--- /dev/null
+# $Id$
+
+
+# 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) \
+ $(lib-base.o)
+
+
+# We now use the variable defined above which switch between debug and
+# optimized mode to select the correct compiler flags and the set of
+# libraries to link with. Included in the list of libraries is the
+# name of the object file which we will produce from the single C++
+# file. Note that by default we use the extension .go for object files
+# compiled in debug mode and .o for object files in optimized mode.
+ifeq ($(debug-mode),on)
+ libraries = $(target).go $(libs.g)
+ flags = $(CXXFLAGS.g)
+else
+ libraries = $(target).o $(libs.o)
+ flags = $(CXXFLAGS.o)
+endif
+
+
+# Now comes the first production rule: how to link the single object
+# file produced from the single C++ file into the executable. Since
+# this is the first rule in the Makefile, it is the one `make' selects
+# if you call it without arguments.
+$(target) : $(libraries)
+ @echo ============================ Linking $@
+ @$(CXX) -o $@ $^ $(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)
+
+
+# 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 *.o *.go *~ Makefile.dep $(target) $(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.
+%.go : %.cc
+ @echo ==============debug========= $(<F)
+ @$(CXX) $(CXXFLAGS.g) -c $< -o $@
+%.o : %.cc
+ @echo ==============optimized===== $(<F)
+ @$(CXX) $(CXXFLAGS.o) -c $< -o $@
+
+
+# The following statement tells make that the rules `run' and `clean'
+# are not expected to produce files of the same name as Makefile rules
+# usually do.
+.PHONY: run clean
+
+
+# Finally there is a rule which you normally need not care much about:
+# since the executable depends on some include files from the library,
+# besides the C++ application file of course, it is necessary to
+# re-generate the executable when one of the files it depends on has
+# changed. The following rule to created a dependency file
+# `Makefile.dep', which `make' uses to determine when to regenerate
+# the executable. This file is automagically remade whenever needed,
+# i.e. whenever one of the cc-(include-path-base)/baseh-files changed. Make detects whether
+# to remake this file upon inclusion at the bottom of this file.
+#
+# The dependency file is created using a perl script. Since the
+# script prefixes the output names by `lib(include-path-base)/baseo' or `lib(include-path-base)/basego' (it was
+# written for the sublibraries' Makefile), we have to strip that again
+# since object files are placed in the present directory for this
+# application. All these things are made in the next rule:
+Makefile.dep: $(target).cc Makefile \
+ $(shell echo $(include-path-base)/base/*.h \
+ $(include-path-lac)/lac/*.h \
+ $(include-path-deal2)/*/*.h)
+ @echo ============================ Remaking Makefile
+ @perl $D/common/scripts/make_dependencies.pl $(INCLUDE) $(target).cc \
+ | perl -pi -e 's!lib/g?o/!!g;' \
+ > Makefile.dep
+
+# To make the dependencies known to `make', we finally have to include
+# them:
+include Makefile.dep
+
+
--- /dev/null
+/* $Id$ */
+/* Author: Wolfgang Bangerth, University of Heidelberg, 2001 */
+
+ // As usual, the program starts with
+ // a rather long list of include
+ // files which you are probably
+ // already used to by now:
+#include <base/quadrature_lib.h>
+#include <base/function.h>
+#include <base/logstream.h>
+#include <lac/vector.h>
+#include <lac/sparse_matrix.h>
+#include <lac/solver_cg.h>
+#include <lac/vector_memory.h>
+#include <lac/precondition.h>
+#include <grid/tria.h>
+#include <grid/grid_generator.h>
+#include <grid/tria_boundary_lib.h>
+#include <grid/tria_accessor.h>
+#include <grid/tria_iterator.h>
+#include <dofs/dof_handler.h>
+#include <dofs/dof_constraints.h>
+#include <dofs/dof_accessor.h>
+#include <dofs/dof_tools.h>
+#include <fe/fe_q.h>
+#include <fe/fe_values.h>
+#include <fe/mapping_q.h>
+#include <numerics/vectors.h>
+#include <numerics/matrices.h>
+
+ // Just this one is new: it declares
+ // a class
+ // ``CompressedSparsityPattern'',
+ // which we will use and explain
+ // further down below.
+#include <lac/compressed_sparsity_pattern.h>
+
+ // We will make use of the std::find
+ // algorithm of the C++ standard
+ // library, so we have to include the
+ // following file for its
+ // declaration:
+#include <algorithm>
+
+
+template <int dim>
+double measure (const DoFHandler<dim> &dof_handler,
+ const Mapping<dim> &mapping)
+{
+ QGauss4<dim> quadrature;
+ FEValues<dim> fe_values (mapping, dof_handler.get_fe(), quadrature,
+ update_JxW_values);
+
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ double measure = 0;
+ for (; cell!=endc; ++cell)
+ {
+ fe_values.reinit (cell);
+ for (unsigned int i=0; i<fe_values.n_quadrature_points; ++i)
+ measure += fe_values.JxW (i);
+ };
+ return measure;
+};
+
+
+template <int dim>
+double measure (const Triangulation<dim> &triangulation,
+ const Mapping<dim> &mapping)
+{
+ FE_Q<dim> dummy_fe(1);
+ DoFHandler<dim> dof_handler (const_cast<Triangulation<dim>&>(triangulation));
+ dof_handler.distribute_dofs(dummy_fe);
+ return measure (dof_handler, mapping);
+};
+
+
+template <int dim>
+double surface (const DoFHandler<dim> &dof_handler,
+ const Mapping<dim> &mapping)
+{
+ QGauss4<dim-1> quadrature;
+ FEFaceValues<dim> fe_values (mapping, dof_handler.get_fe(), quadrature,
+ update_JxW_values);
+
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+ double surface = 0;
+ for (; cell!=endc; ++cell)
+ for (unsigned int face=0; face<GeometryInfo<dim>::faces_per_cell; ++face)
+ if (cell->face(face)->at_boundary())
+ {
+ fe_values.reinit (cell, face);
+ for (unsigned int i=0; i<fe_values.n_quadrature_points; ++i)
+ surface += fe_values.JxW (i);
+ };
+ return surface;
+};
+
+
+template <int dim>
+double surface (const Triangulation<dim> &triangulation,
+ const Mapping<dim> &mapping)
+{
+ FE_Q<dim> dummy_fe(1);
+ DoFHandler<dim> dof_handler (const_cast<Triangulation<dim>&>(triangulation));
+ dof_handler.distribute_dofs(dummy_fe);
+ return surface (dof_handler, mapping);
+};
+
+
+template double surface (const Triangulation<2> &, const Mapping<2> &);
+template double measure (const Triangulation<2> &, const Mapping<2> &);
+
+
+
+
+ // Then we declare a class which
+ // represents the solution of a
+ // Laplace problem. As this example
+ // program is based on step-5, the
+ // class looks rather the same, with
+ // the sole structural difference
+ // that we have merged the functions
+ // ``assemble_system'' and ``solve'',
+ // and the output function was
+ // dropped since the solution
+ // function is so boring that it is
+ // not worth being viewed.
+ //
+ // The only other noteworthy change
+ // is that the constructor takes a
+ // value representing the polynomial
+ // degree of the mapping to be used
+ // later on, and that it has another
+ // member variable representing
+ // exactly this mapping. In general,
+ // this variable will occur in real
+ // applications at the same places
+ // where the finite element is
+ // declared or used.
+template <int dim>
+class LaplaceProblem
+{
+ public:
+ LaplaceProblem (const unsigned int mapping_degree);
+ void run ();
+
+ private:
+ void setup_system ();
+ void assemble_and_solve ();
+ void solve ();
+
+ Triangulation<dim> triangulation;
+ FE_Q<dim> fe;
+ DoFHandler<dim> dof_handler;
+ MappingQ<dim> mapping;
+
+ SparsityPattern sparsity_pattern;
+ SparseMatrix<double> system_matrix;
+ ConstraintMatrix mean_value_constraints;
+
+ Vector<double> solution;
+ Vector<double> system_rhs;
+};
+
+
+
+ // Construct such an object, by
+ // initializing the variables. Here,
+ // we use linear finite elements (the
+ // argument to the ``fe'' variable
+ // denotes the polynomial degree),
+ // and mappings of given order. Print
+ // to screen what we are about to do.
+template <int dim>
+LaplaceProblem<dim>::LaplaceProblem (const unsigned int mapping_degree) :
+ fe (1),
+ dof_handler (triangulation),
+ mapping (mapping_degree)
+{
+ std::cout << "Using mapping with degree " << mapping_degree << ":"
+ << std::endl
+ << "============================"
+ << std::endl;
+};
+
+
+
+ // The first task is to set up the
+ // variables for this problem. This
+ // includes generating a valid
+ // ``DoFHandler'' object, as well as
+ // the sparsity patterns for the
+ // matrix, and the object
+ // representing the constraints that
+ // the mean value of the degrees of
+ // freedom on the boundary be zero.
+template <int dim>
+void LaplaceProblem<dim>::setup_system ()
+{
+ // The first task is trivial:
+ // generate an enumeration of the
+ // degrees of freedom:
+ dof_handler.distribute_dofs (fe);
+
+ // Next task is to construct the
+ // object representing the
+ // constraint that the mean value
+ // of the degrees of freedom on the
+ // boundary shall be zero. For
+ // this, we first want a list of
+ // those nodes which are actually
+ // at the boundary. The
+ // ``DoFTools'' class has a
+ // function that returns an array
+ // of boolean values where ``true''
+ // indicates that the node is at
+ // the boundary. The second
+ // argument denotes a mask
+ // selecting which components of
+ // vector valued finite elements we
+ // want to be considered. Since we
+ // have a scalar finite element
+ // anyway, this mask consists of
+ // only one entry, and its value
+ // must be ``true''.
+ std::vector<bool> boundary_dofs (dof_handler.n_dofs(), false);
+ DoFTools::extract_boundary_dofs (dof_handler, std::vector<bool>(1,true),
+ boundary_dofs);
+
+ // Let us first pick out the first
+ // boundary node from this list. We
+ // do that by searching for the
+ // first ``true'' value in the
+ // array (note that ``std::find''
+ // returns an iterator to this
+ // element), and computing its
+ // distance to the overall first
+ // element in the array to get its
+ // index:
+ const unsigned int first_boundary_dof
+ = std::distance (std::find (boundary_dofs.begin(),
+ boundary_dofs.end(),
+ true),
+ boundary_dofs.begin());
+
+ mean_value_constraints.clear ();
+ mean_value_constraints.add_line (first_boundary_dof);
+ for (unsigned int i=first_boundary_dof+1; i<dof_handler.n_dofs(); ++i)
+ if (boundary_dofs[i] == true)
+ mean_value_constraints.add_entry (first_boundary_dof,
+ i, -1);
+ mean_value_constraints.close ();
+
+ CompressedSparsityPattern csp (dof_handler.n_dofs(),
+ dof_handler.n_dofs());
+ DoFTools::make_sparsity_pattern (dof_handler, csp);
+ mean_value_constraints.condense (csp);
+
+ sparsity_pattern.copy_from (csp);
+
+ system_matrix.reinit (sparsity_pattern);
+
+ solution.reinit (dof_handler.n_dofs());
+ system_rhs.reinit (dof_handler.n_dofs());
+};
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::assemble_and_solve ()
+{
+ QGauss2<dim> cell_quadrature;
+ QGauss2<dim-1> face_quadrature;
+ MatrixTools::create_laplace_matrix (mapping, dof_handler,
+ cell_quadrature,
+ system_matrix);
+ VectorTools::create_right_hand_side (mapping, dof_handler,
+ cell_quadrature,
+ ConstantFunction<dim>(-2),
+ system_rhs);
+
+ Vector<double> tmp (system_rhs.size());
+ VectorTools::create_boundary_right_hand_side (mapping, dof_handler,
+ face_quadrature,
+ ConstantFunction<dim>(1),
+ tmp);
+ system_rhs += tmp;
+
+ mean_value_constraints.condense (system_matrix);
+ mean_value_constraints.condense (system_rhs);
+
+ solve ();
+ mean_value_constraints.distribute (solution);
+
+ Vector<float> difference_per_cell (triangulation.n_active_cells());
+ VectorTools::integrate_difference (mapping, dof_handler,
+ solution,
+ ZeroFunction<dim>(),
+ difference_per_cell,
+ QGauss3<dim>(),
+ H1_seminorm);
+ std::cout << " " << triangulation.n_active_cells() << " cells: "
+ << " |u|_1="
+ << difference_per_cell.l2_norm()
+ << ", error="
+ << fabs(difference_per_cell.l2_norm()-sqrt(3.14159265358/2))
+ << std::endl;
+};
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::solve ()
+{
+ SolverControl solver_control (1000, 1e-12);
+ PrimitiveVectorMemory<> vector_memory;
+ SolverCG<> cg (solver_control, vector_memory);
+
+ PreconditionSSOR<> preconditioner;
+ preconditioner.initialize(system_matrix, 1.2);
+
+ cg.solve (system_matrix, solution, system_rhs,
+ preconditioner);
+};
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::run ()
+{
+ GridGenerator::hyper_ball (triangulation);
+ static const HyperBallBoundary<dim> boundary;
+ triangulation.set_boundary (0, boundary);
+
+ for (unsigned int cycle=0; cycle<6; ++cycle, triangulation.refine_global(1))
+ {
+ setup_system ();
+ assemble_and_solve ();
+ };
+};
+
+
+
+ // Finally the main function. It's
+ // structure is the same as that used
+ // in several of the previous
+ // examples, so probably needs no
+ // more explanation.
+int main ()
+{
+ try
+ {
+ deallog.depth_console (0);
+ std::cout.precision(5);
+
+ // This is the main loop, doing
+ // the computations with
+ // mappings of linear through
+ // cubic mappings. Note that
+ // since we need the object of
+ // type ``LaplaceProblem<2>''
+ // only once, we do not even
+ // name it, but create an
+ // unnamed such object and call
+ // the ``run'' function of it,
+ // subsequent to which it is
+ // immediately destroyed again.
+ for (unsigned int mapping_degree=1; mapping_degree<=3; ++mapping_degree)
+ LaplaceProblem<2>(mapping_degree).run ();
+ }
+ catch (std::exception &exc)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Exception on processing: " << std::endl
+ << exc.what() << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ }
+ catch (...)
+ {
+ std::cerr << std::endl << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ std::cerr << "Unknown exception!" << std::endl
+ << "Aborting!" << std::endl
+ << "----------------------------------------------------"
+ << std::endl;
+ return 1;
+ };
+
+ return 0;
+};
projects / dealii-svn.git / commitdiff