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rMUSPECTRE µSpectre
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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