--- /dev/null
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2017 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+// Trilinos direct solvers on a 2D Poisson equation for linear elements with
+// deal.II's parallel vector
+
+#include "../tests.h"
+
+#include <deal.II/base/function.h>
+#include <deal.II/base/utilities.h>
+#include <deal.II/base/index_set.h>
+#include <deal.II/base/conditional_ostream.h>
+
+#include <deal.II/distributed/tria.h>
+
+#include <deal.II/dofs/dof_handler.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/grid/grid_generator.h>
+#include <deal.II/grid/tria.h>
+
+#include <deal.II/lac/full_matrix.h>
+#include <deal.II/lac/vector.h>
+#include <deal.II/lac/constraint_matrix.h>
+#include <deal.II/lac/sparsity_tools.h>
+#include <deal.II/lac/la_parallel_vector.h>
+#include <deal.II/lac/solver_cg.h>
+
+#include <deal.II/lac/trilinos_solver.h>
+#include <deal.II/lac/trilinos_precondition.h>
+#include <deal.II/lac/trilinos_sparse_matrix.h>
+#include <deal.II/lac/trilinos_vector.h>
+
+#include <deal.II/numerics/vector_tools.h>
+
+
+using namespace dealii;
+
+template <int dim>
+class Step4
+{
+public:
+ Step4 ();
+ void run ();
+
+private:
+ void make_grid ();
+ void setup_system();
+ void assemble_system ();
+ void solve ();
+
+ parallel::distributed::Triangulation<dim> triangulation;
+ FE_Q<dim> fe;
+ DoFHandler<dim> dof_handler;
+
+ ConstraintMatrix constraints;
+ SparsityPattern sparsity_pattern;
+
+ TrilinosWrappers::SparseMatrix system_matrix;
+
+ LinearAlgebra::distributed::Vector<double> solution;
+ LinearAlgebra::distributed::Vector<double> system_rhs;
+ LinearAlgebra::distributed::Vector<double> system_rhs_two;
+};
+
+
+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>
+class BoundaryValues : public Function<dim>
+{
+public:
+ BoundaryValues () : Function<dim>() {}
+
+ virtual double value (const Point<dim> &p,
+ const unsigned int component = 0) const;
+};
+
+
+template <int dim>
+double BoundaryValues<dim>::value (const Point<dim> &p,
+ const unsigned int /*component*/) const
+{
+ return -0.5/dim*p.norm_square();
+}
+
+
+
+template <int dim>
+Step4<dim>::Step4 ()
+ :
+ triangulation(MPI_COMM_WORLD,
+ typename Triangulation<dim>::MeshSmoothing
+ (Triangulation<dim>::smoothing_on_refinement |
+ Triangulation<dim>::smoothing_on_coarsening)),
+ fe (1),
+ dof_handler (triangulation)
+{}
+
+
+template <int dim>
+void Step4<dim>::make_grid ()
+{
+ GridGenerator::hyper_cube (triangulation, -1, 1);
+ triangulation.refine_global (6);
+}
+
+
+
+template <int dim>
+void Step4<dim>::setup_system ()
+{
+ dof_handler.distribute_dofs (fe);
+
+ constraints.clear();
+ std::map<unsigned int,double> boundary_values;
+ VectorTools::interpolate_boundary_values (dof_handler,
+ 0,
+ BoundaryValues<dim>(),
+ constraints);
+ constraints.close();
+
+ IndexSet locally_owned_dofs = dof_handler.locally_owned_dofs();
+ IndexSet locally_relevant_dofs;
+
+ DoFTools::extract_locally_relevant_dofs(dof_handler,
+ locally_relevant_dofs);
+
+
+ DynamicSparsityPattern dsp(dof_handler.n_dofs());
+ DoFTools::make_sparsity_pattern (dof_handler, dsp, constraints, false);
+ SparsityTools::distribute_sparsity_pattern(dsp,
+ dof_handler.n_locally_owned_dofs_per_processor(),
+ MPI_COMM_WORLD,
+ locally_relevant_dofs);
+
+ system_matrix.reinit (locally_owned_dofs,
+ locally_owned_dofs,
+ dsp,
+ MPI_COMM_WORLD);
+
+ solution.reinit (locally_owned_dofs,
+ locally_relevant_dofs,
+ MPI_COMM_WORLD);
+
+ system_rhs.reinit (locally_owned_dofs,
+ locally_relevant_dofs,
+ MPI_COMM_WORLD);
+
+ system_rhs_two.reinit (locally_owned_dofs,
+ locally_relevant_dofs,
+ MPI_COMM_WORLD);
+
+}
+
+
+template <int dim>
+void Step4<dim>::assemble_system ()
+{
+ QGauss<dim> quadrature_formula(fe.degree+1);
+
+ FEValues<dim> fe_values (fe, quadrature_formula,
+ update_values | 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);
+ Vector<double> cell_rhs_two (dofs_per_cell);
+
+ std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);
+
+ typename DoFHandler<dim>::active_cell_iterator
+ cell = dof_handler.begin_active(),
+ endc = dof_handler.end();
+
+ for (; cell!=endc; ++cell)
+ {
+ if (cell->is_locally_owned())
+ {
+ fe_values.reinit (cell);
+ cell_matrix = 0;
+ cell_rhs = 0;
+ cell_rhs_two = 0;
+
+ for (unsigned int q_point=0; q_point<n_q_points; ++q_point)
+ for (unsigned int i=0; i<dofs_per_cell; ++i)
+ {
+ for (unsigned int j=0; j<dofs_per_cell; ++j)
+ cell_matrix(i,j) += (fe_values.shape_grad (i, q_point) *
+ fe_values.shape_grad (j, q_point) *
+ fe_values.JxW (q_point));
+
+ cell_rhs(i) += (fe_values.shape_value (i, q_point) *
+ 1.0 *
+ fe_values.JxW (q_point));
+
+ cell_rhs_two(i) += (fe_values.shape_value (i, q_point) *
+ 2.0 *
+ fe_values.JxW (q_point));
+
+ }
+
+ cell->get_dof_indices (local_dof_indices);
+ constraints.distribute_local_to_global(cell_matrix,
+ local_dof_indices,
+ system_matrix);
+
+ constraints.distribute_local_to_global(cell_rhs,
+ local_dof_indices,
+ system_rhs, cell_matrix);
+ constraints.distribute_local_to_global(cell_rhs_two,
+ local_dof_indices,
+ system_rhs_two, cell_matrix);
+ }
+ }
+ system_matrix.compress(VectorOperation::add);
+ system_rhs.compress(VectorOperation::add);
+ system_rhs_two.compress(VectorOperation::add);
+}
+
+
+
+template <int dim>
+void Step4<dim>::solve ()
+{
+ SolverControl solver_control(100, 1e-12);
+ // factorize matrix for direct solver
+ solution = 0;
+
+ deallog.push("DirectKLU");
+ TrilinosWrappers::SolverDirect::AdditionalData data;
+ data.solver_type = "Amesos_Klu";
+ TrilinosWrappers::SolverDirect direct_solver(solver_control, data);
+ direct_solver.initialize (system_matrix);
+
+ // do solve 1
+ direct_solver.solve (solution, system_rhs);
+ deallog << "Vector norm: " << solution.l2_norm();
+
+ constraints.distribute(solution);
+ deallog << " and " << solution.l2_norm() << std::endl;
+ solution.update_ghost_values();
+
+ Vector<double> cellwise_error(triangulation.n_active_cells());
+ VectorTools::integrate_difference(dof_handler, solution,
+ BoundaryValues<dim>(),
+ cellwise_error,
+ QGauss<dim>(3),
+ VectorTools::L2_norm);
+ deallog << " L2 error: " << VectorTools::compute_global_error(triangulation, cellwise_error,
+ VectorTools::L2_norm) << std::endl;
+
+ // do solve 2 without refactorizing
+ solution = 0;
+ direct_solver.solve (solution, system_rhs_two);
+ deallog << "Vector norm: " << solution.l2_norm();
+
+ constraints.distribute(solution);
+ deallog << " and " << solution.l2_norm() << std::endl;
+
+ deallog.pop();
+
+}
+
+
+
+template <int dim>
+void Step4<dim>::run()
+{
+ make_grid();
+ setup_system();
+ assemble_system();
+ solve();
+}
+
+
+int main (int argc, char **argv)
+{
+ Utilities::MPI::MPI_InitFinalize mpi_initialization (argc, argv, testing_max_num_threads());
+ mpi_initlog();
+ deallog << std::setprecision(10);
+
+ Step4<2> test;
+ test.run();
+}
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