A Class of Nonsymmetric Preconditioners for Saddle Point Problems

Mikhail A. Bochev, G.H. Golub

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    28 Citations (Scopus)
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    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 languageUndefined
    Article number10.1137/040618680
    Pages (from-to)1125-1149
    Number of pages25
    JournalSIAM journal on matrix analysis and applications
    Volume27
    Issue numberTechnical/4
    DOIs
    Publication statusPublished - 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

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