#include "adh.h"

Functions
int	solve_linear_sys_bcgstab (double x, int indptr_diag, int cols_diag, double vals_diag, int indptr_off_diag, int cols_off_diag, double vals_off_diag, double b, double scale_vect, int local_size, int size, int rank, int ghosts, int nghost)
	Solves a system of already scaled equations in split CSR format using bcgstab this is also assuming there is some scaling prior to solve in scale_vect. If no scaling, then scale_vect needs to be all 1's. Preconditioning of block diagonal (local to process) via umfpack is employed. More...

void	umfpack_clear (void)
	Short helper function that clears umfpack structures. More...

int	prep_umfpack (int indptr_diag, int cols_diag, double *vals_diag, int nrow)
	Function that pre-factors matrix, used for preconditioner, modifies the static Symbolic and Numeric structures. More...

int	solve_umfpack (double x, int indptr_diag, int cols_diag, double vals_diag, double *b, int nrow)
	Function that solves system Ax=b using umfpack, provided A is in CSR format. More...

void	free_bcgstab (void)
	Frees all data structures allocate within this file. More...

Detailed Description

This file has functions responsible for solving linear system in split CSR format using BCG-stabilized method

Function Documentation

◆ free_bcgstab()

void free_bcgstab ( void )

Frees all data structures allocate within this file.

Author: Mark Loveland

Bug:: none

Warning: none

Copyright: AdH

◆ prep_umfpack()

int prep_umfpack	(	int *	indptr_diag,
		int *	cols_diag,
		double *	vals_diag,
		int	nrow
	)

Function that pre-factors matrix, used for preconditioner, modifies the static Symbolic and Numeric structures.

Author: Mark Loveland

Bug:: none

Warning: none

Copyright: AdH

Parameters

[in]	indptr_diag	(int*) - array of integers with first/last indeces of each row in CSR matrix
[in]	cols_diag	(int*) - array of integers that are local (to process) column numbers
[in]	vals_diag	(double*) - the values of the sparse matrix
[in]	nrow	(int) - number of equations in system /returns (integer) status of umfpack routine

◆ solve_linear_sys_bcgstab()

int solve_linear_sys_bcgstab	(	double *	x,
		int *	indptr_diag,
		int *	cols_diag,
		double *	vals_diag,
		int *	indptr_off_diag,
		int *	cols_off_diag,
		double *	vals_off_diag,
		double *	b,
		double *	scale_vect,
		int	local_size,
		int	size,
		int	rank,
		int *	ghosts,
		int	nghost
	)

Solves a system of already scaled equations in split CSR format using bcgstab this is also assuming there is some scaling prior to solve in scale_vect. If no scaling, then scale_vect needs to be all 1's. Preconditioning of block diagonal (local to process) via umfpack is employed.

Ref: H. A. vanderVorst, "Bi-CGStab: A fast and smoothly converging variant to Bi-CG for the solution of nonsymmetric systems", SIAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644.

or C. T. Kelley, "Iterative Methods for Linear and Nonlinear Equations", SIAM, Philadelphia, PA, 1995.

In general, the Bi-CGStab solver constructs bases for the Krylov subspaces (A,b) and (A^T,c), where b is the right-hand-side vector and c is usually chosen so that c=b. The method may break down, although this does not seem to happen often in practice.

Author: Mark Loveland

Bug:: none

Warning: none

Copyright: AdH

Parameters

[in,out]	x	(double*) - solution to system Ax=b
[in]	indptr_diag	(int*) - indeces of first/last index for each row in diagonal block (local to process) in split CSR matrix
[in]	cols_diag	(int*) - column numbers (local to process) of diagonal block in split CSR matrix
[in]	vals_diag	(double*) - array of doubles that are the nonzero entries of diagonal block (local to process) in split CSR matrix
[in]	indptr_off_diag	(int*) - indeces of first/last index for each row in off-diagonal block (local to process) in split CSR matrix
[in]	cols_off_diag	(int*) - column numbers (global) of off-diagonal block in split CSR matrix
[in]	vals_off_diag	(double*) - array of doubles that are the nonzero entries of off-diagonal block (local to process) in split CSR matrix
[in]	b	(double*) - scaled rhs of the linear system
[in]	scale_vect	(double*) - the vector that scaled the system of equations prior to solve, used for rescaling after solve is finished
[in]	local_size	(int) - number of equations (rows in the matrix) owned by the process
[in]	size	(int) - number of rows + number of ghost d.o.f.s present
[in]	rank	(int) - MPI rank
[in]	ghosts	(int*) - array of global dof numbers that are ghosts on the process
[in]	nghost	(int) - number of ghost d.o.f.s on the process

Returns: integer that is a code if the solve worked or not

Note

◆ solve_umfpack()

int solve_umfpack	(	double *	x,
		int *	indptr_diag,
		int *	cols_diag,
		double *	vals_diag,
		double *	b,
		int	nrow
	)

Function that solves system Ax=b using umfpack, provided A is in CSR format.

Author: Mark Loveland

Bug:: none

Warning: none

Copyright: AdH

Parameters

[in,out]	x	(double*) - solution array to system Ax=b
[in]	indptr_diag	(int*) - array of integers with first/last indeces of each row in CSR matrix
[in]	cols_diag	(int*) - array of integers that are local (to process) column numbers
[in]	vals_diag	(double*) - the values of the sparse matrix
[in]	b	(double*) - rhs of system Ax=b
[in]	nrow	(int) - number of equations in system /returns (integer) status of umfpack routine

◆ umfpack_clear()

void umfpack_clear ( void )

Short helper function that clears umfpack structures.

Author: Mark Loveland

Bug:: none

Warning: none

Copyright: AdH

Note: Clears structure that factors matrix, should this be done after each solve or only after refinement?

Functions

Detailed Description

Function Documentation

◆ free_bcgstab()

◆ prep_umfpack()

◆ solve_linear_sys_bcgstab()

◆ solve_umfpack()

◆ umfpack_clear()