+++ /dev/null
-/* ------------------------------------------------------------------------
- *
- * SPDX-License-Identifier: LGPL-2.1-or-later
- * Copyright (C) 2003 - 2024 by the deal.II authors
- *
- * This file is part of the deal.II library.
- *
- * Part of the source code is dual licensed under Apache-2.0 WITH
- * LLVM-exception OR LGPL-2.1-or-later. Detailed license information
- * governing the source code and code contributions can be found in
- * LICENSE.md and CONTRIBUTING.md at the top level directory of deal.II.
- *
- * ------------------------------------------------------------------------
- *
- * Authors: Guido Kanschat, University of Heidelberg, 2003
- * Baerbel Janssen, University of Heidelberg, 2010
- * Wolfgang Bangerth, Texas A&M University, 2010
- */
-
-
-// @sect3{Include files}
-
-// Again, the first few include files are already known, so we won't comment
-// on them:
-#include <deal.II/base/quadrature_lib.h>
-#include <deal.II/base/function.h>
-#include <deal.II/base/logstream.h>
-#include <deal.II/base/utilities.h>
-
-#include <deal.II/lac/affine_constraints.h>
-#include <deal.II/lac/vector.h>
-#include <deal.II/lac/full_matrix.h>
-#include <deal.II/lac/sparse_matrix.h>
-#include <deal.II/lac/solver_cg.h>
-#include <deal.II/lac/precondition.h>
-
-#include <deal.II/grid/tria.h>
-#include <deal.II/grid/grid_generator.h>
-#include <deal.II/grid/grid_refinement.h>
-
-#include <deal.II/dofs/dof_tools.h>
-
-#include <deal.II/fe/fe_q.h>
-#include <deal.II/fe/fe_values.h>
-#include <deal.II/fe/mapping_q1.h>
-
-#include <deal.II/numerics/vector_tools.h>
-#include <deal.II/numerics/data_out.h>
-#include <deal.II/numerics/error_estimator.h>
-
-// These, now, are the include necessary for the multilevel methods. The first
-// one declares how to handle Dirichlet boundary conditions on each of the
-// levels of the multigrid method. For the actual description of the degrees
-// of freedom, we do not need any new include file because DoFHandler already
-// has all necessary methods implemented. We will only need to distribute the
-// DoFs for the levels further down.
-//
-// The rest of the include files deals with the mechanics of multigrid as a
-// linear operator (solver or preconditioner).
-#include <deal.II/multigrid/mg_constrained_dofs.h>
-#include <deal.II/multigrid/multigrid.h>
-#include <deal.II/multigrid/mg_transfer.h>
-#include <deal.II/multigrid/mg_tools.h>
-#include <deal.II/multigrid/mg_coarse.h>
-#include <deal.II/multigrid/mg_smoother.h>
-#include <deal.II/multigrid/mg_matrix.h>
-
-// Finally we include the MeshWorker framework. This framework through its
-// function loop() and integration_loop(), automates loops over cells and
-// assembling of data into vectors, matrices, etc. It obeys constraints
-// automatically. Since we have to build several matrices and have to be aware
-// of several sets of constraints, this will save us a lot of headache.
-#include <deal.II/meshworker/dof_info.h>
-#include <deal.II/meshworker/integration_info.h>
-#include <deal.II/meshworker/simple.h>
-#include <deal.II/meshworker/output.h>
-#include <deal.II/meshworker/loop.h>
-
-// In order to save effort, we use the pre-implemented Laplacian found in
-#include <deal.II/integrators/laplace.h>
-#include <deal.II/integrators/l2.h>
-
-// This is C++:
-#include <iostream>
-#include <fstream>
-
-using namespace dealii;
-
-namespace Step16
-{
- // @sect3{The integrator on each cell}
-
- // The MeshWorker::integration_loop() expects a class that provides functions
- // for integration on cells and boundary and interior faces. This is done by
- // the following class. In the constructor, we tell the loop that cell
- // integrals should be computed (the 'true'), but integrals should not be
- // computed on boundary and interior faces (the two 'false'). Accordingly, we
- // only need a cell function, but none for the faces.
- template <int dim>
- class LaplaceIntegrator : public MeshWorker::LocalIntegrator<dim>
- {
- public:
- LaplaceIntegrator();
- virtual void cell(MeshWorker::DoFInfo<dim> &dinfo,
- MeshWorker::IntegrationInfo<dim> &info) const override;
- };
-
-
- template <int dim>
- LaplaceIntegrator<dim>::LaplaceIntegrator()
- : MeshWorker::LocalIntegrator<dim>(true, false, false)
- {}
-
-
- // Next the actual integrator on each cell. We solve a Poisson problem with a
- // coefficient one in the right half plane and one tenth in the left
- // half plane.
-
- // The MeshWorker::LocalResults base class of MeshWorker::DoFInfo contains
- // objects that can be filled in this local integrator. How many objects are
- // created is determined inside the MeshWorker framework by the assembler
- // class. Here, we test for instance that one matrix is required
- // (MeshWorker::LocalResults::n_matrices()). The matrices are accessed through
- // MeshWorker::LocalResults::matrix(), which takes the number of the matrix as
- // its first argument. The second argument is only used for integrals over
- // faces when there are two matrices for each test function used. Then, a
- // second matrix with indicator 'true' would exist with the same index.
-
- // MeshWorker::IntegrationInfo provides one or several FEValues objects, which
- // below are used by LocalIntegrators::Laplace::cell_matrix() or
- // LocalIntegrators::L2::L2(). Since we are assembling only a single PDE,
- // there is also only one of these objects with index zero.
-
- // In addition, we note that this integrator serves to compute the matrices
- // for the multilevel preconditioner as well as the matrix and the right hand
- // side for the global system. Since the assembler for a system requires an
- // additional vector, MeshWorker::LocalResults::n_vectors() is returning a
- // nonzero value. Accordingly, we fill a right hand side vector at the end of
- // this function. Since LocalResults can deal with several BlockVector
- // objects, but we are again in the simplest case here, we enter the
- // information into block zero of vector zero.
- template <int dim>
- void
- LaplaceIntegrator<dim>::cell(MeshWorker::DoFInfo<dim> &dinfo,
- MeshWorker::IntegrationInfo<dim> &info) const
- {
- AssertDimension(dinfo.n_matrices(), 1);
- const double coefficient = (dinfo.cell->center()[0] > 0.) ? .1 : 1.;
-
- LocalIntegrators::Laplace::cell_matrix(dinfo.matrix(0, false).matrix,
- info.fe_values(0),
- coefficient);
-
- if (dinfo.n_vectors() > 0)
- {
- std::vector<double> rhs(info.fe_values(0).n_quadrature_points, 1.);
- LocalIntegrators::L2::L2(dinfo.vector(0).block(0),
- info.fe_values(0),
- rhs);
- }
- }
-
-
- // @sect3{The <code>LaplaceProblem</code> class template}
-
- // This main class is basically the same class as in step-6. As far as
- // member functions is concerned, the only addition is the
- // <code>assemble_multigrid</code> function that assembles the matrices that
- // correspond to the discrete operators on intermediate levels:
- 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 refine_grid();
- void output_results(const unsigned int cycle) const;
-
- Triangulation<dim> triangulation;
- const FE_Q<dim> fe;
- DoFHandler<dim> dof_handler;
-
- SparsityPattern sparsity_pattern;
- SparseMatrix<double> system_matrix;
-
- AffineConstraints<double> constraints;
-
- Vector<double> solution;
- Vector<double> system_rhs;
-
- const unsigned int degree;
-
- // The following members are the essential data structures for the multigrid
- // method. The first two represent the sparsity patterns and the matrices on
- // individual levels of the multilevel hierarchy, very much like the objects
- // for the global mesh above.
- //
- // Then we have two new matrices only needed for multigrid methods with
- // local smoothing on adaptive meshes. They convey data between the interior
- // part of the refined region and the refinement edge, as outlined in detail
- // in the @ref mg_paper "multigrid paper".
- //
- // The last object stores information about the boundary indices on each
- // level and information about indices lying on a refinement edge between
- // two different refinement levels. It thus serves a similar purpose as
- // AffineConstraints, but on each level.
- MGLevelObject<SparsityPattern> mg_sparsity_patterns;
- MGLevelObject<SparseMatrix<double>> mg_matrices;
- MGLevelObject<SparseMatrix<double>> mg_interface_in;
- MGLevelObject<SparseMatrix<double>> mg_interface_out;
- MGConstrainedDoFs mg_constrained_dofs;
- };
-
-
- // @sect3{The <code>LaplaceProblem</code> class implementation}
-
- // Just one short remark about the constructor of the Triangulation:
- // by convention, all adaptively refined triangulations in deal.II never
- // change by more than one level across a face between cells. For our
- // multigrid algorithms, however, we need a slightly stricter guarantee,
- // namely that the mesh also does not change by more than refinement level
- // across vertices that might connect two cells. In other words, we must
- // prevent the following situation:
- //
- // @image html limit_level_difference_at_vertices.png ""
- //
- // This is achieved by passing the
- // Triangulation::limit_level_difference_at_vertices flag to the constructor
- // of the triangulation class.
- template <int dim>
- LaplaceProblem<dim>::LaplaceProblem(const unsigned int degree)
- : triangulation(Triangulation<dim>::limit_level_difference_at_vertices)
- , fe(degree)
- , dof_handler(triangulation)
- , degree(degree)
- {}
-
-
-
- // @sect4{LaplaceProblem::setup_system}
-
- // In addition to just distributing the degrees of freedom in
- // the DoFHandler, we do the same on each level. Then, we follow the
- // same procedure as before to set up the system on the leaf mesh.
- template <int dim>
- void LaplaceProblem<dim>::setup_system()
- {
- dof_handler.distribute_dofs(fe);
- dof_handler.distribute_mg_dofs();
-
- deallog << " Number of degrees of freedom: " << dof_handler.n_dofs()
- << " (by level: ";
- for (unsigned int level = 0; level < triangulation.n_levels(); ++level)
- deallog << dof_handler.n_dofs(level)
- << (level == triangulation.n_levels() - 1 ? ")" : ", ");
- deallog << std::endl;
-
- DynamicSparsityPattern dsp(dof_handler.n_dofs(), dof_handler.n_dofs());
- DoFTools::make_sparsity_pattern(dof_handler, dsp);
-
- solution.reinit(dof_handler.n_dofs());
- system_rhs.reinit(dof_handler.n_dofs());
-
- constraints.clear();
- DoFTools::make_hanging_node_constraints(dof_handler, constraints);
-
- std::set<types::boundary_id> dirichlet_boundary_ids = {0};
- Functions::ZeroFunction<dim> homogeneous_dirichlet_bc;
- const std::map<types::boundary_id, const Function<dim> *>
- dirichlet_boundary_functions = {
- {types::boundary_id(0), &homogeneous_dirichlet_bc}};
- VectorTools::interpolate_boundary_values(dof_handler,
- dirichlet_boundary_functions,
- constraints);
- constraints.close();
- constraints.condense(dsp);
- sparsity_pattern.copy_from(dsp);
- system_matrix.reinit(sparsity_pattern);
-
- // The multigrid constraints have to be initialized. They need to know
- // about the boundary values as well, so we pass the
- // <code>dirichlet_boundary</code> here as well.
- mg_constrained_dofs.clear();
- mg_constrained_dofs.initialize(dof_handler);
- mg_constrained_dofs.make_zero_boundary_constraints(dof_handler,
- dirichlet_boundary_ids);
-
-
- // Now for the things that concern the multigrid data structures. First, we
- // resize the multilevel objects to hold matrices and sparsity patterns for
- // every level. The coarse level is zero (this is mandatory right now but
- // may change in a future revision). Note that these functions take a
- // complete, inclusive range here (not a starting index and size), so the
- // finest level is <code>n_levels-1</code>. We first have to resize the
- // container holding the SparseMatrix classes, since they have to release
- // their SparsityPattern before the can be destroyed upon resizing.
- const unsigned int n_levels = triangulation.n_levels();
-
- mg_interface_in.resize(0, n_levels - 1);
- mg_interface_in.clear_elements();
- mg_interface_out.resize(0, n_levels - 1);
- mg_interface_out.clear_elements();
- mg_matrices.resize(0, n_levels - 1);
- mg_matrices.clear_elements();
- mg_sparsity_patterns.resize(0, n_levels - 1);
-
- // Now, we have to provide a matrix on each level. To this end, we first use
- // the MGTools::make_sparsity_pattern function to generate a preliminary
- // compressed sparsity pattern on each level (see the @ref Sparsity module
- // for more information on this topic) and then copy it over to the one we
- // really want. The next step is to initialize both kinds of level matrices
- // with these sparsity patterns.
- //
- // It may be worth pointing out that the interface matrices only have
- // entries for degrees of freedom that sit at or next to the interface
- // between coarser and finer levels of the mesh. They are therefore even
- // sparser than the matrices on the individual levels of our multigrid
- // hierarchy. If we were more concerned about memory usage (and possibly the
- // speed with which we can multiply with these matrices), we should use
- // separate and different sparsity patterns for these two kinds of matrices.
- for (unsigned int level = 0; level < n_levels; ++level)
- {
- DynamicSparsityPattern dsp(dof_handler.n_dofs(level),
- dof_handler.n_dofs(level));
- MGTools::make_sparsity_pattern(dof_handler, dsp, level);
-
- mg_sparsity_patterns[level].copy_from(dsp);
-
- mg_matrices[level].reinit(mg_sparsity_patterns[level]);
- mg_interface_in[level].reinit(mg_sparsity_patterns[level]);
- mg_interface_out[level].reinit(mg_sparsity_patterns[level]);
- }
- }
-
-
- // @sect4{LaplaceProblem::assemble_system}
-
- // The following function assembles the linear system on the finest level of
- // the mesh. Since we want to reuse the code here for the level assembling
- // below, we use the local integrator class LaplaceIntegrator and leave the
- // loops to the MeshWorker framework. Thus, this function first sets up the
- // objects necessary for this framework, namely
- // - a MeshWorker::IntegrationInfoBox object, which will provide all the
- // required data in quadrature points on the cell. This object can be seen
- // as an extension of FEValues, providing a lot more useful information,
- // - a MeshWorker::DoFInfo object, which on the one hand side extends the
- // functionality of cell iterators, but also provides space for return
- // values in its base class LocalResults,
- // - an assembler, in this case for the whole system. The term 'simple' here
- // refers to the fact that the global system does not have a block
- // structure,
- // - the local integrator, which implements the actual forms.
- //
- // After the loop has combined all of these into a matrix and a right hand
- // side, there is one thing left to do: the assemblers leave matrix rows and
- // columns of constrained degrees of freedom untouched. Therefore, we put a
- // one on the diagonal to make the whole system well posed. The value one, or
- // any fixed value has the advantage, that its effect on the spectrum of the
- // matrix is easily understood. Since the corresponding eigenvectors form an
- // invariant subspace, the value chosen does not affect the convergence of
- // Krylov space solvers.
- template <int dim>
- void LaplaceProblem<dim>::assemble_system()
- {
- MappingQ1<dim> mapping;
- MeshWorker::IntegrationInfoBox<dim> info_box;
- UpdateFlags update_flags =
- update_values | update_gradients | update_hessians;
- info_box.add_update_flags_all(update_flags);
- info_box.initialize(fe, mapping);
-
- MeshWorker::DoFInfo<dim> dof_info(dof_handler);
-
- MeshWorker::Assembler::SystemSimple<SparseMatrix<double>, Vector<double>>
- assembler;
- assembler.initialize(constraints);
- assembler.initialize(system_matrix, system_rhs);
-
- LaplaceIntegrator<dim> matrix_integrator;
- MeshWorker::integration_loop<dim, dim>(dof_handler.begin_active(),
- dof_handler.end(),
- dof_info,
- info_box,
- matrix_integrator,
- assembler);
-
- for (unsigned int i = 0; i < dof_handler.n_dofs(); ++i)
- if (constraints.is_constrained(i))
- system_matrix.set(i, i, 1.);
- }
-
-
- // @sect4{LaplaceProblem::assemble_multigrid}
-
- // The next function is the one that builds the linear operators (matrices)
- // that define the multigrid method on each level of the mesh. The integration
- // core is the same as above, but the loop below will go over all existing
- // cells instead of just the active ones, and the results must be entered into
- // the correct level matrices. Fortunately, MeshWorker hides most of that from
- // us, and thus the difference between this function and the previous lies
- // only in the setup of the assembler and the different iterators in the loop.
- // Also, fixing up the matrices in the end is a little more complicated.
- template <int dim>
- void LaplaceProblem<dim>::assemble_multigrid()
- {
- MappingQ1<dim> mapping;
- MeshWorker::IntegrationInfoBox<dim> info_box;
- UpdateFlags update_flags =
- update_values | update_gradients | update_hessians;
- info_box.add_update_flags_all(update_flags);
- info_box.initialize(fe, mapping);
-
- MeshWorker::DoFInfo<dim> dof_info(dof_handler);
-
- MeshWorker::Assembler::MGMatrixSimple<SparseMatrix<double>> assembler;
- assembler.initialize(mg_constrained_dofs);
- assembler.initialize(mg_matrices);
- assembler.initialize_interfaces(mg_interface_in, mg_interface_out);
-
- LaplaceIntegrator<dim> matrix_integrator;
- MeshWorker::integration_loop<dim, dim>(dof_handler.begin_mg(),
- dof_handler.end_mg(),
- dof_info,
- info_box,
- matrix_integrator,
- assembler);
-
- const unsigned int nlevels = triangulation.n_levels();
- for (unsigned int level = 0; level < nlevels; ++level)
- {
- for (unsigned int i = 0; i < dof_handler.n_dofs(level); ++i)
- if (mg_constrained_dofs.is_boundary_index(level, i) ||
- mg_constrained_dofs.at_refinement_edge(level, i))
- mg_matrices[level].set(i, i, 1.);
- }
- }
-
-
-
- // @sect4{LaplaceProblem::solve}
-
- // This is the other function that is significantly different in support of
- // the multigrid solver (or, in fact, the preconditioner for which we use
- // the multigrid method).
- //
- // Let us start out by setting up two of the components of multilevel
- // methods: transfer operators between levels, and a solver on the coarsest
- // level. In finite element methods, the transfer operators are derived from
- // the finite element function spaces involved and can often be computed in
- // a generic way independent of the problem under consideration. In that
- // case, we can use the MGTransferPrebuilt class that, given the constraints
- // of the final linear system and the MGConstrainedDoFs object that knows
- // about the boundary conditions on the each level and the degrees of
- // freedom on interfaces between different refinement level can build the
- // matrices for those transfer operations from a DoFHandler object with
- // level degrees of freedom.
- //
- // The second part of the following lines deals with the coarse grid
- // solver. Since our coarse grid is very coarse indeed, we decide for a
- // direct solver (a Householder decomposition of the coarsest level matrix),
- // even if its implementation is not particularly sophisticated. If our
- // coarse mesh had many more cells than the five we have here, something
- // better suited would obviously be necessary here.
- template <int dim>
- void LaplaceProblem<dim>::solve()
- {
- MGTransferPrebuilt<Vector<double>> mg_transfer(mg_constrained_dofs);
- mg_transfer.build(dof_handler);
-
- FullMatrix<double> coarse_matrix;
- coarse_matrix.copy_from(mg_matrices[0]);
- MGCoarseGridHouseholder<double, Vector<double>> coarse_grid_solver;
- coarse_grid_solver.initialize(coarse_matrix);
-
- // The next component of a multilevel solver or preconditioner is that we
- // need a smoother on each level. A common choice for this is to use the
- // application of a relaxation method (such as the SOR, Jacobi or Richardson
- // method) or a small number of iterations of a solver method (such as CG or
- // GMRES). The mg::SmootherRelaxation and MGSmootherPrecondition classes
- // provide support for these two kinds of smoothers. Here, we opt for the
- // application of a single SOR iteration. To this end, we define an
- // appropriate alias and then setup a smoother object.
- //
- // The last step is to initialize the smoother object with our level
- // matrices and to set some smoothing parameters. The
- // <code>initialize()</code> function can optionally take additional
- // arguments that will be passed to the smoother object on each level. In
- // the current case for the SOR smoother, this could, for example, include
- // a relaxation parameter. However, we here leave these at their default
- // values. The call to <code>set_steps()</code> indicates that we will use
- // two pre- and two post-smoothing steps on each level; to use a variable
- // number of smoother steps on different levels, more options can be set
- // in the constructor call to the <code>mg_smoother</code> object.
- //
- // The last step results from the fact that we use the SOR method as a
- // smoother - which is not symmetric - but we use the conjugate gradient
- // iteration (which requires a symmetric preconditioner) below, we need to
- // let the multilevel preconditioner make sure that we get a symmetric
- // operator even for nonsymmetric smoothers:
- using Smoother = PreconditionSOR<SparseMatrix<double>>;
- mg::SmootherRelaxation<Smoother, Vector<double>> mg_smoother;
- mg_smoother.initialize(mg_matrices);
- mg_smoother.set_steps(2);
- mg_smoother.set_symmetric(true);
-
- // The next preparatory step is that we must wrap our level and interface
- // matrices in an object having the required multiplication functions. We
- // will create two objects for the interface objects going from coarse to
- // fine and the other way around; the multigrid algorithm will later use
- // the transpose operator for the latter operation, allowing us to
- // initialize both up and down versions of the operator with the matrices
- // we already built:
- mg::Matrix<Vector<double>> mg_matrix(mg_matrices);
- mg::Matrix<Vector<double>> mg_interface_up(mg_interface_in);
- mg::Matrix<Vector<double>> mg_interface_down(mg_interface_out);
-
- // Now, we are ready to set up the V-cycle operator and the multilevel
- // preconditioner.
- Multigrid<Vector<double>> mg(
- mg_matrix, coarse_grid_solver, mg_transfer, mg_smoother, mg_smoother);
- mg.set_edge_matrices(mg_interface_down, mg_interface_up);
-
- PreconditionMG<dim, Vector<double>, MGTransferPrebuilt<Vector<double>>>
- preconditioner(dof_handler, mg, mg_transfer);
-
- // With all this together, we can finally get about solving the linear
- // system in the usual way:
- SolverControl solver_control(1000, 1e-12);
- SolverCG<Vector<double>> solver(solver_control);
-
- solution = 0;
-
- solver.solve(system_matrix, solution, system_rhs, preconditioner);
- constraints.distribute(solution);
- }
-
-
-
- // @sect4{Postprocessing}
-
- // The following two functions postprocess a solution once it is
- // computed. In particular, the first one refines the mesh at the beginning
- // of each cycle while the second one outputs results at the end of each
- // such cycle. The functions are almost unchanged from those in step-6, with
- // the exception of one minor difference: we generate output in VTK
- // format, to use the more modern visualization programs available today
- // compared to those that were available when step-6 was written.
- template <int dim>
- void LaplaceProblem<dim>::refine_grid()
- {
- Vector<float> estimated_error_per_cell(triangulation.n_active_cells());
-
- KellyErrorEstimator<dim>::estimate(
- dof_handler,
- QGauss<dim - 1>(fe.degree + 1),
- std::map<types::boundary_id, const Function<dim> *>(),
- solution,
- estimated_error_per_cell);
- GridRefinement::refine_and_coarsen_fixed_number(triangulation,
- estimated_error_per_cell,
- 0.3,
- 0.03);
- triangulation.execute_coarsening_and_refinement();
- }
-
-
-
- template <int dim>
- void LaplaceProblem<dim>::output_results(const unsigned int cycle) const
- {
- DataOut<dim> data_out;
-
- data_out.attach_dof_handler(dof_handler);
- data_out.add_data_vector(solution, "solution");
- data_out.build_patches();
-
- std::ofstream output("solution-" + std::to_string(cycle) + ".vtk");
- data_out.write_vtk(output);
- }
-
-
- // @sect4{LaplaceProblem::run}
-
- // Like several of the functions above, this is almost exactly a copy of
- // the corresponding function in step-6. The only difference is the call to
- // <code>assemble_multigrid</code> that takes care of forming the matrices
- // on every level that we need in the multigrid method.
- template <int dim>
- void LaplaceProblem<dim>::run()
- {
- for (unsigned int cycle = 0; cycle < 8; ++cycle)
- {
- deallog << "Cycle " << cycle << std::endl;
-
- if (cycle == 0)
- {
- GridGenerator::hyper_ball(triangulation);
- triangulation.refine_global(1);
- }
- else
- refine_grid();
-
- deallog << " Number of active cells: "
- << triangulation.n_active_cells() << std::endl;
-
- setup_system();
-
- assemble_system();
- assemble_multigrid();
-
- solve();
- output_results(cycle);
- }
- }
-} // namespace Step16
-
-
-// @sect3{The main() function}
-//
-// This is again the same function as in step-6:
-int main()
-{
- try
- {
- using namespace Step16;
-
- deallog.depth_console(2);
-
- LaplaceProblem<2> laplace_problem(1);
- laplace_problem.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.git / commitdiff