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rTAMAAS tamaas
bem_polonski.cpp
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/**
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2016 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Tamaas is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Tamaas 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 Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Tamaas. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "bem_polonski.hh"
#include "fft_plan_manager.hh"
#include "fftransform.hh"
#include "surface.hh"
#include <fstream>
#include <iomanip>
#include <iostream>
#include <sstream>
#include <vector>
/* -------------------------------------------------------------------------- */
namespace
tamaas
{
/* -------------------------------------------------------------------------- */
BemPolonski
::
BemPolonski
(
Surface
<
Real
>&
p
)
:
BemFFTBase
(
p
),
surface_t
(
p
.
size
(),
p
.
getL
()),
surface_r
(
p
.
size
(),
p
.
getL
()),
pold
(
p
.
size
(),
p
.
getL
()),
p_sat
(
-
1.
)
{
e_star
=
1.
;
max_iterations
=
2000
;
surface_rms_heights
=
SurfaceStatistics
::
computeStdev
(
this
->
surface
);
}
/* -------------------------------------------------------------------------- */
BemPolonski
::~
BemPolonski
()
{}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeEquilibrium
(
Real
epsilon
,
Real
pressure
)
{
this
->
computeSpectralInfluenceOverDisplacement
();
this
->
surface_t
=
0.
;
this
->
surface_r
=
0.
;
this
->
pold
=
0.
;
this
->
surface_displacements
=
0.
;
Real
delta
=
0.
;
Real
Gold
=
1.
;
Real
f
=
1e300
;
Real
fPrevious
=
1e300
;
Real
current_pressure
=
SurfaceStatistics
::
computeAverage
(
surface_tractions
);
std
::
cout
<<
"current pressure "
<<
current_pressure
<<
std
::
endl
;
if
(
current_pressure
<=
0.
)
surface_tractions
=
pressure
;
this
->
enforcePressureBalance
(
pressure
);
convergence_iterations
.
clear
();
nb_iterations
=
0
;
while
(
f
>
epsilon
&&
nb_iterations
<
max_iterations
)
{
fPrevious
=
f
;
this
->
computeDisplacementsFromTractions
();
this
->
computeGaps
();
Real
gbar
=
this
->
computeMeanGapsInContact
();
this
->
gap
-=
gbar
;
Real
G
=
this
->
computeG
();
this
->
updateT
(
G
,
Gold
,
delta
);
Real
tau
=
this
->
computeTau
();
pold
=
this
->
surface_tractions
;
Gold
=
G
;
delta
=
this
->
updateTractions
(
tau
);
// Projection on admissible space
this
->
enforcePressureBalance
(
pressure
);
// std::cout << std::scientific << std::setprecision(10)
// << SurfaceStatistics::computeAverage(surface_tractions) <<
// std::fixed << std::endl;
//
f
=
this
->
computeF
();
if
(
nb_iterations
%
dump_freq
==
0
)
{
Real
A
=
SurfaceStatistics
::
computeContactAreaRatio
(
surface_tractions
);
std
::
cout
<<
std
::
scientific
<<
std
::
setprecision
(
10
)
<<
nb_iterations
<<
" "
<<
f
<<
" "
<<
f
-
fPrevious
<<
" "
<<
A
<<
std
::
fixed
<<
std
::
endl
;
}
convergence_iterations
.
push_back
(
f
);
++
nb_iterations
;
}
this
->
computeTrueDisplacements
();
return
f
;
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeEquilibriuminit
(
Real
epsilon
,
Real
pressure
,
Surface
<
Real
>&
init
)
{
this
->
computeSpectralInfluenceOverDisplacement
();
this
->
surface_t
=
0.
;
this
->
surface_r
=
0.
;
this
->
pold
=
0.
;
this
->
surface_displacements
=
0.
;
Real
delta
=
0.
;
Real
Gold
=
1.
;
Real
f
=
1e300
;
Real
fPrevious
=
1e300
;
this
->
surface_tractions
=
init
;
Real
current_pressure
=
SurfaceStatistics
::
computeAverage
(
surface_tractions
);
if
(
current_pressure
<=
0.
)
surface_tractions
=
pressure
;
this
->
enforcePressureBalance
(
pressure
);
convergence_iterations
.
clear
();
nb_iterations
=
0
;
this
->
computeDisplacementsFromTractions
();
f
=
this
->
computeF
();
std
::
cout
<<
std
::
scientific
<<
std
::
setprecision
(
10
)
<<
" "
<<
f
<<
std
::
endl
;
while
(
f
>
epsilon
&&
nb_iterations
<
max_iterations
)
{
fPrevious
=
f
;
this
->
computeDisplacementsFromTractions
();
this
->
computeGaps
();
Real
gbar
=
this
->
computeMeanGapsInContact
();
this
->
gap
-=
gbar
;
Real
G
=
this
->
computeG
();
this
->
updateT
(
G
,
Gold
,
delta
);
Real
tau
=
this
->
computeTau
();
pold
=
this
->
surface_tractions
;
Gold
=
G
;
delta
=
this
->
updateTractions
(
tau
);
// Projection on admissible space
this
->
enforcePressureBalance
(
pressure
);
// std::cout << std::scientific << std::setprecision(10)
// << SurfaceStatistics::computeAverage(surface_tractions) <<
// std::fixed << std::endl;
//
f
=
this
->
computeF
();
if
(
nb_iterations
%
dump_freq
==
0
)
{
Real
A
=
SurfaceStatistics
::
computeContactAreaRatio
(
surface_tractions
);
std
::
cout
<<
std
::
scientific
<<
std
::
setprecision
(
10
)
<<
nb_iterations
<<
" "
<<
f
<<
" "
<<
f
-
fPrevious
<<
" "
<<
A
<<
std
::
fixed
<<
std
::
endl
;
}
convergence_iterations
.
push_back
(
f
);
++
nb_iterations
;
}
this
->
computeTrueDisplacements
();
return
f
;
}
/* -------------------------------------------------------------------------- */
void
BemPolonski
::
computeGaps
()
{
UInt
size
=
surface
.
size
();
#pragma omp parallel for
for
(
UInt
i
=
0
;
i
<
size
*
size
;
i
++
)
{
gap
(
i
)
=
surface_displacements
(
i
)
-
surface
(
i
);
}
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeMeanGapsInContact
()
{
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
Real
res
=
0.
;
UInt
nb_contact
=
0
;
#pragma omp parallel for reduction(+ : nb_contact, res)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0
||
std
::
abs
(
this
->
surface_tractions
(
i
)
-
p_sat
)
<
1.0e-10
)
continue
;
++
nb_contact
;
res
+=
this
->
gap
(
i
);
}
res
/=
nb_contact
;
return
res
;
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeG
()
{
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
Real
res
=
0.
;
#pragma omp parallel for reduction(+ : res)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0
||
std
::
abs
(
this
->
surface_tractions
(
i
)
-
p_sat
)
<
1.0e-10
)
continue
;
Real
val
=
this
->
gap
(
i
);
res
+=
val
*
val
;
}
return
res
;
}
/* -------------------------------------------------------------------------- */
void
BemPolonski
::
updateT
(
Real
G
,
Real
Gold
,
Real
delta
)
{
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
Real
factor
=
delta
*
G
/
Gold
;
#pragma omp parallel for
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0
)
this
->
surface_t
(
i
)
=
0.
;
else
{
this
->
surface_t
(
i
)
*=
factor
;
this
->
surface_t
(
i
)
+=
this
->
gap
(
i
);
}
}
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeTau
()
{
this
->
applyInfluenceFunctions
(
surface_t
,
surface_r
);
const
UInt
size
=
surface_t
.
size
()
*
surface_t
.
size
();
Real
rbar
=
0
;
UInt
nb_contact
=
0
;
#pragma omp parallel for reduction(+ : nb_contact, rbar)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0
)
continue
;
++
nb_contact
;
rbar
+=
surface_r
(
i
);
}
rbar
/=
nb_contact
;
surface_r
-=
rbar
;
Real
tau_sum1
=
0.
,
tau_sum2
=
0.
;
#pragma omp parallel for reduction(+ : tau_sum1, tau_sum2)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0
)
continue
;
tau_sum1
+=
this
->
gap
(
i
)
*
surface_t
(
i
);
tau_sum2
+=
surface_r
(
i
)
*
surface_t
(
i
);
}
Real
tau
=
tau_sum1
/
tau_sum2
;
return
tau
;
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
updateTractions
(
Real
tau
)
{
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
#pragma omp parallel for
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0
)
continue
;
this
->
surface_tractions
(
i
)
-=
tau
*
this
->
surface_t
(
i
);
if
(
this
->
surface_tractions
(
i
)
<
0.
)
this
->
surface_tractions
(
i
)
=
0
;
}
// compute number of interpenetration without contact
UInt
nb_iol
=
0
;
#pragma omp parallel for reduction(+ : nb_iol)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
<=
0.
&&
this
->
gap
(
i
)
<
0.
)
{
this
->
surface_tractions
(
i
)
-=
tau
*
this
->
gap
(
i
);
++
nb_iol
;
}
}
// compute number of interpenetration without contact
UInt
nb_sl
=
0
;
#pragma omp parallel for reduction(+ : nb_sl)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
==
p_sat
&&
0.
<
this
->
gap
(
i
))
{
this
->
surface_tractions
(
i
)
-=
tau
*
this
->
gap
(
i
);
++
nb_sl
;
}
}
Real
delta
=
0
;
if
(
nb_iol
>
0
||
nb_sl
>
0
)
delta
=
0.
;
else
delta
=
1.
;
return
delta
;
}
/* -------------------------------------------------------------------------- */
void
BemPolonski
::
enforcePressureBalance
(
Real
applied_pressure
)
{
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
// If we have no saturation, scale to match applied_pressure
if
(
this
->
p_sat
<=
0.
||
SurfaceStatistics
::
computeMaximum
(
this
->
surface_tractions
)
<
this
->
p_sat
)
{
Real
pressure
=
0.
;
#pragma omp parallel for reduction(+ : pressure)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
pressure
+=
this
->
surface_tractions
(
i
);
}
pressure
*=
1.
/
size
;
this
->
surface_tractions
*=
applied_pressure
/
pressure
;
}
// If we have saturation, use secant method to find zero of saturationFunction
else
{
// Checking if we can find a zero
Real
limit
=
this
->
p_sat
*
SurfaceStatistics
::
computeContactArea
(
this
->
surface_tractions
)
-
applied_pressure
;
if
(
limit
<
0
)
SURFACE_FATAL
(
"Saturation pressure is too small for applied pressure"
);
// Initial points
Real
x_n_2
=
0.
,
x_n_1
=
1.
,
x_n
=
0.
;
Real
f_n_2
=
0.
,
f_n_1
=
0.
,
f_n
=
0.
;
// Secant loop
do
{
f_n_2
=
saturationFunction
(
x_n_2
,
applied_pressure
);
f_n_1
=
saturationFunction
(
x_n_1
,
applied_pressure
);
x_n
=
x_n_1
-
f_n_1
*
(
x_n_1
-
x_n_2
)
/
(
f_n_1
-
f_n_2
);
f_n
=
saturationFunction
(
x_n
,
applied_pressure
);
x_n_2
=
x_n_1
;
x_n_1
=
x_n
;
}
while
(
std
::
abs
(
f_n
)
>
1e-16
);
this
->
surface_tractions
*=
x_n
;
// Truncating pressures
#pragma omp parallel for
for
(
UInt
i
=
0
;
i
<
size
;
i
++
)
{
if
(
this
->
surface_tractions
(
i
)
>
this
->
p_sat
)
this
->
surface_tractions
(
i
)
=
this
->
p_sat
;
}
// Real mu_I_sat=0.;
// #pragma omp parallel for reduction(+: mu_I_sat)
// for (UInt i = 0; i < size; ++i) {
// if ( this->p_sat< this->surface_tractions(i) ){
// mu_I_sat+=1.;
// }
// }
// Real pc=0.;
// #pragma omp parallel for reduction(+: pc)
// for (UInt i = 0; i < size; ++i) {
// if ( this->surface_tractions(i) < this->p_sat ){
// pc+=this->surface_tractions(i);}
// }
// #pragma omp parallel for
// for (UInt i = 0; i < size; ++i) {
// if ( this->surface_tractions(i) < this->p_sat ){
// this->surface_tractions(i)=
// this->surface_tractions(i)*((size*applied_pressure-this->p_sat*mu_I_sat)/pc);}
// }
// #pragma omp parallel for
// for (UInt i = 0; i < size; ++i) {
// if ( this->p_sat< this->surface_tractions(i) ){
// this->surface_tractions(i)=this->p_sat;
// }
// }
}
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
saturationFunction
(
Real
alpha
,
Real
applied_pressure
)
{
const
UInt
n
=
surface
.
size
();
const
UInt
size
=
n
*
n
;
Real
sum
=
0.
;
#pragma omp parallel for reduction(+ : sum)
for
(
UInt
i
=
0
;
i
<
size
;
i
++
)
{
Real
alpha_p
=
alpha
*
this
->
surface_tractions
(
i
);
Real
alpha_p_I
=
(
alpha_p
>
this
->
p_sat
)
?
alpha_p
-
this
->
p_sat
:
0.
;
sum
+=
alpha_p
-
alpha_p_I
;
}
sum
/=
size
;
return
sum
-
applied_pressure
;
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeF
()
{
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
Real
res
=
0
;
Real
t_sum
=
SurfaceStatistics
::
computeSum
(
surface_tractions
);
computeTrueDisplacements
();
#pragma omp parallel for reduction(+ : res)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
this
->
surface_tractions
(
i
)
==
this
->
p_sat
)
continue
;
res
+=
surface_tractions
(
i
)
*
(
this
->
true_displacements
(
i
)
-
surface
(
i
));
// res +=
// this->surface_tractions[i].real()
// *(surface_displacements[i].real() - surface[i].real());
}
return
std
::
abs
(
res
/
t_sum
/
surface_rms_heights
/
size
);
}
/* -------------------------------------------------------------------------- */
void
BemPolonski
::
computeTrueDisplacements
()
{
this
->
applyInfluenceFunctions
(
this
->
surface_tractions
,
this
->
surface_displacements
);
this
->
true_displacements
=
this
->
surface_displacements
;
UInt
n
=
surface
.
size
();
UInt
size
=
n
*
n
;
Real
shift
=
1e300
;
#pragma omp parallel for reduction(min : shift)
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
if
(
surface_displacements
(
i
)
-
shift
-
surface
(
i
)
<
0.
&&
(
this
->
p_sat
<
0
||
this
->
surface_tractions
(
i
)
<
this
->
p_sat
))
{
shift
=
surface_displacements
(
i
)
-
surface
(
i
);
}
}
#pragma omp parallel for
for
(
UInt
i
=
0
;
i
<
size
;
++
i
)
{
true_displacements
(
i
)
=
surface_displacements
(
i
)
-
shift
;
}
}
/* -------------------------------------------------------------------------- */
}
// namespace tamaas
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