A Class of Nonsymmetric Preconditioners for Saddle Point Problems

Mikhail A. Bochev; G.H. Golub

doi:10.1137/040618680

A Class of Nonsymmetric Preconditioners for Saddle Point Problems

Mikhail A. Bochev, G.H. Golub

Research output: Contribution to journal › Article › Academic › peer-review

28 Citations (Scopus)

14 Downloads (Pure)

Abstract

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric.

Original language	Undefined
Article number	10.1137/040618680
Pages (from-to)	1125-1149
Number of pages	25
Journal	SIAM journal on matrix analysis and applications
Volume	27
Issue number	Technical/4
DOIs	https://doi.org/10.1137/040618680
Publication status	Published - 2006

Keywords

MSC-65F22
MSC-65F35
MSC-65K10
MSC-65N22
Navier Stokes equations
SSOR
nonsymmetric indefinite linear systems
inner-outer iterations
iterative methods
constraint preconditioners
skew-symmetric preconditioners
preconditioning methods
saddle point problems
EWI-8959
MSC-65F10
METIS-237883
IR-66838

Access to Document

10.1137/040618680

1786
open
Final published version, 488 KB

Cite this

Bochev, M. A., & Golub, G. H. (2006). A Class of Nonsymmetric Preconditioners for Saddle Point Problems. SIAM journal on matrix analysis and applications, 27(Technical/4), 1125-1149. [10.1137/040618680]. https://doi.org/10.1137/040618680

@article{3646a4315bf447e8a2851c042c41fbde,

title = "A Class of Nonsymmetric Preconditioners for Saddle Point Problems",

abstract = "For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric.",

keywords = "MSC-65F22, MSC-65F35, MSC-65K10, MSC-65N22, Navier Stokes equations, SSOR, nonsymmetric indefinite linear systems, inner-outer iterations, iterative methods, constraint preconditioners, skew-symmetric preconditioners, preconditioning methods, saddle point problems, EWI-8959, MSC-65F10, METIS-237883, IR-66838",

author = "Bochev, {Mikhail A.} and G.H. Golub",

note = "Please different possible spellings of the first author's name: {"}Botchev{"} or {"}Bochev{"}",

year = "2006",

doi = "10.1137/040618680",

language = "Undefined",

volume = "27",

pages = "1125--1149",

journal = "SIAM journal on matrix analysis and applications",

issn = "0895-4798",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "Technical/4",

}

TY - JOUR

T1 - A Class of Nonsymmetric Preconditioners for Saddle Point Problems

AU - Bochev, Mikhail A.

AU - Golub, G.H.

N1 - Please different possible spellings of the first author's name: "Botchev" or "Bochev"

PY - 2006

Y1 - 2006

N2 - For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric.

AB - For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the upper-left block is far from symmetric.

KW - MSC-65F22

KW - MSC-65F35

KW - MSC-65K10

KW - MSC-65N22

KW - Navier Stokes equations

KW - SSOR

KW - nonsymmetric indefinite linear systems

KW - inner-outer iterations

KW - iterative methods

KW - constraint preconditioners

KW - skew-symmetric preconditioners

KW - preconditioning methods

KW - saddle point problems

KW - EWI-8959

KW - MSC-65F10

KW - METIS-237883

KW - IR-66838

U2 - 10.1137/040618680

DO - 10.1137/040618680

M3 - Article

VL - 27

SP - 1125

EP - 1149

JO - SIAM journal on matrix analysis and applications

JF - SIAM journal on matrix analysis and applications

SN - 0895-4798

IS - Technical/4

M1 - 10.1137/040618680

ER -