From 6fc76e954a5d19168d99d386a6283417739a4608 Mon Sep 17 00:00:00 2001 From: bangerth Date: Mon, 24 Jul 2006 16:13:04 +0000 Subject: [PATCH] Add step-23, 24, and 25 in its present, partly undocumented, form git-svn-id: https://svn.dealii.org/trunk@13431 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-23/Makefile | 154 ++++ deal.II/examples/step-23/Makefile.dep | 242 ++++++ deal.II/examples/step-23/doc/intro.dox | 2 + deal.II/examples/step-23/doc/results.dox | 2 + deal.II/examples/step-23/step-23 | Bin 0 -> 379718 bytes deal.II/examples/step-23/step-23.cc | 357 ++++++++ deal.II/examples/step-24/Makefile | 154 ++++ deal.II/examples/step-24/Makefile.dep | 252 ++++++ deal.II/examples/step-24/doc/intro.dox | 162 ++++ deal.II/examples/step-24/doc/multi.png | Bin 0 -> 41427 bytes deal.II/examples/step-24/doc/multi_movie.gif | Bin 0 -> 4404094 bytes deal.II/examples/step-24/doc/multi_s.png | Bin 0 -> 27762 bytes deal.II/examples/step-24/doc/multi_s2.png | Bin 0 -> 29963 bytes deal.II/examples/step-24/doc/multi_sf.png | Bin 0 -> 29056 bytes deal.II/examples/step-24/doc/one.png | Bin 0 -> 38358 bytes deal.II/examples/step-24/doc/one_movie.gif | Bin 0 -> 5337113 bytes deal.II/examples/step-24/doc/one_s.png | Bin 0 -> 42393 bytes deal.II/examples/step-24/doc/one_s2.png | Bin 0 -> 31151 bytes deal.II/examples/step-24/doc/one_sf.png | Bin 0 -> 24575 bytes deal.II/examples/step-24/doc/project-1.tex | 91 ++ deal.II/examples/step-24/doc/results.dox | 90 ++ deal.II/examples/step-24/step-24 | Bin 0 -> 634466 bytes deal.II/examples/step-24/step-24.cc | 697 +++++++++++++++ deal.II/examples/step-25/Makefile | 154 ++++ deal.II/examples/step-25/Makefile.dep | 244 ++++++ deal.II/examples/step-25/doc/animate.sh | 38 + .../step-25/doc/christov.1d-breather.gif | Bin 0 -> 397752 bytes .../step-25/doc/christov.1d-breather_stp.png | Bin 0 -> 75606 bytes .../step-25/doc/christov.2d-angled_kink.gif | Bin 0 -> 4032149 bytes .../examples/step-25/doc/christov.2d-kink.gif | Bin 0 -> 1270707 bytes .../examples/step-25/doc/christov.2d-kink.png | Bin 0 -> 81913 bytes .../doc/christov.2d-pseudobreather.gif | Bin 0 -> 2243101 bytes deal.II/examples/step-25/doc/intro.dox | 87 ++ deal.II/examples/step-25/doc/plot.plt | 20 + deal.II/examples/step-25/doc/results.dox | 47 + deal.II/examples/step-25/step-25 | Bin 0 -> 721269 bytes deal.II/examples/step-25/step-25.cc | 819 ++++++++++++++++++ 37 files changed, 3612 insertions(+) create mode 100644 deal.II/examples/step-23/Makefile create mode 100644 deal.II/examples/step-23/Makefile.dep create mode 100644 deal.II/examples/step-23/doc/intro.dox create mode 100644 deal.II/examples/step-23/doc/results.dox create mode 100755 deal.II/examples/step-23/step-23 create mode 100644 deal.II/examples/step-23/step-23.cc create mode 100644 deal.II/examples/step-24/Makefile create mode 100644 deal.II/examples/step-24/Makefile.dep create mode 100644 deal.II/examples/step-24/doc/intro.dox create mode 100644 deal.II/examples/step-24/doc/multi.png create mode 100644 deal.II/examples/step-24/doc/multi_movie.gif create mode 100644 deal.II/examples/step-24/doc/multi_s.png create mode 100644 deal.II/examples/step-24/doc/multi_s2.png create mode 100644 deal.II/examples/step-24/doc/multi_sf.png create mode 100644 deal.II/examples/step-24/doc/one.png create mode 100644 deal.II/examples/step-24/doc/one_movie.gif create mode 100644 deal.II/examples/step-24/doc/one_s.png create mode 100644 deal.II/examples/step-24/doc/one_s2.png create mode 100644 deal.II/examples/step-24/doc/one_sf.png create mode 100644 deal.II/examples/step-24/doc/project-1.tex create mode 100644 deal.II/examples/step-24/doc/results.dox create mode 100755 deal.II/examples/step-24/step-24 create mode 100644 deal.II/examples/step-24/step-24.cc create mode 100644 deal.II/examples/step-25/Makefile create mode 100644 deal.II/examples/step-25/Makefile.dep create mode 100755 deal.II/examples/step-25/doc/animate.sh create mode 100644 deal.II/examples/step-25/doc/christov.1d-breather.gif create mode 100644 deal.II/examples/step-25/doc/christov.1d-breather_stp.png create mode 100644 deal.II/examples/step-25/doc/christov.2d-angled_kink.gif create mode 100644 deal.II/examples/step-25/doc/christov.2d-kink.gif create mode 100644 deal.II/examples/step-25/doc/christov.2d-kink.png create mode 100644 deal.II/examples/step-25/doc/christov.2d-pseudobreather.gif create mode 100644 deal.II/examples/step-25/doc/intro.dox create mode 100644 deal.II/examples/step-25/doc/plot.plt create mode 100644 deal.II/examples/step-25/doc/results.dox create mode 100755 deal.II/examples/step-25/step-25 create mode 100644 deal.II/examples/step-25/step-25.cc diff --git a/deal.II/examples/step-23/Makefile b/deal.II/examples/step-23/Makefile new file mode 100644 index 0000000000..f291d79ad6 --- /dev/null +++ b/deal.II/examples/step-23/Makefile @@ -0,0 +1,154 @@ +# $Id: Makefile 11909 2005-12-21 13:30:36Z guido $ + + +# For the small projects Makefile, you basically need to fill in only +# four fields. +# +# The first is the name of the application. It is assumed that the +# application name is the same as the base file name of the single C++ +# file from which the application is generated. +target = $(basename $(shell echo step-*.cc)) + +# The second field determines whether you want to run your program in +# debug or optimized mode. The latter is significantly faster, but no +# run-time checking of parameters and internal states is performed, so +# you should set this value to `on' while you develop your program, +# and to `off' when running production computations. +debug-mode = on + + +# As third field, we need to give the path to the top-level deal.II +# directory. You need to adjust this to your needs. Since this path is +# probably the most often needed one in the Makefile internals, it is +# designated by a single-character variable, since that can be +# reference using $D only, i.e. without the parentheses that are +# required for most other parameters, as e.g. in $(target). +D = ../../ + + +# The last field specifies the names of data and other files that +# shall be deleted when calling `make clean'. Object and backup files, +# executables and the like are removed anyway. Here, we give a list of +# files in the various output formats that deal.II supports. +clean-up-files = *gmv *gnuplot *gpl *eps *pov + + + + +# +# +# Usually, you will not need to change something beyond this point. +# +# +# The next statement tell the `make' program where to find the +# deal.II top level directory and to include the file with the global +# settings +include $D/common/Make.global_options + + +################################################################ +# Since the whole project consists of only one file, we need not +# consider difficult dependencies. We only have to declare the +# libraries which we want to link to the object file, and there need +# to be two sets of libraries: one for the debug mode version of the +# application and one for the optimized mode. Here we have selected +# the versions for 2d. Note that the order in which the libraries are +# given here is important and that your applications won't link +# properly if they are given in another order. +# +# You may need to augment the lists of libraries when compiling your +# program for other dimensions, or when using third party libraries +libs.g = $(lib-deal2-2d.g) \ + $(lib-lac.g) \ + $(lib-base.g) +libs.o = $(lib-deal2-2d.o) \ + $(lib-lac.o) \ + $(lib-base.o) + + +# We now use the variable defined above which switch between debug and +# optimized mode to select the set of libraries to link with. Included +# in the list of libraries is the name of the object file which we +# will produce from the single C++ file. Note that by default we use +# the extension .g.o for object files compiled in debug mode and .o for +# object files in optimized mode (or whatever the local default on your +# system is instead of .o). +ifeq ($(debug-mode),on) + libraries = $(target).g.$(OBJEXT) $(libs.g) +else + libraries = $(target).$(OBJEXT) $(libs.o) +endif + + +# Now comes the first production rule: how to link the single object +# file produced from the single C++ file into the executable. Since +# this is the first rule in the Makefile, it is the one `make' selects +# if you call it without arguments. +$(target) : $(libraries) + @echo ============================ Linking $@ + @$(CXX) -o $@$(EXEEXT) $^ $(LIBS) $(LDFLAGS) + + +# To make running the application somewhat independent of the actual +# program name, we usually declare a rule `run' which simply runs the +# program. You can then run it by typing `make run'. This is also +# useful if you want to call the executable with arguments which do +# not change frequently. You may then want to add them to the +# following rule: +run: $(target) + @echo ============================ Running $< + @./$(target)$(EXEEXT) + + +# As a last rule to the `make' program, we define what to do when +# cleaning up a directory. This usually involves deleting object files +# and other automatically created files such as the executable itself, +# backup files, and data files. Since the latter are not usually quite +# diverse, you needed to declare them at the top of this file. +clean: + -rm -f *.$(OBJEXT) *~ Makefile.dep $(target)$(EXEEXT) $(clean-up-files) + + +# Since we have not yet stated how to make an object file from a C++ +# file, we should do so now. Since the many flags passed to the +# compiler are usually not of much interest, we suppress the actual +# command line using the `at' sign in the first column of the rules +# and write the string indicating what we do instead. +./%.g.$(OBJEXT) : + @echo ==============debug========= $( $@ \ + || (rm -f $@ ; false) + @if test -s $@ ; then : else rm $@ ; fi + + +# To make the dependencies known to `make', we finally have to include +# them: +include Makefile.dep + diff --git a/deal.II/examples/step-23/Makefile.dep b/deal.II/examples/step-23/Makefile.dep new file mode 100644 index 0000000000..f6e3599a6f --- /dev/null +++ b/deal.II/examples/step-23/Makefile.dep @@ -0,0 +1,242 @@ +./step-23.o: \ + step-23.cc\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/config.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/data_out_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function_time.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/geometry_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/logstream.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/multithread_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/numbers.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/point.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/polynomial.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature_lib.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/smartpointer.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/subscriptor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_product_polynomials.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/thread_management.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/vector_slice.h\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/assert.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/checked_delete.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/posix_features.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_compiler_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_platform_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_stdlib_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/suffix.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/current_function.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_gcc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_win32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/bad_weak_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/interlocked.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lightweight_mutex.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_nop.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_win32_cs.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/quick_allocator.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_ptr_nmt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_cw_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ia64.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_x86.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_nt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_pt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_w32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_impl.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/workaround.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/shared_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/throw_exception.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/tuple/tuple.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/alignment_of.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/type_with_alignment.hpp\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_constraints.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_tools.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/function_map.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_collection.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_poly.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_q.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_update_flags.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_values.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/mapping.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/grid_generator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_faces.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_hex.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_line.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_quad.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/data_out.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/matrices.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/vectors.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/full_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/identity_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_parallel_block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_parallel_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/precondition.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_cg.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_control.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparse_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparsity_pattern.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector_memory.h +./step-23.g.o: \ + step-23.cc\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/config.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/data_out_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function_time.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/geometry_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/logstream.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/multithread_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/numbers.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/point.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/polynomial.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature_lib.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/smartpointer.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/subscriptor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_product_polynomials.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/thread_management.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/vector_slice.h\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/assert.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/checked_delete.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/posix_features.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_compiler_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_platform_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_stdlib_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/suffix.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/current_function.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_gcc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_win32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/bad_weak_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/interlocked.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lightweight_mutex.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_nop.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_win32_cs.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/quick_allocator.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_ptr_nmt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_cw_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ia64.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_x86.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_nt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_pt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_w32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_impl.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/workaround.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/shared_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/throw_exception.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/tuple/tuple.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/alignment_of.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/type_with_alignment.hpp\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_constraints.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_tools.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/function_map.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_collection.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_poly.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_q.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_update_flags.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_values.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/mapping.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/grid_generator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_faces.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_hex.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_line.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_quad.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/data_out.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/matrices.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/vectors.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/full_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/identity_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_parallel_block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_parallel_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/precondition.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_cg.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_control.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparse_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparsity_pattern.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector_memory.h diff --git a/deal.II/examples/step-23/doc/intro.dox b/deal.II/examples/step-23/doc/intro.dox new file mode 100644 index 0000000000..c59cfdf609 --- /dev/null +++ b/deal.II/examples/step-23/doc/intro.dox @@ -0,0 +1,2 @@ + +

Introduction

diff --git a/deal.II/examples/step-23/doc/results.dox b/deal.II/examples/step-23/doc/results.dox new file mode 100644 index 0000000000..e67fccc1c1 --- /dev/null +++ b/deal.II/examples/step-23/doc/results.dox @@ -0,0 +1,2 @@ + +

Results

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@@ +/* $Id: step-4.cc,v 1.34 2006/02/06 21:33:10 wolf Exp $ */ +/* Author: Wolfgang Bangerth, University of Heidelberg, 1999 */ + +/* $Id: step-4.cc,v 1.34 2006/02/06 21:33:10 wolf Exp $ */ +/* Version: $Name: $ */ +/* */ +/* Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006 by the deal.II authors */ +/* */ +/* This file is subject to QPL and may not be distributed */ +/* without copyright and license information. Please refer */ +/* to the file deal.II/doc/license.html for the text and */ +/* further information on this license. */ + + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include + +#include +#include +#include +#include + +#include + + + +template +class WaveEquationProblem +{ + public: + WaveEquationProblem (); + void run (); + + private: + void make_grid_and_dofs (); + void assemble_system (); + void solve_u (); + void solve_v (); + void output_results (const unsigned int timestep_number) const; + + Triangulation triangulation; + FE_Q fe; + DoFHandler dof_handler; + + SparsityPattern sparsity_pattern; + SparseMatrix system_matrix; + SparseMatrix mass_matrix; + SparseMatrix laplace_matrix; + + double time_step; + double theta; + + Vector solution_u, solution_v; + Vector old_solution_u, old_solution_v; + Vector system_rhs; +}; + + + +template +class RightHandSide : public Function +{ + public: + RightHandSide () : Function() {}; + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + + +template +class InitialValuesU : public Function +{ + public: + InitialValuesU () : Function() {}; + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + + + +template +class BoundaryValues : public Function +{ + public: + BoundaryValues () : Function() {}; + + virtual double value (const Point &p, + const unsigned int component = 0) const; +}; + + + + +template +double RightHandSide::value (const Point &/*p*/, + const unsigned int /*component*/) const +{ +// if (get_time() <= 0.25) +// if ((p[0] <=0) && (p[1] <= 0)) +// return 1; + + return 0; +} + + +template +double InitialValuesU::value (const Point &p, + const unsigned int /*component*/) const +{ + // return std::sqrt(p.square()) * std::exp (-p.square()) / 3; + if ((p[0] <=0) && (p[1] <= 0)) + return 1; + + return 0;} + + +template +double BoundaryValues::value (const Point &/*p*/, + const unsigned int /*component*/) const +{ + return 0; +} + + + + + + + +template +WaveEquationProblem::WaveEquationProblem () : + fe (1), + dof_handler (triangulation), + time_step (1./64), + theta (0.5) +{} + + + +template +void WaveEquationProblem::make_grid_and_dofs () +{ + GridGenerator::hyper_cube (triangulation, -1, 1); + triangulation.refine_global (7); + + std::cout << " Number of active cells: " + << triangulation.n_active_cells() + << std::endl + << " Total number of cells: " + << triangulation.n_cells() + << std::endl; + + dof_handler.distribute_dofs (fe); + + std::cout << " Number of degrees of freedom: " + << dof_handler.n_dofs() + << std::endl; + + sparsity_pattern.reinit (dof_handler.n_dofs(), + dof_handler.n_dofs(), + dof_handler.max_couplings_between_dofs()); + DoFTools::make_sparsity_pattern (dof_handler, sparsity_pattern); + sparsity_pattern.compress(); + + system_matrix.reinit (sparsity_pattern); + mass_matrix.reinit (sparsity_pattern); + laplace_matrix.reinit (sparsity_pattern); + + solution_u.reinit (dof_handler.n_dofs()); + solution_v.reinit (dof_handler.n_dofs()); + old_solution_u.reinit (dof_handler.n_dofs()); + old_solution_v.reinit (dof_handler.n_dofs()); + system_rhs.reinit (dof_handler.n_dofs()); +} + + + +template +void WaveEquationProblem::assemble_system () +{ + MatrixCreator::create_mass_matrix (dof_handler, QGauss(3), + mass_matrix); + MatrixCreator::create_laplace_matrix (dof_handler, QGauss(3), + laplace_matrix); + + system_matrix.copy_from (mass_matrix); + system_matrix.add (theta * theta * time_step * time_step, laplace_matrix); +} + + + +template +void WaveEquationProblem::solve_u () +{ + SolverControl solver_control (1000, 1e-8*system_rhs.l2_norm()); + SolverCG<> cg (solver_control); + cg.solve (system_matrix, solution_u, system_rhs, + PreconditionIdentity()); + + std::cout << " " << solver_control.last_step() + << " CG iterations needed to obtain convergence." + << std::endl; +} + + +template +void WaveEquationProblem::solve_v () +{ + SolverControl solver_control (1000, 1e-8*system_rhs.l2_norm()); + SolverCG<> cg (solver_control); + cg.solve (mass_matrix, solution_v, system_rhs, + PreconditionIdentity()); + + std::cout << " " << solver_control.last_step() + << " CG iterations needed to obtain convergence." + << std::endl; +} + + + +template +void WaveEquationProblem::output_results (const unsigned int timestep_number) const +{ + DataOut data_out; + + data_out.attach_dof_handler (dof_handler); + data_out.add_data_vector (solution_u, "U"); + data_out.add_data_vector (solution_v, "V"); + + data_out.build_patches (); + + std::ostringstream filename; + filename << "solution-" + << timestep_number; + std::ofstream output (filename.str().c_str()); + data_out.write_gnuplot (output); +} + + + + +template +void WaveEquationProblem::run () +{ + std::cout << "Solving problem in " << dim << " space dimensions." << std::endl; + + make_grid_and_dofs(); + assemble_system (); + + ConstraintMatrix constraints; + constraints.close(); + VectorTools::project (dof_handler, constraints, QGauss(3), + InitialValuesU(), + old_solution_u); + VectorTools::project (dof_handler, constraints, QGauss(3), + ZeroFunction(), + old_solution_v); + + unsigned int timestep_number = 1; + for (double time = time_step; time<=5; time+=time_step, ++timestep_number) + { + Vector tmp (solution_u.size()); + + mass_matrix.vmult (system_rhs, old_solution_u); + + mass_matrix.vmult (tmp, old_solution_v); + system_rhs.add (time_step, tmp); + + laplace_matrix.vmult (tmp, old_solution_u); + system_rhs.add (-theta * (1-theta) * time_step * time_step, tmp); + + RightHandSide rhs_function; + rhs_function.set_time (time); + VectorTools::create_right_hand_side (dof_handler, QGauss(2), + rhs_function, tmp); + system_rhs.add (theta * theta * time_step * time_step, tmp); + + rhs_function.set_time (time-time_step); + VectorTools::create_right_hand_side (dof_handler, QGauss(2), + rhs_function, tmp); + system_rhs.add (theta * (1-theta) * time_step * time_step, tmp); + + + std::map boundary_values; + VectorTools::interpolate_boundary_values (dof_handler, + 0, + BoundaryValues(), + boundary_values); + MatrixTools::apply_boundary_values (boundary_values, + system_matrix, + solution_u, + system_rhs); + solve_u (); + + + laplace_matrix.vmult (system_rhs, solution_u); + system_rhs *= -theta * time_step; + + mass_matrix.vmult (tmp, old_solution_v); + system_rhs += tmp; + + laplace_matrix.vmult (tmp, old_solution_u); + system_rhs.add (-time_step * (1-theta), tmp); + + rhs_function.set_time (time); + VectorTools::create_right_hand_side (dof_handler, QGauss(2), + rhs_function, tmp); + system_rhs.add (theta * time_step, tmp); + + rhs_function.set_time (time-time_step); + VectorTools::create_right_hand_side (dof_handler, QGauss(2), + rhs_function, tmp); + system_rhs.add ((1-theta) * time_step, tmp); + + solve_v (); + + output_results (timestep_number); + + old_solution_u = solution_u; + old_solution_v = solution_v; + } +} + + + +int main () +{ + deallog.depth_console (0); + { + WaveEquationProblem<2> wave_equation_problem_2d; + wave_equation_problem_2d.run (); + } + + return 0; +} diff --git a/deal.II/examples/step-24/Makefile b/deal.II/examples/step-24/Makefile new file mode 100644 index 0000000000..f291d79ad6 --- /dev/null +++ b/deal.II/examples/step-24/Makefile @@ -0,0 +1,154 @@ +# $Id: Makefile 11909 2005-12-21 13:30:36Z guido $ + + +# For the small projects Makefile, you basically need to fill in only +# four fields. +# +# The first is the name of the application. It is assumed that the +# application name is the same as the base file name of the single C++ +# file from which the application is generated. +target = $(basename $(shell echo step-*.cc)) + +# The second field determines whether you want to run your program in +# debug or optimized mode. The latter is significantly faster, but no +# run-time checking of parameters and internal states is performed, so +# you should set this value to `on' while you develop your program, +# and to `off' when running production computations. +debug-mode = on + + +# As third field, we need to give the path to the top-level deal.II +# directory. You need to adjust this to your needs. Since this path is +# probably the most often needed one in the Makefile internals, it is +# designated by a single-character variable, since that can be +# reference using $D only, i.e. without the parentheses that are +# required for most other parameters, as e.g. in $(target). +D = ../../ + + +# The last field specifies the names of data and other files that +# shall be deleted when calling `make clean'. Object and backup files, +# executables and the like are removed anyway. Here, we give a list of +# files in the various output formats that deal.II supports. +clean-up-files = *gmv *gnuplot *gpl *eps *pov + + + + +# +# +# Usually, you will not need to change something beyond this point. +# +# +# The next statement tell the `make' program where to find the +# deal.II top level directory and to include the file with the global +# settings +include $D/common/Make.global_options + + +################################################################ +# Since the whole project consists of only one file, we need not +# consider difficult dependencies. We only have to declare the +# libraries which we want to link to the object file, and there need +# to be two sets of libraries: one for the debug mode version of the +# application and one for the optimized mode. Here we have selected +# the versions for 2d. Note that the order in which the libraries are +# given here is important and that your applications won't link +# properly if they are given in another order. +# +# You may need to augment the lists of libraries when compiling your +# program for other dimensions, or when using third party libraries +libs.g = $(lib-deal2-2d.g) \ + $(lib-lac.g) \ + $(lib-base.g) +libs.o = $(lib-deal2-2d.o) \ + $(lib-lac.o) \ + $(lib-base.o) + + +# We now use the variable defined above which switch between debug and +# optimized mode to select the set of libraries to link with. Included +# in the list of libraries is the name of the object file which we +# will produce from the single C++ file. Note that by default we use +# the extension .g.o for object files compiled in debug mode and .o for +# object files in optimized mode (or whatever the local default on your +# system is instead of .o). +ifeq ($(debug-mode),on) + libraries = $(target).g.$(OBJEXT) $(libs.g) +else + libraries = $(target).$(OBJEXT) $(libs.o) +endif + + +# Now comes the first production rule: how to link the single object +# file produced from the single C++ file into the executable. Since +# this is the first rule in the Makefile, it is the one `make' selects +# if you call it without arguments. +$(target) : $(libraries) + @echo ============================ Linking $@ + @$(CXX) -o $@$(EXEEXT) $^ $(LIBS) $(LDFLAGS) + + +# To make running the application somewhat independent of the actual +# program name, we usually declare a rule `run' which simply runs the +# program. You can then run it by typing `make run'. This is also +# useful if you want to call the executable with arguments which do +# not change frequently. You may then want to add them to the +# following rule: +run: $(target) + @echo ============================ Running $< + @./$(target)$(EXEEXT) + + +# As a last rule to the `make' program, we define what to do when +# cleaning up a directory. This usually involves deleting object files +# and other automatically created files such as the executable itself, +# backup files, and data files. Since the latter are not usually quite +# diverse, you needed to declare them at the top of this file. +clean: + -rm -f *.$(OBJEXT) *~ Makefile.dep $(target)$(EXEEXT) $(clean-up-files) + + +# Since we have not yet stated how to make an object file from a C++ +# file, we should do so now. Since the many flags passed to the +# compiler are usually not of much interest, we suppress the actual +# command line using the `at' sign in the first column of the rules +# and write the string indicating what we do instead. +./%.g.$(OBJEXT) : + @echo ==============debug========= $( $@ \ + || (rm -f $@ ; false) + @if test -s $@ ; then : else rm $@ ; fi + + +# To make the dependencies known to `make', we finally have to include +# them: +include Makefile.dep + diff --git a/deal.II/examples/step-24/Makefile.dep b/deal.II/examples/step-24/Makefile.dep new file mode 100644 index 0000000000..94cc50a182 --- /dev/null +++ b/deal.II/examples/step-24/Makefile.dep @@ -0,0 +1,252 @@ +./step-24.o: \ + step-24.cc\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/config.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/data_out_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function_time.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/geometry_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/logstream.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/multithread_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/numbers.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/point.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/polynomial.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/qprojector.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature_lib.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/smartpointer.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/subscriptor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_product_polynomials.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/thread_management.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/vector_slice.h\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/assert.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/checked_delete.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/posix_features.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_compiler_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_platform_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_stdlib_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/suffix.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/current_function.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_gcc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_win32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/bad_weak_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/interlocked.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lightweight_mutex.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_nop.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_win32_cs.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/quick_allocator.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_ptr_nmt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_cw_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ia64.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_x86.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_nt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_pt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_w32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_impl.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/workaround.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/shared_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/throw_exception.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/tuple/tuple.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/alignment_of.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/type_with_alignment.hpp\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_constraints.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_tools.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/function_map.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_collection.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_poly.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_q.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_update_flags.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_values.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/mapping.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/mapping_q1.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/grid_generator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/grid_tools.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_boundary.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_boundary_lib.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_faces.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_hex.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_line.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_quad.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/multigrid/mg_dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/data_out.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/matrices.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/numerics/vectors.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/block_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/full_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/identity_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_parallel_block_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_parallel_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/precondition.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_cg.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_control.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparse_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparsity_pattern.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector_memory.h +./step-24.g.o: \ + step-24.cc\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/config.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/data_out_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/exceptions.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/function_time.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/geometry_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/logstream.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/multithread_info.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/numbers.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/point.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/polynomial.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/qprojector.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/quadrature_lib.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/smartpointer.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/subscriptor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/table_indices.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_base.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/tensor_product_polynomials.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/thread_management.h\ + /home/bangerth/p/deal.II/1/deal.II/base/include/base/vector_slice.h\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/assert.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/checked_delete.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/posix_features.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_compiler_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_platform_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/select_stdlib_config.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/config/suffix.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/current_function.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_gcc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/atomic_count_win32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/bad_weak_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/interlocked.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lightweight_mutex.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_nop.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_pthreads.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/lwm_win32_cs.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/quick_allocator.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_count.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/shared_ptr_nmt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_cw_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ia64.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_ppc.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_gcc_x86.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_nt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_pt.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_base_w32.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/sp_counted_impl.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/detail/workaround.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/shared_ptr.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/throw_exception.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/tuple/tuple.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/alignment_of.hpp\ + /home/bangerth/p/deal.II/1/deal.II/contrib/boost/include/boost/type_traits/type_with_alignment.hpp\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_constraints.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_iterator_selector.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/dof_tools.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/function_map.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_handler.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_levels.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/dofs/hp_dof_objects.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_base.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_collection.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_poly.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_q.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_update_flags.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/fe_values.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/mapping.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/fe/mapping_q1.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/grid_generator.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/grid_tools.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_accessor.templates.h\ + /home/bangerth/p/deal.II/1/deal.II/deal.II/include/grid/tria_boundary.h\ + 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/home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/petsc_vector_base.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/precondition.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_cg.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/solver_control.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparse_matrix.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/sparsity_pattern.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector.h\ + /home/bangerth/p/deal.II/1/deal.II/lac/include/lac/vector_memory.h diff --git a/deal.II/examples/step-24/doc/intro.dox b/deal.II/examples/step-24/doc/intro.dox new file mode 100644 index 0000000000..939112b4fa --- /dev/null +++ b/deal.II/examples/step-24/doc/intro.dox @@ -0,0 +1,162 @@ + +

Introduction

+ +This project is to simulate the thermoacoustic tomography imaging. In thermoacoustic +tomography,pulsed electromagnetic energy is delivered into biological issues. +Tissues absorbe the energy and then generate thermoacoustic waves through +thermoelastic expansion. The forward problem is a wave propagation problem. + + +

Problem

+ +Thermal equation without considering thermal diffusion is + +@f[ +\rho C_p \frac{\partial}{\partial t}T(t,\mathbf r) = H(t,\mathbf r) +@f] + +Where $\rho (\mathbf r) $ is the density; $C_p (\mathbf r) $ is the specific heat; +$ T(t,\mathbf r)$ is the temperature rise due to the delivered microwave +energy; and $H(t,\mathbf r)$ is the heating function defined as the thermal energy +per time and volume transformed from deposited microwave energy. + +Assume tissues have heterogeneous dielectric properties but homogeneous acoustic +properties. The basic acoustic generation equation in an acoustically homogeneous +medium is the linear inviscid force equation + +@f[ +\rho \frac{\partial^2}{\partial t^2}u(t,\mathbf r) = +-\nabla p(t,\mathbf r) +@f] + +and the expansion equation: + +@f[ +\nabla \cdot u(t,\mathbf r) = -\frac{p(t,\mathbf r)}{\rho c_0^2}+\beta T(t,\mathbf r) +@f] + +The original problem can be described as: + +@f[ +\Delta p-\frac{1}{c_0^2} \frac{\partial^2 p }{\partial^2 t} = \lambda \delta(t)a(\mathbf r) +@f] + +where $\lambda = - \frac{\beta}{C_p}$. + +The forward propogation problem can be changed to solve a wave equation with +initial conditions as follows: + +@f{eqnarray*} +\Delta \bar{p}- \frac{1}{c_0^2} \frac{\partial^2 \bar{p}}{\partial^2 t} & = & f(t,\mathbf r) \\ + +\bar{p}(0,\mathbf r)=\lambda a(\mathbf r) & = & b(\mathbf r) +@f} + + + +

Weak form and Discretization

+ +One first introduces a second variable, which is defined as the derivative of +the pressure potential. + +@f[ +v = \frac{\partial\bar{p}}{\partial t} +@f] + +With the second variables, one then transform the forward problem into +two seperate equations: + +@f{eqnarray*} +\bar{p}_{t} - v & = & 0 \\ +\Delta\bar{p} - \frac{1}{c_0^2}\,v_{t} & = & f +@f} + +with initial conditions: + +@f{eqnarray*} +\bar{p}(0,\mathbf r) & = & b(r) \\ +v(0,\mathbf r)=\bar{p}_t(0,\mathbf r) & = & 1 +@f} + +In real application, the thermoacoustic source is very small as compared to the medium. +The propagation path of the thermoacoustic waves can be approximated as from the source +to the infinity. And the detector is in limited distance from the source. One only needs to +evaluate the values when the thermoacoustic waves pass through the detectors. For this specific +detection geometry, One then chooses the absorbing boundary condition for the simulation. + +@f[ +\frac{\partial\bar{p}}{\partial\mathbf n} = +-\frac{1}{c_0} \frac{\partial\bar{p}}{\partial t} +@f] + +$\frac{\partial\bar{p}}{\partial\mathbf n}$ is normal derivative at the boundary. This is the +time-varying FEM model. To implement FEM for time dependent problem , one discretizes according +to $t$ and obtains: + +@f{eqnarray*} +(\frac{\bar{p}^n-\bar{p}^{n-1}}{\delta t},\phi)_\Omega- +(\theta v^{n}+(1-\theta)v^{n-1},\phi)_\Omega & = & 0 \\ +-(\Delta((\theta\bar{p}^n+(1-\theta)\bar{p}^{n-1})),\nabla)_\Omega- +\frac{1}{c_0}(\frac{\bar{p}^n-\bar{p}^{n-1}}{\delta t},\phi)_\partial\Omega - +\frac{1}{c_0^2}(\frac{v^n-v^{n-1}}{\delta t},\phi)_\Omega & = +& \theta f^{n}+(1-\theta)f^{n-1} +@f} + +The weak formulation of the problem is obtained by multiplying the above two equations +with test functions and integrating some terms by parts: + +@f{eqnarray*} +M\bar{p}^{n}-(\delta t \theta)M v^{n-1} & = & M\bar{p}^{n-1}+\delta t (1-\theta)Mv^{n-1}\\ + +(-c_0^2\delta t \theta A-c_0 B)\bar{p}^n-Mv^{n} & = & +(c_0^2\delta t(1-\theta)A-c_0B)\bar{p}^{n-1}-Mv^{n-1}+c_0^2\delta t(\theta F^{n}+(1-\theta)F^{n-1}) +@f} + +Here, the absoring boundary conditions are incorporated into the weak form by using + +@f[ +\int_\Omega\varphi(\nabla\cdot(\nabla p))dx = +-\int_\Omega\nabla \varphi \cdot \nabla p dx + +\int_{\partial\Omega}\varphi \frac{\partial p}{\partial t}ds +@f] + +Where $\varphi$ is the test function. + +Pressure and its derivative are the two variables one is interested in the above equations, +One can write the above two equations as a matrix form with the pressure and its derivative as +an unknown vecotor: +@f[ +\left(\begin{array}{cc} + M & -\delta t\theta M \\ +c_0^2\,\delta t\,\theta\,A+c_0\,B & M \\ + \end{array} \right)\\ +\left(\begin{array}{c} + \bar{p}^{n} \\ + \bar{v}^{n} + \end{array}\right)=\\ +\left(\begin{array}{l} + G_1 \\ + G_2 -(\theta F^{n}+(1-\theta)F ^{n-1})c_{0}^{2}\delta t \\ + \end{array}\right) +@f] + +where +@f[ +\left(\begin{array}{c} +G_1 \\ +G_2 \\ + \end{array} \right)=\\ +\left(\begin{array}{l} + M\bar{p}^{n-1}+\delta t(1-\theta)Mv^{n-1}\\ + (-c_{0}^{2}\delta t (1-\theta)A+c_0 B)\bar{p}^{n-1} +Mv^{n-1} + \end{array}\right) +@f] + +By some simply 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