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projection_finite_strain.cc
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projection_finite_strain.cc
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/**
* @file projection_finite_strain.cc
*
* @author Till Junge <till.junge@altermail.ch>
*
* @date 05 Dec 2017
*
* @brief implementation of standard finite strain projection operator
*
* 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 "fft/projection_finite_strain.hh"
#include "fft/fftw_engine.hh"
#include "fft/fft_utils.hh"
#include "common/field_map.hh"
#include "common/tensor_algebra.hh"
#include "common/iterators.hh"
#include "Eigen/Dense"
namespace muSpectre {
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
ProjectionFiniteStrain<DimS, DimM>::
ProjectionFiniteStrain(FFT_Engine_ptr engine)
:Parent{std::move(engine), Formulation::finite_strain}
{}
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
void ProjectionFiniteStrain<DimS, DimM>::
initialise(FFT_PlanFlags flags) {
Parent::initialise(flags);
FFT_freqs<DimS> fft_freqs(this->fft_engine->get_resolutions(),
this->fft_engine->get_lengths());
for (auto && tup: akantu::zip(*this->fft_engine, this->Ghat)) {
const auto & ccoord = std::get<0> (tup);
auto & G = std::get<1>(tup);
auto xi = fft_freqs.get_unit_xi(ccoord);
//! this is simplifiable using Curnier's Méthodes numériques, 6.69(c)
G = Matrices::outer_under(Matrices::I2<DimM>(), xi*xi.transpose());
// The commented block below corresponds to the original
// definition of the operator in de Geus et
// al. (https://doi.org/10.1016/j.cma.2016.12.032). However,
// they use a bizarre definition of the double contraction
// between fourth-order and second-order tensors that has a
// built-in transpose operation (i.e., C = A:B <-> AᵢⱼₖₗBₗₖ =
// Cᵢⱼ , note the inverted ₗₖ instead of ₖₗ), here, we define
// the double contraction without the transposition. As a
// result, the Projection operator produces the transpose of de
// Geus's
// for (Dim_t im = 0; im < DimS; ++im) {
// for (Dim_t j = 0; j < DimS; ++j) {
// for (Dim_t l = 0; l < DimS; ++l) {
// get(G, im, j, l, im) = xi(j)*xi(l);
// }
// }
// }
}
this->Ghat[0].setZero();
}
template class ProjectionFiniteStrain<twoD, twoD>;
template class ProjectionFiniteStrain<threeD, threeD>;
} // muSpectre

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