Block preconditioning for saddle point systems with indefinite (1, 1) block

Authors:
Michele Benzi;Jia Liu
Affiliations:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA;Department of Mathematics and Statistics, University of West Florida, Pensacola, FL, USA
Venue:
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Year:
2007

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Abstract

We investigate the solution of linear systems of saddle point type with an indefinite (1, 1) block by preconditioned iterative methods. Our main focus is on block matrices arising from eigenvalue problems in incompressible fluid dynamics. A block triangular preconditioner based on an augmented Lagrangian formulation is shown to result in fast convergence of the GMRES iteration for a wide range of problem and algorithm parameters. Some theoretical estimates for the eigenvalues of the preconditioned matrices are given. Inexact variants of the preconditioner are also considered.