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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 <vector>
#include "surface.hh"
#include "bem_polonski.hh"
#include "fft_plan_manager.hh"
#include "fftransform.hh"
#include <iostream>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <sstream>
#include <cmath>
/* -------------------------------------------------------------------------- */
#define TIMER
#include "surface_timer.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_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
;
}
/* -------------------------------------------------------------------------- */
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
);
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
;
}
/* -------------------------------------------------------------------------- */
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
(){
STARTTIMER
(
"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
;
STOPTIMER
(
"computeMeanGapsInContact"
);
return
res
;
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeG
(){
STARTTIMER
(
"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
;
}
STOPTIMER
(
"computeG"
);
return
res
;
}
/* -------------------------------------------------------------------------- */
void
BemPolonski
::
updateT
(
Real
G
,
Real
Gold
,
Real
delta
){
STARTTIMER
(
"updateT"
);
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
);
}
}
STOPTIMER
(
"updateT"
);
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
computeTau
(){
STARTTIMER
(
"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
;
STOPTIMER
(
"computeTau"
);
return
tau
;
}
/* -------------------------------------------------------------------------- */
Real
BemPolonski
::
updateTractions
(
Real
tau
){
STARTTIMER
(
"updateTractions"
);
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.
;
STOPTIMER
(
"updateTractions"
);
return
delta
;
}
/* -------------------------------------------------------------------------- */
void
BemPolonski
::
enforcePressureBalance
(
Real
applied_pressure
){
STARTTIMER
(
"enforcePressureBalance"
);
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
;
}
}
}
STOPTIMER
(
"enforcePressureBalance"
);
}
/* -------------------------------------------------------------------------- */
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
=
std
::
abs
(
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
+=
std
::
abs
(
surface_tractions
(
i
)
*
(
this
->
true_displacements
(
i
)
-
surface
(
i
)));
// res +=
// this->surface_tractions[i].real()
// *(surface_displacements[i].real() - surface[i].real());
}
return
res
/
std
::
abs
(
t_sum
);
}
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
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
;
}
}
/* -------------------------------------------------------------------------- */
__END_TAMAAS__
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