article

Constraint Schur complement preconditioners for nonsymmetric saddle point problems

Author:

Zhi-Hao CaoAuthors Info & Claims

Applied Numerical Mathematics, Volume 59, Issue 1

Pages 151 - 169

https://doi.org/10.1016/j.apnum.2008.01.002

Published: 01 January 2009 Publication History

Abstract

We consider constraint preconditioners for block two-by-two generalized saddle point problems, this is the general nonsymmetric, nonsingular case where the (1,2) block need not equal the transposed (2,1) block and the (2,2) block may not be zero. The constraint preconditioners are derived from splittings of the (1,1) block of the generalized saddle point matrix. We show that fast convergence of the preconditioned iterative methods depends mainly on the quality of the splittings and on the effectively solving for the Schur complement systems which arise from the implementation of the constraint preconditioners. Results concerning the eigensolution distribution of the preconditioned matrix and its minimal polynomial are given. To demonstrate the effectiveness of the constraint Schur complement preconditioners we show convergence results and spectra for two model Navier-Stokes problems.

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Cited By

Peng XLi W(2019)An alternating preconditioner for saddle point problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2010.05.003234:12(3411-3423)Online publication date: 3-Jan-2019
https://dl.acm.org/doi/10.1016/j.cam.2010.05.003
Cao Z(2019)Block triangular Schur complement preconditioners for saddle point problems and application to the Oseen equationsApplied Numerical Mathematics10.1016/j.apnum.2009.11.00460:3(193-207)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.apnum.2009.11.004
Yan HHuang Y(2019)Splitting-based block preconditioning methods for block two-by-two matrices of real square blocksApplied Mathematics and Computation10.1016/j.amc.2014.06.040243(825-837)Online publication date: 25-Nov-2019
https://dl.acm.org/doi/10.1016/j.amc.2014.06.040
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Constraint Schur complement preconditioners for nonsymmetric saddle point problems

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Published In

cover image Applied Numerical Mathematics

Applied Numerical Mathematics Volume 59, Issue 1

January, 2009

234 pages

ISSN:0168-9274

Issue’s Table of Contents

Copyright © IMACS © 2008.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 January 2009

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Cited By

Peng XLi W(2019)An alternating preconditioner for saddle point problemsJournal of Computational and Applied Mathematics10.1016/j.cam.2010.05.003234:12(3411-3423)Online publication date: 3-Jan-2019
https://dl.acm.org/doi/10.1016/j.cam.2010.05.003
Cao Z(2019)Block triangular Schur complement preconditioners for saddle point problems and application to the Oseen equationsApplied Numerical Mathematics10.1016/j.apnum.2009.11.00460:3(193-207)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.apnum.2009.11.004
Yan HHuang Y(2019)Splitting-based block preconditioning methods for block two-by-two matrices of real square blocksApplied Mathematics and Computation10.1016/j.amc.2014.06.040243(825-837)Online publication date: 25-Nov-2019
https://dl.acm.org/doi/10.1016/j.amc.2014.06.040
Wang CHuang TWen C(2019)A new preconditioner for indefinite and asymmetric matricesApplied Mathematics and Computation10.1016/j.amc.2013.03.016219:23(11036-11043)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.amc.2013.03.016
Jiang MCao YYao L(2019)On parameterized block triangular preconditioners for generalized saddle point problemsApplied Mathematics and Computation10.1016/j.amc.2009.12.026216:6(1777-1789)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.amc.2009.12.026
Tang JXie YMa C(2015)A modified product preconditioner for indefinite and asymmetric generalized saddle-point matricesApplied Mathematics and Computation10.1016/j.amc.2015.06.032268:C(303-310)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1016/j.amc.2015.06.032
Wu SLi C(2014)Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problemsJournal of Computational and Applied Mathematics10.5555/2823539.2823685260:C(349-355)Online publication date: 1-Apr-2014
https://dl.acm.org/doi/10.5555/2823539.2823685
Wu SLi C(2013)A note on parameterized block triangular preconditioners for generalized saddle point problemsApplied Mathematics and Computation10.1016/j.amc.2013.01.040219:14(7907-7916)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.01.040
Wu SLi C(2013)Indefinite block triangular preconditioner for symmetric saddle point problemsCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-012-0054-450:1(1-15)Online publication date: 1-Mar-2013
https://dl.acm.org/doi/10.1007/s10092-012-0054-4

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