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test_fe_engine_gauss_integration.cc
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test_fe_engine_gauss_integration.cc
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/**
* @file test_fe_engine_precomputation.cc
*
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Mon Jun 14 2010
* @date last modification: Mon Jul 13 2015
*
* @brief test integration on elements, this test consider that mesh is a cube
*
* @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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "fe_engine.hh"
#include "shape_lagrange.hh"
#include "integrator_gauss.hh"
/* -------------------------------------------------------------------------- */
#include <iostream>
/* -------------------------------------------------------------------------- */
using namespace akantu;
typedef FEEngineTemplate<IntegratorGauss, ShapeLagrange> FEM;
const ElementType type = TYPE;
// cst x x^2 x^3
// x^4 x^5
Real alpha[3][6] = {{0.40062394, 0.13703225, 0.51731446, 0.87830084, 0.5410543,
0.71842292}, // x
{0.41861835, 0.11080576, 0.49874043, 0.49077504, 0.85073835,
0.66259755}, // y
{0.92620845, 0.7503478, 0.62962232, 0.31662719, 0.64069644,
0.30878135}}; // z
static Vector<Real> eval_poly(UInt degree, const Vector<Real> & x) {
Vector<Real> res(x.size());
for (UInt i = 0; i < degree + 1; ++i) {
for (UInt d = 0; d < x.size(); ++d) {
res(d) += std::pow(x(d), i) * alpha[d][i];
}
}
return res;
}
static Vector<Real> eval_int(UInt degree, const Vector<Real> & a,
const Vector<Real> & b) {
Vector<Real> res(a.size());
for (UInt i = 0; i < degree + 1; ++i) {
for (UInt d = 0; d < a.size(); ++d) {
res(d) += (std::pow(b(d), i + 1) - std::pow(a(d), i + 1)) * alpha[d][i] / Real(i + 1);
}
}
if (a.size() == 3) {
res(_x) *= std::abs(b(_y) - a(_y)) * std::abs(b(_z) - a(_z));
res(_y) *= std::abs(b(_x) - a(_x)) * std::abs(b(_z) - a(_z));
res(_z) *= std::abs(b(_y) - a(_y)) * std::abs(b(_x) - a(_x));
} else if (a.size() == 2) {
res(_x) *= std::abs(b(_y) - a(_y));
res(_y) *= std::abs(b(_x) - a(_x));
}
return res;
}
template <UInt degree>
static Vector<Real> integrate_poly(UInt poly_degree, FEM & fem) {
Mesh & mesh = fem.getMesh();
UInt dim = mesh.getSpatialDimension();
Matrix<Real> integration_points =
fem.getIntegrator().getIntegrationPoints<type, degree>();
// Vector<Real> integration_weights =
// fem.getIntegrator().getIntegrationWeights<type, degree>();
// for (UInt i = 0; i < integration_points.cols(); ++i) {
// std::cout << "q(" << i << ") = " << Vector<Real>(integration_points(i))
// << " - w(" << i << ") = "<< integration_weights[i] << std::endl;
// }
UInt nb_integration_points = integration_points.cols();
UInt nb_element = mesh.getNbElement(type);
UInt shapes_size = ElementClass<type>::getShapeSize();
Array<Real> shapes(0, shapes_size);
fem.getShapeFunctions().computeShapesOnIntegrationPoints<type>(
mesh.getNodes(), integration_points, shapes, _not_ghost);
UInt vect_size = nb_integration_points * nb_element;
Array<Real> integration_points_pos(vect_size, dim);
fem.getShapeFunctions().interpolateOnIntegrationPoints<type>(
mesh.getNodes(), integration_points_pos, dim, shapes);
Array<Real> polynomial(vect_size, dim);
Array<Real>::vector_iterator P_it = polynomial.begin(dim);
Array<Real>::vector_iterator P_end = polynomial.end(dim);
Array<Real>::const_vector_iterator x_it = integration_points_pos.begin(dim);
for (; P_it != P_end; ++P_it, ++x_it) {
*P_it = eval_poly(poly_degree, *x_it);
// std::cout << "Q = " << *x_it << std::endl;
// std::cout << "P(Q) = " << *P_it << std::endl;
}
Vector<Real> res(dim);
Array<Real> polynomial_1d(vect_size, 1);
for (UInt d = 0; d < dim; ++d) {
Array<Real>::const_vector_iterator P_it = polynomial.begin(dim);
Array<Real>::const_vector_iterator P_end = polynomial.end(dim);
Array<Real>::scalar_iterator P1_it = polynomial_1d.begin();
for (; P_it != P_end; ++P_it, ++P1_it) {
*P1_it = (*P_it)(d);
// std::cout << "P(Q, d) = " << *P1_it << std::endl;
}
res(d) = fem.getIntegrator().integrate<type, degree>(polynomial_1d);
}
return res;
}
int main(int argc, char * argv[]) {
akantu::initialize(argc, argv);
const UInt dim = ElementClass<type>::getSpatialDimension();
Mesh mesh(dim);
std::stringstream meshfilename;
meshfilename << type << ".msh";
mesh.read(meshfilename.str());
FEM fem(mesh, dim, "my_fem");
mesh.computeBoundingBox();
const Vector<Real> & lower = mesh.getLowerBounds();
const Vector<Real> & upper = mesh.getUpperBounds();
bool ok = true;
for (UInt d = 0; d < 6; ++d) {
Vector<Real> res(dim);
switch (d) {
case 0:
res = integrate_poly<1>(d, fem);
break;
case 1:
res = integrate_poly<1>(d, fem);
break;
case 2:
res = integrate_poly<2>(d, fem);
break;
case 3:
res = integrate_poly<3>(d, fem);
break;
case 4:
res = integrate_poly<4>(d, fem);
break;
case 5:
res = integrate_poly<5>(d, fem);
break;
}
Vector<Real> exact(dim);
exact = eval_int(d, lower, upper);
Vector<Real> error(dim);
error = exact - res;
Real error_n = error.norm<L_inf>();
if (error_n > 5e-14) {
std::cout << d << " -> Resultat " << res << " - ";
std::cout << "Exact" << exact << " -- ";
std::cout << error << " {" << error_n << "}" << std::endl;
ok = false;
}
}
finalize();
if (ok)
return 0;
else
return 1;
}

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