Preconditioners for Generalized Saddle-Point Problems

Authors:
Chris Siefert;Eric de Sturler
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2006

Citing 0
Cited 6

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Block triangular Schur complement preconditioners for saddle point problems and application to the Oseen equations

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An alternating preconditioner for saddle point problems

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Schur Complement Preconditioners for Surface Integral-Equation Formulations of Dielectric Problems Solved with the Multilevel Fast Multipole Algorithm

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On generalized parameterized inexact Uzawa method for a block two-by-two linear system

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Abstract

\noindent We propose and examine block-diagonal preconditioners and variants of indefinite preconditioners for block two-by-two generalized saddle-point problems. That is, we consider the nonsymmetric, nonsingular case where the (2,2) block is small in norm, and we are particularly concerned with the case where the (1,2) block is different from the transposed (2,1) block. We provide theoretical and experimental analyses of the convergence and eigenvalue distributions of the preconditioned matrices. We also extend the results of [de Sturler and Liesen, SIAM J. Sci. Comput., 26 (2005), pp. 1598-1619] to matrices with nonzero (2,2) block and to the use of approximate Schur complements. To demonstrate the effectiveness of these preconditioners we show convergence results, spectra, and eigenvalue bounds for two model Navier--Stokes problems.