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solvers.cc
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/**
* @file solvers.cc
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 20 Dec 2017
*
* @brief implementation of solver functions
*
* 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 "solver/solvers.hh"
#include "solver/solver_cg.hh"
#include "common/iterators.hh"
#include <Eigen/IterativeLinearSolvers>
#include <iomanip>
#include <cmath>
namespace
muSpectre
{
template
<
Dim_t
DimS
,
Dim_t
DimM
>
std
::
vector
<
OptimizeResult
>
de_geus
(
SystemBase
<
DimS
,
DimM
>
&
sys
,
const
GradIncrements
<
DimM
>
&
delFs
,
SolverBase
<
DimS
,
DimM
>
&
solver
,
Real
newton_tol
,
Dim_t
verbose
)
{
using
Field_t
=
typename
MaterialBase
<
DimS
,
DimM
>::
StrainField_t
;
auto
solver_fields
{
std
::
make_unique
<
GlobalFieldCollection
<
DimS
,
DimM
>>
()};
solver_fields
->
initialise
(
sys
.
get_resolutions
());
// Corresponds to symbol δF or δε
auto
&
incrF
{
make_field
<
Field_t
>
(
"δF"
,
*
solver_fields
)};
// Corresponds to symbol ΔF or Δε
auto
&
DeltaF
{
make_field
<
Field_t
>
(
"ΔF"
,
*
solver_fields
)};
// field to store the rhs for cg calculations
auto
&
rhs
{
make_field
<
Field_t
>
(
"rhs"
,
*
solver_fields
)};
solver
.
initialise
();
if
(
solver
.
get_maxiter
()
==
0
)
{
solver
.
set_maxiter
(
sys
.
size
()
*
DimM
*
DimM
*
10
);
}
size_t
count_width
{};
const
auto
form
{
sys
.
get_formulation
()};
std
::
string
strain_symb
{};
if
(
verbose
>
0
)
{
//setup of algorithm 5.2 in Nocedal, Numerical Optimization (p. 111)
std
::
cout
<<
"de Geus-"
<<
solver
.
name
()
<<
" for "
;
switch
(
form
)
{
case
Formulation
::
small_strain:
{
strain_symb
=
"ε"
;
std
::
cout
<<
"small"
;
break
;
}
case
Formulation
::
finite_strain:
{
strain_symb
=
"F"
;
std
::
cout
<<
"finite"
;
break
;
}
default
:
throw
SolverError
(
"unknown formulation"
);
break
;
}
std
::
cout
<<
" strain with"
<<
std
::
endl
<<
"newton_tol = "
<<
newton_tol
<<
", cg_tol = "
<<
solver
.
get_tol
()
<<
" maxiter = "
<<
solver
.
get_maxiter
()
<<
" and Δ"
<<
strain_symb
<<
" ="
<<
std
::
endl
;
for
(
auto
&&
tup:
akantu
::
enumerate
(
delFs
))
{
auto
&&
counter
{
std
::
get
<
0
>
(
tup
)};
auto
&&
grad
{
std
::
get
<
1
>
(
tup
)};
std
::
cout
<<
"Step "
<<
counter
+
1
<<
":"
<<
std
::
endl
<<
grad
<<
std
::
endl
;
}
count_width
=
size_t
(
std
::
log10
(
solver
.
get_maxiter
()))
+
1
;
}
// initialise F = I or ε = 0
auto
&
F
{
sys
.
get_strain
()};
switch
(
form
)
{
case
Formulation
::
finite_strain:
{
F
.
get_map
()
=
Matrices
::
I2
<
DimM
>
();
break
;
}
case
Formulation
::
small_strain:
{
F
.
get_map
()
=
Matrices
::
I2
<
DimM
>
().
Zero
();
for
(
const
auto
&
delF:
delFs
)
{
if
(
!
check_symmetry
(
delF
))
{
throw
SolverError
(
"all Δε must be symmetric!"
);
}
}
break
;
}
default
:
throw
SolverError
(
"Unknown formulation"
);
break
;
}
// initialise return value
std
::
vector
<
OptimizeResult
>
ret_val
{};
// initialise materials
constexpr
bool
need_tangent
{
true
};
sys
.
initialise_materials
(
need_tangent
);
Grad_t
<
DimM
>
previous_grad
{
Grad_t
<
DimM
>::
Zero
()};
for
(
const
auto
&
delF:
delFs
)
{
//incremental loop
Real
incrNorm
{
2
*
newton_tol
},
gradNorm
{
1
};
auto
convergence_test
=
[
&
incrNorm
,
&
gradNorm
,
&
newton_tol
]
()
{
return
incrNorm
/
gradNorm
<=
newton_tol
;
};
Uint
newt_iter
{
0
};
for
(;
(
newt_iter
<
solver
.
get_maxiter
())
&&
(
!
convergence_test
()
||
(
newt_iter
==
1
));
++
newt_iter
)
{
// obtain material response
auto
res_tup
{
sys
.
evaluate_stress_tangent
(
F
)};
auto
&
P
{
std
::
get
<
0
>
(
res_tup
)};
auto
&
K
{
std
::
get
<
1
>
(
res_tup
)};
auto
tangent_effect
=
[
&
sys
,
&
K
]
(
const
Field_t
&
dF
,
Field_t
&
dP
)
{
sys
.
directional_stiffness
(
K
,
dF
,
dP
);
};
if
(
newt_iter
==
0
)
{
DeltaF
.
get_map
()
=
-
(
delF
-
previous_grad
);
// neg sign because rhs
tangent_effect
(
DeltaF
,
rhs
);
incrF
.
eigenvec
()
=
solver
.
solve
(
rhs
.
eigenvec
(),
incrF
.
eigenvec
());
F
.
eigen
()
-=
DeltaF
.
eigen
();
}
else
{
rhs
.
eigen
()
=
-
P
.
eigen
();
sys
.
project
(
rhs
);
incrF
.
eigen
()
=
0
;
incrF
.
eigenvec
()
=
solver
.
solve
(
rhs
.
eigenvec
(),
incrF
.
eigenvec
());
}
F
.
eigen
()
+=
incrF
.
eigen
();
incrNorm
=
incrF
.
eigen
().
matrix
().
norm
();
gradNorm
=
F
.
eigen
().
matrix
().
norm
();
if
(
verbose
>
0
)
{
std
::
cout
<<
"at Newton step "
<<
std
::
setw
(
count_width
)
<<
newt_iter
<<
", |δ"
<<
strain_symb
<<
"|/|Δ"
<<
strain_symb
<<
"| = "
<<
std
::
setw
(
17
)
<<
incrNorm
/
gradNorm
<<
", tol = "
<<
newton_tol
<<
std
::
endl
;
if
(
verbose
-
1
>
1
)
{
std
::
cout
<<
"<"
<<
strain_symb
<<
"> ="
<<
std
::
endl
<<
F
.
get_map
().
mean
()
<<
std
::
endl
;
}
}
}
// update previous gradient
previous_grad
=
delF
;
ret_val
.
push_back
(
OptimizeResult
{
F
.
eigen
(),
sys
.
get_stress
().
eigen
(),
convergence_test
(),
Int
(
convergence_test
()),
"message not yet implemented"
,
newt_iter
,
solver
.
get_counter
()});
//!store history variables here
}
return
ret_val
;
}
//! instantiation for two-dimensional cells
template
std
::
vector
<
OptimizeResult
>
de_geus
(
SystemBase
<
twoD
,
twoD
>
&
sys
,
const
GradIncrements
<
twoD
>&
delF0
,
SolverBase
<
twoD
,
twoD
>
&
solver
,
Real
newton_tol
,
Dim_t
verbose
);
// template typename SystemBase<twoD, threeD>::StrainField_t &
// de_geus (SystemBase<twoD, threeD> & sys, const GradIncrements<threeD>& delF0,
// const Real cg_tol, const Real newton_tol, Uint maxiter,
// Dim_t verbose);
//! instantiation for three-dimensional cells
template
std
::
vector
<
OptimizeResult
>
de_geus
(
SystemBase
<
threeD
,
threeD
>
&
sys
,
const
GradIncrements
<
threeD
>&
delF0
,
SolverBase
<
threeD
,
threeD
>
&
solver
,
Real
newton_tol
,
Dim_t
verbose
);
/* ---------------------------------------------------------------------- */
template
<
Dim_t
DimS
,
Dim_t
DimM
>
std
::
vector
<
OptimizeResult
>
newton_cg
(
SystemBase
<
DimS
,
DimM
>
&
sys
,
const
GradIncrements
<
DimM
>
&
delFs
,
SolverBase
<
DimS
,
DimM
>
&
solver
,
Real
newton_tol
,
Dim_t
verbose
)
{
using
Field_t
=
typename
MaterialBase
<
DimS
,
DimM
>::
StrainField_t
;
auto
solver_fields
{
std
::
make_unique
<
GlobalFieldCollection
<
DimS
,
DimM
>>
()};
solver_fields
->
initialise
(
sys
.
get_resolutions
());
// Corresponds to symbol δF or δε
auto
&
incrF
{
make_field
<
Field_t
>
(
"δF"
,
*
solver_fields
)};
// field to store the rhs for cg calculations
auto
&
rhs
{
make_field
<
Field_t
>
(
"rhs"
,
*
solver_fields
)};
solver
.
initialise
();
if
(
solver
.
get_maxiter
()
==
0
)
{
solver
.
set_maxiter
(
sys
.
size
()
*
DimM
*
DimM
*
10
);
}
size_t
count_width
{};
const
auto
form
{
sys
.
get_formulation
()};
std
::
string
strain_symb
{};
if
(
verbose
>
0
)
{
//setup of algorithm 5.2 in Nocedal, Numerical Optimization (p. 111)
std
::
cout
<<
"Newton-"
<<
solver
.
name
()
<<
" for "
;
switch
(
form
)
{
case
Formulation
::
small_strain:
{
strain_symb
=
"ε"
;
std
::
cout
<<
"small"
;
break
;
}
case
Formulation
::
finite_strain:
{
strain_symb
=
"Fy"
;
std
::
cout
<<
"finite"
;
break
;
}
default
:
throw
SolverError
(
"unknown formulation"
);
break
;
}
std
::
cout
<<
" strain with"
<<
std
::
endl
<<
"newton_tol = "
<<
newton_tol
<<
", cg_tol = "
<<
solver
.
get_tol
()
<<
" maxiter = "
<<
solver
.
get_maxiter
()
<<
" and Δ"
<<
strain_symb
<<
" ="
<<
std
::
endl
;
for
(
auto
&&
tup:
akantu
::
enumerate
(
delFs
))
{
auto
&&
counter
{
std
::
get
<
0
>
(
tup
)};
auto
&&
grad
{
std
::
get
<
1
>
(
tup
)};
std
::
cout
<<
"Step "
<<
counter
+
1
<<
":"
<<
std
::
endl
<<
grad
<<
std
::
endl
;
}
count_width
=
size_t
(
std
::
log10
(
solver
.
get_maxiter
()))
+
1
;
}
// initialise F = I or ε = 0
auto
&
F
{
sys
.
get_strain
()};
switch
(
sys
.
get_formulation
())
{
case
Formulation
::
finite_strain:
{
F
.
get_map
()
=
Matrices
::
I2
<
DimM
>
();
break
;
}
case
Formulation
::
small_strain:
{
F
.
get_map
()
=
Matrices
::
I2
<
DimM
>
().
Zero
();
for
(
const
auto
&
delF:
delFs
)
{
if
(
!
check_symmetry
(
delF
))
{
throw
SolverError
(
"all Δε must be symmetric!"
);
}
}
break
;
}
default
:
throw
SolverError
(
"Unknown formulation"
);
break
;
}
// initialise return value
std
::
vector
<
OptimizeResult
>
ret_val
{};
// initialise materials
constexpr
bool
need_tangent
{
true
};
sys
.
initialise_materials
(
need_tangent
);
Grad_t
<
DimM
>
previous_grad
{
Grad_t
<
DimM
>::
Zero
()};
for
(
const
auto
&
delF:
delFs
)
{
//incremental loop
// apply macroscopic strain increment
for
(
auto
&&
grad:
F
.
get_map
())
{
grad
+=
delF
-
previous_grad
;
}
Real
incrNorm
{
2
*
newton_tol
},
gradNorm
{
1
};
auto
convergence_test
=
[
&
incrNorm
,
&
gradNorm
,
&
newton_tol
]
()
{
return
incrNorm
/
gradNorm
<=
newton_tol
;
};
Uint
newt_iter
{
0
};
for
(;
newt_iter
<
solver
.
get_maxiter
()
&&
!
convergence_test
();
++
newt_iter
)
{
// obtain material response
auto
res_tup
{
sys
.
evaluate_stress_tangent
(
F
)};
auto
&
P
{
std
::
get
<
0
>
(
res_tup
)};
rhs
.
eigen
()
=
-
P
.
eigen
();
sys
.
project
(
rhs
);
incrF
.
eigen
()
=
0
;
incrF
.
eigenvec
()
=
solver
.
solve
(
rhs
.
eigenvec
(),
incrF
.
eigenvec
());
F
.
eigen
()
+=
incrF
.
eigen
();
incrNorm
=
incrF
.
eigen
().
matrix
().
norm
();
gradNorm
=
F
.
eigen
().
matrix
().
norm
();
if
(
verbose
>
0
)
{
std
::
cout
<<
"at Newton step "
<<
std
::
setw
(
count_width
)
<<
newt_iter
<<
", |δ"
<<
strain_symb
<<
"|/|Δ"
<<
strain_symb
<<
"| = "
<<
std
::
setw
(
17
)
<<
incrNorm
/
gradNorm
<<
", tol = "
<<
newton_tol
<<
std
::
endl
;
if
(
verbose
-
1
>
1
)
{
std
::
cout
<<
"<"
<<
strain_symb
<<
"> ="
<<
std
::
endl
<<
F
.
get_map
().
mean
()
<<
std
::
endl
;
}
}
}
// update previous gradient
previous_grad
=
delF
;
ret_val
.
push_back
(
OptimizeResult
{
F
.
eigen
(),
sys
.
get_stress
().
eigen
(),
convergence_test
(),
Int
(
convergence_test
()),
"message not yet implemented"
,
newt_iter
,
solver
.
get_counter
()});
//store history variables here
}
return
ret_val
;
}
//! instantiation for two-dimensional cells
template
std
::
vector
<
OptimizeResult
>
newton_cg
(
SystemBase
<
twoD
,
twoD
>
&
sys
,
const
GradIncrements
<
twoD
>&
delF0
,
SolverBase
<
twoD
,
twoD
>
&
solver
,
Real
newton_tol
,
Dim_t
verbose
);
// template typename SystemBase<twoD, threeD>::StrainField_t &
// newton_cg (SystemBase<twoD, threeD> & sys, const GradIncrements<threeD>& delF0,
// const Real cg_tol, const Real newton_tol, Uint maxiter,
// Dim_t verbose);
//! instantiation for three-dimensional cells
template
std
::
vector
<
OptimizeResult
>
newton_cg
(
SystemBase
<
threeD
,
threeD
>
&
sys
,
const
GradIncrements
<
threeD
>&
delF0
,
SolverBase
<
threeD
,
threeD
>
&
solver
,
Real
newton_tol
,
Dim_t
verbose
);
/* ---------------------------------------------------------------------- */
bool
check_symmetry
(
const
Eigen
::
Ref
<
const
Eigen
::
ArrayXXd
>&
eps
,
Real
rel_tol
){
return
rel_tol
>=
(
eps
-
eps
.
transpose
()).
matrix
().
norm
()
/
eps
.
matrix
().
norm
();
}
}
// muSpectre
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