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polonsky_keer_rey.cpp
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rTAMAAS tamaas
polonsky_keer_rey.cpp
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/**
* @file
* @section LICENSE
*
* Copyright (©) 2016-2020 EPFL (École Polytechnique Fédérale de Lausanne),
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "polonsky_keer_rey.hh"
#include "elastic_functional.hh"
#include "logger.hh"
#include "loop.hh"
#include "model_type.hh"
#include <boost/preprocessor/seq.hpp>
#include <iomanip>
/* -------------------------------------------------------------------------- */
namespace
tamaas
{
PolonskyKeerRey
::
PolonskyKeerRey
(
Model
&
model
,
const
GridBase
<
Real
>&
surface
,
Real
tolerance
,
type
variable_type
,
type
constraint_type
)
:
ContactSolver
(
model
,
surface
,
tolerance
),
variable_type
(
variable_type
),
constraint_type
(
constraint_type
)
{
#define SET_VIEWS(_, __, type) \
case type: { \
setViews<type>(); \
break; \
}
switch
(
model
.
getType
())
{
BOOST_PP_SEQ_FOR_EACH
(
SET_VIEWS
,
~
,
TAMAAS_MODEL_TYPES
);
}
#undef SET_VIEWS
search_direction
=
allocateGrid
<
true
,
Real
>
(
operation_type
,
model
.
getBoundaryDiscretization
());
projected_search_direction
=
allocateGrid
<
true
,
Real
>
(
operation_type
,
model
.
getBoundaryDiscretization
());
switch
(
variable_type
)
{
case
gap:
{
model
.
getBEEngine
().
registerDirichlet
();
primal
=
gap_view
.
get
();
dual
=
pressure_view
.
get
();
this
->
functional
.
addFunctionalTerm
(
std
::
make_shared
<
functional
::
ElasticFunctionalGap
>
(
*
integral_op
,
this
->
surface
));
break
;
}
case
pressure:
{
model
.
getBEEngine
().
registerNeumann
();
primal
=
pressure_view
.
get
();
dual
=
gap_view
.
get
();
this
->
functional
.
addFunctionalTerm
(
std
::
make_shared
<
functional
::
ElasticFunctionalPressure
>
(
*
integral_op
,
this
->
surface
));
break
;
}
}
}
/* -------------------------------------------------------------------------- */
Real
PolonskyKeerRey
::
solve
(
std
::
vector
<
Real
>
target_v
)
{
// Update in case of a surface change between solves
this
->
surface_stddev
=
std
::
sqrt
(
this
->
surface
.
var
());
// Printing column headers
Logger
().
get
(
LogLevel
::
info
)
<<
std
::
setw
(
5
)
<<
"Iter"
<<
" "
<<
std
::
setw
(
15
)
<<
"Cost_f"
<<
" "
<<
std
::
setw
(
15
)
<<
"Error"
<<
'\n'
<<
std
::
fixed
;
const
Real
target
=
target_v
.
back
();
// Setting uniform value if constraint
if
(
constraint_type
==
variable_type
&&
std
::
abs
(
primal
->
sum
())
<=
0
)
*
primal
=
target
;
else
if
(
constraint_type
==
variable_type
)
*
primal
*=
target
/
primal
->
mean
();
else
if
(
constraint_type
!=
variable_type
)
*
primal
=
this
->
surface_stddev
;
// Algorithm variables
Real
Gold
=
1
,
error
=
0
;
UInt
n
=
0
;
bool
delta
=
false
;
*
search_direction
=
0
;
do
{
// Computing functional gradient
functional
.
computeGradF
(
*
primal
,
*
dual
);
const
Real
dbar
=
meanOnUnsaturated
(
*
dual
);
// Enforcing dual constraint via gradient
if
(
constraint_type
!=
variable_type
)
{
*
dual
+=
2
*
target
+
dbar
;
}
else
{
// Centering dual on primal > 0
*
dual
-=
dbar
;
}
// Computing gradient norm
const
Real
G
=
computeSquaredNorm
(
*
dual
);
// Updating search direction (conjugate gradient)
updateSearchDirection
(
delta
*
G
/
Gold
);
Gold
=
G
;
// Computing critical step
const
Real
tau
=
computeCriticalStep
(
target
);
// Update primal variable
delta
=
updatePrimal
(
tau
);
// We should scale to constraint
if
(
constraint_type
==
variable_type
)
enforceMeanValue
(
target
);
error
=
computeError
();
const
Real
cost_f
=
functional
.
computeF
(
*
primal
,
*
dual
);
printState
(
n
,
cost_f
,
error
);
}
while
(
error
>
this
->
tolerance
and
n
++
<
this
->
max_iterations
);
// Final update of dual variable
functional
.
computeGradF
(
*
primal
,
*
dual
);
enforceAdmissibleState
();
return
error
;
}
/* -------------------------------------------------------------------------- */
void
PolonskyKeerRey
::
enforceAdmissibleState
()
{
/// Make dual admissible
const
Real
dual_min
=
dual
->
min
();
*
dual
-=
dual_min
;
// Primal is pressure: need to make sure gap is positive
if
(
variable_type
==
pressure
)
{
*
displacement_view
=
*
dual
;
*
displacement_view
+=
this
->
surface
;
}
// Primal is gap: need to make sure dual is positive (pressure + adhesion)
else
{
*
displacement_view
=
*
primal
;
*
displacement_view
+=
this
->
surface
;
integral_op
->
apply
(
*
displacement_view
,
*
pressure_view
);
*
pressure_view
-=
dual_min
;
}
}
/* -------------------------------------------------------------------------- */
/**
* Computes \f$ \frac{1}{\mathrm{card}(\{p > 0\})} \sum_{\{p > 0\}}{f_i} \f$
*/
Real
PolonskyKeerRey
::
meanOnUnsaturated
(
const
GridBase
<
Real
>&
field
)
const
{
// Sum on unsaturated
const
Real
sum
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
Real
&
p
,
const
Real
&
f
)
{
return
(
p
>
0
)
?
f
:
0
;
},
*
primal
,
field
);
// Number of unsaturated points
const
UInt
n_unsat
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
Real
&
p
)
->
UInt
{
return
(
p
>
0
);
},
*
primal
);
return
sum
/
n_unsat
;
}
/* -------------------------------------------------------------------------- */
/**
* Computes \f$ \sum_{\{p > 0\}}{f_i^2} \f$
*/
Real
PolonskyKeerRey
::
computeSquaredNorm
(
const
GridBase
<
Real
>&
field
)
const
{
return
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
Real
&
p
,
const
Real
&
f
)
{
return
(
p
>
0
)
?
f
*
f
:
0
;
},
*
primal
,
field
);
}
/* -------------------------------------------------------------------------- */
/**
* Computes \f$ \tau = \frac{ \sum_{\{p > 0\}}{q_i't_i} }{ \sum_{\{p > 0\}}{r_i'
* t_i} } \f$
*/
Real
PolonskyKeerRey
::
computeCriticalStep
(
Real
target
)
{
integral_op
->
apply
(
*
search_direction
,
*
projected_search_direction
);
const
Real
rbar
=
meanOnUnsaturated
(
*
projected_search_direction
);
if
(
constraint_type
==
variable_type
)
*
projected_search_direction
-=
rbar
;
else
{
*
projected_search_direction
+=
2
*
target
+
rbar
;
}
const
Real
num
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
const
Real
&
p
,
const
Real
&
q
,
const
Real
&
t
)
{
return
(
p
>
0
)
?
q
*
t
:
0
;
},
*
primal
,
*
dual
,
*
search_direction
);
const
Real
denum
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
const
Real
&
p
,
const
Real
&
r
,
const
Real
&
t
)
{
return
(
p
>
0
)
?
r
*
t
:
0
;
},
*
primal
,
*
projected_search_direction
,
*
search_direction
);
return
num
/
denum
;
}
/* -------------------------------------------------------------------------- */
/**
* Update steps:
* 1. \f$\mathbf{p} = \mathbf{p} - \tau \mathbf{t} \f$
* 2. Truncate all \f$p\f$ negative
* 3. For all points in \f$I_\mathrm{na} = \{p = 0 \land q < 0 \}\f$ do \f$p_i =
* p_i - \tau q_i\f$
*/
bool
PolonskyKeerRey
::
updatePrimal
(
Real
step
)
{
const
UInt
na_num
=
Loop
::
reduce
<
operation
::
plus
>
(
[
step
]
CUDA_LAMBDA
(
Real
&
p
,
const
Real
&
q
,
const
Real
&
t
)
->
UInt
{
p
-=
step
*
t
;
// Updating primal
if
(
p
<
0
)
p
=
0
;
// Truncating neg values
if
(
p
==
0
&&
q
<
0
)
{
// If non-admissible state
p
-=
step
*
q
;
return
1
;
}
else
return
0
;
},
*
primal
,
*
dual
,
*
search_direction
);
return
na_num
==
0
;
}
/* -------------------------------------------------------------------------- */
/**
* Error is based on \f$ \sum{p_i q_i} \f$
*/
Real
PolonskyKeerRey
::
computeError
()
{
/// Making sure dual respects constraint
*
dual
-=
dual
->
min
();
/// Complementarity error
const
Real
error
=
primal
->
dot
(
*
dual
);
if
(
std
::
isnan
(
error
))
TAMAAS_EXCEPTION
(
"Encountered NaN in complementarity error: this may be "
"caused by a contact area of a single node."
);
const
Real
norm
=
[
this
]()
{
if
(
variable_type
==
pressure
)
return
std
::
abs
(
primal
->
sum
()
*
this
->
surface_stddev
);
else
return
std
::
abs
(
dual
->
sum
()
*
this
->
surface_stddev
);
}();
return
std
::
abs
(
error
)
/
(
norm
*
primal
->
getGlobalNbPoints
());
}
/* -------------------------------------------------------------------------- */
/**
* Do \f$\mathbf{t} = \mathbf{q}' + \delta \frac{R}{R_\mathrm{old}}\mathbf{t}
* \f$
*/
void
PolonskyKeerRey
::
updateSearchDirection
(
Real
factor
)
{
Loop
::
loop
(
[
factor
]
CUDA_LAMBDA
(
Real
&
p
,
Real
&
q
,
Real
&
t
)
{
t
=
(
p
>
0
)
?
q
+
factor
*
t
:
0
;
},
*
primal
,
*
dual
,
*
search_direction
);
}
/* -------------------------------------------------------------------------- */
void
PolonskyKeerRey
::
enforceMeanValue
(
Real
mean
)
{
*
primal
*=
mean
/
primal
->
mean
();
}
}
// namespace tamaas
/* -------------------------------------------------------------------------- */
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