getmatrix.h File Reference

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Functions
void	Get_Matrix_Pattern (int const nelem, int const ndof_e, int const *const ia, int &nnz, int *&id, int *&ik, double *&sk)
void	CalcElem (int const ial[3], double const xc[], double ske[3][3], double fe[3])
void	AddElem (int const ial[3], double const ske[3][3], double const fe[3], int const id[], int const ik[], double sk[], double f[])
void	DebugMatrix (int const nnode, int const id[], int const ik[], double const sk[])
void	DebugVector (int const nnode, double const v[])
void	GetMatrix (int const nelem, int const ndof_e, int const ia[], int const nnode, double const xc[], int const nnz, int const id[], int const ik[], double sk[], double f[])
void	ApplyDirichletBC (int const nx, int const ny, int const neigh[], double const u[], int const id[], int const ik[], double sk[], double f[])
int	fetch (int const row, int const col, int const id[], int const ik[])
void	Defect (double w[], double const f[], double const u[], int nnode, int const id[], int const ik[], double const sk[])
void	CrsMult (double w[], double const u[], int nnode, int const id[], int const ik[], double const sk[])
void	GetDiag (int nnode, int const id[], int const ik[], double const sk[], double d[])

Function Documentation

AddElem()

void AddElem	(	int const	ial[3],
		double const	ske[3][3],
		double const	fe[3],
		int const	id[],
		int const	ik[],
		double	sk[],
		double	f[]
	)

Adds the element stiffness matrix ske and the element load vector fe of one triangular element with linear shape functions to the appropriate positions in the symmetric stiffness matrix, stored as CSR matrix K(sk,id, ik)

Parameters

[in]	ial	node indices of the three element vertices
[in]	ske	element stiffness matrix
[in]	fe	element load vector
[out]	sk	vector non-zero entries of CSR matrix
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[out]	f	distributed local vector storing the right hand side

Definition at line 97 of file getmatrix.cpp.

ApplyDirichletBC()

void ApplyDirichletBC	(	int const	nx,
		int const	ny,
		int const	neigh[],
		double const	u[],
		int const	id[],
		int const	ik[],
		double	sk[],
		double	f[]
	)

Applies Dirichlet boundary conditions to symmetric CSR matrix (sk,id, ik) and right hand side f of a system of equations resulting from a FEM/FDM discretization

Parameters

[in]	nx	number of discretization intervals in x-direction
[in]	ny	number of discretization intervals in y-direction
[in]	neigh	vector of 4 elements containing the ranks of neighbouring processes, -1 indicates a boundary in this direction
[in]	u	local vector with appropriately initialized b.c.
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[in,out]	sk	vector non-zero entries of CSR matrix
[in,out]	f	right hand side

Definition at line 275 of file getmatrix.cpp.

CalcElem()

void CalcElem	(	int const	ial[3],
		double const	xc[],
		double	ske[3][3],
		double	fe[3]
	)

Calculates the element stiffness matrix ske and the element load vector fe of one triangular element with linear shape functions.

Parameters

[in]	ial	node indices of the three element vertices
[in]	xc	vector of node coordinates with x(2*k,2*k+1) as coodinates of node k
[out]	ske	element stiffness matrix
[out]	fe	element load vector

Definition at line 68 of file getmatrix.cpp.

CrsMult()

void CrsMult	(	double	w[],
		double const	u[],
		int	nnode,
		int const	id[],
		int const	ik[],
		double const	sk[]
	)

Multiplies vector u with a CSR matrix K(id, ik, sk). w := K*u

Parameters

[out]	w	distributed local vector.
[in]	u	accumulated local vector.
[in]	nnode	number of rows
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[in]	sk	vector non-zero entries of CSR matrix

Definition at line 206 of file getmatrix.cpp.

DebugMatrix()

void DebugMatrix	(	int const	nnode,
		int const	id[],
		int const	ik[],
		double const	sk[]
	)

Print entries of the CSR matrix K(id, ik, sk).

Parameters

[in]	nnode	number of rows
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[in]	sk	vector non-zero entries of CSR matrix

Definition at line 132 of file getmatrix.cpp.

DebugVector()

void DebugVector	(	int const	nnode,
		double const	v[]
	)

Print entries of a vector.

Parameters

[in]	nnode	number of entries
[in]	v	vector values

Definition at line 154 of file getmatrix.cpp.

Defect()

void Defect	(	double	w[],
		double const	f[],
		double const	u[],
		int	nnode,
		int const	id[],
		int const	ik[],
		double const	sk[]
	)

Calculates the defect w := f - K*u a CSR matrix K(id, ik, sk).

Parameters

[out]	w	distributed local vector.
[in]	f	distributed local vector.
[in]	u	accumulated local vector.
[in]	nnode	number of rows
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[in]	sk	vector non-zero entries of CSR matrix

Definition at line 191 of file getmatrix.cpp.

fetch()

int fetch	(	int const	row,
		int const	col,
		int const	id[],
		int const	ik[]
	)

Finds in a CRS matrix the access index for an entry at row row and column col.

Parameters

[in]	row	row index
[in]	col	column index
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix

Returns

index for element (row, col). If no appropriate entry exists then -1 will be returned.

Warning

assert() stops the function in case that element (row, col) doesn't exist.

Definition at line 170 of file getmatrix.cpp.

Get_Matrix_Pattern()

void Get_Matrix_Pattern	(	int const	nelem,
		int const	ndof_e,
		int const *const	ia,
		int &	nnz,
		int *&	id,
		int *&	ik,
		double *&	sk
	)

Determines the matrix graph of an CRS matrix (id, ik, sk) based on the element connectivity ia.

The memory for arrays id, ik, sk is allocated inside the function.

Parameters

[in]	nelem	number of triangular elements
[in]	ndof_e	number of f.e. nodes per element
[in]	ia	element connectivity array[nelem][ndof_e] for linear triangular elements
[out]	nnz	number of non-zero elements in matrix
[out]	id	array[nnode+1] storing indices of first entry of a row (is allocated in function)
[out]	ik	array[nnz] storing column indices of non-zero entries (is allocated in function)
[out]	sk	array[nnz] storing values of non-zero entries (is allocated in function)

Definition at line 14 of file getmatrix.cpp.

GetDiag()

void GetDiag	(	int	nnode,
		int const	id[],
		int const	ik[],
		double const	sk[],
		double	d[]
	)

Copies the diagonal entries of a CSR matrix (sk,id, ik) onto a vector d.

Parameters

[in]	nnode	number of rows
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[in]	sk	vector non-zero entries of CSR matrix
[out]	d	accumulated diagonal entries of CSR matrix

Definition at line 223 of file getmatrix.cpp.

GetMatrix()

void GetMatrix	(	int const	nelem,
		int const	ndof_e,
		int const	ia[],
		int const	nnode,
		double const	xc[],
		int const	nnz,
		int const	id[],
		int const	ik[],
		double	sk[],
		double	f[]
	)

Computes the stiffness matrix in CRS format(id, ik, sk) and load vector f for the Poisson problem without incorporating the boundary conditions The matrix pattern has to be generated previously and the memory has to be allocated therein.

See also

Get_Matrix_Pattern

Parameters

[in]	nelem	number of finite elements
[in]	ndof_e	degrees of freedom per element
[in]	ia	element connectivity array[nelem][ndof_e]
[in]	nnode	number of coordinates (== number of unknowns)
[in]	xc	coordinates[nnode][2]
[in]	nnz	number of non-zero entries in CRS matrix
[in]	id	index vector containing the first entry in a CSR row
[in]	ik	column index vector of CSR matrix
[out]	sk	vector of non-zero entries of CSR matrix
[out]	f	distributed local vector storing the right hand side

Definition at line 243 of file getmatrix.cpp.