--- /dev/null
+# $Id: Makefile 22601 2010-11-04 03:26:19Z bangerth $
+
+
+# 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 *vtk *ucd *.d2
+
+
+
+
+#
+#
+# Usually, you will not need to change anything beyond this point.
+#
+#
+# The next statement tells 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. deal.II has two
+# libraries: one for the debug mode version of the
+# application and one for optimized mode.
+libs.g := $(lib-deal2.g)
+libs.o := $(lib-deal2.o)
+
+
+# We now use the variable defined above to switch between debug and
+# optimized mode to select the set of libraries to link with. Included
+# in the list of libraries is the name of the object file which we
+# will produce from the single C++ file. Note that by default we use
+# the extension .g.o for object files compiled in debug mode and .o for
+# object files in optimized mode (or whatever local default on your
+# system is instead of .o)
+ifeq ($(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)$(EXEEXT) : $(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: $(target)$(EXEEXT)
+ @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========= $(<F) -> $@"
+ @$(CXX) $(CXXFLAGS.g) -c $< -o $@
+./%.$(OBJEXT) :
+ @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 creates 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-/h-files changed. Make detects whether
+# to remake this file upon inclusion at the bottom of this file.
+#
+# If the creation of Makefile.dep fails, blow it away and fail
+Makefile.dep: $(target).cc Makefile \
+ $(shell echo $D/include/deal.II/*/*.h)
+ @echo ============================ Remaking $@
+ @$D/common/scripts/make_dependencies $(INCLUDE) -B. $(target).cc \
+ > $@ \
+ || (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
--- /dev/null
+#include <base/polynomial_space.h>
+#include <base/parsed_function.h>
+#include <base/smartpointer.h>
+#include <base/convergence_table.h>
+#include <base/quadrature_lib.h>
+#include <base/quadrature_selector.h>
+#include <base/utilities.h>
+
+#include <lac/full_matrix.h>
+#include <lac/vector.h>
+#include <lac/solver_control.h>
+#include <lac/solver_gmres.h>
+#include <lac/solver_cg.h>
+#include <lac/precondition.h>
+#include <lac/constraint_matrix.h>
+#include <lac/sparse_matrix.h>
+#include <lac/compressed_sparsity_pattern.h>
+
+#include <grid/tria.h>
+#include <grid/tria_iterator.h>
+#include <grid/tria_accessor.h>
+#include <grid/grid_out.h>
+#include <grid/tria_boundary_lib.h>
+#include <grid/grid_generator.h>
+#include <grid/grid_tools.h>
+
+#include <dofs/dof_handler.h>
+#include <dofs/dof_accessor.h>
+#include <dofs/dof_tools.h>
+
+#include <fe/fe_values.h>
+
+#include <numerics/data_out.h>
+#include <numerics/vectors.h>
+#include <numerics/matrices.h>
+
+#include <fstream>
+#include <iostream>
+
+#include <sys/types.h>
+#include <sys/stat.h>
+
+#define deal_II_dimension 3
+
+using std::cout;
+using std::endl;
+using namespace dealii;
+
+
+template <int dim>
+class Solution : public Function<dim>
+{
+public:
+ Solution () : Function<dim>() {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+
+ virtual Tensor<1,dim> gradient (const Point<dim> &p,
+ const unsigned int component = 0) const;
+
+};
+
+template <int dim>
+double Solution<dim>::value (const Point<dim> &p,
+ const unsigned int) const
+{
+ return sin(numbers::PI * p(0))*cos(numbers::PI * p(1))*exp(p(2));
+}
+
+template <int dim>
+Tensor<1,dim> Solution<dim>::gradient (const Point<dim> &p,
+ const unsigned int) const
+{
+ double dPi = numbers::PI;
+
+ Tensor<1,dim> return_value;
+
+ return_value[0] = dPi *cos(dPi * p(0))*cos(dPi * p(1))*exp(p(2));
+ return_value[1] = -dPi *sin(dPi * p(0))*sin(dPi * p(1))*exp(p(2));
+ return_value[2] = sin(dPi * p(0))*cos(dPi * p(1))*exp(p(2));
+
+ // tangential gradient: nabla u - (nabla u nu)nu
+ Point<dim> normal;
+ double dLength;
+
+ dLength = sqrt(p(0)*p(0)+p(1)*p(1)+p(2)*p(2));
+
+ normal[0] = p(0)/dLength;
+ normal[1] = p(1)/dLength;
+ normal[2] = p(2)/dLength;
+
+ return return_value - (return_value*normal)*normal;
+}
+
+template <int dim>
+class RightHandSide : public Function<dim>
+{
+public:
+ RightHandSide () : Function<dim>() {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+};
+
+template <int dim>
+double RightHandSide<dim>::value (const Point<dim> &p,
+ const unsigned int comp) const
+{
+ Assert(dim == 3, ExcInternalError());
+
+ double dPi = numbers::PI;
+
+ // LB: u = Delta u - nu D2 u nu - (Grad u nu ) div (nu)
+
+ Tensor<2,dim> hessian;
+
+ hessian[0][0] = -dPi*dPi*sin(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+ hessian[1][1] = -dPi*dPi*sin(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+ hessian[2][2] = sin(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+
+ hessian[0][1] = -dPi*dPi*cos(dPi*p(0))*sin(dPi*p(1))*exp(p(2));
+ hessian[1][0] = -dPi*dPi*cos(dPi*p(0))*sin(dPi*p(1))*exp(p(2));
+
+ hessian[0][2] = dPi*cos(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+ hessian[2][0] = dPi*cos(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+
+ hessian[1][2] = -dPi*sin(dPi*p(0))*sin(dPi*p(1))*exp(p(2));
+ hessian[2][1] = -dPi*sin(dPi*p(0))*sin(dPi*p(1))*exp(p(2));
+
+ Tensor<1,dim> gradient;
+ gradient[0] = dPi * cos(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+ gradient[1] = - dPi * sin(dPi*p(0))*sin(dPi*p(1))*exp(p(2));
+ gradient[2] = sin(dPi*p(0))*cos(dPi*p(1))*exp(p(2));
+
+ double curvature;
+ Point<dim> normal;
+ double dLength;
+
+ curvature = dim-1;
+ dLength = sqrt(p(0)*p(0)+p(1)*p(1)+p(2)*p(2));
+
+ normal[0] = p(0)/dLength;
+ normal[1] = p(1)/dLength;
+ normal[2] = p(2)/dLength;
+
+ return -trace(hessian) + (hessian * normal) * normal + (gradient * normal)*curvature;
+}
+
+
+
+
+
+
+template <int dim>
+class LaplaceBeltrami
+{
+ public:
+ LaplaceBeltrami (Triangulation<dim-1,dim> *tria, Function<dim> &func_data,
+ unsigned int fe_degree = 1, unsigned int mapping_degree = 1,
+ Function<dim> *pExact = 0);
+ // arguments are:
+ // triangulation
+ // right-hand side
+ // fe_degree for solution
+ // fe_degree for mapping
+ // exact solution is known
+
+ ~LaplaceBeltrami ();
+ void run ();
+ double compute_error (VectorTools::NormType norm_type) const;
+
+ private:
+
+ void setup_system ();
+ void assemble_system ();
+ void solve ();
+ void output_results () const;
+
+
+
+ Triangulation<dim-1,dim> *pTria;
+ FE_Q<dim-1,dim> fe;
+ DoFHandler<dim-1,dim> dh;
+ MappingQ<dim-1, dim> mapping;
+
+ ConstraintMatrix matrix_constraints;
+
+ SparsityPattern sparsity_pattern;
+ SparseMatrix<double> system_matrix;
+
+ Vector<double> solution;
+ Vector<double> system_rhs;
+
+ Function<dim> &rhs_func; // function data
+
+ Function<dim> *pExact; // exact solution if provided
+
+};
+
+
+template <int dim>
+LaplaceBeltrami<dim>::LaplaceBeltrami (Triangulation<dim-1,dim> *tria,
+ Function<dim> &func_data,
+ unsigned int fe_degree,
+ unsigned int mapping_degree,
+ Function<dim> *pExact
+ )
+ :
+ fe (fe_degree),
+ dh(*tria),
+ mapping(mapping_degree),
+ rhs_func(func_data)
+{
+ pTria = tria;
+ this->pExact = pExact;
+
+}
+
+template <int dim>
+LaplaceBeltrami<dim>::~LaplaceBeltrami ()
+{
+ dh.clear ();
+}
+
+template <int dim>
+void LaplaceBeltrami<dim>::setup_system ()
+{
+ dh.distribute_dofs (fe);
+
+ matrix_constraints.clear ();
+ matrix_constraints.close ();
+
+ CompressedSparsityPattern csp (dh.n_dofs(),
+ dh.n_dofs());
+
+ DoFTools::make_sparsity_pattern (dh, csp);
+ matrix_constraints.condense (csp);
+
+ sparsity_pattern.copy_from (csp);
+
+ system_matrix.reinit (sparsity_pattern);
+ solution.reinit (dh.n_dofs());
+ system_rhs.reinit (dh.n_dofs());
+}
+
+template <int dim>
+void LaplaceBeltrami<dim>::assemble_system ()
+{
+
+ system_matrix = 0;
+ system_rhs = 0;
+
+ QGauss<dim-1> quadrature_formula(2);
+
+ FEValues<dim-1,dim> fe_values (mapping,fe, quadrature_formula,
+ update_values | update_cell_normal_vectors |
+ update_gradients |
+ update_quadrature_points | update_JxW_values);
+
+ const unsigned int dofs_per_cell = fe.dofs_per_cell;
+ const unsigned int n_q_points = quadrature_formula.size();
+
+ FullMatrix<double> cell_matrix (dofs_per_cell, dofs_per_cell);
+ Vector<double> cell_rhs (dofs_per_cell);
+
+ std::vector< double > rhs_values(n_q_points);
+ std::vector<unsigned int> local_dof_indices (dofs_per_cell);
+
+ typename DoFHandler<dim-1,dim>::active_cell_iterator
+ cell = dh.begin_active(),
+ endc = dh.end();
+
+ for (; cell!=endc; ++cell)
+ {
+ cell_matrix = 0;
+ cell_rhs = 0;
+
+ fe_values.reinit (cell);
+
+ rhs_func.value_list (fe_values.get_quadrature_points(), rhs_values);
+
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ {
+ for (unsigned int q_point=0; q_point<n_q_points;
+ ++q_point)
+ {
+ cell_matrix(i,j)
+ += fe_values.shape_grad(i,q_point) *
+ fe_values.shape_grad(j,q_point) *
+ fe_values.JxW(q_point);
+ }
+ }
+ }
+
+
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+ cell_rhs(i) += fe_values.shape_value(i,q_point) *
+ rhs_values[q_point]*
+ fe_values.JxW(q_point);
+ }
+
+ 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));
+
+ system_rhs(local_dof_indices[i]) += cell_rhs(i);
+ }
+ }
+
+
+ std::map<unsigned int,double> bdy_values;
+ VectorTools::interpolate_boundary_values (mapping,dh,
+ 0,
+ *pExact,
+ bdy_values
+ );
+
+ MatrixTools::apply_boundary_values (bdy_values,
+ system_matrix,
+ solution,
+ system_rhs,false);
+
+ // condense matrices
+ matrix_constraints.condense (system_matrix);
+ matrix_constraints.condense (system_rhs);
+}
+
+
+template <int dim>
+void LaplaceBeltrami<dim>::solve ()
+{
+ SolverControl solver_control (1000, 1e-7);
+ SolverCG<> cg (solver_control);
+
+ cg.solve (system_matrix, solution, system_rhs,
+ PreconditionIdentity());
+
+
+ matrix_constraints.distribute (solution);
+
+}
+
+
+
+template <int dim>
+void LaplaceBeltrami<dim>::output_results () const
+{
+
+ std::string filename = "solution.vtk";
+
+ std::ofstream output (filename.c_str());
+
+ DataOut<dim-1,DoFHandler<dim-1,dim> > data_out;
+ data_out.attach_dof_handler (dh);
+
+
+
+ data_out.add_data_vector (solution, "solution",DataOut_DoFData<DoFHandler<dim-1,dim>,dim-1,dim>::type_dof_data);
+ data_out.build_patches (mapping,
+ mapping.get_degree());
+ data_out.write_vtk (output);
+}
+
+
+
+template <int dim>
+void LaplaceBeltrami<dim>::run ()
+{
+
+ setup_system();
+ assemble_system();
+ solve();
+ output_results();
+
+}
+
+//################################################################################//
+
+template <int dim>
+double LaplaceBeltrami<dim>::compute_error (VectorTools::NormType norm_type) const
+{
+ Assert(pExact != 0, ExcInternalError());
+
+ Vector<float> difference_per_cell (pTria->n_active_cells());
+ VectorTools::integrate_difference (mapping, dh, solution,
+ *pExact, difference_per_cell,
+ QGauss<(dim-1)>(2*fe.degree+1),
+ norm_type);
+
+ return difference_per_cell.l2_norm();
+}
+
+
+
+
+int main ( int argc, char **argv )
+{
+ std::cout<<std::endl;
+ std::cout<<"================================"<<std::endl;
+ std::cout<<" LB PROBLEM "<<std::endl;
+ std::cout<<"================================"<<std::endl;
+ std::cout<<std::endl;
+
+
+ Triangulation<deal_II_dimension-1,deal_II_dimension> tria;
+
+ // create a mesh consisting on the boundary of the half sphere... thx Seba
+ std::map< Triangulation<deal_II_dimension-1,deal_II_dimension>::cell_iterator,
+ Triangulation<deal_II_dimension,deal_II_dimension>::face_iterator> surface_to_volume_mapping;
+
+ HyperBallBoundary<deal_II_dimension> boundary_description;
+ Triangulation<deal_II_dimension> volume_mesh;
+ GridGenerator::half_hyper_ball(volume_mesh);
+
+ volume_mesh.set_boundary (1, boundary_description);
+ volume_mesh.set_boundary (0, boundary_description);
+ volume_mesh.refine_global (1);
+
+ static HyperBallBoundary<deal_II_dimension-1,deal_II_dimension> surface_description;
+ tria.set_boundary (1, surface_description);
+ tria.set_boundary (0, surface_description);
+
+ std::set<unsigned char> boundary_ids;
+ boundary_ids.insert(0);
+
+ GridTools::extract_boundary_mesh (volume_mesh, tria,
+ surface_to_volume_mapping,
+ boundary_ids);
+
+
+ tria.refine_global(4);
+
+
+ RightHandSide<deal_II_dimension> rhs;
+ Solution<deal_II_dimension> exact;
+
+ LaplaceBeltrami<deal_II_dimension> laplace_beltrami_2d(&tria,rhs,2,2,&exact);
+
+ laplace_beltrami_2d.run();
+
+ std::cout<<laplace_beltrami_2d.compute_error(VectorTools::H1_norm)<<std::endl;
+
+ tria.set_boundary(0);
+ return 0;
+}
+
+
+
+
+
+
+
+
+
+
+
projects / dealii-svn.git / commitdiff
