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rTAMAAS tamaas
kato.hh
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/**
* @file
*
* @author Son Pham-Ba <son.phamba@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2016-2018 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __KATO_HH__
#define __KATO_HH__
/* -------------------------------------------------------------------------- */
#include "contact_solver.hh"
#include "meta_functional.hh"
#include "model_type.hh"
#include "static_types.hh"
#include "tamaas.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_TAMAAS__
class
Kato
:
public
ContactSolver
{
public
:
/// Constructor
Kato
(
Model
&
model
,
const
GridBase
<
Real
>&
surface
,
Real
tolerance
,
Real
mu
);
public
:
/// Solve
Real
solve
(
GridBase
<
Real
>&
p0
,
UInt
proj_iter
);
/// Solve relaxed problem
Real
solveRelaxed
(
GridBase
<
Real
>&
g0
);
/// Solve regularized problem
Real
solveRegularized
(
GridBase
<
Real
>&
p0
,
Real
r
);
/// Compute cost function
Real
computeCost
(
bool
use_tresca
=
false
);
private
:
/// Template for solve function
template
<
model_type
type
>
Real
solveTmpl
(
GridBase
<
Real
>&
p0
,
UInt
proj_iter
);
/// Template for solveRelaxed function
template
<
model_type
type
>
Real
solveRelaxedTmpl
(
GridBase
<
Real
>&
g0
);
/// Template for solveRegularized function
template
<
model_type
type
>
Real
solveRegularizedTmpl
(
GridBase
<
Real
>&
p0
,
Real
r
);
protected
:
/// Creates surfaceComp form surface
template
<
model_type
type
>
void
initSurfaceWithComponents
();
/// Compute gradient of functional
template
<
UInt
comp
>
void
computeGradient
(
bool
use_tresca
=
false
);
/// Project pressure on friction cone
template
<
UInt
comp
>
void
enforcePressureConstraints
(
GridBase
<
Real
>&
p0
,
UInt
proj_iter
);
/// Project on C
template
<
UInt
comp
>
void
enforcePressureMean
(
GridBase
<
Real
>&
p0
);
/// Project on D
template
<
UInt
comp
>
void
enforcePressureCoulomb
();
/// Project on D (Tresca)
template
<
UInt
comp
>
void
enforcePressureTresca
();
/// Comupte mean value of field
template
<
UInt
comp
>
Vector
<
Real
,
comp
>
computeMean
(
GridBase
<
Real
>&
field
);
/// Add vector to each point of field
template
<
UInt
comp
>
void
addUniform
(
GridBase
<
Real
>&
field
,
GridBase
<
Real
>&
vec
);
/// Regularization function with factor r (0 -> unregugularized)
Real
regularize
(
Real
x
,
Real
r
);
/// Compute grids of dual and primal variables
template
<
model_type
type
>
void
computeValuesForCost
(
GridBase
<
Real
>&
lambda
,
GridBase
<
Real
>&
eta
,
GridBase
<
Real
>&
p_N
,
GridBase
<
Real
>&
p_C
);
/// Compute dual and primal variables with Tresca friction
template
<
model_type
type
>
void
computeValuesForCostTresca
(
GridBase
<
Real
>&
lambda
,
GridBase
<
Real
>&
eta
,
GridBase
<
Real
>&
p_N
,
GridBase
<
Real
>&
p_C
);
/// Compute total displacement
template
<
UInt
comp
>
void
computeFinalGap
();
protected
:
BEEngine
&
engine
;
GridBase
<
Real
>*
gap
=
nullptr
;
GridBase
<
Real
>*
pressure
=
nullptr
;
std
::
unique_ptr
<
GridBase
<
Real
>>
surfaceComp
=
nullptr
;
Real
mu
=
0
;
UInt
N
=
0
;
// number of points
};
/* -------------------------------------------------------------------------- */
template
<
UInt
comp
>
void
Kato
::
computeGradient
(
bool
use_tresca
)
{
engine
.
solveNeumann
(
*
pressure
,
*
gap
);
*
gap
-=
*
surfaceComp
;
// Impose zero tangential displacement in non-sliding zone
UInt
count_static
=
0
;
Vector
<
Real
,
comp
>
g_static
;
using
pvector
=
VectorProxy
<
Real
,
comp
>
;
if
(
!
use_tresca
)
{
// with Coulomb friction
count_static
=
Loop
::
reduce
<
operation
::
plus
>
(
[
this
]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
p
)
->
UInt
{
VectorProxy
<
Real
,
comp
-
1
>
p_T
(
p
(
0
));
Real
p_T_norm
=
p_T
.
l2norm
();
Real
p_N
=
p
(
comp
-
1
);
if
(
0.99
*
mu
*
p_N
>
p_T_norm
)
{
// non-sliding contact
return
1
;
}
else
{
return
0
;
}
},
range
<
pvector
>
(
*
pressure
));
g_static
=
Loop
::
reduce
<
operation
::
plus
>
(
[
this
]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
g
,
VectorProxy
<
Real
,
comp
>
p
)
->
Vector
<
Real
,
comp
>
{
VectorProxy
<
Real
,
comp
-
1
>
p_T
(
p
(
0
));
Real
p_T_norm
=
p_T
.
l2norm
();
Real
p_N
=
p
(
comp
-
1
);
if
(
0.99
*
mu
*
p_N
>
p_T_norm
)
{
// non-sliding contact
return
g
;
// to compute mean of g_T
}
else
{
return
0
;
}
},
range
<
pvector
>
(
*
gap
),
range
<
pvector
>
(
*
pressure
));
}
else
{
// with Tresca friction
count_static
=
Loop
::
reduce
<
operation
::
plus
>
(
[
this
]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
p
)
->
UInt
{
VectorProxy
<
Real
,
comp
-
1
>
p_T
(
p
(
0
));
Real
p_T_norm
=
p_T
.
l2norm
();
Real
p_N
=
p
(
comp
-
1
);
if
(
0.99
*
mu
>
p_T_norm
&&
p_N
>
0
)
{
// non-sliding contact
return
1
;
}
else
{
return
0
;
}
},
range
<
pvector
>
(
*
pressure
));
g_static
=
Loop
::
reduce
<
operation
::
plus
>
(
[
this
]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
g
,
VectorProxy
<
Real
,
comp
>
p
)
->
Vector
<
Real
,
comp
>
{
VectorProxy
<
Real
,
comp
-
1
>
p_T
(
p
(
0
));
Real
p_N
=
p
(
comp
-
1
);
Real
p_T_norm
=
p_T
.
l2norm
();
if
(
0.99
*
mu
>
p_T_norm
&&
p_N
>
0
)
{
// non-sliding contact
return
g
;
// to compute mean of g_T
}
else
{
return
0
;
}
},
range
<
pvector
>
(
*
gap
),
range
<
pvector
>
(
*
pressure
));
}
if
(
count_static
!=
0
)
{
g_static
/=
count_static
;
// g_static(comp - 1) = 0;
}
else
{
// if no sticking zone, mean computed on sliding zone
count_static
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
p
)
->
UInt
{
if
(
p
(
comp
-
1
)
>
0
)
{
return
1
;
}
else
{
return
0.0
;
}
},
range
<
pvector
>
(
*
pressure
));
Real
g_N_static
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
g
,
VectorProxy
<
Real
,
comp
>
p
)
{
if
(
p
(
comp
-
1
)
>
0
)
{
return
g
(
comp
-
1
);
}
else
{
return
0.0
;
}
},
range
<
pvector
>
(
*
gap
),
range
<
pvector
>
(
*
pressure
));
g_static
(
comp
-
1
)
=
g_N_static
/
count_static
;
}
// Add frictionnal term to functional
if
(
!
use_tresca
)
{
// with Coulomb friction
Loop
::
loop
(
[
this
,
g_static
]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
g
)
{
g
-=
g_static
;
VectorProxy
<
Real
,
comp
-
1
>
g_T
(
g
(
0
));
Real
g_T_norm
=
g_T
.
l2norm
();
g
(
comp
-
1
)
+=
mu
*
g_T_norm
;
// Frictionnal work
},
range
<
pvector
>
(
*
gap
));
}
else
{
// with Tresca friction
*
gap
-=
g_static
;
// Loop::stridedLoop(
// [this, g_static] CUDA_LAMBDA(VectorProxy<Real, comp>&& g,
// VectorProxy<Real, comp>&& p) {
// g -= g_static;
// VectorProxy<Real, comp - 1> g_T = g(0);
// Real g_T_norm = g_T.l2norm();
// Real p_N = p(comp - 1);
// if (p_N > 0)
// g(comp - 1) += mu/p_N * g_T_norm; // Frictionnal work
// },
// *gap, *pressure);
}
// Loop::stridedLoop(
// [this] CUDA_LAMBDA(VectorProxy<Real, comp>&& g, VectorProxy<Real, comp>&& p) {
// VectorProxy<Real, comp - 1> g_T = g(0);
// Real g_T_norm = g_T.l2norm();
// VectorProxy<Real, 1> g_N = g(comp - 1);
// VectorProxy<Real, comp - 1> p_T = p(0);
// Real p_T_norm = p_T.l2norm();
// VectorProxy<Real, 1> p_N = p(comp - 1);
// if (p_T_norm != 0) {
// g_T = p_T;
// g_T *= -g_T_norm / p_T_norm;
// }
// g_N += mu * g_T_norm; // Frictionnal work
// },
// *gap, *pressure);
}
/* -------------------------------------------------------------------------- */
/**
* Projects $\vec{p}$ on $\mathcal{C}$ and $\mathcal{D}$.
*/
// template <UInt comp>
// void Kato::enforcePressureConstraints(GridBase<Real>& p0, UInt proj_iter) {
// for (UInt i = 0; i < proj_iter; i++) {
// enforcePressureMean<comp>(p0);
// enforcePressureCoulomb<comp>();
// }
// }
/* -------------------------------------------------------------------------- */
/**
* Projects $\vec{p}$ on $\mathcal{C}$ and $\mathcal{D}$.
*/
template
<
UInt
comp
>
void
Kato
::
enforcePressureConstraints
(
GridBase
<
Real
>&
p0
,
UInt
proj_iter
)
{
for
(
UInt
i
=
0
;
i
<
proj_iter
;
i
++
)
{
enforcePressureMean
<
comp
>
(
p0
);
enforcePressureCoulomb
<
comp
>
();
}
}
/* -------------------------------------------------------------------------- */
template
<
UInt
comp
>
void
Kato
::
enforcePressureCoulomb
()
{
Loop
::
loop
(
[
this
]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
p
)
{
VectorProxy
<
Real
,
comp
-
1
>
p_T
(
p
(
0
));
Real
p_N
=
p
(
comp
-
1
);
Real
p_T_sqrd
=
p_T
.
l2squared
();
// Projection normale au cône de friction
bool
cond1
=
(
p_N
>=
0
&&
p_T_sqrd
<=
mu
*
mu
*
p_N
*
p_N
);
bool
cond2
=
(
p_N
<=
0
&&
p_T_sqrd
<=
p_N
*
p_N
/
mu
/
mu
);
if
(
cond2
)
{
p_T
=
0
;
p
(
comp
-
1
)
=
0
;
}
else
if
(
!
cond1
)
{
Real
p_T_norm
=
std
::
sqrt
(
p_T_sqrd
);
Real
k
=
(
p_N
+
mu
*
p_T_norm
)
/
(
1
+
mu
*
mu
);
p_T
*=
k
*
mu
/
p_T_norm
;
p
(
comp
-
1
)
=
k
;
}
},
range
<
VectorProxy
<
Real
,
comp
>>
(
*
pressure
));
}
/* -------------------------------------------------------------------------- */
/**
* Compute mean of the field taking each component separately.
*/
template
<
UInt
comp
>
Vector
<
Real
,
comp
>
Kato
::
computeMean
(
GridBase
<
Real
>&
field
)
{
Vector
<
Real
,
comp
>
mean
=
Loop
::
reduce
<
operation
::
plus
>
(
[]
CUDA_LAMBDA
(
VectorProxy
<
Real
,
comp
>
f
)
->
Vector
<
Real
,
comp
>
{
return
f
;
},
range
<
VectorProxy
<
Real
,
comp
>>
(
field
));
mean
/=
N
;
return
mean
;
}
/* -------------------------------------------------------------------------- */
template
<
UInt
comp
>
void
Kato
::
addUniform
(
GridBase
<
Real
>&
field
,
GridBase
<
Real
>&
vec
)
{
VectorProxy
<
Real
,
comp
>
_vec
(
vec
(
0
));
field
+=
_vec
;
}
__END_TAMAAS__
#endif
// __KATO_HH__
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