--- /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 *vtk
+
+
+
+
+#
+#
+# Usually, you will not need to change anything 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-deal2-3d.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========= $(<F)
+ @$(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 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-/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/*/*.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
+/* $Id$ */
+/* Author: Martin Kronbichler, Uppsala University, 2009 */
+
+/* $Id$ */
+/* */
+/* Copyright (C) 2009 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. */
+
+
+ // The include files are mostly similar to
+ // the ones in step-16.
+#include <base/quadrature_lib.h>
+#include <base/function.h>
+#include <base/logstream.h>
+
+#include <lac/vector.h>
+#include <lac/full_matrix.h>
+#include <lac/solver_cg.h>
+#include <lac/precondition.h>
+
+#include <dofs/dof_handler.h>
+#include <dofs/dof_accessor.h>
+#include <dofs/dof_tools.h>
+
+#include <fe/fe_q.h>
+#include <fe/fe_values.h>
+
+#include <grid/tria.h>
+#include <grid/tria_accessor.h>
+#include <grid/tria_iterator.h>
+#include <grid/tria_boundary_lib.h>
+#include <grid/grid_generator.h>
+
+#include <multigrid/multigrid.h>
+#include <multigrid/mg_dof_handler.h>
+#include <multigrid/mg_dof_accessor.h>
+#include <multigrid/mg_transfer.h>
+#include <multigrid/mg_tools.h>
+#include <multigrid/mg_coarse.h>
+#include <multigrid/mg_smoother.h>
+#include <multigrid/mg_matrix.h>
+
+#include <numerics/vectors.h>
+#include <numerics/matrices.h>
+#include <numerics/data_out.h>
+
+#include <fstream>
+#include <sstream>
+
+using namespace dealii;
+
+
+
+ // @sect3{Equation data.}
+
+ // We define a variable coefficient
+ // function for the Poisson problem. It is
+ // similar to the function in step-5. As a
+ // difference, we use the formulation
+ // $\frac{1}{0.1 + \|\bf x\|^2}$ instead of
+ // a discontinuous one. It is merely to
+ // demonstrate the possibilities of this
+ // implemenation, rather than being
+ // physically reasonable.
+template <int dim>
+class Coefficient : public Function<dim>
+{
+ public:
+ Coefficient () : Function<dim>() {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+
+ virtual void value_list (const std::vector<Point<dim> > &points,
+ std::vector<double> &values,
+ const unsigned int component = 0) const;
+};
+
+
+
+template <int dim>
+double Coefficient<dim>::value (const Point<dim> &p,
+ const unsigned int /*component*/) const
+{
+ return 1./(0.1+p.square());
+}
+
+
+
+template <int dim>
+void Coefficient<dim>::value_list (const std::vector<Point<dim> > &points,
+ std::vector<double> &values,
+ const unsigned int component) const
+{
+ Assert (values.size() == points.size(),
+ ExcDimensionMismatch (values.size(), points.size()));
+ Assert (component == 0,
+ ExcIndexRange (component, 0, 1));
+
+ const unsigned int n_points = points.size();
+
+ for (unsigned int i=0; i<n_points; ++i)
+ values[i] = 1./(0.1+points[i].square());
+}
+
+
+
+ // @sect3{Matrix-free implementation.}
+
+ // Next comes the implemenation of the
+ // Matrix-Free class. It provides standard
+ // information we expect for matrices (like
+ // the size of the matrix), and it is able
+ // to perform matrix-vector
+ // multiplications.
+ //
+ // TODO: Use WorkStream for parallelization
+ // instead of apply_to_subranges, once we
+ // have realized the best way for doing
+ // that.
+template <typename number, class Transformation>
+class MatrixFree : public Subscriptor
+{
+public:
+ MatrixFree ();
+
+ void reinit (const unsigned int n_dofs,
+ const unsigned int n_cells,
+ const FullMatrix<double> &cell_matrix,
+ const unsigned int n_points_per_cell);
+
+ void clear();
+
+ unsigned int m () const;
+ unsigned int n () const;
+
+ ConstraintMatrix & get_constraints ();
+
+ void set_local_dof_indices (const unsigned int cell_no,
+ const std::vector<unsigned int> &local_dof_indices);
+
+ void set_derivative_data (const unsigned int cell_no,
+ const unsigned int quad_point,
+ const Transformation &trans_in);
+
+ template <typename number2>
+ void vmult_on_subrange (const unsigned int first_cell,
+ const unsigned int last_cell,
+ Vector<number2> &dst,
+ const Vector<number2> &src) const;
+
+ template <typename number2>
+ void vmult (Vector<number2> &dst,
+ const Vector<number2> &src) const;
+
+ template <typename number2>
+ void Tvmult (Vector<number2> &dst,
+ const Vector<number2> &src) const;
+
+ template <typename number2>
+ void vmult_add (Vector<number2> &dst,
+ const Vector<number2> &src) const;
+
+ template <typename number2>
+ void Tvmult_add (Vector<number2> &dst,
+ const Vector<number2> &src) const;
+
+ number el (const unsigned int row, const unsigned int col) const;
+
+ std::size_t memory_consumption () const;
+
+private:
+ FullMatrix<number> small_matrix;
+ ConstraintMatrix constraints;
+
+ Table<2,unsigned int> indices_local_to_global;
+ Table<2,Transformation> derivatives;
+
+ mutable Vector<number> diagonal_values;
+ mutable bool diagonal_is_calculated;
+
+ struct SmallMatrixData
+ {
+ unsigned int m;
+ unsigned int n;
+ unsigned int n_points;
+ unsigned int n_comp;
+ };
+ unsigned int n_dofs, n_cols, n_cells;
+ SmallMatrixData matrix_data;
+};
+
+
+
+template <typename number, class Transformation>
+MatrixFree<number,Transformation>::MatrixFree ()
+:
+ Subscriptor()
+{}
+
+
+
+template <typename number, class Transformation>
+void MatrixFree<number,Transformation>::
+reinit (const unsigned int n_dofs_in,
+ const unsigned int n_cells_in,
+ const FullMatrix<double> &small_matrix_in,
+ const unsigned int n_points_per_cell)
+{
+ n_dofs = n_dofs_in;
+ n_cells = n_cells_in;
+ small_matrix = small_matrix_in;
+ matrix_data.m = small_matrix.m();
+ matrix_data.n = small_matrix.n();
+ matrix_data.n_points = n_points_per_cell;
+ matrix_data.n_comp = small_matrix.n()/matrix_data.n_points;
+
+ Assert(matrix_data.n_comp * n_points_per_cell == small_matrix.n(),
+ ExcInternalError());
+
+ derivatives.reinit (n_cells, n_points_per_cell);
+ indices_local_to_global.reinit (n_cells, small_matrix.m());
+ diagonal_is_calculated = false;
+}
+
+
+
+template <typename number, class Transformation>
+void
+MatrixFree<number,Transformation>::clear ()
+{
+ n_dofs = 0;
+ n_cells = 0;
+ small_matrix.reinit(0,0);
+ derivatives.reinit (0,0);
+ indices_local_to_global.reinit(0,0);
+ diagonal_values.reinit (0);
+ constraints.clear();
+ diagonal_is_calculated = false;
+}
+
+
+
+template <typename number, class Transformation>
+unsigned int
+MatrixFree<number,Transformation>::m () const
+{
+ return n_dofs;
+}
+
+
+
+template <typename number, class Transformation>
+unsigned int
+MatrixFree<number,Transformation>::n () const
+{
+ return n_dofs;
+}
+
+
+
+template <typename number, class Transformation>
+ConstraintMatrix &
+MatrixFree<number,Transformation>::get_constraints ()
+{
+ return constraints;
+}
+
+
+
+template <typename number, class Transformation>
+void MatrixFree<number,Transformation>::
+set_local_dof_indices (const unsigned int cell_no,
+ const std::vector<unsigned int> &local_dof_indices)
+{
+ Assert (local_dof_indices.size() == matrix_data.m,
+ ExcDimensionMismatch(local_dof_indices.size(),
+ matrix_data.m));
+ for (unsigned int i=0; i<matrix_data.m; ++i)
+ {
+ Assert (local_dof_indices[i] < n_dofs, ExcInternalError());
+ indices_local_to_global(cell_no,i) = local_dof_indices[i];
+ }
+ diagonal_is_calculated = false;
+}
+
+
+
+template <typename number, class Transformation>
+void MatrixFree<number,Transformation>::
+set_derivative_data (const unsigned int cell_no,
+ const unsigned int quad_point,
+ const Transformation &trans_in)
+{
+ derivatives(cell_no,quad_point) = trans_in;
+ diagonal_is_calculated = false;
+}
+
+
+
+template <typename number, class Transformation>
+template <typename number2>
+void
+MatrixFree<number,Transformation>::
+vmult_on_subrange (const unsigned int first_cell,
+ const unsigned int last_cell,
+ Vector<number2> &dst,
+ const Vector<number2> &src) const
+{
+ FullMatrix<number> solution_cells, solution_points;
+
+ const unsigned int n_chunks = (last_cell-first_cell)/100 + 1;
+ const unsigned int chunk_size =
+ (last_cell-first_cell)/n_chunks + ((last_cell-first_cell)%n_chunks>0);
+
+ for (unsigned int k=first_cell; k<last_cell; k+=chunk_size)
+ {
+ const unsigned int current_chunk_size =
+ k+chunk_size>last_cell ? last_cell-k : chunk_size;
+
+ solution_cells.reinit (current_chunk_size,matrix_data.m, true);
+ solution_points.reinit (current_chunk_size,matrix_data.n, true);
+
+ for (unsigned int i=0; i<current_chunk_size; ++i)
+ for (unsigned int j=0; j<matrix_data.m; ++j)
+ solution_cells(i,j) = (number)src(indices_local_to_global(i+k,j));
+
+ solution_cells.mmult (solution_points, small_matrix);
+
+ for (unsigned int i=0; i<current_chunk_size; ++i)
+ for (unsigned int j=0; j<matrix_data.n_points; ++j)
+ derivatives(i+k,j).transform(&solution_points(i, j*matrix_data.n_comp));
+
+ solution_points.mTmult (solution_cells, small_matrix);
+
+ static Threads::Mutex mutex;
+ Threads::Mutex::ScopedLock lock (mutex);
+ for (unsigned int i=0; i<current_chunk_size; ++i)
+ for (unsigned int j=0; j<matrix_data.m; ++j)
+ dst(indices_local_to_global(i+k,j)) += (number2)solution_cells(i,j);
+ }
+}
+
+
+
+template <typename number, class Transformation>
+template <typename number2>
+void
+MatrixFree<number,Transformation>::vmult (Vector<number2> &dst,
+ const Vector<number2> &src) const
+{
+ dst = 0;
+ vmult_add (dst, src);
+}
+
+
+
+template <typename number, class Transformation>
+template <typename number2>
+void
+MatrixFree<number,Transformation>::Tvmult (Vector<number2> &dst,
+ const Vector<number2> &src) const
+{
+ dst = 0;
+ Tvmult_add (dst,src);
+}
+
+
+
+template <typename number, class Transformation>
+template <typename number2>
+void
+MatrixFree<number,Transformation>::vmult_add (Vector<number2> &dst,
+ const Vector<number2> &src) const
+{
+ Vector<number2> src_copy (src);
+ constraints.distribute(src_copy);
+
+ vmult_on_subrange (0, n_cells, dst, src_copy);
+ constraints.condense (dst);
+
+ // Need to do this in order to be
+ // consistent even at constrained
+ // dofs. Need to find a better solution in
+ // the future (e.g. by switching to smaller
+ // vectors that do not contain any
+ // constrained entries).
+ for (unsigned int i=0; i<n_dofs; ++i)
+ if (constraints.is_constrained(i) == true)
+ dst(i) = el(i,i) * src(i);
+}
+
+
+
+template <typename number, class Transformation>
+template <typename number2>
+void
+MatrixFree<number,Transformation>::Tvmult_add (Vector<number2> &dst,
+ const Vector<number2> &src) const
+{
+ vmult_add (dst,src);
+}
+
+
+
+template <typename number, class Transformation>
+number
+MatrixFree<number,Transformation>::el (const unsigned int row,
+ const unsigned int col) const
+{
+ Assert (row == col, ExcNotImplemented());
+
+ if (diagonal_is_calculated == false)
+ {
+ diagonal_values.reinit (n_dofs);
+ std::vector<number> calculation (matrix_data.n_comp);
+ for (unsigned int cell=0; cell<n_cells; ++cell)
+ for (unsigned int dof=0; dof<matrix_data.m; ++dof)
+ {
+ double diag_value = 0;
+ for (unsigned int j=0; j<matrix_data.n_points; ++j)
+ {
+ for (unsigned int d=0; d<matrix_data.n_comp; ++d)
+ calculation[d] = small_matrix(dof,j*matrix_data.n_comp+d);
+ derivatives(cell,j).transform(&calculation[0]);
+ for (unsigned int d=0; d<matrix_data.n_comp; ++d)
+ diag_value += calculation[d]*small_matrix(dof,j*matrix_data.n_comp+d);
+ }
+ diagonal_values(indices_local_to_global(cell,dof)) += diag_value;
+ }
+ diagonal_is_calculated = true;
+ }
+
+ return diagonal_values(row);
+}
+
+
+
+template <typename number, class Transformation>
+std::size_t MatrixFree<number,Transformation>::memory_consumption () const
+{
+ std::size_t glob_size = derivatives.memory_consumption() +
+ indices_local_to_global.memory_consumption() +
+ constraints.memory_consumption() +
+ small_matrix.memory_consumption() + sizeof(*this);
+ return glob_size;
+}
+
+
+
+ // @sect3{Laplace operator.}
+
+ // This implements the local action of a
+ // Laplace preconditioner.
+template <int dim,typename number>
+class LaplaceOperator
+{
+public:
+ LaplaceOperator ();
+
+ LaplaceOperator (const Tensor<2,dim> &tensor);
+
+ void transform (number * result) const;
+
+ LaplaceOperator<dim,number>&
+ operator = (const Tensor<2,dim> &tensor);
+
+ number transformation[dim][dim];
+};
+
+template<int dim,typename number>
+LaplaceOperator<dim,number>::LaplaceOperator()
+{}
+
+template<int dim,typename number>
+LaplaceOperator<dim,number>::LaplaceOperator(const Tensor<2,dim> &tensor)
+{
+ *this = tensor;
+}
+
+template <int dim, typename number>
+void LaplaceOperator<dim,number>::transform (number* result) const
+{
+ number temp_result[dim];
+ for (unsigned int d=0; d<dim; ++d)
+ temp_result[d] = result[d];
+ for (unsigned int d=0; d<dim; ++d)
+ {
+ number output = 0;
+ for (unsigned int e=0; e<dim; ++e)
+ output += transformation[d][e] * temp_result[e];
+ result[d] = output;
+ }
+}
+
+template <int dim, typename number>
+LaplaceOperator<dim,number>&
+LaplaceOperator<dim,number>::operator=(const Tensor<2,dim> &tensor)
+{
+ for (unsigned int d=0;d<dim;++d)
+ for (unsigned int e=0;e<dim;++e)
+ transformation[d][e] = tensor[d][e];
+ return *this;
+}
+
+
+
+ // @sect3{LaplaceProblem class.}
+
+ // This class is based on the same class in
+ // step-16. We replaced the
+ // SparseMatrix<double> class by our
+ // matrix-free implementation, which means
+ // that we can skip the sparsity patterns.
+template <int dim>
+class LaplaceProblem
+{
+ public:
+ LaplaceProblem (const unsigned int degree);
+ void run ();
+
+ private:
+ void setup_system ();
+ void assemble_system ();
+ void assemble_multigrid ();
+ void solve ();
+ void output_results (const unsigned int cycle) const;
+
+ Triangulation<dim> triangulation;
+ FE_Q<dim> fe;
+ MGDoFHandler<dim> mg_dof_handler;
+
+ MatrixFree<double,LaplaceOperator<dim,double> > system_matrix;
+ typedef MatrixFree<float,LaplaceOperator<dim,float> > MatrixFreeType;
+ MGLevelObject<MatrixFreeType> mg_matrices;
+ FullMatrix<float> coarse_matrix;
+
+ Vector<double> solution;
+ Vector<double> system_rhs;
+};
+
+
+
+template <int dim>
+LaplaceProblem<dim>::LaplaceProblem (const unsigned int degree) :
+ fe (degree),
+ mg_dof_handler (triangulation)
+{}
+
+
+
+ // This is the function of step-16 with
+ // relevant changes due to the MatrixFree
+ // class.
+template <int dim>
+void LaplaceProblem<dim>::setup_system ()
+{
+ system_matrix.clear();
+ mg_matrices.clear();
+
+ mg_dof_handler.distribute_dofs (fe);
+
+ std::cout << "Number of degrees of freedom: "
+ << mg_dof_handler.n_dofs()
+ << std::endl;
+
+ const unsigned int nlevels = triangulation.n_levels();
+ mg_matrices.resize(0, nlevels-1);
+
+ QGauss<dim> quadrature_formula(fe.degree+1);
+ FEValues<dim> fe_values2 (fe, quadrature_formula,
+ update_gradients);
+ Triangulation<dim> tria;
+ GridGenerator::hyper_cube (tria, 0, 1);
+ fe_values2.reinit (tria.begin());
+ FullMatrix<double> data_matrix (fe.dofs_per_cell,
+ quadrature_formula.size()*dim);
+ for (unsigned int i=0; i<fe.dofs_per_cell; ++i)
+ {
+ for (unsigned int j=0; j<quadrature_formula.size(); ++j)
+ {
+ for (unsigned int d=0; d<dim; ++d)
+ data_matrix(i,j*dim+d) = fe_values2.shape_grad(i,j)[d];
+ }
+ }
+ system_matrix.reinit (mg_dof_handler.n_dofs(), triangulation.n_active_cells(),
+ data_matrix, quadrature_formula.size());
+ VectorTools::interpolate_boundary_values (mg_dof_handler,
+ 0,
+ ZeroFunction<dim>(),
+ system_matrix.get_constraints());
+ system_matrix.get_constraints().close();
+ std::cout.precision(4);
+ std::cout << "System matrix memory consumption: "
+ << (double)system_matrix.memory_consumption()*std::pow(2.,-20.) << " MBytes."
+ << std::endl;
+
+ solution.reinit (mg_dof_handler.n_dofs());
+ system_rhs.reinit (mg_dof_handler.n_dofs());
+
+ // Initialize the matrices for the
+ // multigrid method on all the levels.
+ typename FunctionMap<dim>::type dirichlet_boundary;
+ ZeroFunction<dim> homogeneous_dirichlet_bc (1);
+ dirichlet_boundary[0] = &homogeneous_dirichlet_bc;
+ std::vector<std::set<unsigned int> > boundary_indices(triangulation.n_levels());
+ MGTools::make_boundary_list (mg_dof_handler,
+ dirichlet_boundary,
+ boundary_indices);
+ for (unsigned int level=0;level<nlevels;++level)
+ {
+ mg_matrices[level].reinit(mg_dof_handler.n_dofs(level),
+ triangulation.n_cells(level),
+ data_matrix,
+ quadrature_formula.size());
+ std::set<unsigned int>::iterator bc_it = boundary_indices[level].begin();
+ for ( ; bc_it != boundary_indices[level].end(); ++bc_it)
+ mg_matrices[level].get_constraints().add_line(*bc_it);
+ mg_matrices[level].get_constraints().close();
+ }
+ coarse_matrix.reinit (mg_dof_handler.n_dofs(0),
+ mg_dof_handler.n_dofs(0));
+}
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::assemble_system ()
+{
+ QGauss<dim> quadrature_formula(fe.degree+1);
+ MappingQ<dim> mapping (fe.degree);
+ FEValues<dim> fe_values (mapping, fe, quadrature_formula,
+ update_values | update_inverse_jacobians |
+ 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();
+
+ std::vector<unsigned int> local_dof_indices (dofs_per_cell);
+ const Coefficient<dim> coefficient;
+ std::vector<double> coefficient_values (n_q_points);
+
+ unsigned int cell_no = 0;
+
+ typename DoFHandler<dim>::active_cell_iterator cell = mg_dof_handler.begin_active(),
+ endc = mg_dof_handler.end();
+ for (; cell!=endc; ++cell, ++cell_no)
+ {
+ cell->get_dof_indices (local_dof_indices);
+ fe_values.reinit (cell);
+ coefficient.value_list (fe_values.get_quadrature_points(),
+ coefficient_values);
+
+ system_matrix.set_local_dof_indices (cell_no, local_dof_indices);
+ for (unsigned int q=0; q<n_q_points; ++q)
+ system_matrix.set_derivative_data
+ (cell_no, q,
+ (transpose(fe_values.inverse_jacobian(q)) *
+ fe_values.inverse_jacobian(q)) *
+ fe_values.JxW(q) * coefficient_values[q]);
+
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+ double rhs_val = 0;
+ for (unsigned int q=0; q<n_q_points; ++q)
+ rhs_val += (fe_values.shape_value(i,q) * 1.0 *
+ fe_values.JxW(q));
+ system_rhs(local_dof_indices[i]) += rhs_val;
+ }
+ }
+ system_matrix.get_constraints().condense(system_rhs);
+}
+
+
+ // Here is another assemble
+ // function. The integration core is
+ // the same as above. Only the loop
+ // goes over all existing cells now
+ // and the results must be entered
+ // into the correct matrix.
+
+ // Since we only do multi-level
+ // preconditioning, no right-hand
+ // side is assembled here.
+template <int dim>
+void LaplaceProblem<dim>::assemble_multigrid ()
+{
+ coarse_matrix = 0;
+ QGauss<dim> quadrature_formula(fe.degree+1);
+ MappingQ<dim> mapping (fe.degree);
+ FEValues<dim> fe_values (mapping, fe, quadrature_formula,
+ update_gradients | update_inverse_jacobians |
+ 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();
+
+ std::vector<unsigned int> local_dof_indices (dofs_per_cell);
+ const Coefficient<dim> coefficient;
+ std::vector<double> coefficient_values (n_q_points);
+
+ std::vector<unsigned int> cell_no(triangulation.n_levels());
+ typename MGDoFHandler<dim>::cell_iterator cell = mg_dof_handler.begin(),
+ endc = mg_dof_handler.end();
+ for (; cell!=endc; ++cell)
+ {
+ const unsigned int level = cell->level();
+ cell->get_mg_dof_indices (local_dof_indices);
+ fe_values.reinit (cell);
+ coefficient.value_list (fe_values.get_quadrature_points(),
+ coefficient_values);
+
+ mg_matrices[level].set_local_dof_indices (cell_no[level],
+ local_dof_indices);
+ for (unsigned int q=0; q<n_q_points; ++q)
+ mg_matrices[level].set_derivative_data
+ (cell_no[level], q,
+ (transpose(fe_values.inverse_jacobian(q)) *
+ fe_values.inverse_jacobian(q)) *
+ fe_values.JxW(q) * coefficient_values[q]);
+
+ ++cell_no[level];
+ if (level == 0)
+ {
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ {
+ double add_value = 0;
+ for (unsigned int q=0; q<n_q_points; ++q)
+ add_value += (fe_values.shape_grad(i,q) *
+ fe_values.shape_grad(j,q) *
+ coefficient_values[q] *
+ fe_values.JxW(q));
+ coarse_matrix(local_dof_indices[i],
+ local_dof_indices[j]) += add_value;
+ }
+ }
+ }
+ for (unsigned int i=0; i<coarse_matrix.m(); ++i)
+ if (mg_matrices[0].get_constraints().is_constrained(i))
+ for (unsigned int j=0; j<coarse_matrix.n(); ++j)
+ if (i!=j)
+ {
+ coarse_matrix(i,j) = 0;
+ coarse_matrix(j,i) = 0;
+ }
+}
+
+
+
+ // The solution process again looks like
+ // step-16. We now use a Chebyshev smoother
+ // instead of SSOR (which is difficult to
+ // implement if we do not have the matrix
+ // elements explicitly available).
+template <int dim>
+void LaplaceProblem<dim>::solve ()
+{
+ GrowingVectorMemory<> vector_memory;
+
+ MGTransferPrebuilt<Vector<double> > mg_transfer;
+ mg_transfer.build_matrices(mg_dof_handler);
+
+ MGCoarseGridHouseholder<float, Vector<double> > mg_coarse;
+ mg_coarse.initialize(coarse_matrix);
+
+ typedef PreconditionChebyshev<MatrixFreeType,Vector<double> > SMOOTHER;
+ MGSmootherPrecondition<MatrixFreeType, SMOOTHER, Vector<double> >
+ mg_smoother(vector_memory);
+
+ // Initialize the smoother with our level
+ // matrices and the required, additional
+ // data for the Chebyshev smoother. Use a
+ // higher polynomial degree for higher
+ // order elements, since smoothing gets
+ // more difficult then. Smooth out a
+ // range of
+ // $[\lambda_{\max}/8,\lambda_{\max}]$.
+ typename SMOOTHER::AdditionalData smoother_data;
+ smoother_data.smoothing_range = 8.;
+ smoother_data.degree = fe.degree+1;
+ mg_smoother.initialize(mg_matrices, smoother_data);
+
+ MGMatrix<MatrixFreeType, Vector<double> >
+ mg_matrix(&mg_matrices);
+
+ Multigrid<Vector<double> > mg(mg_dof_handler,
+ mg_matrix,
+ mg_coarse,
+ mg_transfer,
+ mg_smoother,
+ mg_smoother);
+ PreconditionMG<dim, Vector<double>,
+ MGTransferPrebuilt<Vector<double> > >
+ preconditioner(mg_dof_handler, mg, mg_transfer);
+
+ double multigrid_memory =
+ (double)mg_matrices.memory_consumption() +
+ (double)mg_transfer.memory_consumption() +
+ (double)coarse_matrix.memory_consumption();
+
+ std::cout << "Multigrid objects memory consumption: "
+ << multigrid_memory*std::pow(2.,-20.)
+ << " MBytes."
+ << std::endl;
+
+ // Finally, create the solver
+ // object and solve the system
+ SolverControl solver_control (1000, 1e-12);
+ SolverCG<> cg (solver_control);
+
+ cg.solve (system_matrix, solution, system_rhs,
+ preconditioner);
+
+ std::cout << "Convergence in " << solver_control.last_step()
+ << " CG iterations." << std::endl;
+}
+
+
+
+ // Here is the data output, which is
+ // a simplified version of step-5. We
+ // do a standard vtk output for
+ // each grid produced in the
+ // refinement process.
+template <int dim>
+void LaplaceProblem<dim>::output_results (const unsigned int cycle) const
+{
+ DataOut<dim> data_out;
+
+ data_out.attach_dof_handler (mg_dof_handler);
+ data_out.add_data_vector (solution, "solution");
+ data_out.build_patches ();
+
+ std::ostringstream filename;
+ filename << "solution-"
+ << cycle
+ << ".vtk";
+
+ std::ofstream output (filename.str().c_str());
+ data_out.write_vtk (output);
+}
+
+
+
+template <int dim>
+void LaplaceProblem<dim>::run ()
+{
+ for (unsigned int cycle=0; cycle<6; ++cycle)
+ {
+ std::cout << "Cycle " << cycle << std::endl;
+
+ if (cycle == 0)
+ {
+ // Generate a simple hyperball grid.
+ GridGenerator::hyper_ball(triangulation);
+ static const HyperBallBoundary<dim> boundary;
+ triangulation.set_boundary (0, boundary);
+ triangulation.refine_global (0);
+ }
+ triangulation.refine_global (1);
+ setup_system ();
+ assemble_system ();
+ assemble_multigrid ();
+ solve ();
+ output_results (cycle);
+ std::cout << std::endl;
+ };
+}
+
+
+
+int main ()
+{
+ deallog.depth_console (0);
+ LaplaceProblem<2> laplace_problem (2);
+ laplace_problem.run ();
+
+ return 0;
+}