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rAKA/test/test_fe_engine/test_gradient.cc
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test_gradient.cc
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/**
* @file test_gradient.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Peter Spijker <peter.spijker@epfl.ch>
*
* @date creation: Fri Sep 03 2010
* @date last modification: Thu Oct 15 2015
*
* @brief test of the fem class
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014, 2015 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/>.
*
* @section DESCRIPTION
*
* This code is computing the gradient of a linear field and check that it gives
* a constant result. It also compute the gradient the coordinates of the mesh
* and check that it gives the identity
*
*/
/* -------------------------------------------------------------------------- */
#include "fe_engine.hh"
#include "shape_lagrange.hh"
#include "integrator_gauss.hh"
/* -------------------------------------------------------------------------- */
#include <cstdlib>
#include <iostream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
int main(int argc, char *argv[]) {
akantu::initialize(argc, argv);
debug::setDebugLevel(dblTest);
const ElementType type = TYPE;
UInt dim = ElementClass<type>::getSpatialDimension();
Real eps = 1e-12;
std::cout << "Epsilon : " << eps << std::endl;
Mesh my_mesh(dim);
std::stringstream meshfilename; meshfilename << type << ".msh";
my_mesh.read(meshfilename.str());
FEEngine *fem = new FEEngineTemplate<IntegratorGauss,ShapeLagrange>(my_mesh, dim, "my_fem");
fem->initShapeFunctions();
Real alpha[2][3] = {{13, 23, 31},
{11, 7, 5}};
/// create the 2 component field
const Array<Real> & position = fem->getMesh().getNodes();
Array<Real> const_val(fem->getMesh().getNbNodes(), 2, "const_val");
UInt nb_element = my_mesh.getNbElement(type);
UInt nb_quadrature_points = fem->getNbIntegrationPoints(type) * nb_element;
Array<Real> grad_on_quad(nb_quadrature_points, 2 * dim, "grad_on_quad");
for (UInt i = 0; i < const_val.getSize(); ++i) {
const_val(i, 0) = 0;
const_val(i, 1) = 0;
for (UInt d = 0; d < dim; ++d) {
const_val(i, 0) += alpha[0][d] * position(i, d);
const_val(i, 1) += alpha[1][d] * position(i, d);
}
}
/// compute the gradient
fem->gradientOnIntegrationPoints(const_val, grad_on_quad, 2, type);
std::cout << "Linear array on nodes : " << const_val << std::endl;
std::cout << "Gradient on quad : " <<grad_on_quad << std::endl;
/// check the results
Array<Real>::matrix_iterator it = grad_on_quad.begin(2,dim);
Array<Real>::matrix_iterator it_end = grad_on_quad.end(2,dim);
for (;it != it_end; ++it) {
for (UInt d = 0; d < dim; ++d) {
Matrix<Real> & grad = *it;
if(!(std::abs(grad(0, d) - alpha[0][d]) < eps) ||
!(std::abs(grad(1, d) - alpha[1][d]) < eps)) {
std::cout << "Error gradient is not correct "
<< (*it)(0, d) << " " << alpha[0][d] << " (" << std::abs((*it)(0, d) - alpha[0][d]) << ")"
<< " - "
<< (*it)(1, d) << " " << alpha[1][d] << " (" << std::abs((*it)(1, d) - alpha[1][d]) << ")"
<< " - " << d << std::endl;
std::cout << *it << std::endl;
exit(EXIT_FAILURE);
}
}
}
// compute gradient of coordinates
Array<Real> grad_coord_on_quad(nb_quadrature_points, dim * dim, "grad_coord_on_quad");
fem->gradientOnIntegrationPoints(my_mesh.getNodes(), grad_coord_on_quad, my_mesh.getSpatialDimension(), type);
std::cout << "Node positions : " << my_mesh.getNodes() << std::endl;
std::cout << "Gradient of nodes : " << grad_coord_on_quad << std::endl;
Array<Real>::matrix_iterator itp = grad_coord_on_quad.begin(dim, dim);
Array<Real>::matrix_iterator itp_end = grad_coord_on_quad.end(dim, dim);
for (;itp != itp_end; ++itp) {
for (UInt i = 0; i < dim; ++i) {
for (UInt j = 0; j < dim; ++j) {
if(!(std::abs((*itp)(i,j) - (i == j)) < eps)) {
std::cout << *itp << std::endl;
exit(EXIT_FAILURE);
}
}
}
}
delete fem;
finalize();
return EXIT_SUCCESS;
}
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