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test_gradient.cc
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Mon, Jul 1, 14:27

test_gradient.cc
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/**
* @file test_gradient.cc
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief test the gradient computation for the igfem elements
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
#include "fe_engine.hh"
#include "integrator_gauss_igfem.hh"
#include "shape_igfem.hh"
/* -------------------------------------------------------------------------- */
#include <cstdlib>
#include <fstream>
#include <iostream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
bool gradient(const ElementType type);
void generateIGFEMMesh(const ElementType type, Mesh & mesh,
const std::string & filename);
int main(int argc, char * argv[]) {
akantu::initialize(argc, argv);
debug::setDebugLevel(dblTest);
bool test_passed = false;
/// integrate test of _igfem_triangle_4
AKANTU_DEBUG_INFO("integrating _igfem_triangle_4...");
test_passed = gradient(_igfem_triangle_4);
if (!test_passed) {
finalize();
return EXIT_FAILURE;
}
/// integrate test of _igfem_triangle_5
AKANTU_DEBUG_INFO("integrating _igfem_triangle_5...");
test_passed = gradient(_igfem_triangle_5);
if (!test_passed) {
finalize();
return EXIT_FAILURE;
}
finalize();
return EXIT_SUCCESS;
}
/* -------------------------------------------------------------------------- */
bool gradient(const ElementType type) {
bool correct_result = true;
Int dim = 2;
std::stringstream mesh_info;
mesh_info << "mesh_info" << type << ".txt";
Mesh my_mesh(dim);
generateIGFEMMesh(type, my_mesh, mesh_info.str());
Real eps = 3e-13;
std::cout << "Epsilon : " << eps << std::endl;
FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_igfem> * fem =
new FEEngineTemplate<IntegratorGauss, ShapeLagrange, _ek_igfem>(
my_mesh, dim, "my_fem");
fem->initShapeFunctions();
Real alpha[2][3] = {{13, 23, 31}, {11, 7, 5}};
/// create the 2 component field
/// for field to be constant the enriched values need to be zero!! Therefore
/// non-zero values
/// are only imposed on standard nodes
UInt nb_standard_nodes = 9;
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 (Int i = 0; i < nb_standard_nodes; ++i) {
const_val(i, 0) = 0;
const_val(i, 1) = 0;
for (Int 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);
}
}
/// impose zero at enriched nodes
for (Int i = nb_standard_nodes; i < const_val.getSize(); ++i) {
const_val(i, 0) = 0;
const_val(i, 1) = 0;
}
/// 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 (Int 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;
correct_result = false;
return correct_result;
}
}
}
// compute gradient of coordinates
Array<Real> grad_coord_on_quad(nb_quadrature_points, dim * dim,
"grad_coord_on_quad");
/// create an array with the nodal coordinates that need to be
/// interpolated. The nodal coordinates of the enriched nodes need
/// to be set to zero, because they represent the enrichment of the
/// position field, and the enrichments for this field are all zero!
/// There is no gap in the mesh!
Array<Real> igfem_nodes(my_mesh.getNbNodes(), dim);
const ShapeLagrange<_ek_igfem> & shapes = fem->getShapeFunctions();
shapes.extractValuesAtStandardNodes(my_mesh.getNodes(), igfem_nodes,
_not_ghost);
fem->gradientOnIntegrationPoints(igfem_nodes, 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 (Int i = 0; i < dim; ++i) {
for (Int j = 0; j < dim; ++j) {
if (!(std::abs((*itp)(i, j) - (i == j)) < eps)) {
std::cout << *itp << std::endl;
correct_result = false;
return correct_result;
}
}
}
}
delete fem;
return correct_result;
}

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