Preconditioned schemes for nonsymmetric saddle-point problems

Ahmed Sameh, Abdelkader Baggag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 from the numerical solution of the mixed finite element discretization of particulate flows - flow of solid particles in incompressible fluids. 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 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-particles system, and its "scalability".

Original languageEnglish
Title of host publicationECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering
Publication statusPublished - 2004
Externally publishedYes
EventEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 - Jyvaskyla
Duration: 24 Jul 200428 Jul 2004

Other

OtherEuropean Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004
CityJyvaskyla
Period24/7/0428/7/04

Fingerprint

Saddle Point Problems
Iteration
Flow of solids
Fluids
Preconditioner
Linear systems
Scalability
Indefinite Systems
Preconditioning Techniques
Krylov Subspace Methods
Mixed Finite Elements
Particle System
Finite Element Discretization
Incompressible Fluid
Convergence Properties
Experiments
Linear Systems
Numerical Experiment
Numerical Solution
Robustness

Keywords

  • Indefinite systems
  • Inner-outer scheme
  • Krylov subspace methods
  • Preconditioners
  • Richardson iteration
  • Saddle-point problem

ASJC Scopus subject areas

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Sameh, A., & Baggag, A. (2004). Preconditioned schemes for nonsymmetric saddle-point problems. In ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering

Preconditioned schemes for nonsymmetric saddle-point problems. / Sameh, Ahmed; Baggag, Abdelkader.

ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering. 2004.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sameh, A & Baggag, A 2004, Preconditioned schemes for nonsymmetric saddle-point problems. in ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004, Jyvaskyla, 24/7/04.
Sameh A, Baggag A. Preconditioned schemes for nonsymmetric saddle-point problems. In ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering. 2004
Sameh, Ahmed ; Baggag, Abdelkader. / Preconditioned schemes for nonsymmetric saddle-point problems. ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering. 2004.
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