A general approach to analyse preconditioners for two‐by‐two block matrices. Issue 5 (14th December 2011)

• Record Type: Journal Article
• Authors: Axelsson, Owe; Neytcheva, Maya
• Is Part Of: Numerical linear algebra with applications. Volume 20:Issue 5(2013:Sep.)
• Page Start: 723
• Page End: 742
• Publication Date: 2011-12-14
• Subjects: saddle point systems -- nonsymmetric matrices -- block preconditioning; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.830
• Languages: English
• ISSNs: 1070-5325

Abstract

SUMMARY: Two‐by‐two block matrices arise in various applications, such as in domain decomposition methods or when solving boundary value problems discretised by finite elements from the separation of the node set of the mesh into 'fine' and 'coarse' nodes. Matrices with such a structure, in saddle point form arise also in mixed variable finite element methods and in constrained optimisation problems. A general algebraic approach to construct, analyse and control the accuracy of preconditioners for matrices in two‐by‐two block form is presented. This includes both symmetric and nonsymmetric matrices, as well as indefinite matrices. The action of the preconditioners can involve element‐by‐element approximations and/or geometric or algebraic multigrid/multilevel methods. Copyright © 2011 John Wiley & Sons, Ltd.