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test_solver_petsc.cc
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test_solver_petsc.cc
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/**
* @file test_solver_petsc.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
* @date creation: Sun Oct 19 2014
* @date last modification: Tue Jan 01 2019
*
* @brief test the PETSc solver interface
*
*
* @section LICENSE
*
* Copyright (©) 2015-2021 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can 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 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
#include <cstdlib>
/* -------------------------------------------------------------------------- */
#include "aka_common.hh"
#include "aka_csr.hh"
#include "communicator.hh"
#include "dof_synchronizer.hh"
#include "element_synchronizer.hh"
#include "fe_engine.hh"
#include "mesh.hh"
#include "mesh_io.hh"
#include "mesh_utils.hh"
#include "solver_petsc.hh"
#include "sparse_matrix_petsc.hh"
#include "mesh_partition_scotch.hh"
using namespace akantu;
int main(int argc, char * argv[]) {
initialize(argc, argv);
const ElementType element_type = _segment_2;
const GhostType ghost_type = _not_ghost;
UInt spatial_dimension = 1;
const auto & comm = akantu::Communicator::getStaticCommunicator();
Int psize = comm.getNbProc();
Int prank = comm.whoAmI();
/// read the mesh and partition it
Mesh mesh(spatial_dimension);
/* ------------------------------------------------------------------------ */
/* Parallel initialization */
/* ------------------------------------------------------------------------ */
ElementSynchronizer * communicator = NULL;
if (prank == 0) {
/// creation mesh
mesh.read("1D_bar.msh");
MeshPartitionScotch * partition =
new MeshPartitionScotch(mesh, spatial_dimension);
partition->partitionate(psize);
communicator =
ElementSynchronizer::createDistributedSynchronizerMesh(mesh, partition);
delete partition;
} else {
communicator =
ElementSynchronizer::createDistributedSynchronizerMesh(mesh, NULL);
}
FEEngine * fem =
new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_regular>(
mesh, spatial_dimension, "my_fem");
DOFSynchronizer dof_synchronizer(mesh, spatial_dimension);
UInt nb_global_nodes = mesh.getNbGlobalNodes();
dof_synchronizer.initGlobalDOFEquationNumbers();
// fill the matrix with
UInt nb_element = mesh.getNbElement(element_type);
UInt nb_nodes_per_element = mesh.getNbNodesPerElement(element_type);
UInt nb_dofs_per_element = spatial_dimension * nb_nodes_per_element;
SparseMatrix K(nb_global_nodes * spatial_dimension, _symmetric);
K.buildProfile(mesh, dof_synchronizer, spatial_dimension);
Matrix<Real> element_input(nb_dofs_per_element, nb_dofs_per_element, 0);
for (UInt i = 0; i < nb_dofs_per_element; ++i) {
for (UInt j = 0; j < nb_dofs_per_element; ++j) {
element_input(i, j) = ((i == j) ? 1 : -1);
}
}
Array<Real> K_e =
Array<Real>(nb_element, nb_dofs_per_element * nb_dofs_per_element, "K_e");
Array<Real>::matrix_iterator K_e_it =
K_e.begin(nb_dofs_per_element, nb_dofs_per_element);
Array<Real>::matrix_iterator K_e_end =
K_e.end(nb_dofs_per_element, nb_dofs_per_element);
for (; K_e_it != K_e_end; ++K_e_it)
*K_e_it = element_input;
// assemble the test matrix
fem->assembleMatrix(K_e, K, spatial_dimension, element_type, ghost_type);
// apply boundary: block first node
const Array<Real> & position = mesh.getNodes();
UInt nb_nodes = mesh.getNbNodes();
Array<bool> boundary = Array<bool>(nb_nodes, spatial_dimension, false);
for (UInt i = 0; i < nb_nodes; ++i) {
if (std::abs(position(i, 0)) < Math::getTolerance())
boundary(i, 0) = true;
}
K.applyBoundary(boundary);
/// create the PETSc matrix for the solve step
PETScMatrix petsc_matrix(nb_global_nodes * spatial_dimension, _symmetric);
petsc_matrix.buildProfile(mesh, dof_synchronizer, spatial_dimension);
/// copy the stiffness matrix into the petsc matrix
petsc_matrix.add(K, 1);
// initialize internal forces: they are zero because imposed displacement is
// zero
Array<Real> internal_forces(nb_nodes, spatial_dimension, 0.);
// compute residual: apply nodal force on last node
Array<Real> residual(nb_nodes, spatial_dimension, 0.);
for (UInt i = 0; i < nb_nodes; ++i) {
if (std::abs(position(i, 0) - 10) < Math::getTolerance())
residual(i, 0) += 2;
}
residual -= internal_forces;
/// initialize solver and solution
Array<Real> solution(nb_nodes, spatial_dimension, 0.);
SolverPETSc solver(petsc_matrix);
solver.initialize();
solver.setOperators();
solver.setRHS(residual);
solver.solve(solution);
/// verify solution
Math::setTolerance(1e-11);
for (UInt i = 0; i < nb_nodes; ++i) {
if (!dof_synchronizer.isPureGhostDOF(i) &&
!Math::are_float_equal(2 * position(i, 0), solution(i, 0))) {
std::cout << "The solution is not correct!!!!" << std::endl;
finalize();
return EXIT_FAILURE;
}
}
delete communicator;
finalize();
return EXIT_SUCCESS;
}

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