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rTAMAAS tamaas
bem_grid.cpp
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/**
*
* @author Lucas Frérot <lucas.frerot@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_grid.hh"
#include "grid.hh"
#include "types.hh"
#include "fft_plan_manager.hh"
#include <cmath>
/* -------------------------------------------------------------------------- */
__BEGIN_TAMAAS__
BemGrid
::
BemGrid
(
Surface
<
Real
>
&
surface
)
:
E
(
1.
),
nu
(
0.3
),
surface
(
surface
),
surface_normals
(
surface
.
sizes
(),
surface
.
lengths
(),
3
),
tractions
(
surface
.
sizes
(),
surface
.
lengths
(),
3
),
displacements
(
surface
.
sizes
(),
surface
.
lengths
(),
3
),
gaps
(
surface
.
sizes
(),
surface
.
lengths
(),
3
),
true_tractions
(
NULL
),
true_displacements
(
NULL
),
dump_freq
(
100
)
{
UInt
hermitian_sizes
[
2
]
=
{
surface
.
sizes
()[
0
],
surface
.
sizes
()[
1
]
/
2
+
1
};
influence
.
setNbComponents
(
9
);
spectral_tractions
.
setNbComponents
(
3
);
spectral_displacements
.
setNbComponents
(
3
);
influence
.
resize
(
hermitian_sizes
);
spectral_tractions
.
resize
(
hermitian_sizes
);
spectral_displacements
.
resize
(
hermitian_sizes
);
//computeSurfaceNormals();
}
/* -------------------------------------------------------------------------- */
BemGrid
::~
BemGrid
()
{
FFTPlanManager
::
get
().
clean
();
delete
true_tractions
;
delete
true_displacements
;
}
/* -------------------------------------------------------------------------- */
const
Grid2dReal
&
BemGrid
::
getTrueTractions
()
const
{
if
(
true_tractions
==
NULL
)
TAMAAS_EXCEPTION
(
"True tractions were not allocated"
);
return
*
true_tractions
;
}
const
Grid2dReal
&
BemGrid
::
getTrueDisplacements
()
const
{
if
(
true_displacements
==
NULL
)
TAMAAS_EXCEPTION
(
"True displacements were not allocated"
);
return
*
true_displacements
;
}
/* -------------------------------------------------------------------------- */
/// This function computes surface slopes in fourier space and fills the normals grid
void
BemGrid
::
computeSurfaceNormals
()
{
SurfaceComplex
<
Real
>
spectral_surface
(
surface
.
size
(),
surface
.
getL
());
GridHermitian
<
Real
,
2
>
spectral_slopes
(
spectral_surface
.
sizes
(),
spectral_surface
.
lengths
(),
3
);
FFTransform
<
Real
,
2
>
&
plan1
=
FFTPlanManager
::
get
().
createPlan
(
surface
,
spectral_surface
);
FFTransform
<
Real
,
2
>
&
plan2
=
FFTPlanManager
::
get
().
createPlan
(
surface_normals
,
spectral_slopes
);
plan1
.
forwardTransform
();
// Loops should be with signed integers
const
Int
*
n
=
reinterpret_cast
<
const
Int
*
>
(
spectral_surface
.
sizes
());
constexpr
Complex
I
(
0
,
1
);
#pragma omp parallel
{
#pragma omp for collapse(2)
for
(
Int
i
=
0
;
i
<=
n
[
0
]
/
2
;
i
++
)
{
for
(
Int
j
=
0
;
j
<
n
[
1
]
;
j
++
)
{
Real
q1
=
2
*
M_PI
*
j
;
Real
q2
=
2
*
M_PI
*
i
;
spectral_slopes
(
i
,
j
,
0
)
=
-
q1
*
I
*
spectral_surface
(
i
,
j
);
spectral_slopes
(
i
,
j
,
1
)
=
-
q2
*
I
*
spectral_surface
(
i
,
j
);
spectral_slopes
(
i
,
j
,
2
)
=
0
;
}
}
#pragma omp for collapse(2)
for
(
Int
i
=
n
[
0
]
/
2
+
1
;
i
<
n
[
0
]
;
i
++
)
{
for
(
Int
j
=
0
;
j
<
n
[
1
]
;
j
++
)
{
Real
q1
=
2
*
M_PI
*
j
;
Real
q2
=
2
*
M_PI
*
(
i
-
n
[
0
]);
spectral_slopes
(
i
,
j
,
0
)
=
-
q1
*
I
*
spectral_surface
(
i
,
j
);
spectral_slopes
(
i
,
j
,
1
)
=
-
q2
*
I
*
spectral_surface
(
i
,
j
);
spectral_slopes
(
i
,
j
,
2
)
=
0
;
}
}
}
// end #pragma omp parallel
// Dirac
spectral_slopes
(
0
,
0
,
2
)
=
n
[
0
]
*
n
[
0
];
plan2
.
backwardTransform
();
FFTPlanManager
::
get
().
destroyPlan
(
surface
,
spectral_surface
);
FFTPlanManager
::
get
().
destroyPlan
(
surface_normals
,
spectral_slopes
);
// Make surface normal
VectorProxy
<
Real
>
sn
(
nullptr
,
3
);
const
UInt
N
=
surface_normals
.
getNbPoints
();
#pragma omp parallel for firstprivate(sn)
for
(
UInt
i
=
0
;
i
<
N
;
i
++
)
{
sn
.
setPointer
(
surface_normals
.
getInternalData
()
+
i
*
sn
.
dataSize
());
sn
/=
sn
.
l2norm
();
}
}
/* -------------------------------------------------------------------------- */
void
BemGrid
::
computeDisplacementsFromTractions
()
{
applyInfluenceFunctions
(
tractions
,
displacements
);
}
void
BemGrid
::
computeTractionsFromDisplacements
()
{
applyInverseInfluenceFunctions
(
tractions
,
displacements
);
}
/* -------------------------------------------------------------------------- */
void
BemGrid
::
computeGaps
(
Grid
<
Real
,
2
>
&
disp
)
{
const
UInt
*
n
=
surface
.
sizes
();
#pragma omp parallel for collapse(2)
for
(
UInt
i
=
0
;
i
<
n
[
0
]
;
i
++
)
{
for
(
UInt
j
=
0
;
j
<
n
[
1
]
;
j
++
)
{
gaps
(
i
,
j
,
0
)
=
disp
(
i
,
j
,
0
);
gaps
(
i
,
j
,
1
)
=
disp
(
i
,
j
,
1
);
gaps
(
i
,
j
,
2
)
=
disp
(
i
,
j
,
2
)
-
surface
(
i
,
j
);
}
}
}
/* -------------------------------------------------------------------------- */
void
BemGrid
::
applyInfluenceFunctions
(
Grid
<
Real
,
2
>
&
input
,
Grid
<
Real
,
2
>
&
output
)
{
TAMAAS_ASSERT
(
input
.
dataSize
()
==
output
.
dataSize
(),
"input and output have different size"
);
FFTransform
<
Real
,
2
>
&
plan_1
=
FFTPlanManager
::
get
().
createPlan
(
input
,
spectral_tractions
);
FFTransform
<
Real
,
2
>
&
plan_2
=
FFTPlanManager
::
get
().
createPlan
(
output
,
spectral_displacements
);
plan_1
.
forwardTransform
();
Complex
*
F
=
influence
.
getInternalData
(),
*
p
=
spectral_tractions
.
getInternalData
(),
*
u
=
spectral_displacements
.
getInternalData
();
VectorProxy
<
Complex
>
spectral_p
(
nullptr
,
3
),
spectral_u
(
nullptr
,
3
);
MatrixProxy
<
Complex
>
spectral_F
(
nullptr
,
3
,
3
);
spectral_displacements
=
0
;
const
UInt
N
=
influence
.
getNbPoints
();
// OpenMP not very cool with this: best to have a POD iteration variable
#pragma omp parallel for firstprivate(spectral_p, spectral_u, spectral_F)
for
(
UInt
i
=
0
;
i
<
N
;
++
i
)
{
spectral_p
.
setPointer
(
p
+
i
*
spectral_p
.
dataSize
());
spectral_u
.
setPointer
(
u
+
i
*
spectral_u
.
dataSize
());
spectral_F
.
setPointer
(
F
+
i
*
spectral_F
.
dataSize
());
spectral_u
.
mul
(
spectral_F
,
spectral_p
);
}
plan_2
.
backwardTransform
();
}
/* -------------------------------------------------------------------------- */
void
BemGrid
::
applyInverseInfluenceFunctions
(
Grid
<
Real
,
2
>
&
__attribute__
((
unused
))
input
,
Grid
<
Real
,
2
>
&
__attribute__
((
unused
))
output
)
{
TAMAAS_EXCEPTION
(
"applyInverseInfluenceFunctions not yet implemented"
);
}
/* -------------------------------------------------------------------------- */
// warning: this function will suck your soul out
// loops must be written with signed integers
void
BemGrid
::
computeInfluence
()
{
// Iterator over points of surface
MatrixProxy
<
Complex
>
it
(
influence
.
getInternalData
(),
3
,
3
);
// Imaginary unit
constexpr
Complex
I
(
0
,
1
);
const
Int
size
=
this
->
surface
.
size
();
const
Real
L_1
=
this
->
surface
.
lengths
()[
0
];
const
Real
L_2
=
this
->
surface
.
lengths
()[
1
];
this
->
influence
=
0
;
// Influence functions matrix, ask Lucas
#define INFLUENCE(q_1, q_2, q, E, nu) { \
2./(E*q*q*q)*(-nu*nu*q_1*q_1 - nu*q_2*q_2 + q*q), \
-q_1*q_2/(E*q*q*q)*(1+nu)*2*nu, \
I*q_1/(E*q*q)*(1+nu)*(1-2*nu), \
-q_1*q_2/(E*q*q*q)*(1+nu)*2*nu, \
2./(E*q*q*q)*(-nu*nu*q_2*q_2 - nu*q_1*q_1 + q*q), \
I*q_2/(E*q*q)*(1+nu)*(1-2*nu), \
-I*q_1/(E*q*q)*(1+nu)*(1-2*nu), \
-I*q_2/(E*q*q)*(1+nu)*(1-2*nu), \
2./(E*q)*(1-nu*nu)}
// Fill influence for single point
#define FILL_INFLUENCE(k, l) do { \
Real q_1 = 2*M_PI*(l)/L_1; \
Real q_2 = 2*M_PI*(k)/L_2; \
Real q = std::sqrt(q_1*q_1+q_2*q_2); \
Complex influence_1[] = INFLUENCE(q_1, q_2, q, E, nu); \
MatrixProxy<Complex> inf_mat(influence_1, 3, 3); \
it.setPointer(&influence(i, j, 0)); \
it = inf_mat; \
} while(0)
// Fill influence points for "symetric" areas
#define FILL_SYM_INFLUENCE(k, l) do { \
Real q_1 = 2*M_PI*(l)/L_1; \
Real q_2 = 2*M_PI*(k)/L_2; \
Real q = std::sqrt(q_1*q_1+q_2*q_2); \
Complex influence_1[] = INFLUENCE(q_1, q_2, q, E, nu); \
Complex influence_2[] = INFLUENCE(q_2, q_1, q, E, nu); \
MatrixProxy<Complex> inf_mat(influence_1, 3, 3); \
it.setPointer(&influence(i, j, 0)); \
it = inf_mat; \
inf_mat.setPointer(influence_2); \
it.setPointer(&influence(j, i, 0)); \
it = inf_mat; \
} while(0)
#pragma omp parallel firstprivate(it)
// all the following loops are independent
{
// Loops over parts of surface
/*
[ ][ ][ ][ ]
[ ][x][ ][ ]
[ ][ ][ ][ ]
[ ][ ][ ][o]
*/
#pragma omp for schedule(dynamic)
// can't collapse triangluar loops
for
(
Int
i
=
1
;
i
<
size
/
2
;
i
++
)
{
for
(
Int
j
=
i
;
j
<
size
/
2
;
j
++
)
{
FILL_SYM_INFLUENCE
(
i
,
j
);
}
}
/*
[ ][ ][ ][ ]
[ ][ ][ ][o]
[ ][ ][ ][ ]
[ ][x][ ][ ]
*/
#pragma omp for collapse(2)
for
(
Int
i
=
size
/
2
+
1
;
i
<
size
;
i
++
)
{
for
(
Int
j
=
1
;
j
<
size
/
2
;
j
++
)
{
FILL_INFLUENCE
(
i
-
size
,
j
);
}
}
/*
[ ][x][x][o]
[x][ ][x][ ]
[x][x][x][ ]
[ ][ ][ ][ ]
*/
#pragma omp for
for
(
Int
i
=
1
;
i
<=
size
/
2
;
i
++
)
{
{
Int
j
=
size
/
2
;
FILL_SYM_INFLUENCE
(
i
,
j
);
}
{
Int
j
=
0
;
FILL_SYM_INFLUENCE
(
i
,
j
);
}
}
/*
[ ][ ][ ][ ]
[ ][ ][ ][ ]
[ ][ ][ ][o]
[x][ ][x][ ]
*/
#pragma omp for
for
(
Int
i
=
size
/
2
+
1
;
i
<
size
;
i
++
)
{
{
Int
j
=
size
/
2
;
FILL_INFLUENCE
(
i
-
size
,
j
);
}
{
Int
j
=
0
;
FILL_INFLUENCE
(
i
-
size
,
j
);
}
}
}
// End #pragma omp parallel
/* State of surface now:
[0][x][x][o]
[x][x][x][o]
[x][x][x][o]
[x][x][x][o]
Legend: x => explicitely filled
o => hermitian symetry
0 => actually 0
*/
computeInfluenceLipschitz
();
#undef INFLUENCE
#undef FILL_INFLUENCE
#undef FILL_SYM_INFLUENCE
}
/* -------------------------------------------------------------------------- */
/// Computing L_2 norm of influence functions
void
BemGrid
::
computeInfluenceLipschitz
()
{
const
UInt
N
=
influence
.
getNbPoints
();
VectorProxy
<
Complex
>
m
(
nullptr
,
9
);
Real
norm
=
0.
;
#pragma omp parallel for firstprivate(m) reduction(+:norm)
for
(
UInt
i
=
0
;
i
<
N
;
i
++
)
{
m
.
setPointer
(
influence
.
getInternalData
()
+
i
*
m
.
dataSize
());
norm
+=
std
::
pow
(
std
::
norm
(
m
.
l2norm
()),
2
);
}
lipschitz
=
std
::
sqrt
(
norm
);
}
/* -------------------------------------------------------------------------- */
/* Friction related computations */
/* -------------------------------------------------------------------------- */
void
BemGrid
::
projectOnFrictionCone
(
Grid
<
Real
,
2
>
&
field
,
Real
mu
)
{
VectorProxy
<
Real
>
p_proxy
(
nullptr
,
3
);
const
UInt
N
=
field
.
getNbPoints
();
#pragma omp parallel for firstprivate(p_proxy)
for
(
UInt
i
=
0
;
i
<
N
;
i
++
)
{
p_proxy
.
setPointer
(
field
.
getInternalData
()
+
i
*
p_proxy
.
dataSize
());
projectOnFrictionCone
(
p_proxy
,
mu
);
}
}
/* -------------------------------------------------------------------------- */
void
BemGrid
::
enforceMeanValue
(
Grid
<
Real
,
2
>
&
field
,
const
Grid
<
Real
,
1
>
&
target
)
{
Real
red_0
=
0
,
red_1
=
0
,
red_2
=
0
;
const
UInt
*
n
=
field
.
sizes
();
#pragma omp parallel for collapse(2) reduction(+:red_0, red_1, red_2)
for
(
UInt
i
=
0
;
i
<
n
[
0
]
;
i
++
)
{
for
(
UInt
j
=
0
;
j
<
n
[
1
]
;
j
++
)
{
red_0
+=
field
(
i
,
j
,
0
);
red_1
+=
field
(
i
,
j
,
1
);
red_2
+=
field
(
i
,
j
,
2
);
}
}
red_0
/=
n
[
0
]
*
n
[
1
];
red_1
/=
n
[
0
]
*
n
[
1
];
red_2
/=
n
[
0
]
*
n
[
1
];
Real
p1_data
[
3
]
=
{
red_0
,
red_1
,
red_2
};
// Loop for pressure shifting
VectorProxy
<
Real
>
p1
(
p1_data
,
3
);
VectorProxy
<
Real
>
p0
((
Real
*
)
target
.
getInternalData
(),
3
);
VectorProxy
<
Real
>
p
(
nullptr
,
3
);
const
UInt
N
=
field
.
getNbPoints
();
#pragma omp parallel for firstprivate(p0, p1)
for
(
UInt
i
=
0
;
i
<
N
;
i
++
)
{
p
.
setPointer
(
field
.
getInternalData
()
+
i
*
p
.
dataSize
());
p
-=
p1
;
p
+=
p0
;
}
}
/* -------------------------------------------------------------------------- */
void
BemGrid
::
computeMeanValueError
(
Grid
<
Real
,
2
>
&
field
,
const
Grid
<
Real
,
1
>
&
target
,
Grid
<
Real
,
1
>
&
error_vec
)
{
Real
p0
=
0
,
p1
=
0
,
p2
=
0
;
const
UInt
*
n
=
field
.
sizes
();
#pragma omp parallel for collapse(2) reduction(+:p0, p1, p2)
for
(
UInt
i
=
0
;
i
<
n
[
0
]
;
i
++
)
{
for
(
UInt
j
=
0
;
j
<
n
[
1
]
;
j
++
)
{
p0
+=
field
(
i
,
j
,
0
);
p1
+=
field
(
i
,
j
,
1
);
p2
+=
field
(
i
,
j
,
2
);
}
}
p0
/=
n
[
0
]
*
n
[
1
];
p1
/=
n
[
0
]
*
n
[
1
];
p2
/=
n
[
0
]
*
n
[
1
];
Real
error
[
3
]
=
{
p0
-
target
(
0
),
p1
-
target
(
1
),
p2
-
target
(
2
)};
VectorProxy
<
Real
>
e
(
error
,
3
);
error_vec
=
e
;
}
/* -------------------------------------------------------------------------- */
Real
BemGrid
::
computeMeanValueError
(
Grid
<
Real
,
2
>
&
field
,
const
Grid
<
Real
,
1
>
&
target
)
{
Real
e
[
3
]
=
{
0.
};
VectorProxy
<
Real
>
error
(
e
,
3
);
computeMeanValueError
(
field
,
target
,
error
);
Real
norm
=
target
(
0
)
*
target
(
0
)
+
target
(
1
)
*
target
(
1
)
+
target
(
2
)
*
target
(
2
);
return
error
.
l2norm
()
/
std
::
sqrt
(
norm
);
}
/* -------------------------------------------------------------------------- */
__END_TAMAAS__
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