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MatrixPartitioned.h
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rGOOSEFEM GooseFEM
MatrixPartitioned.h
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/*
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
*/
#ifndef GOOSEFEM_MATRIXPARTITIONED_H
#define GOOSEFEM_MATRIXPARTITIONED_H
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
namespace
GooseFEM
{
template
<
class
Solver
=
Eigen
::
SimplicialLDLT
<
Eigen
::
SparseMatrix
<
double
>>>
class
MatrixPartitioned
{
public:
// Constructors
MatrixPartitioned
()
=
default
;
MatrixPartitioned
(
const
xt
::
xtensor
<
size_t
,
2
>&
conn
,
const
xt
::
xtensor
<
size_t
,
2
>&
dofs
,
const
xt
::
xtensor
<
size_t
,
1
>&
iip
);
// Dimensions
size_t
nelem
()
const
;
// number of elements
size_t
nne
()
const
;
// number of nodes per element
size_t
nnode
()
const
;
// number of nodes
size_t
ndim
()
const
;
// number of dimensions
size_t
ndof
()
const
;
// number of DOFs
size_t
nnu
()
const
;
// number of unknown DOFs
size_t
nnp
()
const
;
// number of prescribed DOFs
// DOF lists
xt
::
xtensor
<
size_t
,
2
>
dofs
()
const
;
// DOFs
xt
::
xtensor
<
size_t
,
1
>
iiu
()
const
;
// unknown DOFs
xt
::
xtensor
<
size_t
,
1
>
iip
()
const
;
// prescribed DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
void
assemble
(
const
xt
::
xtensor
<
double
,
3
>&
elemmat
);
// Solve:
// x_u = A_uu \ ( b_u - A_up * x_p )
void
solve
(
const
xt
::
xtensor
<
double
,
2
>&
b
,
xt
::
xtensor
<
double
,
2
>&
x
);
// modified with "x_u"
void
solve
(
const
xt
::
xtensor
<
double
,
1
>&
b
,
xt
::
xtensor
<
double
,
1
>&
x
);
// modified with "x_u"
void
solve_u
(
const
xt
::
xtensor
<
double
,
1
>&
b_u
,
const
xt
::
xtensor
<
double
,
1
>&
x_p
,
xt
::
xtensor
<
double
,
1
>&
x_u
);
// Get right-hand-size for corresponding to the prescribed DOFs:
// b_p = A_pu * x_u + A_pp * x_p = A_pp * x_p
void
reaction
(
const
xt
::
xtensor
<
double
,
2
>&
x
,
xt
::
xtensor
<
double
,
2
>&
b
)
const
;
// modified with "b_p"
void
reaction
(
const
xt
::
xtensor
<
double
,
1
>&
x
,
xt
::
xtensor
<
double
,
1
>&
b
)
const
;
// modified with "b_p"
void
reaction_p
(
const
xt
::
xtensor
<
double
,
1
>&
x_u
,
const
xt
::
xtensor
<
double
,
1
>&
x_p
,
xt
::
xtensor
<
double
,
1
>&
b_p
)
const
;
// Auto-allocation of the functions above
xt
::
xtensor
<
double
,
2
>
Solve
(
const
xt
::
xtensor
<
double
,
2
>&
b
,
const
xt
::
xtensor
<
double
,
2
>&
x
);
xt
::
xtensor
<
double
,
1
>
Solve
(
const
xt
::
xtensor
<
double
,
1
>&
b
,
const
xt
::
xtensor
<
double
,
1
>&
x
);
xt
::
xtensor
<
double
,
1
>
Solve_u
(
const
xt
::
xtensor
<
double
,
1
>&
b_u
,
const
xt
::
xtensor
<
double
,
1
>&
x_p
);
xt
::
xtensor
<
double
,
2
>
Reaction
(
const
xt
::
xtensor
<
double
,
2
>&
x
,
const
xt
::
xtensor
<
double
,
2
>&
b
)
const
;
xt
::
xtensor
<
double
,
1
>
Reaction
(
const
xt
::
xtensor
<
double
,
1
>&
x
,
const
xt
::
xtensor
<
double
,
1
>&
b
)
const
;
xt
::
xtensor
<
double
,
1
>
Reaction_p
(
const
xt
::
xtensor
<
double
,
1
>&
x_u
,
const
xt
::
xtensor
<
double
,
1
>&
x_p
)
const
;
private:
// The matrix
Eigen
::
SparseMatrix
<
double
>
m_Auu
;
Eigen
::
SparseMatrix
<
double
>
m_Aup
;
Eigen
::
SparseMatrix
<
double
>
m_Apu
;
Eigen
::
SparseMatrix
<
double
>
m_App
;
// Matrix entries
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tuu
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tup
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tpu
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tpp
;
// Solver (re-used to solve different RHS)
Solver
m_solver
;
// Signal changes to data compare to the last inverse
bool
m_factor
=
false
;
// Bookkeeping
xt
::
xtensor
<
size_t
,
2
>
m_conn
;
// connectivity [nelem, nne ]
xt
::
xtensor
<
size_t
,
2
>
m_dofs
;
// DOF-numbers per node [nnode, ndim]
xt
::
xtensor
<
size_t
,
2
>
m_part
;
// DOF-numbers per node, renumbered [nnode, ndim]
xt
::
xtensor
<
size_t
,
1
>
m_iiu
;
// unknown DOFs [nnu]
xt
::
xtensor
<
size_t
,
1
>
m_iip
;
// prescribed DOFs [nnp]
// Dimensions
size_t
m_nelem
;
// number of elements
size_t
m_nne
;
// number of nodes per element
size_t
m_nnode
;
// number of nodes
size_t
m_ndim
;
// number of dimensions
size_t
m_ndof
;
// number of DOFs
size_t
m_nnu
;
// number of unknown DOFs
size_t
m_nnp
;
// number of prescribed DOFs
// Compute inverse (automatically evaluated by "solve")
void
factorize
();
// Convert arrays (Eigen version of VectorPartitioned, which contains public functions)
Eigen
::
VectorXd
asDofs_u
(
const
xt
::
xtensor
<
double
,
1
>&
dofval
)
const
;
Eigen
::
VectorXd
asDofs_u
(
const
xt
::
xtensor
<
double
,
2
>&
nodevec
)
const
;
Eigen
::
VectorXd
asDofs_p
(
const
xt
::
xtensor
<
double
,
1
>&
dofval
)
const
;
Eigen
::
VectorXd
asDofs_p
(
const
xt
::
xtensor
<
double
,
2
>&
nodevec
)
const
;
};
}
// namespace GooseFEM
#include "MatrixPartitioned.hpp"
#endif
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