[current_vertex].size(); ++k)
- if (colors_used[j].count(graph[current_vertex][k])==1)
+ // Compute the degree of each vertex of the graph using the
+ // intersection of the conflict indices.
+ std::vector<types::global_dof_index> conflict_indices_intersection;
+ std::vector<types::global_dof_index>::iterator intersection_it;
+ for (unsigned int i=0; i<partition_size; ++i)
+ for (unsigned int j=i+1; j<partition_size; ++j)
{
- unused_color = false;
- break;
+ conflict_indices_intersection.resize(std::max(conflict_indices[i].size(),
+ conflict_indices[j].size()));
+ intersection_it = std::set_intersection(conflict_indices[i].begin(),
+ conflict_indices[i].end(),
+ conflict_indices[j].begin(),
+ conflict_indices[j].end(),
+ conflict_indices_intersection.begin());
+ // If the two iterators share indices then we increase the degree of the
+ // vertices and create an ''edge'' in the graph.
+ if (intersection_it!=conflict_indices_intersection.begin())
+ {
+ ++degrees[i];
+ ++degrees[j];
+ graph[i].push_back(j);
+ graph[j].push_back(i);
+ }
}
- if (unused_color)
+
+ // Sort the vertices by decreasing degree.
+ std::vector<int>::iterator degrees_it;
+ for (unsigned int i=0; i<partition_size; ++i)
{
- partition_coloring[j].push_back(partition[current_vertex]);
- colors_used[j].insert(current_vertex);
- new_color = false;
- break;
+ // Find the largest element.
+ degrees_it = std::max_element(degrees.begin(),degrees.end());
+ sorted_vertices[i] = degrees_it-degrees.begin();
+ // Put the largest element to -1 so it cannot be chosen again.
+ *degrees_it = -1;
}
- }
- // Add a new color.
- if (new_color)
- {
- partition_coloring.push_back(std::vector<Iterator> (1,
- partition[current_vertex]));
- boost::unordered_set<unsigned int> tmp;
- tmp.insert(current_vertex);
- colors_used.push_back(tmp);
- }
- }
- return partition_coloring;
- }
+ // Color the graph.
+ std::vector<boost::unordered_set<unsigned int> > colors_used;
+ for (unsigned int i=0; i<partition_size; ++i)
+ {
+ const unsigned int current_vertex(sorted_vertices[i]);
+ bool new_color(true);
+ // Try to use an existing color, i.e., try to find a color which is not
+ // associated to one of the vertices linked to current_vertex.
+ // Loop over the color.
+ for (unsigned int j=0; j<partition_coloring.size(); ++j)
+ {
+ // Loop on the vertices linked to current_vertex. If one vertex linked
+ // to current_vertex is already using the color j, this color cannot
+ // be used anymore.
+ bool unused_color(true);
+ for (unsigned int k=0; k<graph[current_vertex].size(); ++k)
+ if (colors_used[j].count(graph[current_vertex][k])==1)
+ {
+ unused_color = false;
+ break;
+ }
+ if (unused_color)
+ {
+ partition_coloring[j].push_back(partition[current_vertex]);
+ colors_used[j].insert(current_vertex);
+ new_color = false;
+ break;
+ }
+ }
+ // Add a new color.
+ if (new_color)
+ {
+ partition_coloring.push_back(std::vector<Iterator> (1,
+ partition[current_vertex]));
+ boost::unordered_set<unsigned int> tmp;
+ tmp.insert(current_vertex);
+ colors_used.push_back(tmp);
+ }
+ }
+ }
- /**
- * Given a partition-coloring graph, gather the colors together. All the
- * colors on even (resp. odd) partition can be executed simultaneously. This
- * function tries to create colors of similar number of elements.
- */
- template <typename Iterator>
- std::vector<std::vector<Iterator> >
- gather_colors(std::vector<std::vector<std::vector<Iterator> > > const &partition_coloring)
- {
- std::vector<std::vector<Iterator> > coloring;
-
- // Count the number of iterators in each color.
- const unsigned int partition_size(partition_coloring.size());
- std::vector<std::vector<unsigned int> > colors_counter(partition_size);
- for (unsigned int i=0; i<partition_size; ++i)
+ /**
+ * Given a partition-coloring graph, i.e., a set of zones (partitions) each
+ * of which is colored, produce a combined coloring for the entire set of
+ * iterators. This is possible because any color on an
+ * even (resp. odd) zone does not conflict with any color of any other even
+ * (resp. odd) zone. Consequently, we can combine colors from all even and all
+ * odd zones. This function tries to create colors of similar number of elements.
+ */
+ template <typename Iterator>
+ std::vector<std::vector<Iterator> >
+ gather_colors(const std::vector<std::vector<std::vector<Iterator> > > &partition_coloring)
{
- const unsigned int n_colors(partition_coloring[i].size());
- colors_counter[i].resize(n_colors);
- for (unsigned int j=0; j<n_colors; ++j)
- colors_counter[i][j] = partition_coloring[i][j].size();
- }
+ std::vector<std::vector<Iterator> > coloring;
- // Find the partition with the largest number of colors for the even partition.
- unsigned int i_color(0);
- unsigned int max_even_n_colors(0);
- const unsigned int colors_size(colors_counter.size());
- for (unsigned int i=0; i<colors_size; i+=2)
- {
- if (max_even_n_colors<colors_counter[i].size())
- {
- max_even_n_colors = colors_counter[i].size();
- i_color = i;
- }
- }
- coloring.resize(max_even_n_colors);
- for (unsigned int j=0; j<colors_counter[i_color].size(); ++j)
- coloring[j] = partition_coloring[i_color][j];
+ // Count the number of iterators in each color.
+ const unsigned int partition_size(partition_coloring.size());
+ std::vector<std::vector<unsigned int> > colors_counter(partition_size);
+ for (unsigned int i=0; i<partition_size; ++i)
+ {
+ const unsigned int n_colors(partition_coloring[i].size());
+ colors_counter[i].resize(n_colors);
+ for (unsigned int j=0; j<n_colors; ++j)
+ colors_counter[i][j] = partition_coloring[i][j].size();
+ }
- for (unsigned int i=0; i<partition_size; i+=2)
- {
- if (i!=i_color)
- {
- boost::unordered_set<unsigned int> used_k;
- for (unsigned int j=0; j<colors_counter[i].size(); ++j)
+ // Find the partition with the largest number of colors for the even partition.
+ unsigned int i_color(0);
+ unsigned int max_even_n_colors(0);
+ const unsigned int colors_size(colors_counter.size());
+ for (unsigned int i=0; i<colors_size; i+=2)
{
- // Find the color in the current partition with the largest number of
- // iterators.
- std::vector<unsigned int>::iterator it;
- it = std::max_element(colors_counter[i].begin(),colors_counter[i].end());
- unsigned int min_iterators(-1);
- unsigned int pos(0);
- // Find the color of coloring with the least number of colors among
- // the colors that have not been used yet.
- for (unsigned int k=0; k<max_even_n_colors; ++k)
- if (used_k.count(k)==0)
- if (colors_counter[i_color][k]<min_iterators)
- {
- min_iterators = colors_counter[i_color][k];
- pos = k;
- }
- colors_counter[i_color][pos] += *it;
- // Concatenate the current color with the existing coloring.
- coloring[pos].insert(coloring[pos].end(),
- partition_coloring[i][it-colors_counter[i].begin()].begin(),
- partition_coloring[i][it-colors_counter[i].begin()].end());
- used_k.insert(pos);
- // Put the number of iterators to the current color to zero.
- *it = 0;
+ if (max_even_n_colors<colors_counter[i].size())
+ {
+ max_even_n_colors = colors_counter[i].size();
+ i_color = i;
+ }
}
- }
- }
+ coloring.resize(max_even_n_colors);
+ for (unsigned int j=0; j<colors_counter[i_color].size(); ++j)
+ coloring[j] = partition_coloring[i_color][j];
- // Do the same thing that we did for the even partitions to the odd
- // partitions
- unsigned int max_odd_n_colors(0);
- for (unsigned int i=1; i<partition_size; i+=2)
- {
- if (max_odd_n_colors<colors_counter[i].size())
- {
- max_odd_n_colors = colors_counter[i].size();
- i_color = i;
- }
- }
- coloring.resize(max_even_n_colors+max_odd_n_colors);
- for (unsigned int j=0; j<colors_counter[i_color].size(); ++j)
- coloring[max_even_n_colors+j] = partition_coloring[i_color][j];
+ for (unsigned int i=0; i<partition_size; i+=2)
+ {
+ if (i!=i_color)
+ {
+ boost::unordered_set<unsigned int> used_k;
+ for (unsigned int j=0; j<colors_counter[i].size(); ++j)
+ {
+ // Find the color in the current partition with the largest number of
+ // iterators.
+ std::vector<unsigned int>::iterator it;
+ it = std::max_element(colors_counter[i].begin(),colors_counter[i].end());
+ unsigned int min_iterators(-1);
+ unsigned int pos(0);
+ // Find the color of coloring with the least number of colors among
+ // the colors that have not been used yet.
+ for (unsigned int k=0; k<max_even_n_colors; ++k)
+ if (used_k.count(k)==0)
+ if (colors_counter[i_color][k]<min_iterators)
+ {
+ min_iterators = colors_counter[i_color][k];
+ pos = k;
+ }
+ colors_counter[i_color][pos] += *it;
+ // Concatenate the current color with the existing coloring.
+ coloring[pos].insert(coloring[pos].end(),
+ partition_coloring[i][it-colors_counter[i].begin()].begin(),
+ partition_coloring[i][it-colors_counter[i].begin()].end());
+ used_k.insert(pos);
+ // Put the number of iterators to the current color to zero.
+ *it = 0;
+ }
+ }
+ }
- for (unsigned int i=1; i<partition_size; i+=2)
- {
- if (i!=i_color)
- {
- boost::unordered_set<unsigned int> used_k;
- for (unsigned int j=0; j<colors_counter[i].size(); ++j)
+ // If there is more than one partition, do the same thing that we did for the even partitions
+ // to the odd partitions
+ if (partition_size>1)
{
- // Find the color in the current partition with the largest number of
- // iterators.
- std::vector<unsigned int>::iterator it;
- it = std::max_element(colors_counter[i].begin(),colors_counter[i].end());
- unsigned int min_iterators(-1);
- unsigned int pos(0);
- // Find the color of coloring with the least number of colors among
- // the colors that have not been used yet.
- for (unsigned int k=0; k<max_odd_n_colors; ++k)
- if (used_k.count(k)==0)
- if (colors_counter[i_color][k]<min_iterators)
- {
- min_iterators = colors_counter[i_color][k];
- pos = k;
- }
- colors_counter[i_color][pos] += *it;
- // Concatenate the current color with the existing coloring.
- coloring[max_even_n_colors+pos].insert(coloring[max_even_n_colors+pos].end(),
- partition_coloring[i][it-colors_counter[i].begin()].begin(),
- partition_coloring[i][it-colors_counter[i].begin()].end());
- used_k.insert(pos);
- // Put the number of iterators to the current color to zero.
- *it = 0;
+ unsigned int max_odd_n_colors(0);
+ for (unsigned int i=1; i<partition_size; i+=2)
+ {
+ if (max_odd_n_colors<colors_counter[i].size())
+ {
+ max_odd_n_colors = colors_counter[i].size();
+ i_color = i;
+ }
+ }
+ coloring.resize(max_even_n_colors+max_odd_n_colors);
+ for (unsigned int j=0; j<colors_counter[i_color].size(); ++j)
+ coloring[max_even_n_colors+j] = partition_coloring[i_color][j];
+
+ for (unsigned int i=1; i<partition_size; i+=2)
+ {
+ if (i!=i_color)
+ {
+ boost::unordered_set<unsigned int> used_k;
+ for (unsigned int j=0; j<colors_counter[i].size(); ++j)
+ {
+ // Find the color in the current partition with the largest number of
+ // iterators.
+ std::vector<unsigned int>::iterator it;
+ it = std::max_element(colors_counter[i].begin(),colors_counter[i].end());
+ unsigned int min_iterators(-1);
+ unsigned int pos(0);
+ // Find the color of coloring with the least number of colors among
+ // the colors that have not been used yet.
+ for (unsigned int k=0; k<max_odd_n_colors; ++k)
+ if (used_k.count(k)==0)
+ if (colors_counter[i_color][k]<min_iterators)
+ {
+ min_iterators = colors_counter[i_color][k];
+ pos = k;
+ }
+ colors_counter[i_color][pos] += *it;
+ // Concatenate the current color with the existing coloring.
+ coloring[max_even_n_colors+pos].insert(coloring[max_even_n_colors+pos].end(),
+ partition_coloring[i][it-colors_counter[i].begin()].begin(),
+ partition_coloring[i][it-colors_counter[i].begin()].end());
+ used_k.insert(pos);
+ // Put the number of iterators to the current color to zero.
+ *it = 0;
+ }
+ }
+ }
}
- }
- }
- return coloring;
+ return coloring;
+ }
}
-
/**
- * This function creates a coloring given two iterators on the DoFHandler
- * and a function that return the conflict indices given an iterator. When
- * using continuous finite elements, the conflict_indices can be the dofs
- * indices.
+ * Create a partitioning of the given range of iterators so that
+ * iterators that point to conflicting objects will be placed
+ * into different partitions, where the question whether two objects conflict
+ * is determined by a user-provided function.
+ *
+ * This function can also be considered as a graph coloring: each object
+ * pointed to by an iterator is considered to be a node and there is an
+ * edge between each two nodes that conflict. The graph coloring algorithm
+ * then assigns a color to each node in such a way that two nodes connected
+ * by an edge do not have the same color.
+ *
+ * A typical use case for this function is in assembling a matrix in parallel.
+ * There, one would like to assemble local contributions on different cells
+ * at the same time (an operation that is purely local and so requires
+ * no synchronization) but then we need to add these local contributions
+ * to the global matrix. In general, the contributions from different cells
+ * may be to the same matrix entries if the cells share degrees of freedom
+ * and, consequently, can not happen at the same time unless we want to
+ * risk a race condition (see http://en.wikipedia.org/wiki/Race_condition ).
+ * Thus, we call these two cells in conflict, and we can only allow operations
+ * in parallel from cells that do not conflict. In other words, two cells
+ * are in conflict if the set of matrix entries (for example characterized
+ * by the rows) have a nonempty intersection.
+ *
+ * In this generality, computing the graph of conflicts would require calling
+ * a function that determines whether two iterators (or the two objects they
+ * represent) conflict, and calling it for every pair of iterators, i.e.,
+ * $\frac 12 N (N-1)$ times. This is too expensive in general. A better
+ * approach is to require a user-defined function that returns for every
+ * iterator it is called for a set of indicators of some kind that characterize
+ * a conflict; two iterators are in conflict if their conflict indicator sets
+ * have a nonempty intersection. In the example of assembling a matrix,
+ * the conflict indicator set would contain the indices of all degrees of
+ * freedom on the cell pointed to (in the case of continuous Galerkin methods)
+ * or the union of indices of degree of freedom on the current cell and all
+ * cells adjacent to the faces of the current cell (in the case of
+ * discontinuous Galerkin methods, because there one computes face integrals
+ * coupling the degrees of freedom connected by a common face -- see step-12).
+ *
+ * @note The conflict set returned by the user defined function passed as
+ * third argument needs to accurately describe <i>all</i> degrees of
+ * freedom for which anything is written into the matrix or right hand side.
+ * In other words, if the writing happens through a function like
+ * ConstraintMatrix::copy_local_to_global(), then the set of conflict indices
+ * must actually contain not only the degrees of freedom on the current
+ * cell, but also those they are linked to by constraints such as hanging
+ * nodes.
+ *
+ * In other situations, the conflict indicator sets may represent
+ * something different altogether -- it is up to the caller of this function
+ * to describe what it means for two iterators to conflict. Given this,
+ * computing conflict graph edges can be done significantly more cheaply
+ * than with ${\cal O}(N^2)$ operations.
+ *
+ * In any case, the result of the function will be so that iterators whose
+ * conflict indicator sets have overlap will not be assigned to the same
+ * color.
+ *
+ * @param[in] begin The first element of a range of iterators for which a
+ * coloring is sought.
+ * @param[in] end The element past the end of the range of iterators.
+ * @param[in] get_conflict_indices A user defined function object returning
+ * a set of indicators that are descriptive of what represents a
+ * conflict. See above for a more thorough discussion.
+ * @return A set of sets of iterators (where sets are represented by
+ * std::vector for efficiency). Each element of the outermost set
+ * corresponds to the iterators pointing to objects that are in the
+ * same partition (have the same color) and consequently do not
+ * conflict. The elements of different sets may conflict.
+ *
+ * @author Martin Kronbichler, Bruno Turcksin
*/
template <typename Iterator>
- std::vector<std::vector<Iterator> >
- make_graph_coloring(Iterator const &begin,typename identity<Iterator>::type const &end,
- std_cxx1x::function<std::vector<types::global_dof_index> (Iterator const &)>
- const &get_conflict_indices)
+ std::vector<std::vector<Iterator> >
+ make_graph_coloring(const Iterator &begin,
+ const typename identity<Iterator>::type &end,
+ const std_cxx1x::function<std::vector<types::global_dof_index> (const typename identity<Iterator>::type &)> &get_conflict_indices)
{
+ Assert (begin != end, ExcMessage ("GraphColoring is not prepared to deal with empty ranges!"));
+
// Create the partitioning.
- std::vector<std::vector<Iterator> > partitioning = create_partitioning(begin,end,
- get_conflict_indices);
+ std::vector<std::vector<Iterator> >
+ partitioning = internal::create_partitioning (begin,
+ end,
+ get_conflict_indices);
// Color the iterators within each partition.
+ // Run the coloring algorithm on each zone in parallel
const unsigned int partitioning_size(partitioning.size());
- std::vector<std::vector<std::vector<Iterator> > > partition_coloring(
- partitioning_size);
- for (unsigned int i=0; i<partitioning_size; ++i)
- {
- // Compute the coloring of the graph using the DSATUR algorithm
- partition_coloring[i] = make_dsatur_coloring(partitioning[i],get_conflict_indices);
- }
+ std::vector<std::vector<std::vector<Iterator> > >
+ partition_coloring(partitioning_size);
- // Gather the colors together.
- std::vector<std::vector<Iterator> > coloring = gather_colors(partition_coloring);
-
- return coloring;
+ Threads::TaskGroup<> tasks;
+ for (unsigned int i=0; i<partitioning_size; ++i)
+ tasks += Threads::new_task (&internal::make_dsatur_coloring<Iterator>,
+ partitioning[i],
+ get_conflict_indices,
+ partition_coloring[i]);
+ tasks.join_all();
+
+ // Gather the colors together.
+ return internal::gather_colors(partition_coloring);
}
} // End graph_coloring namespace
DEAL_II_NAMESPACE_OPEN
//TODO: Allow long input lines to be broken by appending a backslash character
-//TODO: Provide an "include" command for parameter files
// public classes; to be declared below
* While we have only one of these
* objects per thread, several
* Threads::Thread objects may refer to
- * this descriptor.
- *
- * Note, however, that since this
- * object holds the location
- * where we store the return
- * value of the thread, the
- * object has to live at least as
- * long as the thread
- * executes. This means that even
- * if all Threads::Thread objects
- * that referred to this
- * descriptor (through a
- * std::shared_ptr) have gone out
- * of scope, we must still hold
- * on to the object. We do this
- * by having the descriptor keep
- * a pointer to itself and reset
- * it to zero once it is done --
- * effectively keeping the use
- * pointer above zero as long as
- * work is going on.
- *
- * To enable the current class to
- * obtain a shared_ptr from
- * itself, we derive from the
- * class
- * std::enable_shared_from_this.
+ * this descriptor. If all Thread
+ * objects go out of scope the
+ * ThreadDescriptor will detach from
+ * the thread before being destructed.
*/
template <typename RT>
- struct ThreadDescriptor : public std_cxx1x::enable_shared_from_this<ThreadDescriptor<RT> >
+ struct ThreadDescriptor
{
- /**
- * A pointer to the current
- * object, kept nonzero as
- * long as the thread is
- * executing to avoid
- * destroying the current
- * object while we are still
- * expecting to write
- * something into the return
- * value location.
- */
- std_cxx1x::shared_ptr<ThreadDescriptor<RT> > self;
-
/**
* An object that represents the
* thread started.
* An object that will hold the value
* returned by the function called on
* the thread.
+ *
+ * The return value is stored
+ * in a shared_ptr because we might
+ * abandon the the ThreadDescriptor.
+ * This makes sure the object stays
+ * alive until the thread exits.
*/
- return_value<RT> ret_val;
+ std_cxx1x::shared_ptr<return_value<RT> > ret_val;
/**
* A bool variable that is initially
thread_is_active (false)
{}
+ ~ThreadDescriptor ()
+ {
+ if (!thread_is_active)
+ return;
+ thread.detach();
+ thread_is_active = false;
+ }
/**
* Start the thread and let
* it put its return value
* into the ret_val object.
- *
- * Note that we cannot
- * already do this in the
- * constructor of this class:
- * we will call
- * enable_shared_from_this::shared_from_this
- * which requires that there
- * is already a shared_ptr
- * that owns this object;
- * however, at the time of
- * creation, there can of
- * course be no shared_ptr
- * that owns the object -- it
- * is, after all, just being
- * created and can not
- * already have been handed
- * off to a shared_ptr; as a
- * consequence, we first
- * create the object, give it
- * to a shared_ptr, and then
- * call shared_from_this.
*/
void start (const std_cxx1x::function<RT ()> &function)
{
- // set the self pointer
- // and then start the
- // thread
- self = this->shared_from_this ();
thread_is_active = true;
- thread = std_cxx1x::thread (thread_entry_point, function, this);
+ ret_val.reset(new return_value<RT>());
+ thread = std_cxx1x::thread (thread_entry_point, function, ret_val);
}
*/
static
void thread_entry_point (const std_cxx1x::function<RT ()> function,
- ThreadDescriptor<RT> *descriptor)
+ std_cxx1x::shared_ptr<return_value<RT> > ret_val)
{
// call the function
// in question. since an
internal::register_thread ();
try
{
- call (function, descriptor->ret_val);
+ call (function, *ret_val);
}
catch (const std::exception &exc)
{
internal::handle_unknown_exception ();
}
internal::deregister_thread ();
-
- // once we are done,
- // we can release our
- // hold on the thread
- // descriptor
- // object. if all
- // Threads::Thread
- // objects that
- // pointed here
- // should have gone
- // out of scope
- // already, then this
- // will trigger
- // destruction of the
- // descriptor object
- Assert (descriptor->self.use_count () > 0,
- ExcInternalError());
- descriptor->self.reset ();
}
};
* returned by the function called on
* the thread.
*/
- return_value<RT> ret_val;
+ std_cxx1x::shared_ptr<return_value<RT> > ret_val;
/**
* Start the thread and
*/
void start (const std_cxx1x::function<RT ()> &function)
{
- call (function, ret_val);
+ ret_val.reset(new return_value<RT>());
+ call (function, *ret_val);
}
/**
thread_descriptor (new internal::ThreadDescriptor<RT>())
{
// in a second step, start
- // the thread. this needs
- // to be done in two steps
- // because inside the start
- // function we call
- // enable_shared_from_this::shared_from_this
- // which requires that
- // there is already a
- // shared_ptr that owns the
- // object
+ // the thread.
thread_descriptor->start (function);
}
RT return_value ()
{
join ();
- return thread_descriptor->ret_val.get();
+ return thread_descriptor->ret_val->get();
}
/**
* sure that that object lives
* as long as there is at least
* one subscriber to it.
- *
- * Note that since the
- * descriptor holds the
- * location where the return
- * value is stored, even if all
- * Threads::Thread objects that
- * point to the descriptor go
- * out of scope, we must make
- * sure that the descriptor is
- * not yet destroyed. Rather,
- * the descriptor must be
- * destroyed when the last
- * Threads::Thread object that
- * points to it goes out of
- * scope or whenever the thread
- * is finished, whatever
- * happens later. We do this by
- * having the descriptor keep a
- * pointer to itself and reset
- * it to zero once it is done
- * -- effectively keeping the use
- * pointer above zero as long
- * as work is going on.
*/
std_cxx1x::shared_ptr<internal::ThreadDescriptor<RT> > thread_descriptor;
};
// and that is available also as a fall-back whenever via boost or similar
/**
- * A class that creates a sequence of items from a range of iterators.
+ * A namespace for the implementation of details of the WorkStream pattern
+ * and function. This namespace holds classes that deal with the second
+ * implementation described in the paper by Turcksin, Kronbichler and
+ * Bangerth.
+ *
+ * Even though this implementation is slower than the third implementation
+ * discussed in that paper, we need to keep it around for two reasons:
+ * (i) a user may not give us a graph coloring, (ii) we want to use
+ * this implementation for colors that are just too small.
*/
- template <typename Iterator,
- typename ScratchData,
- typename CopyData>
- class IteratorRangeToItemStream : public tbb::filter
+ namespace Implementation2
{
- public:
/**
- * A data type that we use to identify items to be worked on. This is
- * the structure that is passed around between the different parts of
- * the WorkStream implementation to identify what needs to be done by
- * the various stages of the pipeline.
+ * A class that creates a sequence of items from a range of iterators.
*/
- struct ItemType
+ template <typename Iterator,
+ typename ScratchData,
+ typename CopyData>
+ class IteratorRangeToItemStream : public tbb::filter
{
+ public:
/**
- * A structure that contains a pointer to a scratch data object along
- * with a flag that indicates whether this object is currently in use.
+ * A data type that we use to identify items to be worked on. This is
+ * the structure that is passed around between the different parts of
+ * the WorkStream implementation to identify what needs to be done by
+ * the various stages of the pipeline.
*/
- struct ScratchDataObject
+ struct ItemType
{
- std_cxx1x::shared_ptr<ScratchData> scratch_data;
- bool currently_in_use;
-
/**
- * Default constructor.
+ * A structure that contains a pointer to a scratch data object along
+ * with a flag that indicates whether this object is currently in use.
*/
- ScratchDataObject ()
- :
- currently_in_use (false)
- {}
-
- ScratchDataObject (ScratchData *p,
- const bool in_use)
- :
- scratch_data (p),
- currently_in_use (in_use)
- {}
-
-//TODO: when we push back an object to the list of scratch objects, in
-// Worker::operator(), we first create an object and then copy
-// it to the end of this list. this involves having two objects
+ struct ScratchDataObject
+ {
+ std_cxx1x::shared_ptr<ScratchData> scratch_data;
+ bool currently_in_use;
+
+ /**
+ * Default constructor.
+ */
+ ScratchDataObject ()
+ :
+ currently_in_use (false)
+ {}
+
+ ScratchDataObject (ScratchData *p,
+ const bool in_use)
+ :
+ scratch_data (p),
+ currently_in_use (in_use)
+ {}
+
+//TODO: when we push back an object to the list of scratch objects, in
+// Worker::operator(), we first create an object and then copy
+// it to the end of this list. this involves having two objects
// of the current type having pointers to it, each with their own
// currently_in_use flag. there is probably little harm in this because
// the original one goes out of scope right away again, but it's
// certainly awkward. one way to avoid this would be to use unique_ptr
// but we'd need to figure out a way to use it in non-C++11 mode
- ScratchDataObject (const ScratchDataObject &o)
+ ScratchDataObject (const ScratchDataObject &o)
+ :
+ scratch_data (o.scratch_data),
+ currently_in_use (o.currently_in_use)
+ {}
+ };
+
+
+ /**
+ * Typedef to a list of scratch data objects. The rationale for this
+ * list is provided in the variables that use these lists.
+ */
+ typedef std::list<ScratchDataObject> ScratchDataList;
+
+ /**
+ * A list of iterators that need to be worked on. Only the first
+ * n_items are relevant.
+ */
+ std::vector<Iterator> work_items;
+
+ /**
+ * The CopyData objects that the Worker part of the pipeline
+ * fills for each work item. Again, only the first n_items
+ * elements are what we care about.
+ */
+ std::vector<CopyData> copy_datas;
+
+ /**
+ * Number of items identified by the work_items array that the
+ * Worker and Copier pipeline stage need to work on. The maximum
+ * value of this variable will be chunk_size.
+ */
+ unsigned int n_items;
+
+ /**
+ * Pointer to a thread local variable identifying the scratch data objects
+ * this thread will use. The initial implementation of this
+ * class using thread local variables provided only a single
+ * scratch object per thread. This doesn't work, because
+ * the worker functions may start tasks itself and then call
+ * Threads::TaskGroup::join_all() or a similar function, which the
+ * TBB scheduler may use to run something else on the current
+ * thread -- for example another instance of the worker function.
+ * Consequently, there would be two instances of the worker
+ * function that use the same scratch object if we only
+ * provided a single scratch object per thread. The solution is
+ * to provide a list of scratch objects for each thread, together
+ * with a flag indicating whether this scratch object is currently
+ * used. If a thread needs a scratch object, it walks this list
+ * until it finds an unused object, or, if there is none, creates one
+ * itself. Note that we need not use synchronization primitives
+ * for this process since the lists are thread-local and
+ * we are guaranteed that only a single thread accesses them as long
+ * as we have no yield point in between the accesses to the list.
+ *
+ * The pointers to scratch objects stored in each of these lists must
+ * be so that they are deleted on all threads when the thread
+ * local object is destroyed. This is achieved by using shared_ptr.
+ *
+ * Note that when a worker needs to create a scratch object, it allocates
+ * it using sample_scratch_data to copy from. This has
+ * the advantage of a first-touch initialization, i.e., the
+ * memory for the scratch data object is allocated and initialized
+ * by the same thread that will later use it.
+ */
+ Threads::ThreadLocalStorage<ScratchDataList> *scratch_data;
+
+ /**
+ * Pointer to a sample scratch data object, to be used to initialize
+ * the scratch data objects created for each individual thread.
+ */
+ const ScratchData *sample_scratch_data;
+
+
+ /**
+ * Default constructor.
+ * Initialize everything that doesn't have a default constructor
+ * itself.
+ */
+ ItemType ()
:
- scratch_data (o.scratch_data),
- currently_in_use (o.currently_in_use)
+ n_items (0),
+ scratch_data (0),
+ sample_scratch_data (0)
{}
};
/**
- * Typedef to a list of scratch data objects. The rationale for this
- * list is provided in the variables that use these lists.
+ * Constructor. Take an iterator range, the size of a buffer that can
+ * hold items, and the sample additional data object that will be passed
+ * to each worker and copier function invokation.
*/
- typedef std::list<ScratchDataObject> ScratchDataList;
+ IteratorRangeToItemStream (const Iterator &begin,
+ const Iterator &end,
+ const unsigned int buffer_size,
+ const unsigned int chunk_size,
+ const ScratchData &sample_scratch_data,
+ const CopyData &sample_copy_data)
+ :
+ tbb::filter (/*is_serial=*/true),
+ remaining_iterator_range (begin, end),
+ ring_buffer (buffer_size),
+ sample_scratch_data (sample_scratch_data),
+ n_emitted_items (0),
+ chunk_size (chunk_size)
+ {
+ // initialize the elements of the ring buffer
+ for (unsigned int element=0; element<ring_buffer.size(); ++element)
+ {
+ Assert (ring_buffer[element].n_items == 0,
+ ExcInternalError());
+
+ ring_buffer[element].work_items.resize (chunk_size,
+ remaining_iterator_range.second);
+ ring_buffer[element].scratch_data = &thread_local_scratch;
+ ring_buffer[element].sample_scratch_data = &sample_scratch_data;
+ ring_buffer[element].copy_datas.resize (chunk_size,
+ sample_copy_data);
+ }
+ }
+
/**
- * A list of iterators that need to be worked on. Only the first
- * n_items are relevant.
+ * Create an item and return a
+ * pointer to it.
*/
- std::vector<Iterator> work_items;
+ virtual void *operator () (void *)
+ {
+ // store the current
+ // position of the pointer
+ ItemType *current_item
+ = &ring_buffer[n_emitted_items % ring_buffer.size()];
+
+ // initialize the next item. it may
+ // consist of at most chunk_size
+ // elements
+ current_item->n_items = 0;
+ while ((remaining_iterator_range.first !=
+ remaining_iterator_range.second)
+ &&
+ (current_item->n_items < chunk_size))
+ {
+ current_item->work_items[current_item->n_items]
+ = remaining_iterator_range.first;
+
+ ++remaining_iterator_range.first;
+ ++current_item->n_items;
+ }
+
+ if (current_item->n_items == 0)
+ // there were no items
+ // left. terminate the pipeline
+ return 0;
+ else
+ {
+ ++n_emitted_items;
+ return current_item;
+ }
+ }
+ private:
/**
- * The CopyData objects that the Worker part of the pipeline
- * fills for each work item. Again, only the first n_items
- * elements are what we care about.
+ * The interval of iterators still to
+ * be worked on. This range will shrink
+ * over time.
*/
- std::vector<CopyData> copy_datas;
+ std::pair<Iterator,Iterator> remaining_iterator_range;
/**
- * Number of items identified by the work_items array that the
- * Worker and Copier pipeline stage need to work on. The maximum
- * value of this variable will be chunk_size.
+ * A ring buffer that will store items.
*/
- unsigned int n_items;
+ std::vector<ItemType> ring_buffer;
/**
* Pointer to a thread local variable identifying the scratch data objects
* memory for the scratch data object is allocated and initialized
* by the same thread that will later use it.
*/
- Threads::ThreadLocalStorage<ScratchDataList> *scratch_data;
+ Threads::ThreadLocalStorage<typename ItemType::ScratchDataList> thread_local_scratch;
/**
- * Pointer to a sample scratch data object, to be used to initialize
- * the scratch data objects created for each individual thread.
+ * A reference to a sample scratch data that will be used to
+ * initialize the thread-local pointers to a scratch data object
+ * each of the worker tasks uses.
*/
- const ScratchData *sample_scratch_data;
+ const ScratchData &sample_scratch_data;
+ /**
+ * Counter for the number of emitted
+ * items. Each item may consist of up
+ * to chunk_size iterator elements.
+ */
+ unsigned int n_emitted_items;
/**
- * Default constructor.
- * Initialize everything that doesn't have a default constructor
- * itself.
+ * Number of elements of the
+ * iterator range that each
+ * thread should work on
+ * sequentially; a large number
+ * makes sure that each thread
+ * gets a significant amount of
+ * work before the next task
+ * switch happens, whereas a
+ * small number is better for
+ * load balancing.
*/
- ItemType ()
- :
- n_items (0),
- scratch_data (0),
- sample_scratch_data (0)
- {}
+ const unsigned int chunk_size;
+
+ /**
+ * Initialize the pointers and vector
+ * elements in the specified entry of
+ * the ring buffer.
+ */
+ void init_buffer_elements (const unsigned int element,
+ const CopyData &sample_copy_data)
+ {
+ Assert (ring_buffer[element].n_items == 0,
+ ExcInternalError());
+
+ ring_buffer[element].work_items
+ .resize (chunk_size, remaining_iterator_range.second);
+ ring_buffer[element].scratch_data
+ = &thread_local_scratch;
+ ring_buffer[element].sample_scratch_data
+ = &sample_scratch_data;
+ ring_buffer[element].copy_datas
+ .resize (chunk_size, sample_copy_data);
+ }
};
+
/**
- * Constructor. Take an iterator range, the size of a buffer that can
- * hold items, and the sample additional data object that will be passed
- * to each worker and copier function invokation.
+ * A class that manages calling the
+ * worker function on a number of
+ * parallel threads. Note that it is, in
+ * the TBB notation, a filter that can
+ * run in parallel.
*/
- IteratorRangeToItemStream (const Iterator &begin,
- const Iterator &end,
- const unsigned int buffer_size,
- const unsigned int chunk_size,
- const ScratchData &sample_scratch_data,
- const CopyData &sample_copy_data)
- :
- tbb::filter (/*is_serial=*/true),
- remaining_iterator_range (new std::pair<Iterator,Iterator> (begin, end)),
- ring_buffer (buffer_size),
- sample_scratch_data (sample_scratch_data),
- color(false),
- n_emitted_items (0),
- chunk_size (chunk_size)
+ template <typename Iterator,
+ typename ScratchData,
+ typename CopyData>
+ class Worker : public tbb::filter
{
- // initialize the elements of the ring buffer
- for (unsigned int element=0; element<ring_buffer.size(); ++element)
+ public:
+ /**
+ * Constructor. Takes a
+ * reference to the object on
+ * which we will operate as
+ * well as a pointer to the
+ * function that will do the
+ * assembly.
+ */
+ Worker (const std_cxx1x::function<void (const Iterator &,
+ ScratchData &,
+ CopyData &)> &worker)
+ :
+ tbb::filter (/* is_serial= */ false),
+ worker (worker)
+ {}
+
+
+ /**
+ * Work on an item.
+ */
+ void *operator () (void *item)
{
- Assert (ring_buffer[element].n_items == 0,
- ExcInternalError());
-
- ring_buffer[element].work_items.resize (chunk_size,
- remaining_iterator_range->second);
- ring_buffer[element].scratch_data = &thread_local_scratch;
- ring_buffer[element].sample_scratch_data = &sample_scratch_data;
- ring_buffer[element].copy_datas.resize (chunk_size,
- sample_copy_data);
+ // first unpack the current item
+ typedef
+ typename IteratorRangeToItemStream<Iterator,ScratchData,CopyData>::ItemType
+ ItemType;
+
+ ItemType *current_item = static_cast<ItemType *> (item);
+
+ // we need to find an unused scratch data object in the list that
+ // corresponds to the current thread and then mark it as used. if
+ // we can't find one, create one
+ //
+ // as discussed in the discussion of the documentation of the
+ // IteratorRangeToItemStream::scratch_data variable, there is no
+ // need to synchronize access to this variable using a mutex
+ // as long as we have no yield-point in between. this means that
+ // we can't take an iterator into the list now and expect it to
+ // still be valid after calling the worker, but we at least do
+ // not have to lock the following section
+ ScratchData *scratch_data = 0;
+ {
+ typename ItemType::ScratchDataList &
+ scratch_data_list = current_item->scratch_data->get();
+
+ // see if there is an unused object. if so, grab it and mark
+ // it as used
+ for (typename ItemType::ScratchDataList::iterator
+ p = scratch_data_list.begin();
+ p != scratch_data_list.end(); ++p)
+ if (p->currently_in_use == false)
+ {
+ scratch_data = p->scratch_data.get();
+ p->currently_in_use = true;
+ break;
+ }
+
+ // if no object was found, create one and mark it as used
+ if (scratch_data == 0)
+ {
+ scratch_data = new ScratchData(*current_item->sample_scratch_data);
+
+ typename ItemType::ScratchDataList::value_type
+ new_scratch_object (scratch_data, true);
+ scratch_data_list.push_back (new_scratch_object);
+ }
+ }
+
+ // then call the worker function on each element of the chunk we were
+ // given. since these worker functions are called on separate threads,
+ // nothing good can happen if they throw an exception and we are best
+ // off catching it and showing an error message
+ for (unsigned int i=0; i<current_item->n_items; ++i)
+ {
+ try
+ {
+ if (worker)
+ worker (current_item->work_items[i],
+ *scratch_data,
+ current_item->copy_datas[i]);
+ }
+ catch (const std::exception &exc)
+ {
+ Threads::internal::handle_std_exception (exc);
+ }
+ catch (...)
+ {
+ Threads::internal::handle_unknown_exception ();
+ }
+ }
+
+ // finally mark the scratch object as unused again. as above, there
+ // is no need to lock anything here since the object we work on
+ // is thread-local
+ {
+ typename ItemType::ScratchDataList &
+ scratch_data_list = current_item->scratch_data->get();
+
+ for (typename ItemType::ScratchDataList::iterator p =
+ scratch_data_list.begin(); p != scratch_data_list.end();
+ ++p)
+ if (p->scratch_data.get() == scratch_data)
+ {
+ Assert(p->currently_in_use == true, ExcInternalError());
+ p->currently_in_use = false;
+ }
+ }
+
+
+
+ // then return the original pointer
+ // to the now modified object
+ return item;
}
- }
- IteratorRangeToItemStream (const typename std::vector<Iterator>::iterator &begin,
- const typename std::vector<Iterator>::iterator &end,
- const unsigned int buffer_size,
- const unsigned int chunk_size,
- const ScratchData &sample_scratch_data,
- const CopyData &sample_copy_data)
- :
- tbb::filter (/*is_serial=*/true),
- color_remaining_iterator_range (new std::pair<typename std::vector<Iterator>::iterator,
- typename std::vector<Iterator>::iterator> (begin,end)),
- ring_buffer (buffer_size),
- sample_scratch_data (sample_scratch_data),
- color(true),
- n_emitted_items (0),
- chunk_size (chunk_size)
+
+ private:
+ /**
+ * Pointer to the function
+ * that does the assembling
+ * on the sequence of cells.
+ */
+ const std_cxx1x::function<void (const Iterator &,
+ ScratchData &,
+ CopyData &)> worker;
+ };
+
+
+
+ /**
+ * A class that manages calling the
+ * copier function. Note that it is, in
+ * the TBB notation, a filter that runs
+ * sequentially, ensuring that all items
+ * are copied in the same order in which
+ * they are created.
+ */
+ template <typename Iterator,
+ typename ScratchData,
+ typename CopyData>
+ class Copier : public tbb::filter
{
- for (unsigned int element=0; element<ring_buffer.size(); ++element)
+ public:
+ /**
+ * Constructor. Takes a
+ * reference to the object on
+ * which we will operate as
+ * well as a pointer to the
+ * function that will do the
+ * copying from the
+ * additional data object to
+ * the global matrix or
+ * similar.
+ */
+ Copier (const std_cxx1x::function<void (const CopyData &)> &copier)
+ :
+ tbb::filter (/*is_serial=*/true),
+ copier (copier)
+ {}
+
+
+ /**
+ * Work on a single item.
+ */
+ void *operator () (void *item)
{
- Assert (ring_buffer[element].n_items == 0,
- ExcInternalError());
-
- // work_items is templated on iterator. Therefore, the resize must
- // be done given *(color_remaining_iterator_range->firts) because
- // iterator may not have a default constructor and
- // *(color_remaining_iterator_range->second) is invalid.
- ring_buffer[element].work_items.resize (chunk_size,
- *(color_remaining_iterator_range->first));
- ring_buffer[element].scratch_data = &thread_local_scratch;
- ring_buffer[element].sample_scratch_data = &sample_scratch_data;
- ring_buffer[element].copy_datas.resize (chunk_size,
- sample_copy_data);
+ // first unpack the current item
+ typedef
+ typename IteratorRangeToItemStream<Iterator,ScratchData,CopyData>::ItemType
+ ItemType;
+
+ ItemType *current_item = static_cast<ItemType *> (item);
+
+ // initiate copying data. for the same reasons as in the worker class
+ // above, catch exceptions rather than letting it propagate into
+ // unknown territories
+ for (unsigned int i=0; i<current_item->n_items; ++i)
+ {
+ try
+ {
+ if (copier)
+ copier (current_item->copy_datas[i]);
+ }
+ catch (const std::exception &exc)
+ {
+ Threads::internal::handle_std_exception (exc);
+ }
+ catch (...)
+ {
+ Threads::internal::handle_unknown_exception ();
+ }
+ }
+
+
+ // return an invalid item since we are at the end of the
+ // pipeline
+ return 0;
}
- }
+
+ private:
+ /**
+ * Pointer to the function that does the copying of data.
+ */
+ const std_cxx1x::function<void (const CopyData &)> copier;
+ };
+
+ }
+
+
+ /**
+ * A namespace for the implementation of details of the WorkStream pattern
+ * and function. This namespace holds classes that deal with the third
+ * implementation described in the paper by Turcksin, Kronbichler and
+ * Bangerth.
+ */
+ namespace Implementation3
+ {
/**
- * Create a item and return a
- * pointer to it.
+ * A class that creates a sequence of items from a range of iterators.
*/
- virtual void *operator () (void *)
+ template <typename Iterator,
+ typename ScratchData,
+ typename CopyData>
+ class IteratorRangeToItemStream : public tbb::filter
{
- // store the current
- // position of the pointer
- ItemType *current_item
- = &ring_buffer[n_emitted_items % ring_buffer.size()];
-
- // initialize the next item. it may
- // consist of at most chunk_size
- // elements
- current_item->n_items = 0;
- if (color==false)
- while ((remaining_iterator_range->first !=
- remaining_iterator_range->second)
- &&
- (current_item->n_items < chunk_size))
+ public:
+ /**
+ * A data type that we use to identify items to be worked on. This is
+ * the structure that is passed around between the different parts of
+ * the WorkStream implementation to identify what needs to be done by
+ * the various stages of the pipeline.
+ */
+ struct ItemType
+ {
+ /**
+ * A structure that contains a pointer to scratch and copy data objects along
+ * with a flag that indicates whether this object is currently in use.
+ */
+ struct ScratchAndCopyDataObjects
{
- current_item->work_items[current_item->n_items]
- = remaining_iterator_range->first;
+ std_cxx1x::shared_ptr<ScratchData> scratch_data;
+ std_cxx1x::shared_ptr<CopyData> copy_data;
+ bool currently_in_use;
+
+ /**
+ * Default constructor.
+ */
+ ScratchAndCopyDataObjects ()
+ :
+ currently_in_use (false)
+ {}
+
+ ScratchAndCopyDataObjects (ScratchData *p,
+ CopyData *q,
+ const bool in_use)
+ :
+ scratch_data (p),
+ copy_data (q),
+ currently_in_use (in_use)
+ {}
+
+//TODO: when we push back an object to the list of scratch objects, in
+// Worker::operator(), we first create an object and then copy
+// it to the end of this list. this involves having two objects
+// of the current type having pointers to it, each with their own
+// currently_in_use flag. there is probably little harm in this because
+// the original one goes out of scope right away again, but it's
+// certainly awkward. one way to avoid this would be to use unique_ptr
+// but we'd need to figure out a way to use it in non-C++11 mode
+ ScratchAndCopyDataObjects (const ScratchAndCopyDataObjects &o)
+ :
+ scratch_data (o.scratch_data),
+ copy_data (o.copy_data),
+ currently_in_use (o.currently_in_use)
+ {}
+ };
- ++remaining_iterator_range->first;
- ++current_item->n_items;
- }
- else
- while ((color_remaining_iterator_range->first !=
- color_remaining_iterator_range->second)
- &&
- (current_item->n_items < chunk_size))
- {
- current_item->work_items[current_item->n_items]
- = *(color_remaining_iterator_range->first);
- ++color_remaining_iterator_range->first;
- ++current_item->n_items;
- }
+ /**
+ * Typedef to a list of scratch data objects. The rationale for this
+ * list is provided in the variables that use these lists.
+ */
+ typedef std::list<ScratchAndCopyDataObjects> ScratchAndCopyDataList;
- if (current_item->n_items == 0)
- // there were no items
- // left. terminate the pipeline
- return 0;
- else
+ /**
+ * A list of iterators that need to be worked on. Only the first
+ * n_items are relevant.
+ */
+ std::vector<Iterator> work_items;
+
+ /**
+ * Number of items identified by the work_items array that the
+ * Worker and Copier pipeline stage need to work on. The maximum
+ * value of this variable will be chunk_size.
+ */
+ unsigned int n_items;
+
+ /**
+ * Pointer to a thread local variable identifying the scratch
+ * and copy data objects this thread will use. The same considerations
+ * apply as documented in the Implementation2::IteratorRangeToItemStream
+ * class as well as in the paper by Turcksin, Kronbichler and Bangerth.
+ */
+ Threads::ThreadLocalStorage<ScratchAndCopyDataList> *scratch_and_copy_data;
+
+ /**
+ * Pointer to a sample scratch data object, to be used to initialize
+ * the scratch data objects created for each individual thread.
+ */
+ const ScratchData *sample_scratch_data;
+
+ /**
+ * Pointer to a sample copy data object.
+ */
+ const CopyData *sample_copy_data;
+
+ /**
+ * Flag is true if the buffer is used and false if the buffer can be
+ * used.
+ */
+ bool currently_in_use;
+
+ /**
+ * Default constructor.
+ * Initialize everything that doesn't have a default constructor
+ * itself.
+ */
+ ItemType ()
+ :
+ n_items (0),
+ sample_scratch_data (0),
+ sample_copy_data (0),
+ currently_in_use (false)
+ {}
+ };
+
+
+ /**
+ * Constructor. Take range of iterators into an array of the kind of object we
+ * want to loop over, the size of a buffer that can
+ * hold items, and the sample additional data object that will be passed
+ * to each worker and copier function invokation.
+ */
+ IteratorRangeToItemStream (const typename std::vector<Iterator>::const_iterator &begin,
+ const typename std::vector<Iterator>::const_iterator &end,
+ const unsigned int buffer_size,
+ const unsigned int chunk_size,
+ const ScratchData &sample_scratch_data,
+ const CopyData &sample_copy_data)
+ :
+ tbb::filter (/*is_serial=*/true),
+ remaining_iterator_range (begin, end),
+ item_buffer (buffer_size),
+ sample_scratch_data (sample_scratch_data),
+ sample_copy_data (sample_copy_data),
+ chunk_size (chunk_size)
{
- ++n_emitted_items;
- return current_item;
+ Assert (begin != end, ExcMessage ("This class is not prepared to deal with empty ranges!"));
+ // initialize the elements of the item_buffer
+ for (unsigned int element=0; element<item_buffer.size(); ++element)
+ {
+ Assert (item_buffer[element].n_items == 0,
+ ExcInternalError());
+
+ // resize the item_buffer. we have to initialize the new
+ // elements with something and because we can't rely on there
+ // being a default constructor for 'Iterator', we take the first
+ // element in the range [begin,end) pointed to.
+ item_buffer[element].work_items.resize (chunk_size,*begin);
+ item_buffer[element].scratch_and_copy_data = &thread_local_scratch_and_copy;
+ item_buffer[element].sample_scratch_data = &sample_scratch_data;
+ item_buffer[element].sample_copy_data = &sample_copy_data;
+ item_buffer[element].currently_in_use = false;
+ }
}
- }
- private:
- /**
- * The interval of iterators still to
- * be worked on. This range will shrink
- * over time.
- */
- std_cxx1x::shared_ptr<std::pair<Iterator,Iterator> > remaining_iterator_range;
- /**
- * When graph coloring is used the iterators to be worked on are given
- * in a vector defined by a pair of iterators.
- */
- std_cxx1x::shared_ptr<std::pair<typename std::vector<Iterator>::iterator,
- typename std::vector<Iterator>::iterator> >
- color_remaining_iterator_range;
+ /**
+ * Create an item and return a
+ * pointer to it.
+ */
+ virtual void *operator () (void *)
+ {
+ // find first unused item. we know that there must be one
+ // because we have set the maximal number of tokens in flight
+ // and have set the ring buffer to have exactly this size. so
+ // if this function is called, we know that less than the
+ // maximal number of items in currently in flight
+ ItemType *current_item = 0;
+ for (unsigned int i=0; i<item_buffer.size(); ++i)
+ if (item_buffer[i].currently_in_use == false)
+ {
+ item_buffer[i].currently_in_use = true;
+ current_item = &item_buffer[i];
+ break;
+ }
+ Assert (current_item != 0, ExcMessage ("This can't be. There must be a free item!"));
+
+
+ // initialize the next item. it may
+ // consist of at most chunk_size
+ // elements
+ current_item->n_items = 0;
+ while ((remaining_iterator_range.first !=
+ remaining_iterator_range.second)
+ &&
+ (current_item->n_items < chunk_size))
+ {
+ // initialize the iterators to work on with the elements
+ // of the vector that remaining_iterator_range
+ // points into
+ current_item->work_items[current_item->n_items]
+ = *remaining_iterator_range.first;
+
+ ++remaining_iterator_range.first;
+ ++current_item->n_items;
+ }
+
+ if (current_item->n_items == 0)
+ // there were no items
+ // left. terminate the pipeline
+ return 0;
+ else
+ return current_item;
+ }
- /**
- * A ring buffer that will store items.
- */
- std::vector<ItemType> ring_buffer;
+ private:
+ /**
+ * The interval of iterators still to
+ * be worked on. This range will shrink
+ * over time.
+ */
+ std::pair<typename std::vector<Iterator>::const_iterator,typename std::vector<Iterator>::const_iterator> remaining_iterator_range;
- /**
- * Pointer to a thread local variable identifying the scratch data objects
- * this thread will use. The initial implementation of this
- * class using thread local variables provided only a single
- * scratch object per thread. This doesn't work, because
- * the worker functions may start tasks itself and then call
- * Threads::TaskGroup::join_all() or a similar function, which the
- * TBB scheduler may use to run something else on the current
- * thread -- for example another instance of the worker function.
- * Consequently, there would be two instances of the worker
- * function that use the same scratch object if we only
- * provided a single scratch object per thread. The solution is
- * to provide a list of scratch objects for each thread, together
- * with a flag indicating whether this scratch object is currently
- * used. If a thread needs a scratch object, it walks this list
- * until it finds an unused object, or, if there is none, creates one
- * itself. Note that we need not use synchronization primitives
- * for this process since the lists are thread-local and
- * we are guaranteed that only a single thread accesses them as long
- * as we have no yield point in between the accesses to the list.
- *
- * The pointers to scratch objects stored in each of these lists must
- * be so that they are deleted on all threads when the thread
- * local object is destroyed. This is achieved by using shared_ptr.
- *
- * Note that when a worker needs to create a scratch object, it allocates
- * it using sample_scratch_data to copy from. This has
- * the advantage of a first-touch initialization, i.e., the
- * memory for the scratch data object is allocated and initialized
- * by the same thread that will later use it.
- */
- Threads::ThreadLocalStorage<typename ItemType::ScratchDataList> thread_local_scratch;
+ /**
+ * A ring buffer that will store items.
+ */
+ std::vector<ItemType> item_buffer;
- /**
- * A reference to a sample scratch data that will be used to
- * initialize the thread-local pointers to a scratch data object
- * each of the worker tasks uses.
- */
- const ScratchData &sample_scratch_data;
+ /**
+ * Pointer to a thread local variable identifying the scratch and
+ * copy data objects each thread will use. The same is true as
+ * discussed for the implementation in the
+ * Implementation2::IteratorRangeToItemStream class and the paper
+ * by Turcksin, Kronbichler and Bangerth.
+ */
+ Threads::ThreadLocalStorage<typename ItemType::ScratchAndCopyDataList> thread_local_scratch_and_copy;
- /**
- * This flag is used to know if graph coloring is used or not.
- */
- bool color;
+ /**
+ * A reference to a sample scratch data that will be used to
+ * initialize the thread-local pointers to a scratch data object
+ * each of the worker tasks uses.
+ */
+ const ScratchData &sample_scratch_data;
+
+ /**
+ * A reference to a sample scratch data that will be used to
+ * initialize the thread-local pointers to a scratch data object
+ * each of the worker tasks uses.
+ */
+ const CopyData &sample_copy_data;
+
+ /**
+ * Number of elements of the
+ * iterator range that each
+ * thread should work on
+ * sequentially; a large number
+ * makes sure that each thread
+ * gets a significant amount of
+ * work before the next task
+ * switch happens, whereas a
+ * small number is better for
+ * load balancing.
+ */
+ const unsigned int chunk_size;
+
+ /**
+ * Initialize the pointers and vector
+ * elements in the specified entry of
+ * the item_buffer.
+ */
+ void init_buffer_elements (const unsigned int element)
+ {
+ Assert (item_buffer[element].n_items == 0,
+ ExcInternalError());
+
+ item_buffer[element].work_items
+ .resize (chunk_size, remaining_iterator_range.second);
+ item_buffer[element].scratch_and_copy_data
+ = &thread_local_scratch_and_copy;
+ item_buffer[element].sample_scratch_data
+ = &sample_scratch_data;
+ item_buffer[element].sample_copy_data
+ = &sample_copy_data;
+ }
+ };
- /**
- * Counter for the number of emitted
- * items. Each item may consist of up
- * to chunk_size iterator elements.
- */
- unsigned int n_emitted_items;
- /**
- * Number of elements of the
- * iterator range that each
- * thread should work on
- * sequentially; a large number
- * makes sure that each thread
- * gets a significant amount of
- * work before the next task
- * switch happens, whereas a
- * small number is better for
- * load balancing.
- */
- const unsigned int chunk_size;
/**
- * Initialize the pointers and vector
- * elements in the specified entry of
- * the ring buffer.
+ * A class that manages calling the
+ * worker function on a number of
+ * parallel threads. Note that it is, in
+ * the TBB notation, a filter that can
+ * run in parallel.
*/
- void init_buffer_elements (const unsigned int element,
- const CopyData &sample_copy_data)
+ template <typename Iterator,
+ typename ScratchData,
+ typename CopyData>
+ class WorkerAndCopier : public tbb::filter
{
- Assert (ring_buffer[element].n_items == 0,
- ExcInternalError());
-
- ring_buffer[element].work_items
- .resize (chunk_size, remaining_iterator_range->second);
- ring_buffer[element].scratch_data
- = &thread_local_scratch;
- ring_buffer[element].sample_scratch_data
- = &sample_scratch_data;
- ring_buffer[element].copy_datas
- .resize (chunk_size, sample_copy_data);
- }
- };
+ public:
+ /**
+ * Constructor. Takes a
+ * reference to the object on
+ * which we will operate as
+ * well as a pointer to the
+ * function that will do the
+ * assembly.
+ */
+ WorkerAndCopier (const std_cxx1x::function<void (const Iterator &,
+ ScratchData &,
+ CopyData &)> &worker,
+ const std_cxx1x::function<void (const CopyData &)> &copier)
+ :
+ tbb::filter (/* is_serial= */ false),
+ worker (worker),
+ copier (copier)
+ {}
+
+ /**
+ * Work on an item.
+ */
+ void *operator () (void *item)
+ {
+ // first unpack the current item
+ typedef
+ typename IteratorRangeToItemStream<Iterator,ScratchData,CopyData>::ItemType
+ ItemType;
+
+ ItemType *current_item = static_cast<ItemType *> (item);
+
+ // we need to find an unused scratch and corresponding copy
+ // data object in the list that
+ // corresponds to the current thread and then mark it as used. if
+ // we can't find one, create one
+ //
+ // as discussed in the discussion of the documentation of the
+ // IteratorRangeToItemStream::scratch_data variable, there is no
+ // need to synchronize access to this variable using a mutex
+ // as long as we have no yield-point in between. this means that
+ // we can't take an iterator into the list now and expect it to
+ // still be valid after calling the worker, but we at least do
+ // not have to lock the following section
+ ScratchData *scratch_data = 0;
+ CopyData *copy_data = 0;
+ {
+ typename ItemType::ScratchAndCopyDataList &
+ scratch_and_copy_data_list = current_item->scratch_and_copy_data->get();
+
+ // see if there is an unused object. if so, grab it and mark
+ // it as used
+ for (typename ItemType::ScratchAndCopyDataList::iterator
+ p = scratch_and_copy_data_list.begin();
+ p != scratch_and_copy_data_list.end(); ++p)
+ if (p->currently_in_use == false)
+ {
+ scratch_data = p->scratch_data.get();
+ copy_data = p->copy_data.get();
+ p->currently_in_use = true;
+ break;
+ }
+
+ // if no element in the list was found, create one and mark it as used
+ if (scratch_data == 0)
+ {
+ Assert (copy_data==0, ExcInternalError());
+ scratch_data = new ScratchData(*current_item->sample_scratch_data);
+ copy_data = new CopyData(*current_item->sample_copy_data);
+
+ typename ItemType::ScratchAndCopyDataList::value_type
+ new_scratch_object (scratch_data, copy_data, true);
+ scratch_and_copy_data_list.push_back (new_scratch_object);
+ }
+ }
+ // then call the worker and copier function on each element of the chunk we were
+ // given. since these functions are called on separate threads,
+ // nothing good can happen if they throw an exception and we are best
+ // off catching it and showing an error message
+ for (unsigned int i=0; i<current_item->n_items; ++i)
+ {
+ try
+ {
+ if (worker)
+ worker (current_item->work_items[i],
+ *scratch_data,
+ *copy_data);
+ if (copier)
+ copier (*copy_data);
+ }
+ catch (const std::exception &exc)
+ {
+ Threads::internal::handle_std_exception (exc);
+ }
+ catch (...)
+ {
+ Threads::internal::handle_unknown_exception ();
+ }
+ }
+
+ // finally mark the scratch object as unused again. as above, there
+ // is no need to lock anything here since the object we work on
+ // is thread-local
+ {
+ typename ItemType::ScratchAndCopyDataList &
+ scratch_and_copy_data_list = current_item->scratch_and_copy_data->get();
+
+ for (typename ItemType::ScratchAndCopyDataList::iterator p =
+ scratch_and_copy_data_list.begin(); p != scratch_and_copy_data_list.end();
+ ++p)
+ if (p->scratch_data.get() == scratch_data)
+ {
+ Assert(p->currently_in_use == true, ExcInternalError());
+ p->currently_in_use = false;
+ }
+ }
- /**
- * A class that manages calling the
- * worker function on a number of
- * parallel threads. Note that it is, in
- * the TBB notation, a filter that can
- * run in parallel.
- */
- template <typename Iterator,
- typename ScratchData,
- typename CopyData>
- class Worker : public tbb::filter
- {
- public:
- /**
- * Constructor. Takes a
- * reference to the object on
- * which we will operate as
- * well as a pointer to the
- * function that will do the
- * assembly.
- */
- Worker (const std_cxx1x::function<void (const Iterator &,
- ScratchData &,
- CopyData &)> &worker)
- :
- tbb::filter (/* is_serial= */ false),
- worker (worker)
- {}
-
-
- /**
- * Work on an item.
- */
- void *operator () (void *item)
- {
- // first unpack the current item
- typedef
- typename IteratorRangeToItemStream<Iterator,ScratchData,CopyData>::ItemType
- ItemType;
-
- ItemType *current_item = static_cast<ItemType *> (item);
-
- // we need to find an unused scratch data object in the list that
- // corresponds to the current thread and then mark it as used. if
- // we can't find one, create one
- //
- // as discussed in the discussion of the documentation of the
- // IteratorRangeToItemStream::scratch_data variable, there is no
- // need to synchronize access to this variable using a mutex
- // as long as we have no yield-point in between. this means that
- // we can't take an iterator into the list now and expect it to
- // still be valid after calling the worker, but we at least do
- // not have to lock the following section
- ScratchData *scratch_data = 0;
- {
- typename ItemType::ScratchDataList &
- scratch_data_list = current_item->scratch_data->get();
-
- // see if there is an unused object. if so, grab it and mark
- // it as used
- for (typename ItemType::ScratchDataList::iterator
- p = scratch_data_list.begin();
- p != scratch_data_list.end(); ++p)
- if (p->currently_in_use == false)
- {
- scratch_data = p->scratch_data.get();
- p->currently_in_use = true;
- break;
- }
-
- // if no object was found, create one and mark it as used
- if (scratch_data == 0)
- {
- scratch_data = new ScratchData(*current_item->sample_scratch_data);
-
- typename ItemType::ScratchDataList::value_type
- new_scratch_object (scratch_data, true);
- scratch_data_list.push_back (new_scratch_object);
- }
- }
-
- // then call the worker function on each element of the chunk we were
- // given. since these worker functions are called on separate threads,
- // nothing good can happen if they throw an exception and we are best
- // off catching it and showing an error message
- for (unsigned int i=0; i<current_item->n_items; ++i)
- {
- try
- {
- if (worker)
- worker (current_item->work_items[i],
- *scratch_data,
- current_item->copy_datas[i]);
- }
- catch (const std::exception &exc)
- {
- Threads::internal::handle_std_exception (exc);
- }
- catch (...)
- {
- Threads::internal::handle_unknown_exception ();
- }
- }
-
- // finally mark the scratch object as unused again. as above, there
- // is no need to lock anything here since the object we work on
- // is thread-local
- {
- typename ItemType::ScratchDataList &
- scratch_data_list = current_item->scratch_data->get();
-
- for (typename ItemType::ScratchDataList::iterator p =
- scratch_data_list.begin(); p != scratch_data_list.end();
- ++p)
- if (p->scratch_data.get() == scratch_data)
- {
- Assert(p->currently_in_use == true, ExcInternalError());
- p->currently_in_use = false;
- }
- }
-
-
-
- // then return the original pointer
- // to the now modified object
- return item;
- }
-
-
- private:
- /**
- * Pointer to the function
- * that does the assembling
- * on the sequence of cells.
- */
- const std_cxx1x::function<void (const Iterator &,
- ScratchData &,
- CopyData &)> worker;
- };
+ // mark current item as usable again
+ current_item->currently_in_use = false;
+ // return an invalid item since we are at the end of the
+ // pipeline
+ return 0;
+ }
- /**
- * A class that manages calling the
- * copier function. Note that it is, in
- * the TBB notation, a filter that runs
- * sequentially, ensuring that all items
- * are copied in the same order in which
- * they are created.
- */
- template <typename Iterator,
- typename ScratchData,
- typename CopyData>
- class Copier : public tbb::filter
- {
- public:
- /**
- * Constructor. Takes a
- * reference to the object on
- * which we will operate as
- * well as a pointer to the
- * function that will do the
- * copying from the
- * additional data object to
- * the global matrix or
- * similar.
- */
- Copier (const std_cxx1x::function<void (const CopyData &)> &copier,bool is_serial)
- :
- tbb::filter (is_serial),
- copier (copier)
- {}
-
-
- /**
- * Work on a single item.
- */
- void *operator () (void *item)
- {
- // first unpack the current item
- typedef
- typename IteratorRangeToItemStream<Iterator,ScratchData,CopyData>::ItemType
- ItemType;
-
- ItemType *current_item = static_cast<ItemType *> (item);
-
- // initiate copying data. for the same reasons as in the worker class
- // above, catch exceptions rather than letting it propagate into
- // unknown territories
- for (unsigned int i=0; i<current_item->n_items; ++i)
- {
- try
- {
- if (copier)
- copier (current_item->copy_datas[i]);
- }
- catch (const std::exception &exc)
- {
- Threads::internal::handle_std_exception (exc);
- }
- catch (...)
- {
- Threads::internal::handle_unknown_exception ();
- }
- }
-
-
- // return an invalid item since we are at the end of the
- // pipeline
- return 0;
- }
-
-
- private:
- /**
- * Pointer to the function that does the copying of data.
- */
- const std_cxx1x::function<void (const CopyData &)> copier;
- };
+ private:
+ /**
+ * Pointer to the function
+ * that does the assembling
+ * on the sequence of cells.
+ */
+ const std_cxx1x::function<void (const Iterator &,
+ ScratchData &,
+ CopyData &)> worker;
+ /**
+ * Pointer to the function that does the copying from
+ * local contribution to global object.
+ */
+ const std_cxx1x::function<void (const CopyData &)> copier;
+ };
+ }
}
-
#endif // DEAL_II_WITH_THREADS
/**
- * This is the main function of the WorkStream concept, doing work as
- * described in the introduction to this namespace.
+ * This is one of two main functions of the WorkStream concept, doing work as
+ * described in the introduction to this namespace. It corresponds to
+ * implementation 2 of the paper by Turcksin, Kronbichler and Bangerth.
*
- * This is the function that can be used for worker and copier objects that
+ * This function that can be used for worker and copier objects that
* are either pointers to non-member functions or objects that allow to be
* called with an operator(), for example objects created by std::bind.
*
typename Iterator,
typename ScratchData,
typename CopyData>
- void
- run (const Iterator &begin,
+ void
+ run (const Iterator &begin,
const typename identity<Iterator>::type &end,
Worker worker,
Copier copier,
{
// need to check if the function is not the zero function. To
// check zero-ness, create a C++ function out of it and check that
- if (static_cast<const std_cxx1x::function<void (const Iterator &,
- ScratchData &,
- CopyData &)>& >(worker))
- worker (i, scratch_data, copy_data);
- if (static_cast<const std_cxx1x::function<void (const CopyData &)>& >
- (copier))
- copier (copy_data);
+ if (static_cast<const std_cxx1x::function<void (const Iterator &,
+ ScratchData &,
+ CopyData &)>& >(worker))
+ worker (i, scratch_data, copy_data);
+ if (static_cast<const std_cxx1x::function<void (const CopyData &)>& >
+ (copier))
+ copier (copy_data);
}
}
#ifdef DEAL_II_WITH_THREADS
else // have TBB and use more than one thread
{
// create the three stages of the pipeline
- internal::IteratorRangeToItemStream<Iterator,ScratchData,CopyData>
+ internal::Implementation2::IteratorRangeToItemStream<Iterator,ScratchData,CopyData>
iterator_range_to_item_stream (begin, end,
- queue_length,
- chunk_size,
- sample_scratch_data,
- sample_copy_data);
+ queue_length,
+ chunk_size,
+ sample_scratch_data,
+ sample_copy_data);
- internal::Worker<Iterator, ScratchData, CopyData> worker_filter (worker);
- internal::Copier<Iterator, ScratchData, CopyData> copier_filter (copier,true);
+ internal::Implementation2::Worker<Iterator, ScratchData, CopyData> worker_filter (worker);
+ internal::Implementation2::Copier<Iterator, ScratchData, CopyData> copier_filter (copier);
// now create a pipeline from these stages
tbb::pipeline assembly_line;
}
-
/**
- * This is the main function of the WorkStream concept, doing work as
- * described in the introduction to this namespace.
+ * This is one of two main functions of the WorkStream concept, doing work as
+ * described in the introduction to this namespace. It corresponds to
+ * implementation 3 of the paper by Turcksin, Kronbichler and Bangerth.
+ * As such, it takes not a range of iterators described by a begin
+ * and end iterator, but a "colored" graph of iterators where each
+ * color represents cells for which writing the cell contributions into
+ * the global object does not conflict (in other words, these cells
+ * are not neighbors). Each "color" is represented by std::vectors of cells.
+ * The first argument to this function, a set of sets of cells (which are
+ * represent as a vector of vectors, for efficiency), is typically
+ * constructed by calling GraphColoring::make_graph_coloring().
*
- * This is the function that can be used for worker and copier objects that
+ * This function that can be used for worker and copier objects that
* are either pointers to non-member functions or objects that allow to be
* called with an operator(), for example objects created by std::bind.
*
- * The argument passed as @p end must be convertible to the same type as @p
- * begin, but doesn't have to be of the same type itself. This allows to
- * write code like <code>WorkStream().run(dof_handler.begin_active(),
- * dof_handler.end(), ...</code> where the first is of type
- * DoFHandler::active_cell_iterator whereas the second is of type
- * DoFHandler::raw_cell_iterator.
- *
* The two data types <tt>ScratchData</tt> and <tt>CopyData</tt> need to
* have a working copy constructor. <tt>ScratchData</tt> is only used in the
* <tt>worker</tt> function, while <tt>CopyData</tt> is the object passed
* from the <tt>worker</tt> to the <tt>copier</tt>.
*
- * The @p get_conflict_indices argument, is a function that given an
- * iterator computes the conflict indices necessary for the
- * graph_coloring. Graph coloring is necessary to be able to copy the data
- * in parallel. If the number of elements in some colors is less than @p
- * chunk_size time multithread_info.n_threads(), these elements are
- * aggregated and copied serially.
- *
* The @p queue_length argument indicates the number of items that can be
* live at any given time. Each item consists of @p chunk_size elements of
* the input stream that will be worked on by the worker and copier
typename Iterator,
typename ScratchData,
typename CopyData>
- void
- run (const Iterator &begin,
- const typename identity<Iterator>::type &end,
+ void
+ run (const std::vector<std::vector<Iterator> > &colored_iterators,
Worker worker,
Copier copier,
const ScratchData &sample_scratch_data,
const CopyData &sample_copy_data,
- const std_cxx1x::function<std::vector<types::global_dof_index> (const Iterator &)>
- &get_conflict_indices,
const unsigned int queue_length = 2*multithread_info.n_threads(),
const unsigned int chunk_size = 8)
{
ExcMessage ("The chunk_size must be at least one."));
(void)chunk_size; // removes -Wunused-parameter warning in optimized mode
- // if no work then skip. (only use
- // operator!= for iterators since we may
- // not have an equality comparison
- // operator)
- if (!(begin != end))
- return;
-
// we want to use TBB if we have support and if it is not disabled at
// runtime:
- #ifdef DEAL_II_WITH_THREADS
- if (multithread_info.n_threads()==1)
- #endif
- {
- // need to copy the sample since it is
- // marked const
- ScratchData scratch_data = sample_scratch_data;
- CopyData copy_data = sample_copy_data;
-
- for (Iterator i=begin; i!=end; ++i)
- {
- if (static_cast<const std_cxx1x::function<void (const Iterator &,
- ScratchData &,
- CopyData &)>& >(worker))
- worker (i, scratch_data, copy_data);
- if (static_cast<const std_cxx1x::function<void (const CopyData &)>& >
- (copier))
- copier (copy_data);
- }
- }
#ifdef DEAL_II_WITH_THREADS
- else
- {
- // color the graph
- std::vector<std::vector<Iterator> > coloring = graph_coloring::make_graph_coloring(
- begin,end,get_conflict_indices);
-
- // colors that do not have cells, i.e., less than chunk_size times
- // multithread_info.n_threads(), are gathered and the copier is
- // called serially.
- const unsigned int serial_limit(chunk_size*multithread_info.n_threads());
- std::vector<Iterator> serial_copying;
-
- for (unsigned int color=0; color<coloring.size(); ++color)
- {
- if (coloring[color].size()<serial_limit)
- serial_copying.insert(serial_copying.end(),coloring[color].begin(),coloring[color].end());
- else
- {
- // create the three stages of the
- // pipeline
- internal::IteratorRangeToItemStream<Iterator,ScratchData,CopyData>
- iterator_range_to_item_stream (coloring[color].begin(), coloring[color].end(),
- queue_length,
- chunk_size,
- sample_scratch_data,
- sample_copy_data);
-
- internal::Worker<Iterator, ScratchData, CopyData> worker_filter (worker);
- internal::Copier<Iterator, ScratchData, CopyData> copier_filter (copier,false);
-
- // now create a pipeline from
- // these stages
- tbb::pipeline assembly_line;
- assembly_line.add_filter (iterator_range_to_item_stream);
- assembly_line.add_filter (worker_filter);
- assembly_line.add_filter (copier_filter);
-
- // and run it
- assembly_line.run (queue_length);
-
- assembly_line.clear ();
- }
- }
-
- // use the serial copier for all the colors that do not have enough cells
- if (serial_copying.size()!=0)
- {
- internal::IteratorRangeToItemStream<Iterator,ScratchData,CopyData>
- iterator_range_to_item_stream (serial_copying.begin(), serial_copying.end(),
- queue_length,
- chunk_size,
- sample_scratch_data,
- sample_copy_data);
-
- internal::Worker<Iterator, ScratchData, CopyData> worker_filter (worker);
- internal::Copier<Iterator, ScratchData, CopyData> copier_filter (copier,true);
-
- tbb::pipeline assembly_line;
- assembly_line.add_filter (iterator_range_to_item_stream);
- assembly_line.add_filter (worker_filter);
- assembly_line.add_filter (copier_filter);
-
- // and run it
- assembly_line.run (queue_length);
-
- assembly_line.clear ();
- }
- }
+ if (multithread_info.n_threads()==1)
#endif
- }
-
-
+ {
+ // need to copy the sample since it is marked const
+ ScratchData scratch_data = sample_scratch_data;
+ CopyData copy_data = sample_copy_data;
- /**
- * This is the main function of the WorkStream concept, doing work as
- * described in the introduction to this namespace.
- *
- * This is the function that can be used for worker and copier functions
- * that are member functions of a class.
- *
- * The argument passed as @p end must be convertible to the same type as @p
- * begin, but doesn't have to be of the same type itself. This allows to
- * write code like <code>WorkStream().run(dof_handler.begin_active(),
- * dof_handler.end(), ...</code> where the first is of type
- * DoFHandler::active_cell_iterator whereas the second is of type
- * DoFHandler::raw_cell_iterator.
- *
- * The @p queue_length argument indicates the number of items that can be
- * live at any given time. Each item consists of @p chunk_size elements of
- * the input stream that will be worked on by the worker and copier
- * functions one after the other on the same thread.
- *
- * @note If your data objects are large, or their constructors are
- * expensive, it is helpful to keep in mind that <tt>queue_length</tt>
- * copies of the <tt>ScratchData</tt> object and
- * <tt>queue_length*chunk_size</tt> copies of the <tt>CopyData</tt> object
- * are generated.
- */
- template <typename MainClass,
- typename Iterator,
- typename ScratchData,
- typename CopyData>
- void
- run (const Iterator &begin,
- const typename identity<Iterator>::type &end,
- MainClass &main_object,
- void (MainClass::*worker) (const Iterator &,
- ScratchData &,
- CopyData &),
- void (MainClass::*copier) (const CopyData &),
- const ScratchData &sample_scratch_data,
- const CopyData &sample_copy_data,
- const unsigned int queue_length = 2*multithread_info.n_threads(),
- const unsigned int chunk_size = 8)
- {
- // forward to the other function
- run (begin, end,
- std_cxx1x::bind (worker,
- std_cxx1x::ref (main_object),
- std_cxx1x::_1, std_cxx1x::_2, std_cxx1x::_3),
- std_cxx1x::bind (copier,
- std_cxx1x::ref (main_object),
- std_cxx1x::_1),
- sample_scratch_data,
- sample_copy_data,
- queue_length,
- chunk_size);
+ for (unsigned int color=0; color<colored_iterators.size(); ++color)
+ for (typename std::vector<Iterator>::const_iterator p = colored_iterators[color].begin();
+ p != colored_iterators[color].end(); ++p)
+ {
+ // need to check if the function is not the zero function. To
+ // check zero-ness, create a C++ function out of it and check that
+ if (static_cast<const std_cxx1x::function<void (const Iterator &,
+ ScratchData &,
+ CopyData &)>& >(worker))
+ worker (*p, scratch_data, copy_data);
+ if (static_cast<const std_cxx1x::function<void (const CopyData &)>& >(copier))
+ copier (copy_data);
+ }
+ }
+#ifdef DEAL_II_WITH_THREADS
+ else // have TBB and use more than one thread
+ {
+ // loop over the various colors of what we're given
+ for (unsigned int color=0; color<colored_iterators.size(); ++color)
+ if (colored_iterators[color].size() > 0)
+ {
+ // create the three stages of the pipeline
+ internal::Implementation3::IteratorRangeToItemStream<Iterator,ScratchData,CopyData>
+ iterator_range_to_item_stream (colored_iterators[color].begin(),
+ colored_iterators[color].end(),
+ queue_length,
+ chunk_size,
+ sample_scratch_data,
+ sample_copy_data);
+
+
+ internal::Implementation3::WorkerAndCopier<Iterator, ScratchData, CopyData>
+ worker_and_copier_filter (worker, copier);
+
+ // now create a pipeline from these stages
+ tbb::pipeline assembly_line;
+ assembly_line.add_filter (iterator_range_to_item_stream);
+ assembly_line.add_filter (worker_and_copier_filter);
+
+ // and run it
+ assembly_line.run (queue_length);
+
+ assembly_line.clear ();
+ }
+ }
+#endif
}
+
/**
- * This is the main function of the WorkStream concept, doing work as
- * described in the introduction to this namespace.
+ * This is a variant of one of the two main functions of the WorkStream
+ * concept, doing work as described in the introduction to this namespace.
+ * It corresponds to implementation 2 of the paper by Turcksin, Kronbichler
+ * and Bangerth.
*
* This is the function that can be used for worker and copier functions
* that are member functions of a class.
* DoFHandler::active_cell_iterator whereas the second is of type
* DoFHandler::raw_cell_iterator.
*
- * The @p get_conflict_indices argument, is a function that given an
- * iterator computes the conflict indices necessary for the
- * graph_coloring. Graph coloring is necessary to be able to copy the data
- * in parallel. If the number of elements in some colors is less than @p
- * chunk_size time multithread_info.n_threads(), these elements are
- * aggregated and copied serially.
- *
* The @p queue_length argument indicates the number of items that can be
* live at any given time. Each item consists of @p chunk_size elements of
* the input stream that will be worked on by the worker and copier
void (MainClass::*copier) (const CopyData &),
const ScratchData &sample_scratch_data,
const CopyData &sample_copy_data,
- std::vector<types::global_dof_index> (MainClass::*get_conflict_indices)(const Iterator &),
const unsigned int queue_length = 2*multithread_info.n_threads(),
const unsigned int chunk_size = 8)
{
std_cxx1x::_1),
sample_scratch_data,
sample_copy_data,
- std_cxx1x::bind(get_conflict_indices,
- std_cxx1x::ref (main_object)),
queue_length,
chunk_size);
}
* results. However, after all there is no algorithm that
* accomplishes this within reasonable time. There are situations
* where the lack of optimality even leads to worse results than with
- * the original, crude, levelwise numering scheme; one of these
+ * the original, crude, levelwise numbering scheme; one of these
* examples is a mesh of four cells of which always those cells are
* refined which are neighbors to the center (you may call this mesh a
* `zoom in' mesh). In one such example the bandwidth was increased by
* after DoFHandler::distribute_dofs. The minimum degree algorithm does not
* attempt to minimize the bandwidth of a matrix but to minimize the amount
* of fill-in a LU decomposition would produce, i.e. the number of places in
- * the matrix that would be occupied by elements of an LU decompisition that
+ * the matrix that would be occupied by elements of an LU decomposition that
* are not already occupied by elements of the original matrix. The resulting
* sparsity pattern obviously has an entirely different structure than the
* ones produced by algorithms trying to minimize the bandwidth.
/**
- * Point based comparator for downstream
- * directions: it returns @p true if the
- * second point is downstream of the first
- * one with respect to the direction given
- * to the constructor. If the points are
- * the same with respect to the downstream
- * direction, the point with the lower DoF
- * number is considered smaller.
+ * Point based comparator for downstream directions: it returns @p true if
+ * the second point is downstream of the first one with respect to the
+ * direction given to the constructor. If the points are the same with
+ * respect to the downstream direction, the point with the lower DoF number
+ * is considered smaller.
*/
template <int dim>
struct ComparePointwiseDownstream
};
/**
- * A namespace for the
- * implementation of some
- * renumbering algorithms based
- * on algorithms implemented in
- * the Boost Graph Library (BGL)
- * by Jeremy Siek and others.
+ * A namespace for the implementation of some renumbering algorithms based
+ * on algorithms implemented in the Boost Graph Library (BGL) by Jeremy Siek
+ * and others.
*
- * While often slighty slower to
- * compute, the algorithms using
- * BOOST often lead to matrices
- * with smaller bandwidths and
- * sparse ILUs based on this
- * numbering are therefore more
- * efficient.
+ * While often slightly slower to compute, the algorithms using BOOST often
+ * lead to matrices with smaller bandwidths and sparse ILUs based on this
+ * numbering are therefore more efficient.
*
- * For a comparison of these
- * algorithms with the ones
- * defined in DoFRenumbering, see
- * the comparison section in the
- * documentation of the
+ * For a comparison of these algorithms with the ones defined in
+ * DoFRenumbering, see the comparison section in the documentation of the
* DoFRenumbering namespace.
*/
namespace boost
{
/**
- * Renumber the degrees of
- * freedom according to the
- * Cuthill-McKee method,
- * eventually using the reverse
- * numbering scheme.
+ * Renumber the degrees of freedom according to the Cuthill-McKee method,
+ * eventually using the reverse numbering scheme.
*
- * See the general
- * documentation of the
- * parent class for details
- * on the different methods.
+ * See the general documentation of the parent class for details on the
+ * different methods.
*
- * As an example of the
- * results of this algorithm,
- * take a look at the
- * comparison of various
- * algorithms in the
- * documentation of the
+ * As an example of the results of this algorithm, take a look at the
+ * comparison of various algorithms in the documentation of the
* DoFRenumbering namespace.
*/
template <class DH>
const bool use_constraints = false);
/**
- * Computes the renumbering
- * vector needed by the
- * Cuthill_McKee() function. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the Cuthill_McKee()
+ * function. Does not perform the renumbering on the DoFHandler dofs but
+ * returns the renumbering vector.
*/
template <class DH>
void
const bool use_constraints = false);
/**
- * Renumber the degrees of
- * freedom based on the BOOST
- * implementation of the King
- * algorithm. This often
- * results in slightly larger
- * (by a few percent)
- * bandwidths than the
- * Cuthill-McKee algorithm,
- * but sparse ILUs are often
- * slightly (also by a few
- * percent) better
- * preconditioners.
+ * Renumber the degrees of freedom based on the BOOST implementation of
+ * the King algorithm. This often results in slightly larger (by a few
+ * percent) bandwidths than the Cuthill-McKee algorithm, but sparse ILUs
+ * are often slightly (also by a few percent) better preconditioners.
*
- * As an example of the
- * results of this algorithm,
- * take a look at the
- * comparison of various
- * algorithms in the
- * documentation of the
+ * As an example of the results of this algorithm, take a look at the
+ * comparison of various algorithms in the documentation of the
* DoFRenumbering namespace.
*
- * This algorithm is used in
- * step-22.
+ * This algorithm is used in step-22.
*/
template <class DH>
void
const bool use_constraints = false);
/**
- * Compute the renumbering
- * for the King algorithm but
- * do not actually renumber
- * the degrees of freedom in
- * the DoF handler argument.
+ * Compute the renumbering for the King algorithm but do not actually
+ * renumber the degrees of freedom in the DoF handler argument.
*/
template <class DH>
void
const bool use_constraints = false);
/**
- * Renumber the degrees of
- * freedom based on the BOOST
- * implementation of the
- * minimum degree
- * algorithm. Unlike the
- * Cuthill-McKee algorithm,
- * this algorithm does not
- * attempt to minimize the
- * bandwidth of a matrix but
- * to minimize the amount of
- * fill-in when doing an LU
- * decomposition. It may
- * sometimes yield better
- * ILUs because of this
- * property.
+ * Renumber the degrees of freedom based on the BOOST implementation of
+ * the minimum degree algorithm. Unlike the Cuthill-McKee algorithm, this
+ * algorithm does not attempt to minimize the bandwidth of a matrix but to
+ * minimize the amount of fill-in when doing an LU decomposition. It may
+ * sometimes yield better ILUs because of this property.
*
- * As an example of the
- * results of this algorithm,
- * take a look at the
- * comparison of various
- * algorithms in the
- * documentation of the
+ * As an example of the results of this algorithm, take a look at the
+ * comparison of various algorithms in the documentation of the
* DoFRenumbering namespace.
*/
template <class DH>
const bool use_constraints = false);
/**
- * Compute the renumbering
- * for the minimum degree
- * algorithm but do not
- * actually renumber the
- * degrees of freedom in the
- * DoF handler argument.
+ * Compute the renumbering for the minimum degree algorithm but do not
+ * actually renumber the degrees of freedom in the DoF handler argument.
*/
template <class DH>
void
}
/**
- * Renumber the degrees of
- * freedom according to the
- * Cuthill-McKee method,
- * eventually using the reverse
- * numbering scheme.
+ * Renumber the degrees of freedom according to the Cuthill-McKee method,
+ * eventually using the reverse numbering scheme.
*
- * See the general documentation
- * of this class for details on
- * the different methods.
+ * See the general documentation of this class for details on the different
+ * methods.
*
- * As an example of the results
- * of this algorithm, take a look
- * at the comparison of various
- * algorithms in the
- * documentation of the
+ * As an example of the results of this algorithm, take a look at the
+ * comparison of various algorithms in the documentation of the
* DoFRenumbering namespace.
*/
template <class DH>
const std::vector<types::global_dof_index> &starting_indices = std::vector<types::global_dof_index>());
/**
- * Computes the renumbering
- * vector needed by the
- * Cuthill_McKee() function. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the Cuthill_McKee()
+ * function. Does not perform the renumbering on the DoFHandler dofs but
+ * returns the renumbering vector.
*/
template <class DH>
void
const std::vector<types::global_dof_index> &starting_indices = std::vector<types::global_dof_index>());
/**
- * Renumber the degrees of
- * freedom according to the
- * Cuthill-McKee method,
- * eventually using the reverse
- * numbering scheme, in this case
- * for a multigrid numbering of
- * degrees of freedom.
+ * Renumber the degrees of freedom according to the Cuthill-McKee method,
+ * eventually using the reverse numbering scheme, in this case for a
+ * multigrid numbering of degrees of freedom.
*
- * You can give a triangulation
- * level to which this function
- * is to be applied. Since with
- * a level-wise numbering there
- * are no hanging nodes, no
- * constraints can be used, so
- * the respective parameter of
- * the previous function is
- * ommitted.
+ * You can give a triangulation level to which this function is to be
+ * applied. Since with a level-wise numbering there are no hanging nodes,
+ * no constraints can be used, so the respective parameter of the previous
+ * function is omitted.
*
- * See the general documentation
- * of this class for details on
- * the different methods.
+ * See the general documentation of this class for details on the different
+ * methods.
*/
template <class DH>
void
*/
/**
- * Sort the degrees of freedom by
- * vector component. The
- * numbering within each
- * component is not touched, so a
- * degree of freedom with index
- * $i$, belonging to some
- * component, and another degree
- * of freedom with index $j$
- * belonging to the same
- * component will be assigned new
- * indices $n(i)$ and $n(j)$ with
- * $n(i)<n(j)$ if $i<j$ and
- * $n(i)>n(j)$ if $i>j$.
+ * Sort the degrees of freedom by vector component. The numbering within
+ * each component is not touched, so a degree of freedom with index $i$,
+ * belonging to some component, and another degree of freedom with index $j$
+ * belonging to the same component will be assigned new indices $n(i)$ and
+ * $n(j)$ with $n(i)<n(j)$ if $i<j$ and $n(i)>n(j)$ if $i>j$.
*
- * You can specify that the
- * components are ordered in a
- * different way than suggested
- * by the FESystem object you
- * use. To this end, set up the
- * vector @p target_component
- * such that the entry at index
- * @p i denotes the number of the
- * target component for dofs with
- * component @p i in the
- * FESystem. Naming the same
- * target component more than once is
- * possible and results in a
- * blocking of several components
- * into one. This is discussed in
- * step-22. If you
- * omit this argument, the same
- * order as given by the finite
- * element is used.
+ * You can specify that the components are ordered in a different way than
+ * suggested by the FESystem object you use. To this end, set up the vector
+ * @p target_component such that the entry at index @p i denotes the number
+ * of the target component for dofs with component @p i in the
+ * FESystem. Naming the same target component more than once is possible and
+ * results in a blocking of several components into one. This is discussed
+ * in step-22. If you omit this argument, the same order as given by the
+ * finite element is used.
*
- * If one of the base finite
- * elements from which the global
- * finite element under
- * consideration here, is a
- * non-primitive one, i.e. its
- * shape functions have more than
- * one non-zero component, then
- * it is not possible to
- * associate these degrees of
- * freedom with a single vector
- * component. In this case, they
- * are associated with the first
- * vector component to which they
- * belong.
+ * If one of the base finite elements from which the global finite element
+ * under consideration here, is a non-primitive one, i.e. its shape
+ * functions have more than one non-zero component, then it is not possible
+ * to associate these degrees of freedom with a single vector component. In
+ * this case, they are associated with the first vector component to which
+ * they belong.
*
- * For finite elements with only
- * one component, or a single
- * non-primitive base element,
- * this function is the identity
- * operation.
+ * For finite elements with only one component, or a single non-primitive
+ * base element, this function is the identity operation.
*
- * @note A similar function, which
- * renumbered all levels existed
- * for MGDoFHandler. This function
- * was deleted. Thus, you have to
- * call the level function for each
- * level now.
+ * @note A similar function, which renumbered all levels existed for
+ * MGDoFHandler. This function was deleted. Thus, you have to call the level
+ * function for each level now.
*/
template <int dim, int spacedim>
void
/**
- * Sort the degrees of freedom by
- * component. It does the same
- * thing as the above function.
+ * Sort the degrees of freedom by component. It does the same thing as the
+ * above function.
*/
template <int dim>
void
const std::vector<unsigned int> &target_component = std::vector<unsigned int> ());
/**
- * Sort the degrees of freedom by
- * component. It does the same
- * thing as the above function,
- * only that it does this for one
- * single level of a multi-level
- * discretization. The
- * non-multigrid part of the
- * MGDoFHandler is not touched.
+ * Sort the degrees of freedom by component. It does the same thing as the
+ * above function, only that it does this for one single level of a
+ * multi-level discretization. The non-multigrid part of the MGDoFHandler is
+ * not touched.
*/
template <class DH>
void
/**
- * Sort the degrees of freedom by
- * component. It does the same
- * thing as the previous
- * functions, but more: it
- * renumbers not only every level
- * of the multigrid part, but
- * also the global,
- * i.e. non-multigrid components.
+ * Sort the degrees of freedom by component. It does the same thing as the
+ * previous functions, but more: it renumbers not only every level of the
+ * multigrid part, but also the global, i.e. non-multigrid components.
*/
template <int dim>
void
const std::vector<unsigned int> &target_component = std::vector<unsigned int>());
/**
- * Computes the renumbering
- * vector needed by the
- * component_wise()
- * functions. Does not perform
- * the renumbering on the
- * DoFHandler dofs but returns
- * the renumbering vector.
+ * Computes the renumbering vector needed by the component_wise()
+ * functions. Does not perform the renumbering on the DoFHandler dofs but
+ * returns the renumbering vector.
*/
template <int dim, int spacedim, class ITERATOR, class ENDITERATOR>
types::global_dof_index
*/
/**
- * Sort the degrees of freedom by
- * vector block. The
- * numbering within each
- * block is not touched, so a
- * degree of freedom with index
- * $i$, belonging to some
- * block, and another degree
- * of freedom with index $j$
- * belonging to the same
- * block will be assigned new
- * indices $n(i)$ and $n(j)$ with
- * $n(i)<n(j)$ if $i<j$ and
- * $n(i)>n(j)$ if $i>j$.
+ * Sort the degrees of freedom by vector block. The numbering within each
+ * block is not touched, so a degree of freedom with index $i$, belonging to
+ * some block, and another degree of freedom with index $j$ belonging to the
+ * same block will be assigned new indices $n(i)$ and $n(j)$ with
+ * $n(i)<n(j)$ if $i<j$ and $n(i)>n(j)$ if $i>j$.
*/
template <int dim, int spacedim>
void
/**
- * Sort the degrees of freedom by
- * block. It does the same
- * thing as the above function.
- *
- * This function only succeeds if each of
- * the elements in the hp::FECollection
- * attached to the hp::DoFHandler argument
- * has exactly the same number of blocks
- * (see @ref GlossBlock "the glossary" for
- * more information). Note that this is not
- * always given: while the hp::FECollection
- * class ensures that all of its elements
- * have the same number of vector
- * components, they need not have the same
- * number of blocks. At the same time, this
- * function here needs to match individual
- * blocks across elements and therefore
- * requires that elements have the same
- * number of blocks and that subsequent
- * blocks in one element have the same
- * meaning as in another element.
+ * Sort the degrees of freedom by block. It does the same thing as the above
+ * function.
+ *
+ * This function only succeeds if each of the elements in the
+ * hp::FECollection attached to the hp::DoFHandler argument has exactly the
+ * same number of blocks (see @ref GlossBlock "the glossary" for more
+ * information). Note that this is not always given: while the
+ * hp::FECollection class ensures that all of its elements have the same
+ * number of vector components, they need not have the same number of
+ * blocks. At the same time, this function here needs to match individual
+ * blocks across elements and therefore requires that elements have the same
+ * number of blocks and that subsequent blocks in one element have the same
+ * meaning as in another element.
*/
template <int dim>
void
block_wise (hp::DoFHandler<dim> &dof_handler);
/**
- * Sort the degrees of freedom by
- * block. It does the same
- * thing as the above function,
- * only that it does this for one
- * single level of a multi-level
- * discretization. The
- * non-multigrid part of the
- * MGDoFHandler is not touched.
+ * Sort the degrees of freedom by block. It does the same thing as the above
+ * function, only that it does this for one single level of a multi-level
+ * discretization. The non-multigrid part of the MGDoFHandler is not
+ * touched.
*/
template <int dim>
void
/**
- * Sort the degrees of freedom by
- * block. It does the same
- * thing as the previous
- * functions, but more: it
- * renumbers not only every level
- * of the multigrid part, but
- * also the global,
- * i.e. non-multigrid components.
+ * Sort the degrees of freedom by block. It does the same thing as the
+ * previous functions, but more: it renumbers not only every level of the
+ * multigrid part, but also the global, i.e. non-multigrid components.
*/
template <int dim>
void
block_wise (MGDoFHandler<dim> &dof_handler);
/**
- * Computes the renumbering
- * vector needed by the
- * block_wise()
- * functions. Does not perform
- * the renumbering on the
- * DoFHandler dofs but returns
- * the renumbering vector.
+ * Computes the renumbering vector needed by the block_wise()
+ * functions. Does not perform the renumbering on the DoFHandler dofs but
+ * returns the renumbering vector.
*/
template <int dim, int spacedim, class ITERATOR, class ENDITERATOR>
types::global_dof_index
*/
/**
- * Renumber the degrees cell by cell in hierarchical order
- * (also known as z-order). The main usage is that this
- * guarantees the same ordering independent of the
- * number of processors involved in a parallel
+ * Renumber the degrees cell by cell in hierarchical order (also known as
+ * z-order). The main usage is that this guarantees the same ordering
+ * independent of the number of processors involved in a parallel
* distributed computation.
*/
template <int dim>
hierarchical (DoFHandler<dim> &dof_handler);
/**
- * Cell-wise renumbering. This function takes
- * the ordered set of cells in
- * <tt>cell_order</tt>, and makes
- * sure that all degrees of
- * freedom in a cell with higher
- * index are behind all degrees
- * of freedom of a cell with
- * lower index. The order inside
- * a cell block will be the same
- * as before this renumbering.
+ * Cell-wise renumbering. This function takes the ordered set of cells in
+ * <tt>cell_order</tt>, and makes sure that all degrees of freedom in a cell
+ * with higher index are behind all degrees of freedom of a cell with lower
+ * index. The order inside a cell block will be the same as before this
+ * renumbering.
*/
template <class DH>
void
const std::vector<typename DH::active_cell_iterator> &cell_order);
/**
- * Computes the renumbering
- * vector needed by the
- * cell_wise() function. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the cell_wise() function. Does
+ * not perform the renumbering on the DoFHandler dofs but returns the
+ * renumbering vector.
*/
template <class DH>
void
const std::vector<typename DH::active_cell_iterator> &cell_order);
/**
- * Cell-wise renumbering on one
- * level. See the other function
- * with the same name.
+ * Cell-wise renumbering on one level. See the other function with the same
+ * name.
*/
template <class DH>
void
const std::vector<typename DH::level_cell_iterator> &cell_order);
/**
- * Computes the renumbering
- * vector needed by the
- * cell_wise() level renumbering function. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the cell_wise() level
+ * renumbering function. Does not perform the renumbering on the DoFHandler
+ * dofs but returns the renumbering vector.
*/
template <class DH>
void
*/
/**
- * Downstream numbering with respect to a
- * constant flow direction. If the
- * additional argument @p
- * dof_wise_renumbering is set to @p false,
- * the numbering is performed cell-wise,
- * otherwise it is performed based on the
+ * Downstream numbering with respect to a constant flow direction. If the
+ * additional argument @p dof_wise_renumbering is set to @p false, the
+ * numbering is performed cell-wise, otherwise it is performed based on the
* location of the support points.
*
- * The cells are sorted such that
- * the centers of higher numbers
- * are further downstream with
- * respect to the constant vector
- * @p direction than the centers
- * of lower numbers. Even if this
- * yields a downstream numbering
- * with respect to the flux on
- * the edges for fairly general
- * grids, this might not be
- * guaranteed for all meshes.
+ * The cells are sorted such that the centers of higher numbers are further
+ * downstream with respect to the constant vector @p direction than the
+ * centers of lower numbers. Even if this yields a downstream numbering with
+ * respect to the flux on the edges for fairly general grids, this might not
+ * be guaranteed for all meshes.
*
- * If the @p dof_wise_renumbering argument
- * is set to @p false, this function
- * produces a downstream ordering of the
- * mesh cells and calls
- * cell_wise(). Therefore, the output only
- * makes sense for Discontinuous Galerkin
- * Finite Elements (all degrees of freedom
- * have to be associated with the interior
- * of the cell in that case) in that case.
+ * If the @p dof_wise_renumbering argument is set to @p false, this function
+ * produces a downstream ordering of the mesh cells and calls
+ * cell_wise(). Therefore, the output only makes sense for Discontinuous
+ * Galerkin Finite Elements (all degrees of freedom have to be associated
+ * with the interior of the cell in that case) in that case.
*
- * If @p dof_wise_renumbering is set to @p
- * true, the degrees of freedom are
- * renumbered based on the support point
- * location of the individual degrees of
- * freedom (obviously, the finite element
- * needs to define support points for this
- * to work). The numbering of points with
- * the same position in downstream location
- * (e.g. those parallel to the flow
- * direction, or several dofs within a
- * FESystem) will be unaffected.
+ * If @p dof_wise_renumbering is set to @p true, the degrees of freedom are
+ * renumbered based on the support point location of the individual degrees
+ * of freedom (obviously, the finite element needs to define support points
+ * for this to work). The numbering of points with the same position in
+ * downstream location (e.g. those parallel to the flow direction, or
+ * several dofs within a FESystem) will be unaffected.
*/
template <class DH>
void
/**
- * Cell-wise downstream numbering
- * with respect to a constant
- * flow direction on one
- * level. See the other function
- * with the same name.
+ * Cell-wise downstream numbering with respect to a constant flow direction
+ * on one level. See the other function with the same name.
*/
template <class DH>
void
const bool dof_wise_renumbering = false);
/**
- * This function does the downstream numbering for the individual
- * levels of a multigrid hierarchy, but not for the global degrees
- * of freedom.
+ * This function does the downstream numbering for the individual levels of
+ * a multigrid hierarchy, but not for the global degrees of freedom.
*
- * @deprecated Call downstream() function that takes a level
- * argument for each of the levels of the multigrid hierarchy.
+ * @deprecated Call downstream() function that takes a level argument for
+ * each of the levels of the multigrid hierarchy.
*/
template <int dim, int spacedim>
void
}
/**
- * Computes the renumbering
- * vector needed by the
- * downstream() function. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the downstream() function. Does
+ * not perform the renumbering on the DoFHandler dofs but returns the
+ * renumbering vector.
*/
template <class DH>
void
const bool dof_wise_renumbering);
/**
- * Computes the renumbering
- * vector needed by the
- * downstream() function. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the downstream() function. Does
+ * not perform the renumbering on the DoFHandler dofs but returns the
+ * renumbering vector.
*/
template <class DH>
void
/**
* Cell-wise clockwise numbering.
*
- * This function produces a
- * (counter)clockwise ordering of
- * the mesh cells with respect to
- * the hub @p center and calls
- * cell_wise(). Therefore, it
- * only works with Discontinuous
- * Galerkin Finite Elements,
- * i.e. all degrees of freedom
- * have to be associated with the
- * interior of the cell.
+ * This function produces a (counter)clockwise ordering of the mesh cells
+ * with respect to the hub @p center and calls cell_wise(). Therefore, it
+ * only works with Discontinuous Galerkin Finite Elements, i.e. all degrees
+ * of freedom have to be associated with the interior of the cell.
*/
template <class DH>
void
const bool counter = false);
/**
- * Cell-wise clockwise numbering
- * on one level. See the other
- * function with the same name.
+ * Cell-wise clockwise numbering on one level. See the other function with
+ * the same name.
*/
template <class DH>
void
const bool counter = false);
/**
- * Computes the renumbering
- * vector needed by the
- * clockwise_dg() functions. Does
- * not perform the renumbering on
- * the DoFHandler dofs but
- * returns the renumbering
- * vector.
+ * Computes the renumbering vector needed by the clockwise_dg()
+ * functions. Does not perform the renumbering on the DoFHandler dofs but
+ * returns the renumbering vector.
*/
template <class DH>
void
*/
/**
- * Sort those degrees of freedom
- * which are tagged with @p true
- * in the @p selected_dofs array
- * to the back of the DoF
- * numbers. The sorting is
- * stable, i.e. the relative
- * order within the tagged
- * degrees of freedom is
- * preserved, as is the relative
- * order within the untagged
- * ones.
+ * Sort those degrees of freedom which are tagged with @p true in the @p
+ * selected_dofs array to the back of the DoF numbers. The sorting is
+ * stable, i.e. the relative order within the tagged degrees of freedom is
+ * preserved, as is the relative order within the untagged ones.
*
- * @pre The @p selected_dofs
- * array must have as many elements as
- * the @p dof_handler has degrees of
- * freedom.
+ * @pre The @p selected_dofs array must have as many elements as the @p
+ * dof_handler has degrees of freedom.
*/
template <class DH>
void
const std::vector<bool> &selected_dofs);
/**
- * Sort those degrees of freedom which are tagged with @p true in
- * the @p selected_dofs array on the level @p level to the back of
- * the DoF numbers. The sorting is stable, i.e. the relative order
- * within the tagged degrees of freedom is preserved, as is the
- * relative order within the untagged ones.
+ * Sort those degrees of freedom which are tagged with @p true in the @p
+ * selected_dofs array on the level @p level to the back of the DoF
+ * numbers. The sorting is stable, i.e. the relative order within the tagged
+ * degrees of freedom is preserved, as is the relative order within the
+ * untagged ones.
*
- * @pre The @p selected_dofs array must have as many elements as the
- * @p dof_handler has degrees of freedom on the given level.
+ * @pre The @p selected_dofs array must have as many elements as the @p
+ * dof_handler has degrees of freedom on the given level.
*/
template <class DH>
void
const unsigned int level);
/**
- * Computes the renumbering
- * vector needed by the
- * sort_selected_dofs_back()
- * function. Does not perform the
- * renumbering on the DoFHandler
- * dofs but returns the
- * renumbering vector.
+ * Computes the renumbering vector needed by the sort_selected_dofs_back()
+ * function. Does not perform the renumbering on the DoFHandler dofs but
+ * returns the renumbering vector.
*
- * @pre The @p selected_dofs
- * array must have as many elements as
- * the @p dof_handler has degrees of
- * freedom.
+ * @pre The @p selected_dofs array must have as many elements as the @p
+ * dof_handler has degrees of freedom.
*/
template <class DH>
void
const std::vector<bool> &selected_dofs);
/**
- * Computes the renumbering
- * vector on each level
- * needed by the
- * sort_selected_dofs_back()
- * function. Does not perform the
- * renumbering on the MGDoFHandler
- * dofs but returns the
- * renumbering vector.
+ * Computes the renumbering vector on each level needed by the
+ * sort_selected_dofs_back() function. Does not perform the renumbering on
+ * the MGDoFHandler dofs but returns the renumbering vector.
*
- * @pre The @p selected_dofs
- * array must have as many elements as
- * the @p dof_handler has degrees of
- * freedom on the given level.
+ * @pre The @p selected_dofs array must have as many elements as the @p
+ * dof_handler has degrees of freedom on the given level.
*/
template <class DH>
void
const unsigned int level);
/**
- * Renumber the degrees of
- * freedom in a random way.
+ * Renumber the degrees of freedom in a random way.
*/
template <class DH>
void
random (DH &dof_handler);
/**
- * Computes the renumbering
- * vector needed by the random()
- * function. Does not perform the
- * renumbering on the DoFHandler
- * dofs but returns the
+ * Computes the renumbering vector needed by the random() function. Does not
+ * perform the renumbering on the DoFHandler dofs but returns the
* renumbering vector.
*/
template <class DH>
*/
/**
- * Renumber the degrees of
- * freedom such that they are
- * associated with the subdomain
- * id of the cells they are
- * living on, i.e. first all
- * degrees of freedom that belong
- * to cells with subdomain zero,
- * then all with subdomain one,
- * etc. This is useful when doing
- * parallel computations after
- * assigning subdomain ids using
- * a partitioner (see the
- * GridTools::partition_triangulation
- * function for this).
+ * Renumber the degrees of freedom such that they are associated with the
+ * subdomain id of the cells they are living on, i.e. first all degrees of
+ * freedom that belong to cells with subdomain zero, then all with subdomain
+ * one, etc. This is useful when doing parallel computations after assigning
+ * subdomain ids using a partitioner (see the
+ * GridTools::partition_triangulation function for this).
*
- * Note that degrees of freedom
- * associated with faces, edges,
- * and vertices may be associated
- * with multiple subdomains if
- * they are sitting on partition
- * boundaries. It would therefore
- * be undefined with which
- * subdomain they have to be
- * associated. For this, we use
- * what we get from the
- * DoFTools::get_subdomain_association
- * function.
+ * Note that degrees of freedom associated with faces, edges, and vertices
+ * may be associated with multiple subdomains if they are sitting on
+ * partition boundaries. It would therefore be undefined with which
+ * subdomain they have to be associated. For this, we use what we get from
+ * the DoFTools::get_subdomain_association function.
*
- * The algorithm is stable, i.e. if
- * two dofs i,j have <tt>i<j</tt> and belong
- * to the same subdomain, then they
- * will be in this order also after
+ * The algorithm is stable, i.e. if two dofs i,j have <tt>i<j</tt> and
+ * belong to the same subdomain, then they will be in this order also after
* reordering.
*/
template <class DH>
subdomain_wise (DH &dof_handler);
/**
- * Computes the renumbering
- * vector needed by the
- * subdomain_wise()
- * function. Does not perform the
- * renumbering on the @p
- * DoFHandler dofs but returns
- * the renumbering vector.
+ * Computes the renumbering vector needed by the subdomain_wise()
+ * function. Does not perform the renumbering on the @p DoFHandler dofs but
+ * returns the renumbering vector.
*/
template <class DH>
void
types::boundary_id boundary_id;
types::material_id material_id;
};
- /**
- * Manifold identificator of this
- * object. This identificator
- * should be used to identify the
- * manifold to which this object
- * belongs, and from which this
- * object will collect information
- * on how to add points upon
- * refinement.*/
+ /**
+ * Manifold identificator of this object. This identificator should
+ * be used to identify the manifold to which this object belongs,
+ * and from which this object will collect information on how to add
+ * points upon refinement.*/
types::manifold_id manifold_id;
+
+ /**
+ * Default constructor. Sets the vertex indices to invalid values and the boundary or material
+ * id the default value (zero).
+ */
+ CellData ();
};
#ifndef DOXYGEN
+
+template <int structdim>
+inline
+CellData<structdim>::CellData ()
+{
+ for (unsigned int i=0; i<GeometryInfo<structdim>::vertices_per_cell; ++i)
+ vertices[i] = numbers::invalid_unsigned_int;
+
+ material_id = 0;
+}
+
+
+
namespace internal
{
namespace Triangulation
* sparsity patterns of the
* parameter.
*
- * The elements of the matrix are
- * set to zero by this function.
+ * You have to make sure that the lifetime of the sparsity structure is at
+ * least as long as that of this matrix or as long as reinit(const
+ * SparsityPattern &) is not called with a new sparsity structure.
+ *
+ * The elements of the matrix are set to zero by this function.
*/
virtual void reinit (const BlockSparsityPattern &sparsity);
//@}
}
+/**
+ * @}
+ */
+
//TODO: Add multithreading to the other vmult functions.
* elements in a row are written in ascending column order.
*/
template <class STREAM>
- void print (STREAM &out, bool across=false, bool diagonal_first=true) const;
+ void print (STREAM &out,
+ const bool across = false,
+ const bool diagonal_first = true) const;
/**
* Print the matrix in the usual format, i.e. as a matrix and not as a list
template <typename,bool> friend class SparseMatrixIterators::Accessor;
};
-/**
- * @}
- */
-
#ifndef DOXYGEN
/*---------------------- Inline functions -----------------------------------*/
template <typename number>
template <class STREAM>
inline
-void SparseMatrix<number>::print (STREAM &out, bool across, bool diagonal_first) const
+void SparseMatrix<number>::print (STREAM &out,
+ const bool across,
+ const bool diagonal_first) const
{
Assert (cols != 0, ExcNotInitialized());
Assert (val != 0, ExcNotInitialized());
bool hanging_diagonal = false;
- number diagonal;
+ number diagonal = number();
for (size_type i=0; i<cols->rows; ++i)
{
ADD_SUBDIRECTORY(matrix_free)
ADD_SUBDIRECTORY(meshworker)
+# A custom target to build the library:
+ADD_CUSTOM_TARGET(build_library)
+
FOREACH(build ${DEAL_II_BUILD_TYPES})
STRING(TOLOWER ${build} build_lowercase)
${deal_ii_objects_${build_lowercase}}
)
+ ADD_DEPENDENCIES(build_library ${DEAL_II_BASE_NAME}${DEAL_II_${_build}_SUFFIX})
ADD_DEPENDENCIES(library ${DEAL_II_BASE_NAME}${DEAL_II_${_build}_SUFFIX})
SET_TARGET_PROPERTIES(${DEAL_II_BASE_NAME}${DEAL_II_${build}_SUFFIX}
AssertThrow (out, ExcIO());
}
+template <>
+void DataOutBase::write_svg<1,1> (const std::vector<Patch<1,1> > &patches,
+ const std::vector<std::string> &data_names,
+ const std::vector<std_cxx1x::tuple<unsigned int, unsigned int, std::string> > &vector_data_ranges,
+ const SvgFlags &flags,
+ std::ostream &out)
+{
+ AssertThrow (false, ExcNotImplemented());
+}
+
template <int dim, int spacedim>
void DataOutBase::write_svg (const std::vector<Patch<dim,spacedim> > &patches,
if (flags.margin) margin_in_percent = 5;
-// determine the bounding box in the model space
- double x_min, y_min, z_min;
- double x_max, y_max, z_max;
+ // determine the bounding box in the model space
double x_dimension, y_dimension, z_dimension;
typename std::vector<Patch<dim,spacedim> >::const_iterator patch = patches.begin();
patch->data.n_rows() == 0,
ExcIndexRange (flags.height_vector, 0, patch->data.n_rows()));
- x_min = projected_point[0];
- x_max = x_min;
- y_min = projected_point[1];
- y_max = y_min;
- z_min = patch->data.n_rows() != 0 ? patch->data(flags.height_vector,0) : 0;
- z_max = z_min;
+ double x_min = projected_point[0];
+ double x_max = x_min;
+ double y_min = projected_point[1];
+ double y_max = y_min;
+ double z_min = patch->data.n_rows() != 0 ? patch->data(flags.height_vector,0) : 0;
+ double z_max = z_min;
// iterate over the patches
for (; patch != patches.end(); ++patch)
camera_focus = .5 * z_dimension;
- Point<3> camera_position_temp(true);
- Point<3> camera_direction_temp(true);
- Point<3> camera_horizontal_temp(true);
+ Point<3> camera_position_temp;
+ Point<3> camera_direction_temp;
+ Point<3> camera_horizontal_temp;
const float angle_factor = 3.14159265 / 180.;
const std::vector<std_cxx1x::tuple<unsigned int, unsigned int, std::string> > &vector_data_ranges,
const TecplotFlags &flags,
std::ostream &out);
+
+#if deal_II_space_dimension >1
template
void
DataOutBase::write_svg (const std::vector<Patch<deal_II_dimension,deal_II_space_dimension> > &patches,
const std::vector<std_cxx1x::tuple<unsigned int, unsigned int, std::string> > &vector_data_ranges,
const SvgFlags &flags,
std::ostream &out);
+#endif
template
void
DataOutBase::write_deal_II_intermediate (const std::vector<Patch<deal_II_dimension,deal_II_space_dimension> > &patches,
# include <sys/sysctl.h>
#endif
-#ifdef DEAL_II_WITH_THREADS
+#if defined(__FreeBSD__)
+# include <stdlib.h>
+#endif
+#ifdef DEAL_II_WITH_THREADS
# include <deal.II/base/thread_management.h>
# include <tbb/task_scheduler_init.h>
#endif
template void
downstream<DoFHandler<deal_II_dimension> >
- (DoFHandler<deal_II_dimension>&, const Point<deal_II_dimension>&,
+ (DoFHandler<deal_II_dimension>&, const Point<DoFHandler<deal_II_dimension>::space_dimension>&,
const bool);
template void
template void
downstream<hp::DoFHandler<deal_II_dimension> >
(hp::DoFHandler<deal_II_dimension>&,
- const Point<deal_II_dimension>&,
+ const Point<hp::DoFHandler<deal_II_dimension>::space_dimension>&,
const bool);
template void
downstream<MGDoFHandler<deal_II_dimension> >
(MGDoFHandler<deal_II_dimension>&,
- const Point<deal_II_dimension>&,
+ const Point<MGDoFHandler<deal_II_dimension>::space_dimension>&,
const bool);
template void
template
void downstream
- (DoFHandler<deal_II_dimension>&, const unsigned int,
+ (DoFHandler<deal_II_dimension>&,
+ const unsigned int,
const Point<deal_II_dimension>&,
const bool);
* the generated Xcode project.
*/
-const int _global_symbol_42 = 42;
+const int global_symbol_42 = 42;
const VectorBase &V,
const bool transpose_left)
{
+#ifdef DEAL_II_USE_LARGE_INDEX_TYPE
+ Assert(false,ExcNotImplemented())
+#endif
const bool use_vector = (V.size() == inputright.m() ? true : false);
if (transpose_left == false)
{
const SparseMatrix &B,
const VectorBase &V) const
{
+#ifdef DEAL_II_USE_LARGE_INDEX_TYPE
+ Assert(false,ExcNotImplemented())
+#endif
internals::perform_mmult (*this, B, C, V, false);
}
const SparseMatrix &B,
const VectorBase &V) const
{
+#ifdef DEAL_II_USE_LARGE_INDEX_TYPE
+ Assert(false,ExcNotImplemented())
+#endif
internals::perform_mmult (*this, B, C, V, true);
}
)
ADD_DEPENDENCIES(setup_tests setup_tests_${_category})
- # depend on a valid build directory:
- ADD_DEPENDENCIES(setup_tests_${_category} setup_build_dir)
+ # depend on a compiled library:
+ ADD_DEPENDENCIES(setup_tests_${_category} build_library)
ADD_CUSTOM_TARGET(regen_tests_${_category}
COMMAND [ ! -d ${_category} ] || ${CMAKE_COMMAND}
--- /dev/null
+====================================================
+MESH CONVERSION TOOL
+v. 1.2
+
+Use: Convert an ABAQUS .inp file to an AVS UCD file.
+
+Author: Jean-Paul Pelteret
+ jppelteret.uct@gmail.com
+ modified by: Timo Heister, heister@clemson.edu
+===================================================
+
+
+This tool is intended to support converting ABAQUS .inp files into a
+format that deal.II can read. To use this tool, you need to configure
+deal.II using the "-DDEAL_II_COMPONENT_MESH_CONVERTER=ON" argument
+when calling 'cmake'. The resulting executable will then be placed in
+the installation directory.
+
+
+
+Cubit features captured by ABAQUS .inp files:
+---------------------------------------------
+1. Multiple material-id's can be defined in the mesh. This is done by specifying blocksets in the pre-processor.
+2. Arbitrary surface boundaries can be defined in the mesh. This is done by specifying sidesets in the pre-processor. In particular, boundaries are not confined to just surfaces (in 3d) - individual element faces can be added to the sideset as well. This is useful when a boundary condition is to be applied on a complex shape boundary that is difficult to define using "surfaces" alone. Similar can be done in 2d.
+
+How to use:
+-----------
+1. It is necessary to save the mesh as an Abaqus input file .inp. In Cubit, this is done as follows:
+1.1. Go to "Analysis setup mode" by clicking on the disc icon in the toolbar on the right.
+1.2. Select "Export Mesh" under "Operation" by clicking on the necessary icon in the toolbar on the right.
+1.3. Select an output file. I have found that in Cubit version 11.0 and 12.0 that it is necessary to click on the browse button and type it in the dialogue that pops up.
+1.4. Select the dimension to output in.
+1.5. Tick the overwrite box.
+1.6. If using Cubit v12.0 onwards, uncheck the box "Export using Cubit ID's". The conversion process will encounter errors if box if left checked.
+1.7. Click apply.
+
+2. Converting the mesh
+IMPORTANT NOTE: From v12.0 onwards, the format of the Abaqus file that Cubit outputted changed. This has been accounted for but an requires a flag to be passed to the conversion program.
+ I describe outputs from before v12.0 as "Abaqus OLD" and v12.0 an on (up to v12.1 at this point) as "Abaqus NEW".
+2.1. Compile the program using 'make' or another suitable tool
+2.2. Run the program with the following command line arguments:
+ './convert_mesh <spatial_dimension> /path/to/input_file.inp /path/to/output_file.ucd'
+
+ The first input argument is the spatial dimension of the input file, the second is the path to the read-in Abaqus .inp file, and the third is the name of the file to which you wish to write the output AVS .ucd file to.
+ An example of the correct program usage is:
+e.g. './convert_mesh 3 mesh/3d/test_in.inp mesh/3d/test_out.ucd'
+
+
+Notes:
+------
+1. A few example / test meshes are provided in the directory "mesh". The .inp files that have been generated are all of the Abaqus OLD format except for one - CC.cub has been converted into both the "new" and "old" formats and both subsequently converted into deal.II readable meshes.
+
+Copyright:
+----------
+This program is distributed under the GNU GPL v2.0 copyright. Details can be found at:
+http://www.gnu.org/licenses/gpl-2.0.html
+
+This copyright is extended to the example mesh files distributed with this program, namely
+./mesh/2d/2d_test.*
+./mesh/2d/quad.*
+./mesh/3d/CC.*
+./mesh/3d/CC_cubit_new.*
+./mesh/3d/CC_cubit_old.*
+./mesh/3d/test_cube_1.*
+./mesh/3d/test_cube_pave_1.*
+./mesh/3d/test_cube_two_materials.*
make_quicktest("p4est" ${_mybuild} 10)
ENDIF()
+# Test petsc
+IF (DEAL_II_WITH_PETSC)
+ make_quicktest("step-petsc" ${_mybuild} "")
+ENDIF()
+
+# Test slepc
+IF (DEAL_II_WITH_PETSC AND DEAL_II_WITH_SLEPC)
+ make_quicktest("step-slepc" ${_mybuild} "")
+ENDIF()
# A custom test target:
ADD_CUSTOM_TARGET(test
COMMAND ${CMAKE_CTEST_COMMAND} --force-new-ctest-process
WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
)
+ADD_DEPENDENCIES(test build_library)
MESSAGE(STATUS "Setup quick_tests in ${_mybuild} mode - Done")
--- /dev/null
+/* ---------------------------------------------------------------------\r
+ * $Id: step-petsc.cc $\r
+ *\r
+ * Copyright (C) 2013 by the deal.II authors\r
+ *\r
+ * This file is part of the deal.II library.\r
+ *\r
+ * The deal.II library is free software; you can use it, redistribute\r
+ * it, and/or modify it under the terms of the GNU Lesser General\r
+ * Public License as published by the Free Software Foundation; either\r
+ * version 2.1 of the License, or (at your option) any later version.\r
+ * The full text of the license can be found in the file LICENSE at\r
+ * the top level of the deal.II distribution.\r
+ *\r
+ * ---------------------------------------------------------------------\r
+ */\r
+\r
+#include <deal.II/base/logstream.h>\r
+#include <deal.II/base/table_handler.h>\r
+#include <deal.II/base/quadrature_lib.h>\r
+#include <deal.II/base/function.h>\r
+#include <deal.II/base/utilities.h>\r
+#include <deal.II/grid/tria.h>\r
+#include <deal.II/grid/grid_generator.h>\r
+#include <deal.II/grid/tria_accessor.h>\r
+#include <deal.II/grid/tria_iterator.h>\r
+#include <deal.II/dofs/dof_handler.h>\r
+#include <deal.II/dofs/dof_accessor.h>\r
+#include <deal.II/dofs/dof_tools.h>\r
+#include <deal.II/fe/fe_q.h>\r
+#include <deal.II/fe/fe_values.h>\r
+#include <deal.II/numerics/vector_tools.h>\r
+#include <deal.II/numerics/matrix_tools.h>\r
+#include <deal.II/numerics/data_out.h>\r
+#include <deal.II/lac/full_matrix.h>\r
+#include <deal.II/lac/petsc_sparse_matrix.h>\r
+#include <deal.II/lac/petsc_vector.h>\r
+#include <deal.II/lac/petsc_solver.h>\r
+#include <deal.II/lac/petsc_precondition.h>\r
+\r
+#include <fstream>\r
+#include <iostream>\r
+\r
+using namespace dealii;\r
+\r
+// Test that deal.II is working with PETSc by solving the Laplace's\r
+// problem in 2d.\r
+class LaplaceProblem\r
+{\r
+public:\r
+ LaplaceProblem ();\r
+ void run ();\r
+ \r
+private:\r
+ void setup_system ();\r
+ void assemble_system ();\r
+ void solve ();\r
+ \r
+ Triangulation<2> triangulation;\r
+ FE_Q<2> fe;\r
+ DoFHandler<2> dof_handler;\r
+ \r
+ PETScWrappers::SparseMatrix A;\r
+ PETScWrappers::Vector b, x; \r
+ ConstraintMatrix constraints;\r
+\r
+ TableHandler output_table;\r
+};\r
+\r
+LaplaceProblem::LaplaceProblem ()\r
+ :\r
+ fe (1),\r
+ dof_handler (triangulation)\r
+{}\r
+\r
+void LaplaceProblem::setup_system ()\r
+{\r
+ dof_handler.distribute_dofs (fe);\r
+\r
+ constraints.clear ();\r
+ DoFTools::make_zero_boundary_constraints (dof_handler, constraints);\r
+ constraints.close ();\r
+ \r
+ A.reinit (dof_handler.n_dofs(), dof_handler.n_dofs(),\r
+ dof_handler.max_couplings_between_dofs());\r
+ b.reinit (dof_handler.n_dofs());\r
+ x.reinit (dof_handler.n_dofs());\r
+\r
+ // some output\r
+ output_table.add_value ("cells", triangulation.n_active_cells());\r
+ output_table.add_value ("dofs", dof_handler.n_dofs());\r
+}\r
+\r
+void LaplaceProblem::assemble_system ()\r
+{\r
+ QGauss<2> quadrature_formula(2);\r
+ \r
+ FEValues<2> fe_values (fe, quadrature_formula,\r
+ update_values | \r
+ update_gradients |\r
+ update_quadrature_points | \r
+ update_JxW_values);\r
+ \r
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;\r
+ const unsigned int n_q_points = quadrature_formula.size();\r
+ \r
+ FullMatrix<double> cell_A (dofs_per_cell, dofs_per_cell);\r
+ Vector<double> cell_b (dofs_per_cell);\r
+ \r
+ std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);\r
+ \r
+ typename DoFHandler<2>::active_cell_iterator\r
+ cell = dof_handler.begin_active (),\r
+ endc = dof_handler.end ();\r
+ \r
+ for (; cell!=endc; ++cell)\r
+ {\r
+ fe_values.reinit (cell);\r
+ cell_A = 0;\r
+ cell_b = 0;\r
+ \r
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)\r
+ for (unsigned int i=0; i<dofs_per_cell; ++i)\r
+ {\r
+ for (unsigned int j=0; j<dofs_per_cell; ++j)\r
+ {\r
+ cell_A (i, j)\r
+ += \r
+ fe_values.shape_grad (i, q_point) *\r
+ fe_values.shape_grad (j, q_point)\r
+ * \r
+ fe_values.JxW (q_point);\r
+ }\r
+\r
+ cell_b (i)\r
+ += \r
+ fe_values.shape_value (i, q_point)\r
+ * \r
+ fe_values.JxW (q_point);\r
+ }\r
+ \r
+ cell->get_dof_indices (local_dof_indices);\r
+ \r
+ constraints.distribute_local_to_global (cell_A, local_dof_indices, A);\r
+ constraints.distribute_local_to_global (cell_b, local_dof_indices, b);\r
+ }\r
+ \r
+ A.compress (VectorOperation::add);\r
+ b.compress (VectorOperation::add);\r
+}\r
+\r
+void LaplaceProblem::solve ()\r
+{\r
+ SolverControl solver_control (1e03, 1e-03);\r
+ PETScWrappers::SolverCG cg_solver (solver_control);\r
+ PETScWrappers::PreconditionBlockJacobi preconditioner (A);\r
+ cg_solver.solve (A, x, b, preconditioner);\r
+\r
+ // some output\r
+ // ?\r
+}\r
+\r
+void LaplaceProblem::run ()\r
+{\r
+ GridGenerator::hyper_cube (triangulation, -1, 1);\r
+\r
+ for (unsigned int c=0; c<5; ++c)\r
+ {\r
+ triangulation.refine_global (1);\r
+ setup_system ();\r
+ assemble_system ();\r
+ solve ();\r
+ }\r
+\r
+ // finialise output\r
+ output_table.write_text (std::cout);\r
+ deallog << std::endl;\r
+}\r
+\r
+\r
+int main (int argc, char **argv)\r
+{\r
+ try\r
+ {\r
+ dealii::Utilities::MPI::MPI_InitFinalize mpi_initialization (argc, argv, 1);\r
+ {\r
+ deallog.depth_console (0);\r
+ LaplaceProblem problem;\r
+ problem.run ();\r
+ deallog << "OK" << std::endl;\r
+ }\r
+ }\r
+\r
+ catch (std::exception &exc)\r
+ {\r
+ std::cerr << std::endl << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+ std::cerr << "Exception on processing: " << std::endl\r
+ << exc.what() << std::endl\r
+ << "Aborting!" << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+\r
+ return 1;\r
+ }\r
+ catch (...)\r
+ {\r
+ std::cerr << std::endl << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+ std::cerr << "Unknown exception!" << std::endl\r
+ << "Aborting!" << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+ return 1;\r
+ }\r
+\r
+ return 0;\r
+}\r
--- /dev/null
+/* ---------------------------------------------------------------------\r
+ * $Id$\r
+ *\r
+ * Copyright (C) 2013 by the deal.II authors\r
+ *\r
+ * This file is part of the deal.II library.\r
+ *\r
+ * The deal.II library is free software; you can use it, redistribute\r
+ * it, and/or modify it under the terms of the GNU Lesser General\r
+ * Public License as published by the Free Software Foundation; either\r
+ * version 2.1 of the License, or (at your option) any later version.\r
+ * The full text of the license can be found in the file LICENSE at\r
+ * the top level of the deal.II distribution.\r
+ *\r
+ * ---------------------------------------------------------------------\r
+ */\r
+\r
+#include <deal.II/base/logstream.h>\r
+#include <deal.II/base/table_handler.h>\r
+#include <deal.II/base/quadrature_lib.h>\r
+#include <deal.II/base/function.h>\r
+#include <deal.II/base/utilities.h>\r
+#include <deal.II/grid/tria.h>\r
+#include <deal.II/grid/grid_generator.h>\r
+#include <deal.II/grid/tria_accessor.h>\r
+#include <deal.II/grid/tria_iterator.h>\r
+#include <deal.II/dofs/dof_handler.h>\r
+#include <deal.II/dofs/dof_accessor.h>\r
+#include <deal.II/dofs/dof_tools.h>\r
+#include <deal.II/fe/fe_q.h>\r
+#include <deal.II/fe/fe_values.h>\r
+#include <deal.II/numerics/vector_tools.h>\r
+#include <deal.II/numerics/matrix_tools.h>\r
+#include <deal.II/numerics/data_out.h>\r
+#include <deal.II/lac/full_matrix.h>\r
+#include <deal.II/lac/petsc_sparse_matrix.h>\r
+#include <deal.II/lac/petsc_vector.h>\r
+#include <deal.II/lac/slepc_solver.h>\r
+\r
+#include <fstream>\r
+#include <iostream>\r
+\r
+using namespace dealii;\r
+\r
+// Test that deal.II is working with SLEPc by solving the Laplace's\r
+// eigenspectrum problem in 2d.\r
+class LaplaceEigenspectrumProblem\r
+{\r
+public:\r
+ LaplaceEigenspectrumProblem ();\r
+ void run ();\r
+ \r
+private:\r
+ void setup_system ();\r
+ void assemble_system ();\r
+ void solve ();\r
+ \r
+ Triangulation<2> triangulation;\r
+ FE_Q<2> fe;\r
+ DoFHandler<2> dof_handler;\r
+ \r
+ PETScWrappers::SparseMatrix A, B;\r
+ std::vector<PETScWrappers::Vector> x;\r
+ std::vector<double> lambda; \r
+ ConstraintMatrix constraints;\r
+\r
+ TableHandler output_table;\r
+};\r
+\r
+LaplaceEigenspectrumProblem::LaplaceEigenspectrumProblem ()\r
+ :\r
+ fe (1),\r
+ dof_handler (triangulation)\r
+{}\r
+\r
+void LaplaceEigenspectrumProblem::setup_system ()\r
+{\r
+ dof_handler.distribute_dofs (fe);\r
+ \r
+ constraints.clear ();\r
+ DoFTools::make_zero_boundary_constraints (dof_handler, constraints);\r
+ constraints.close ();\r
+ \r
+ A.reinit (dof_handler.n_dofs(), dof_handler.n_dofs(),\r
+ dof_handler.max_couplings_between_dofs());\r
+ B.reinit (dof_handler.n_dofs(), dof_handler.n_dofs(),\r
+ dof_handler.max_couplings_between_dofs());\r
+ \r
+ x.resize (1);\r
+ x[0].reinit (dof_handler.n_dofs ());\r
+ lambda.resize (1);\r
+ lambda[0] = 0.;\r
+\r
+ // some output\r
+ output_table.add_value ("cells", triangulation.n_active_cells());\r
+ output_table.add_value ("dofs", dof_handler.n_dofs());\r
+}\r
+\r
+void LaplaceEigenspectrumProblem::assemble_system ()\r
+{\r
+ QGauss<2> quadrature_formula(2);\r
+ \r
+ FEValues<2> fe_values (fe, quadrature_formula,\r
+ update_values | \r
+ update_gradients |\r
+ update_quadrature_points | \r
+ update_JxW_values);\r
+ \r
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;\r
+ const unsigned int n_q_points = quadrature_formula.size();\r
+ \r
+ FullMatrix<double> cell_A (dofs_per_cell, dofs_per_cell);\r
+ FullMatrix<double> cell_B (dofs_per_cell, dofs_per_cell);\r
+ \r
+ std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);\r
+ \r
+ typename DoFHandler<2>::active_cell_iterator\r
+ cell = dof_handler.begin_active (),\r
+ endc = dof_handler.end ();\r
+ \r
+ for (; cell!=endc; ++cell)\r
+ {\r
+ fe_values.reinit (cell);\r
+ cell_A = 0;\r
+ cell_B = 0;\r
+ \r
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)\r
+ for (unsigned int i=0; i<dofs_per_cell; ++i)\r
+ for (unsigned int j=0; j<dofs_per_cell; ++j)\r
+ {\r
+ cell_A (i, j)\r
+ += \r
+ fe_values.shape_grad (i, q_point) *\r
+ fe_values.shape_grad (j, q_point)\r
+ * \r
+ fe_values.JxW (q_point);\r
+ \r
+ cell_B (i, j)\r
+ += \r
+ fe_values.shape_value (i, q_point) *\r
+ fe_values.shape_value (j, q_point)\r
+ * \r
+ fe_values.JxW (q_point);\r
+ }\r
+ \r
+ cell->get_dof_indices (local_dof_indices);\r
+ \r
+ constraints.distribute_local_to_global (cell_A, local_dof_indices, A);\r
+ constraints.distribute_local_to_global (cell_B, local_dof_indices, B);\r
+ }\r
+ \r
+ A.compress (VectorOperation::add);\r
+ B.compress (VectorOperation::add);\r
+}\r
+\r
+void LaplaceEigenspectrumProblem::solve ()\r
+{\r
+ SolverControl solver_control (1000, 1e-03);\r
+ SLEPcWrappers::SolverArnoldi eigensolver (solver_control);\r
+ eigensolver.set_which_eigenpairs (EPS_SMALLEST_REAL);\r
+ eigensolver.solve (A, B, lambda, x, x.size());\r
+\r
+ // some output\r
+ output_table.add_value ("lambda", lambda[0]);\r
+ output_table.add_value ("error", std::fabs(2.-lambda[0]));\r
+}\r
+\r
+void LaplaceEigenspectrumProblem::run ()\r
+{\r
+ const double radius = dealii::numbers::PI/2.;\r
+ GridGenerator::hyper_cube (triangulation, -radius, radius);\r
+\r
+ // set the old eigenvalue to a silly number.\r
+ double old_lambda = 1000;\r
+\r
+ for (unsigned int c=0; c<5; ++c)\r
+ {\r
+ // obtain numerical result\r
+ triangulation.refine_global (1);\r
+ setup_system ();\r
+ assemble_system ();\r
+ solve ();\r
+\r
+ // check energy convergence with previous result\r
+ AssertThrow (lambda[0]<old_lambda, ExcMessage("solution is not converging"));\r
+ old_lambda = lambda[0];\r
+ }\r
+\r
+ // push back analytic result\r
+ output_table.add_value ("cells", "inf");\r
+ output_table.add_value ("dofs", "inf");\r
+ output_table.add_value ("lambda", 2.);\r
+ output_table.add_value ("error", "-");\r
+\r
+ // finialise output\r
+ output_table.write_text (std::cout);\r
+ deallog << std::endl;\r
+}\r
+\r
+\r
+int main (int argc, char **argv)\r
+{\r
+ try\r
+ {\r
+ dealii::Utilities::MPI::MPI_InitFinalize mpi_initialization (argc, argv, 1);\r
+ {\r
+ deallog.depth_console (0);\r
+ LaplaceEigenspectrumProblem problem;\r
+ problem.run ();\r
+ }\r
+ }\r
+\r
+ catch (std::exception &exc)\r
+ {\r
+ std::cerr << std::endl << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+ std::cerr << "Exception on processing: " << std::endl\r
+ << exc.what() << std::endl\r
+ << "Aborting!" << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+\r
+ return 1;\r
+ }\r
+ catch (...)\r
+ {\r
+ std::cerr << std::endl << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+ std::cerr << "Unknown exception!" << std::endl\r
+ << "Aborting!" << std::endl\r
+ << "----------------------------------------------------"\r
+ << std::endl;\r
+ return 1;\r
+ }\r
+\r
+ return 0;\r
+}\r
projects / dealii-svn.git / commitdiff
