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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 "test_fe_engine_fixture.hh"
/* -------------------------------------------------------------------------- */
#include <cstdlib>
#include <iostream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
namespace {
TYPED_TEST(TestFEMFixture, GradientPoly) {
this->fem->initShapeFunctions();
Real alpha[2][3] = {{13, 23, 31}, {11, 7, 5}};
const auto dim = this->dim;
const auto type = this->type;
const auto & position = this->fem->getMesh().getNodes();
Array<Real> const_val(this->fem->getMesh().getNbNodes(), 2, "const_val");
for (auto && pair : zip(make_view(position, dim), make_view(const_val, 2))) {
auto & pos = std::get<0>(pair);
auto & const_ = std::get<1>(pair);
const_.set(0.);
for (UInt d = 0; d < dim; ++d) {
const_(0) += alpha[0][d] * pos(d);
const_(1) += alpha[1][d] * pos(d);
}
}
/// compute the gradient
Array<Real> grad_on_quad(this->nb_quadrature_points_total, 2 * dim,
"grad_on_quad");
this->fem->gradientOnIntegrationPoints(const_val, grad_on_quad, 2, type);
/// check the results
for (auto && grad : make_view(grad_on_quad, 2, dim)) {
for (UInt d = 0; d < dim; ++d) {
EXPECT_NEAR(grad(0, d), alpha[0][d], 5e-13);
EXPECT_NEAR(grad(1, d), alpha[1][d], 5e-13);
}
}
}
TYPED_TEST(TestFEMFixture, GradientPositions) {
this->fem->initShapeFunctions();
const auto dim = this->dim;
const auto type = this->type;
UInt nb_quadrature_points =
this->fem->getNbIntegrationPoints(type) * this->nb_element;
Array<Real> grad_coord_on_quad(nb_quadrature_points, dim * dim,
"grad_coord_on_quad");
const auto & position = this->mesh->getNodes();
this->fem->gradientOnIntegrationPoints(position, grad_coord_on_quad, dim,
type);
auto I = Matrix<Real>::eye(UInt(dim));
for (auto && grad : make_view(grad_coord_on_quad, dim, dim)) {
auto diff = (I - grad).template norm<L_inf>();
EXPECT_NEAR(0., diff, 2e-14);
}
}
}
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