A preconditioned scheme for nonsymmetric saddle-point problems

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Abstract

In this paper, we present an effective preconditioning technique for solving nonsymmetric saddle-point problems. In particular, we consider those saddle-point problems that arise in the numerical simulation of particulate flows-flow of solid particles in incompressible fluids, using mixed finite element discretization of the Navier-Stokes equations. These indefinite linear systems are solved using a preconditioned Krylov subspace method with an indefinite preconditioner. This creates an inner-outer iteration, in which the inner iteration is handled via a preconditioned Richardson scheme. We provide an analysis of our approach that relates the convergence properties of the inner to the outer iterations. Also optimal approaches are proposed for the implicit construction of the Richardson's iteration preconditioner. The analysis is validated by numerical experiments that demonstrate the robustness of our scheme, its lack of sensitivity to changes in the fluid-particle system, and its scalability.

Original languageEnglish
Title of host publicationHigh-Performance Scientific Computing: Algorithms and Applications
PublisherSpringer-Verlag London Ltd
Pages219-250
Number of pages32
Volume9781447124375
ISBN (Electronic)9781447124375
ISBN (Print)1447124367, 9781447124368
DOIs
Publication statusPublished - 1 Oct 2012
Externally publishedYes

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ASJC Scopus subject areas

  • Computer Science(all)

Cite this

Baggag, A. (2012). A preconditioned scheme for nonsymmetric saddle-point problems. In High-Performance Scientific Computing: Algorithms and Applications (Vol. 9781447124375, pp. 219-250). Springer-Verlag London Ltd. https://doi.org/10.1007/978-1-4471-2437-5_11