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MatrixPartitionedTyings.h
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rGOOSEFEM GooseFEM
MatrixPartitionedTyings.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_MATRIXPARTITIONEDTYINGS_H
#define GOOSEFEM_MATRIXPARTITIONEDTYINGS_H
// -------------------------------------------------------------------------------------------------
#include "config.h"
#include <Eigen/Eigen>
#include <Eigen/Sparse>
#include <Eigen/SparseCholesky>
// =================================================================================================
namespace
GooseFEM
{
// -------------------------------------------------------------------------------------------------
class
MatrixPartitionedTyings
{
public:
// Constructors
MatrixPartitionedTyings
()
=
default
;
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
);
// 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 independent, unknown DOFs
size_t
nnp
()
const
;
// number of independent, prescribed DOFs
size_t
nni
()
const
;
// number of independent DOFs
size_t
nnd
()
const
;
// number of dependent DOFs
// DOF lists
xt
::
xtensor
<
size_t
,
2
>
dofs
()
const
;
// DOFs
xt
::
xtensor
<
size_t
,
1
>
iiu
()
const
;
// independent, unknown DOFs
xt
::
xtensor
<
size_t
,
1
>
iip
()
const
;
// independent, prescribed DOFs
xt
::
xtensor
<
size_t
,
1
>
iii
()
const
;
// independent DOFs
xt
::
xtensor
<
size_t
,
1
>
iid
()
const
;
// dependent DOFs
// Assemble from matrices stored per element [nelem, nne*ndim, nne*ndim]
void
assemble
(
const
xt
::
xtensor
<
double
,
3
>
&
elemmat
);
// Solve:
// A' = A_ii + K_id * C_di + C_di^T * K_di + C_di^T * K_dd * C_di
// b' = b_i + C_di^T * b_d
// x_u = A'_uu \ ( b'_u - A'_up * x_p )
// x_i = [x_u, x_p]
// x_d = C_di * x_i
void
solve
(
const
xt
::
xtensor
<
double
,
2
>
&
b
,
xt
::
xtensor
<
double
,
2
>
&
x
);
// modified with "x_u", "x_d"
void
solve
(
const
xt
::
xtensor
<
double
,
1
>
&
b
,
xt
::
xtensor
<
double
,
1
>
&
x
);
// modified with "x_u", "x_d"
void
solve_u
(
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
);
// overwritten
private:
// The matrix
Eigen
::
SparseMatrix
<
double
>
m_Auu
;
Eigen
::
SparseMatrix
<
double
>
m_Aup
;
Eigen
::
SparseMatrix
<
double
>
m_Apu
;
Eigen
::
SparseMatrix
<
double
>
m_App
;
Eigen
::
SparseMatrix
<
double
>
m_Aud
;
Eigen
::
SparseMatrix
<
double
>
m_Apd
;
Eigen
::
SparseMatrix
<
double
>
m_Adu
;
Eigen
::
SparseMatrix
<
double
>
m_Adp
;
Eigen
::
SparseMatrix
<
double
>
m_Add
;
// The matrix for which the tyings have been applied
Eigen
::
SparseMatrix
<
double
>
m_ACuu
;
Eigen
::
SparseMatrix
<
double
>
m_ACup
;
Eigen
::
SparseMatrix
<
double
>
m_ACpu
;
Eigen
::
SparseMatrix
<
double
>
m_ACpp
;
// 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
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tud
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tpd
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tdu
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tdp
;
std
::
vector
<
Eigen
::
Triplet
<
double
>>
m_Tdd
;
// Solver (re-used to solve different RHS)
Eigen
::
SimplicialLDLT
<
Eigen
::
SparseMatrix
<
double
>>
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
,
1
>
m_iiu
;
// unknown DOFs [nnu]
xt
::
xtensor
<
size_t
,
1
>
m_iip
;
// prescribed DOFs [nnp]
xt
::
xtensor
<
size_t
,
1
>
m_iid
;
// dependent DOFs [nnd]
// 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 independent, unknown DOFs
size_t
m_nnp
;
// number of independent, prescribed DOFs
size_t
m_nni
;
// number of independent DOFs
size_t
m_nnd
;
// number of dependent DOFs
// Tyings
Eigen
::
SparseMatrix
<
double
>
m_Cdu
;
Eigen
::
SparseMatrix
<
double
>
m_Cdp
;
Eigen
::
SparseMatrix
<
double
>
m_Cud
;
Eigen
::
SparseMatrix
<
double
>
m_Cpd
;
// 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
;
Eigen
::
VectorXd
asDofs_d
(
const
xt
::
xtensor
<
double
,
1
>
&
dofval
)
const
;
Eigen
::
VectorXd
asDofs_d
(
const
xt
::
xtensor
<
double
,
2
>
&
nodevec
)
const
;
};
// -------------------------------------------------------------------------------------------------
}
// namespace ...
// =================================================================================================
#include "MatrixPartitionedTyings.hpp"
// =================================================================================================
#endif
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