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muSpectre/tests/test_solver_newton_cg.cc
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test_solver_newton_cg.cc
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/**
* @file test_solver_newton_cg.cc
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 20 Dec 2017
*
* @brief Tests for the standard Newton-Raphson + Conjugate Gradient solver
*
* Copyright © 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre 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
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#include "tests.hh"
#include "solver/solvers.hh"
#include "solver/solver_cg.hh"
#include "solver/solver_cg_eigen.hh"
#include "fft/fftw_engine.hh"
#include "fft/projection_finite_strain_fast.hh"
#include "materials/material_linear_elastic1.hh"
#include "common/iterators.hh"
#include "common/ccoord_operations.hh"
#include "cell/cell_factory.hh"
namespace muSpectre {
BOOST_AUTO_TEST_SUITE(newton_cg_tests);
BOOST_AUTO_TEST_CASE(manual_construction_test) {
// constexpr Dim_t dim{twoD};
constexpr Dim_t dim{threeD};
// constexpr Ccoord_t<dim> resolutions{3, 3};
// constexpr Rcoord_t<dim> lengths{2.3, 2.7};
constexpr Ccoord_t<dim> resolutions{5, 5, 5};
constexpr Rcoord_t<dim> lengths{5, 5, 5};
auto fft_ptr{std::make_unique<FFTWEngine<dim, dim>>(resolutions)};
auto proj_ptr{std::make_unique<ProjectionFiniteStrainFast<dim, dim>>(std::move(fft_ptr), lengths)};
CellBase<dim, dim> sys(std::move(proj_ptr));
using Mat_t = MaterialLinearElastic1<dim, dim>;
//const Real Young{210e9}, Poisson{.33};
const Real Young{1.0030648180242636}, Poisson{0.29930675909878679};
// const Real lambda{Young*Poisson/((1+Poisson)*(1-2*Poisson))};
// const Real mu{Young/(2*(1+Poisson))};
auto& Material_hard = Mat_t::make(sys, "hard", 10*Young, Poisson);
auto& Material_soft = Mat_t::make(sys, "soft", Young, Poisson);
for (auto && tup: akantu::enumerate(sys)) {
auto && pixel = std::get<1>(tup);
if (std::get<0>(tup) == 0) {
Material_hard.add_pixel(pixel);
} else {
Material_soft.add_pixel(pixel);
}
}
sys.initialise();
Grad_t<dim> delF0;
delF0 << 0, 1., 0, 0, 0, 0, 0, 0, 0;
constexpr Real cg_tol{1e-8}, newton_tol{1e-5};
constexpr Uint maxiter{CcoordOps::get_size(resolutions)*ipow(dim, secondOrder)*10};
constexpr bool verbose{false};
GradIncrements<dim> grads; grads.push_back(delF0);
SolverCG<dim> cg{sys, cg_tol, maxiter, bool(verbose)};
Eigen::ArrayXXd res1{de_geus(sys, grads, cg, newton_tol, verbose)[0].grad};
SolverCG<dim> cg2{sys, cg_tol, maxiter, bool(verbose)};
Eigen::ArrayXXd res2{newton_cg(sys, grads, cg2, newton_tol, verbose)[0].grad};
BOOST_CHECK_LE(abs(res1-res2).mean(), cg_tol);
}
BOOST_AUTO_TEST_CASE(small_strain_patch_test) {
constexpr Dim_t dim{twoD};
using Ccoord = Ccoord_t<dim>;
using Rcoord = Rcoord_t<dim>;
constexpr Ccoord resolutions{CcoordOps::get_cube<dim>(3)};
constexpr Rcoord lengths{CcoordOps::get_cube<dim>(1.)};
constexpr Formulation form{Formulation::small_strain};
// number of layers in the hard material
constexpr Uint nb_lays{1};
constexpr Real contrast{2};
static_assert(nb_lays < resolutions[0],
"the number or layers in the hard material must be smaller "
"than the total number of layers in dimension 0");
auto sys{make_cell(resolutions, lengths, form)};
using Mat_t = MaterialLinearElastic1<dim, dim>;
constexpr Real Young{2.}, Poisson{.33};
auto material_hard{std::make_unique<Mat_t>("hard", contrast*Young, Poisson)};
auto material_soft{std::make_unique<Mat_t>("soft", Young, Poisson)};
for (const auto & pixel: sys) {
if (pixel[0] < Dim_t(nb_lays)) {
material_hard->add_pixel(pixel);
} else {
material_soft->add_pixel(pixel);
}
}
sys.add_material(std::move(material_hard));
sys.add_material(std::move(material_soft));
sys.initialise();
Grad_t<dim> delEps0{Grad_t<dim>::Zero()};
constexpr Real eps0 = 1.;
//delEps0(0, 1) = delEps0(1, 0) = eps0;
delEps0(0, 0) = eps0;
constexpr Real cg_tol{1e-8}, newton_tol{1e-5}, equil_tol{1e-10};
constexpr Uint maxiter{dim*10};
constexpr Dim_t verbose{0};
SolverCGEigen<dim> cg{sys, cg_tol, maxiter, bool(verbose)};
auto result = de_geus(sys, delEps0, cg, newton_tol,
equil_tol, verbose);
if (verbose) {
std::cout << "result:" << std::endl << result.grad << std::endl;
std::cout << "mean strain = " << std::endl
<< sys.get_strain().get_map().mean() << std::endl;
}
/**
* verification of resultant strains: subscript ₕ for hard and ₛ
* for soft, Nₕ is nb_lays and Nₜₒₜ is resolutions, k is contrast
*
* Δl = εl = Δlₕ + Δlₛ = εₕlₕ+εₛlₛ
* => ε = εₕ Nₕ/Nₜₒₜ + εₛ (Nₜₒₜ-Nₕ)/Nₜₒₜ
*
* σ is constant across all layers
* σₕ = σₛ
* => Eₕ εₕ = Eₛ εₛ
* => εₕ = 1/k εₛ
* => ε / (1/k Nₕ/Nₜₒₜ + (Nₜₒₜ-Nₕ)/Nₜₒₜ) = εₛ
*/
constexpr Real factor{1/contrast * Real(nb_lays)/resolutions[0]
+ 1.-nb_lays/Real(resolutions[0])};
constexpr Real eps_soft{eps0/factor};
constexpr Real eps_hard{eps_soft/contrast};
if (verbose) {
std::cout << "εₕ = " << eps_hard << ", εₛ = " << eps_soft << std::endl;
std::cout << "ε = εₕ Nₕ/Nₜₒₜ + εₛ (Nₜₒₜ-Nₕ)/Nₜₒₜ" << std::endl;
}
Grad_t<dim> Eps_hard; Eps_hard << eps_hard, 0, 0, 0;
Grad_t<dim> Eps_soft; Eps_soft << eps_soft, 0, 0, 0;
// verify uniaxial tension patch test
for (const auto & pixel: sys) {
if (pixel[0] < Dim_t(nb_lays)) {
BOOST_CHECK_LE((Eps_hard-sys.get_strain().get_map()[pixel]).norm(), tol);
} else {
BOOST_CHECK_LE((Eps_soft-sys.get_strain().get_map()[pixel]).norm(), tol);
}
}
delEps0 = Grad_t<dim>::Zero();
delEps0(0, 1) = delEps0(1, 0) = eps0;
SolverCG<dim> cg2{sys, cg_tol, maxiter, bool(verbose)};
result = newton_cg(sys, delEps0, cg2, newton_tol,
equil_tol, verbose);
Eps_hard << 0, eps_hard, eps_hard, 0;
Eps_soft << 0, eps_soft, eps_soft, 0;
// verify pure shear patch test
for (const auto & pixel: sys) {
if (pixel[0] < Dim_t(nb_lays)) {
BOOST_CHECK_LE((Eps_hard-sys.get_strain().get_map()[pixel]).norm(), tol);
} else {
BOOST_CHECK_LE((Eps_soft-sys.get_strain().get_map()[pixel]).norm(), tol);
}
}
}
BOOST_AUTO_TEST_SUITE_END();
} // muSpectre
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