krylov.c File Reference

Source file of Krylov subspace methods. More...

#include "krylov.h"
#include "precon.h"
#include <math.h>
#include <omp.h>

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Functions
ucfd_status_t	serial_gmres (sparse_matrix_t op, ucfd_precon_type_t precon_type, int bn, int block, int m, int *iter, double tol, int *row_ptr, int *col_ind, int *diag_ind, double *precon_nnz_data, double *x, double *b, double *H, double *V, double *g, double *y, double *w, double *r)
	Serial GMRES routine. More...
ucfd_status_t	step_gmres (sparse_matrix_t op, ucfd_precon_solve psolve, const struct matrix_descr descr, int bn, int m, int *flag, int *row_ptr, int *col_ind, int *diag_ind, double *precon_nnz_data, double *x, double *b, double *H, double *V, double *g, double *y, double *w, double *r)
	Single GMRES iteration routine. More...
ucfd_status_t	serial_bicgstab (sparse_matrix_t op, ucfd_precon_type_t precon_type, int bn, int *iter, double tol, int *row_ptr, int *col_ind, int *diag_ind, double *precon_nnz_data, double *x, double *b, double *r, double *p, double *v, double *s, double *t)
	Serial BiCGstab routine. More...

Detailed Description

Source file of Krylov subspace methods.

======================================================================================================================

There are two Krylov subspace methods, GMRES and BiCGstab methods.

         (1) GMRES (Generalized Minimal RESidual)  
         GMRES method is introduced by Saad and Schultz, which is the one of the Krylov subspace methods.
         GMRES algorithm consists of sparse matrix-vector multiplication, vector-vector product, L-2 norm,
         and these BLAS functions are implemented by using `Intel MKL` library.
         Restart version is used.  

         (2) BiCGstab (Bi-Conjugate Gradient stabilized)  
         Bi-CGSTAB method is introduced by H.A. van der Vorst, which is one of the Krylov subspace methods.
         It takes for q_k a product of appropriate 1-step Minimal Residual polynomials so that can converge
         rather smoothly than bi-conjugate gradient (Bi-CG) method.
         However, its computation process is slightly more expensive than CGS.

Note

For system matrix A, any sparse matrix storage format (CSR, CSC, BSR) is available. However, Preconditioner arrays must be stored as Block Sparse Row(BSR) format.

Author

• Namhyoung Kim (knhks.nosp@m.e@in.nosp@m.ha.ed.nosp@m.u), Department of Aerospace Engineering, Inha University
• Jin Seok Park (jinse.nosp@m.ok.p.nosp@m.ark@i.nosp@m.nha..nosp@m.ac.kr), Department of Aerospace Engineering, Inha University

Date

Dec 2024

Version

1.0

Copyright

Copyright (c) 2024, Namhyoung Kim and Jin Seok Park, Inha University, All rights reserved.

License

This project is release under the terms of the MIT License (see LICENSE file).

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Definition in file krylov.c.

Function Documentation

serial_bicgstab()

ucfd_status_t serial_bicgstab	(	sparse_matrix_t	op,
		ucfd_precon_type_t	precon_type,
		int	bn,
		int *	iter,
		double	tol,
		int *	row_ptr,
		int *	col_ind,
		int *	diag_ind,
		double *	precon_nnz_data,
		double *	x,
		double *	b,
		double *	r,
		double *	p,
		double *	v,
		double *	s,
		double *	t
	)

Serial BiCGstab routine.

Overall process of BiCGstab routine. Outer iteration ends when solution is converged or reached in maximum iteration number. UCFD_STATUS_CONVERGED is returned when L-2 norm of the residual vector becomes smaller than tol, and UCFD_STATUS_NOT_CONVERGED is returned when maximum iteration finished.

Definition at line 286 of file krylov.c.

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serial_gmres()

ucfd_status_t serial_gmres	(	sparse_matrix_t	op,
		ucfd_precon_type_t	precon_type,
		int	bn,
		int	block,
		int	m,
		int *	iter,
		double	tol,
		int *	row_ptr,
		int *	col_ind,
		int *	diag_ind,
		double *	precon_nnz_data,
		double *	x,
		double *	b,
		double *	H,
		double *	V,
		double *	g,
		double *	y,
		double *	w,
		double *	r
	)

Serial GMRES routine.

Overall process of GMRES routine. Outer iteration ends when solution is converged or reached in maximum iteration number. UCFD_STATUS_CONVERGED is returned when L-2 norm of the residual vector becomes smaller than tol, and UCFD_STATUS_NOT_CONVERGED is returned when maximum iteration finished.

Definition at line 46 of file krylov.c.

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step_gmres()

ucfd_status_t step_gmres	(	sparse_matrix_t	op,
		ucfd_precon_solve	psolve,
		const struct matrix_descr	descr,
		int	bn,
		int	m,
		int *	flag,
		int *	row_ptr,
		int *	col_ind,
		int *	diag_ind,
		double *	precon_nnz_data,
		double *	x,
		double *	b,
		double *	H,
		double *	V,
		double *	g,
		double *	y,
		double *	w,
		double *	r
	)

Single GMRES iteration routine.

Single iteration of GMRES.

Note

Residual array r must be initialized, r := b - A @ x.

Definition at line 185 of file krylov.c.