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MatrixPartitionedTyings.hpp
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rGOOSEFEM GooseFEM
MatrixPartitionedTyings.hpp
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/**
Implementation of MatrixPartitionedTyings.h
\file MatrixPartitionedTyings.hpp
\copyright Copyright 2017. Tom de Geus. All rights reserved.
\license This project is released under the GNU Public License (GPLv3).
*/
#ifndef GOOSEFEM_MATRIXPARTITIONEDTYINGS_HPP
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_HPP
#include "MatrixPartitionedTyings.h"
namespace
GooseFEM
{
inline
MatrixPartitionedTyings
::
MatrixPartitionedTyings
(
const
xt
::
xtensor
<
size_t
,
2
>&
conn
,
const
xt
::
xtensor
<
size_t
,
2
>&
dofs
,
const
Eigen
::
SparseMatrix
<
double
>&
Cdu
,
const
Eigen
::
SparseMatrix
<
double
>&
Cdp
)
{
GOOSEFEM_ASSERT
(
Cdu
.
rows
()
==
Cdp
.
rows
());
m_conn
=
conn
;
m_dofs
=
dofs
;
m_Cdu
=
Cdu
;
m_Cdp
=
Cdp
;
m_nnu
=
static_cast
<
size_t
>
(
m_Cdu
.
cols
());
m_nnp
=
static_cast
<
size_t
>
(
m_Cdp
.
cols
());
m_nnd
=
static_cast
<
size_t
>
(
m_Cdp
.
rows
());
m_nni
=
m_nnu
+
m_nnp
;
m_ndof
=
m_nni
+
m_nnd
;
m_iiu
=
xt
::
arange
<
size_t
>
(
m_nnu
);
m_iip
=
xt
::
arange
<
size_t
>
(
m_nnu
,
m_nnu
+
m_nnp
);
m_iid
=
xt
::
arange
<
size_t
>
(
m_nni
,
m_nni
+
m_nnd
);
m_nelem
=
m_conn
.
shape
(
0
);
m_nne
=
m_conn
.
shape
(
1
);
m_nnode
=
m_dofs
.
shape
(
0
);
m_ndim
=
m_dofs
.
shape
(
1
);
m_Cud
=
m_Cdu
.
transpose
();
m_Cpd
=
m_Cdp
.
transpose
();
m_Tuu
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tup
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tpu
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tpp
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tud
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tpd
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tdu
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tdp
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Tdd
.
reserve
(
m_nelem
*
m_nne
*
m_ndim
*
m_nne
*
m_ndim
);
m_Auu
.
resize
(
m_nnu
,
m_nnu
);
m_Aup
.
resize
(
m_nnu
,
m_nnp
);
m_Apu
.
resize
(
m_nnp
,
m_nnu
);
m_App
.
resize
(
m_nnp
,
m_nnp
);
m_Aud
.
resize
(
m_nnu
,
m_nnd
);
m_Apd
.
resize
(
m_nnp
,
m_nnd
);
m_Adu
.
resize
(
m_nnd
,
m_nnu
);
m_Adp
.
resize
(
m_nnd
,
m_nnp
);
m_Add
.
resize
(
m_nnd
,
m_nnd
);
GOOSEFEM_ASSERT
(
m_ndof
<=
m_nnode
*
m_ndim
);
GOOSEFEM_ASSERT
(
m_ndof
==
xt
::
amax
(
m_dofs
)()
+
1
);
}
inline
size_t
MatrixPartitionedTyings
::
nnu
()
const
{
return
m_nnu
;
}
inline
size_t
MatrixPartitionedTyings
::
nnp
()
const
{
return
m_nnp
;
}
inline
size_t
MatrixPartitionedTyings
::
nni
()
const
{
return
m_nni
;
}
inline
size_t
MatrixPartitionedTyings
::
nnd
()
const
{
return
m_nnd
;
}
inline
xt
::
xtensor
<
size_t
,
1
>
MatrixPartitionedTyings
::
iiu
()
const
{
return
m_iiu
;
}
inline
xt
::
xtensor
<
size_t
,
1
>
MatrixPartitionedTyings
::
iip
()
const
{
return
m_iip
;
}
inline
xt
::
xtensor
<
size_t
,
1
>
MatrixPartitionedTyings
::
iii
()
const
{
return
xt
::
arange
<
size_t
>
(
m_nni
);
}
inline
xt
::
xtensor
<
size_t
,
1
>
MatrixPartitionedTyings
::
iid
()
const
{
return
m_iid
;
}
inline
void
MatrixPartitionedTyings
::
assemble
(
const
xt
::
xtensor
<
double
,
3
>&
elemmat
)
{
GOOSEFEM_ASSERT
(
xt
::
has_shape
(
elemmat
,
{
m_nelem
,
m_nne
*
m_ndim
,
m_nne
*
m_ndim
}));
m_Tuu
.
clear
();
m_Tup
.
clear
();
m_Tpu
.
clear
();
m_Tpp
.
clear
();
m_Tud
.
clear
();
m_Tpd
.
clear
();
m_Tdu
.
clear
();
m_Tdp
.
clear
();
m_Tdd
.
clear
();
for
(
size_t
e
=
0
;
e
<
m_nelem
;
++
e
)
{
for
(
size_t
m
=
0
;
m
<
m_nne
;
++
m
)
{
for
(
size_t
i
=
0
;
i
<
m_ndim
;
++
i
)
{
size_t
di
=
m_dofs
(
m_conn
(
e
,
m
),
i
);
for
(
size_t
n
=
0
;
n
<
m_nne
;
++
n
)
{
for
(
size_t
j
=
0
;
j
<
m_ndim
;
++
j
)
{
size_t
dj
=
m_dofs
(
m_conn
(
e
,
n
),
j
);
if
(
di
<
m_nnu
&&
dj
<
m_nnu
)
{
m_Tuu
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
,
dj
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
di
<
m_nnu
&&
dj
<
m_nni
)
{
m_Tup
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
,
dj
-
m_nnu
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
di
<
m_nnu
)
{
m_Tud
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
,
dj
-
m_nni
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
di
<
m_nni
&&
dj
<
m_nnu
)
{
m_Tpu
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
-
m_nnu
,
dj
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
di
<
m_nni
&&
dj
<
m_nni
)
{
m_Tpp
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
-
m_nnu
,
dj
-
m_nnu
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
di
<
m_nni
)
{
m_Tpd
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
-
m_nnu
,
dj
-
m_nni
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
dj
<
m_nnu
)
{
m_Tdu
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
-
m_nni
,
dj
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
if
(
dj
<
m_nni
)
{
m_Tdp
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
-
m_nni
,
dj
-
m_nnu
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
else
{
m_Tdd
.
push_back
(
Eigen
::
Triplet
<
double
>
(
di
-
m_nni
,
dj
-
m_nni
,
elemmat
(
e
,
m
*
m_ndim
+
i
,
n
*
m_ndim
+
j
)));
}
}
}
}
}
}
m_Auu
.
setFromTriplets
(
m_Tuu
.
begin
(),
m_Tuu
.
end
());
m_Aup
.
setFromTriplets
(
m_Tup
.
begin
(),
m_Tup
.
end
());
m_Apu
.
setFromTriplets
(
m_Tpu
.
begin
(),
m_Tpu
.
end
());
m_App
.
setFromTriplets
(
m_Tpp
.
begin
(),
m_Tpp
.
end
());
m_Aud
.
setFromTriplets
(
m_Tud
.
begin
(),
m_Tud
.
end
());
m_Apd
.
setFromTriplets
(
m_Tpd
.
begin
(),
m_Tpd
.
end
());
m_Adu
.
setFromTriplets
(
m_Tdu
.
begin
(),
m_Tdu
.
end
());
m_Adp
.
setFromTriplets
(
m_Tdp
.
begin
(),
m_Tdp
.
end
());
m_Add
.
setFromTriplets
(
m_Tdd
.
begin
(),
m_Tdd
.
end
());
m_changed
=
true
;
}
inline
Eigen
::
VectorXd
MatrixPartitionedTyings
::
AsDofs_u
(
const
xt
::
xtensor
<
double
,
1
>&
dofval
)
const
{
GOOSEFEM_ASSERT
(
dofval
.
size
()
==
m_ndof
);
Eigen
::
VectorXd
dofval_u
(
m_nnu
,
1
);
#pragma omp parallel for
for
(
size_t
d
=
0
;
d
<
m_nnu
;
++
d
)
{
dofval_u
(
d
)
=
dofval
(
m_iiu
(
d
));
}
return
dofval_u
;
}
inline
Eigen
::
VectorXd
MatrixPartitionedTyings
::
AsDofs_u
(
const
xt
::
xtensor
<
double
,
2
>&
nodevec
)
const
{
GOOSEFEM_ASSERT
(
xt
::
has_shape
(
nodevec
,
{
m_nnode
,
m_ndim
}));
Eigen
::
VectorXd
dofval_u
=
Eigen
::
VectorXd
::
Zero
(
m_nnu
,
1
);
#pragma omp parallel for
for
(
size_t
m
=
0
;
m
<
m_nnode
;
++
m
)
{
for
(
size_t
i
=
0
;
i
<
m_ndim
;
++
i
)
{
if
(
m_dofs
(
m
,
i
)
<
m_nnu
)
{
dofval_u
(
m_dofs
(
m
,
i
))
=
nodevec
(
m
,
i
);
}
}
}
return
dofval_u
;
}
inline
Eigen
::
VectorXd
MatrixPartitionedTyings
::
AsDofs_p
(
const
xt
::
xtensor
<
double
,
1
>&
dofval
)
const
{
GOOSEFEM_ASSERT
(
dofval
.
size
()
==
m_ndof
);
Eigen
::
VectorXd
dofval_p
(
m_nnp
,
1
);
#pragma omp parallel for
for
(
size_t
d
=
0
;
d
<
m_nnp
;
++
d
)
{
dofval_p
(
d
)
=
dofval
(
m_iip
(
d
));
}
return
dofval_p
;
}
inline
Eigen
::
VectorXd
MatrixPartitionedTyings
::
AsDofs_p
(
const
xt
::
xtensor
<
double
,
2
>&
nodevec
)
const
{
GOOSEFEM_ASSERT
(
xt
::
has_shape
(
nodevec
,
{
m_nnode
,
m_ndim
}));
Eigen
::
VectorXd
dofval_p
=
Eigen
::
VectorXd
::
Zero
(
m_nnp
,
1
);
#pragma omp parallel for
for
(
size_t
m
=
0
;
m
<
m_nnode
;
++
m
)
{
for
(
size_t
i
=
0
;
i
<
m_ndim
;
++
i
)
{
if
(
m_dofs
(
m
,
i
)
>=
m_nnu
&&
m_dofs
(
m
,
i
)
<
m_nni
)
{
dofval_p
(
m_dofs
(
m
,
i
)
-
m_nnu
)
=
nodevec
(
m
,
i
);
}
}
}
return
dofval_p
;
}
inline
Eigen
::
VectorXd
MatrixPartitionedTyings
::
AsDofs_d
(
const
xt
::
xtensor
<
double
,
1
>&
dofval
)
const
{
GOOSEFEM_ASSERT
(
dofval
.
size
()
==
m_ndof
);
Eigen
::
VectorXd
dofval_d
(
m_nnd
,
1
);
#pragma omp parallel for
for
(
size_t
d
=
0
;
d
<
m_nnd
;
++
d
)
{
dofval_d
(
d
)
=
dofval
(
m_iip
(
d
));
}
return
dofval_d
;
}
inline
Eigen
::
VectorXd
MatrixPartitionedTyings
::
AsDofs_d
(
const
xt
::
xtensor
<
double
,
2
>&
nodevec
)
const
{
GOOSEFEM_ASSERT
(
xt
::
has_shape
(
nodevec
,
{
m_nnode
,
m_ndim
}));
Eigen
::
VectorXd
dofval_d
=
Eigen
::
VectorXd
::
Zero
(
m_nnd
,
1
);
#pragma omp parallel for
for
(
size_t
m
=
0
;
m
<
m_nnode
;
++
m
)
{
for
(
size_t
i
=
0
;
i
<
m_ndim
;
++
i
)
{
if
(
m_dofs
(
m
,
i
)
>=
m_nni
)
{
dofval_d
(
m_dofs
(
m
,
i
)
-
m_nni
)
=
nodevec
(
m
,
i
);
}
}
}
return
dofval_d
;
}
template
<
class
Solver
>
inline
void
MatrixPartitionedTyingsSolver
<
Solver
>::
factorize
(
MatrixPartitionedTyings
&
matrix
)
{
if
(
!
matrix
.
m_changed
&&
!
m_factor
)
{
return
;
}
matrix
.
m_ACuu
=
matrix
.
m_Auu
+
matrix
.
m_Aud
*
matrix
.
m_Cdu
+
matrix
.
m_Cud
*
matrix
.
m_Adu
+
matrix
.
m_Cud
*
matrix
.
m_Add
*
matrix
.
m_Cdu
;
matrix
.
m_ACup
=
matrix
.
m_Aup
+
matrix
.
m_Aud
*
matrix
.
m_Cdp
+
matrix
.
m_Cud
*
matrix
.
m_Adp
+
matrix
.
m_Cud
*
matrix
.
m_Add
*
matrix
.
m_Cdp
;
// matrix.m_ACpu = matrix.m_Apu + matrix.m_Apd * matrix.m_Cdu + matrix.m_Cpd * matrix.m_Adu
// + matrix.m_Cpd * matrix.m_Add * matrix.m_Cdu;
// matrix.m_ACpp = matrix.m_App + matrix.m_Apd * matrix.m_Cdp + matrix.m_Cpd * matrix.m_Adp
// + matrix.m_Cpd * matrix.m_Add * matrix.m_Cdp;
m_solver
.
compute
(
matrix
.
m_ACuu
);
m_factor
=
false
;
matrix
.
m_changed
=
false
;
}
template
<
class
Solver
>
inline
void
MatrixPartitionedTyingsSolver
<
Solver
>::
solve
(
MatrixPartitionedTyings
&
matrix
,
const
xt
::
xtensor
<
double
,
2
>&
b
,
xt
::
xtensor
<
double
,
2
>&
x
)
{
GOOSEFEM_ASSERT
(
xt
::
has_shape
(
b
,
{
matrix
.
m_nnode
,
matrix
.
m_ndim
}));
GOOSEFEM_ASSERT
(
xt
::
has_shape
(
x
,
{
matrix
.
m_nnode
,
matrix
.
m_ndim
}));
this
->
factorize
(
matrix
);
Eigen
::
VectorXd
B_u
=
matrix
.
AsDofs_u
(
b
);
Eigen
::
VectorXd
B_d
=
matrix
.
AsDofs_d
(
b
);
Eigen
::
VectorXd
X_p
=
matrix
.
AsDofs_p
(
x
);
B_u
+=
matrix
.
m_Cud
*
B_d
;
Eigen
::
VectorXd
X_u
=
m_solver
.
solve
(
Eigen
::
VectorXd
(
B_u
-
matrix
.
m_ACup
*
X_p
));
Eigen
::
VectorXd
X_d
=
matrix
.
m_Cdu
*
X_u
+
matrix
.
m_Cdp
*
X_p
;
#pragma omp parallel for
for
(
size_t
m
=
0
;
m
<
matrix
.
m_nnode
;
++
m
)
{
for
(
size_t
i
=
0
;
i
<
matrix
.
m_ndim
;
++
i
)
{
if
(
matrix
.
m_dofs
(
m
,
i
)
<
matrix
.
m_nnu
)
{
x
(
m
,
i
)
=
X_u
(
matrix
.
m_dofs
(
m
,
i
));
}
else
if
(
matrix
.
m_dofs
(
m
,
i
)
>=
matrix
.
m_nni
)
{
x
(
m
,
i
)
=
X_d
(
matrix
.
m_dofs
(
m
,
i
)
-
matrix
.
m_nni
);
}
}
}
}
template
<
class
Solver
>
inline
void
MatrixPartitionedTyingsSolver
<
Solver
>::
solve
(
MatrixPartitionedTyings
&
matrix
,
const
xt
::
xtensor
<
double
,
1
>&
b
,
xt
::
xtensor
<
double
,
1
>&
x
)
{
GOOSEFEM_ASSERT
(
b
.
size
()
==
matrix
.
m_ndof
);
GOOSEFEM_ASSERT
(
x
.
size
()
==
matrix
.
m_ndof
);
this
->
factorize
(
matrix
);
Eigen
::
VectorXd
B_u
=
matrix
.
AsDofs_u
(
b
);
Eigen
::
VectorXd
B_d
=
matrix
.
AsDofs_d
(
b
);
Eigen
::
VectorXd
X_p
=
matrix
.
AsDofs_p
(
x
);
Eigen
::
VectorXd
X_u
=
m_solver
.
solve
(
Eigen
::
VectorXd
(
B_u
-
matrix
.
m_ACup
*
X_p
));
Eigen
::
VectorXd
X_d
=
matrix
.
m_Cdu
*
X_u
+
matrix
.
m_Cdp
*
X_p
;
#pragma omp parallel for
for
(
size_t
d
=
0
;
d
<
matrix
.
m_nnu
;
++
d
)
{
x
(
matrix
.
m_iiu
(
d
))
=
X_u
(
d
);
}
#pragma omp parallel for
for
(
size_t
d
=
0
;
d
<
matrix
.
m_nnd
;
++
d
)
{
x
(
matrix
.
m_iid
(
d
))
=
X_d
(
d
);
}
}
template
<
class
Solver
>
inline
void
MatrixPartitionedTyingsSolver
<
Solver
>::
solve_u
(
MatrixPartitionedTyings
&
matrix
,
const
xt
::
xtensor
<
double
,
1
>&
b_u
,
const
xt
::
xtensor
<
double
,
1
>&
b_d
,
const
xt
::
xtensor
<
double
,
1
>&
x_p
,
xt
::
xtensor
<
double
,
1
>&
x_u
)
{
UNUSED
(
b_d
);
GOOSEFEM_ASSERT
(
b_u
.
size
()
==
matrix
.
m_nnu
);
GOOSEFEM_ASSERT
(
b_d
.
size
()
==
matrix
.
m_nnd
);
GOOSEFEM_ASSERT
(
x_p
.
size
()
==
matrix
.
m_nnp
);
GOOSEFEM_ASSERT
(
x_u
.
size
()
==
matrix
.
m_nnu
);
this
->
factorize
(
matrix
);
Eigen
::
Map
<
Eigen
::
VectorXd
>
(
x_u
.
data
(),
x_u
.
size
()).
noalias
()
=
m_solver
.
solve
(
Eigen
::
VectorXd
(
Eigen
::
Map
<
const
Eigen
::
VectorXd
>
(
b_u
.
data
(),
b_u
.
size
())
-
matrix
.
m_ACup
*
Eigen
::
Map
<
const
Eigen
::
VectorXd
>
(
x_p
.
data
(),
x_p
.
size
())));
}
template
<
class
Solver
>
inline
xt
::
xtensor
<
double
,
2
>
MatrixPartitionedTyingsSolver
<
Solver
>::
Solve
(
MatrixPartitionedTyings
&
matrix
,
const
xt
::
xtensor
<
double
,
2
>&
b
,
const
xt
::
xtensor
<
double
,
2
>&
x
)
{
xt
::
xtensor
<
double
,
2
>
ret
=
x
;
this
->
solve
(
matrix
,
b
,
ret
);
return
ret
;
}
template
<
class
Solver
>
inline
xt
::
xtensor
<
double
,
1
>
MatrixPartitionedTyingsSolver
<
Solver
>::
Solve
(
MatrixPartitionedTyings
&
matrix
,
const
xt
::
xtensor
<
double
,
1
>&
b
,
const
xt
::
xtensor
<
double
,
1
>&
x
)
{
xt
::
xtensor
<
double
,
1
>
ret
=
x
;
this
->
solve
(
matrix
,
b
,
ret
);
return
ret
;
}
template
<
class
Solver
>
inline
xt
::
xtensor
<
double
,
1
>
MatrixPartitionedTyingsSolver
<
Solver
>::
Solve_u
(
MatrixPartitionedTyings
&
matrix
,
const
xt
::
xtensor
<
double
,
1
>&
b_u
,
const
xt
::
xtensor
<
double
,
1
>&
b_d
,
const
xt
::
xtensor
<
double
,
1
>&
x_p
)
{
xt
::
xtensor
<
double
,
1
>
x_u
=
xt
::
empty
<
double
>
({
matrix
.
m_nnu
});
this
->
solve_u
(
matrix
,
b_u
,
b_d
,
x_p
,
x_u
);
return
x_u
;
}
}
// namespace GooseFEM
#endif
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