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solvers.hh
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/**
* @file solvers.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 20 Dec 2017
*
* @brief Free functions for solving
*
* 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.
*/
#ifndef SOLVERS_H
#define SOLVERS_H
#include "solver/solver_base.hh"
#include <Eigen/Dense>
#include <vector>
#include <string>
namespace muSpectre {
/**
* emulates scipy.optimize.OptimizeResult
*/
struct OptimizeResult
{
//! Strain ε or Gradient F at solution
Eigen::ArrayXXd grad;
//! Cauchy stress σ or first Piola-Kirchhoff stress P at solution
Eigen::ArrayXXd stress;
//! whether or not the solver exited successfully
bool success;
//! Termination status of the optimizer. Its value depends on the
//! underlying solver. Refer to message for details.
Int status;
//! Description of the cause of the termination.
std::string message;
//! number of iterations
Uint nb_it;
//! number of system evaluations
Uint nb_fev;
};
/**
* Field type that solvers expect gradients to be expressed in
*/
template <Dim_t Dim>
using Grad_t = Matrices::Tens2_t<Dim>;
/**
* multiple increments can be submitted at once (useful for
* path-dependent materials)
*/
template <Dim_t Dim>
using GradIncrements = std::vector<Grad_t<Dim>,
Eigen::aligned_allocator<Grad_t<Dim>>>;
/* ---------------------------------------------------------------------- */
/**
* Uses the Newton-conjugate Gradient method to find the static
* equilibrium of a cell given a series of mean applied strains
*/
template <Dim_t DimS, Dim_t DimM=DimS>
std::vector<OptimizeResult>
newton_cg (SystemBase<DimS, DimM> & sys,
const GradIncrements<DimM> & delF0,
SolverBase<DimS, DimM> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose = 0);
/* ---------------------------------------------------------------------- */
/**
* Uses the Newton-conjugate Gradient method to find the static
* equilibrium of a cell given a mean applied strain
*/
template <Dim_t DimS, Dim_t DimM=DimS>
inline OptimizeResult
newton_cg (SystemBase<DimS, DimM> & sys, const Grad_t<DimM> & delF0,
SolverBase<DimS, DimM> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose = 0){
return newton_cg(sys, GradIncrements<DimM>{delF0},
solver, newton_tol, equil_tol, verbose)[0];
}
/* ---------------------------------------------------------------------- */
/**
* Uses the method proposed by de Geus method to find the static
* equilibrium of a cell given a series of mean applied strains
*/
template <Dim_t DimS, Dim_t DimM=DimS>
std::vector<OptimizeResult>
de_geus (SystemBase<DimS, DimM> & sys,
const GradIncrements<DimM> & delF0,
SolverBase<DimS, DimM> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose = 0);
/* ---------------------------------------------------------------------- */
/**
* Uses the method proposed by de Geus method to find the static
* equilibrium of a cell given a mean applied strain
*/
template <Dim_t DimS, Dim_t DimM=DimS>
OptimizeResult
de_geus (SystemBase<DimS, DimM> & sys, const Grad_t<DimM> & delF0,
SolverBase<DimS, DimM> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose = 0){
return de_geus(sys, GradIncrements<DimM>{delF0},
solver, newton_tol, equil_tol, verbose)[0];
}
/* ---------------------------------------------------------------------- */
/**
* check whether a strain is symmetric, for the purposes of small
* strain problems
*/
bool check_symmetry(const Eigen::Ref<const Eigen::ArrayXXd>& eps,
Real rel_tol = 1e-8);
} // muSpectre
#endif /* SOLVERS_H */

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