An adaptive multilevel factorized sparse approximate inverse preconditioning

• ID: 2753, RIV: 10331041
• ISSN: 0965-9978, ISBN: not specified
• source: Advances in Engineering Software
• keywords: preconditioning; multilevel methods; iterative solvers
• authors: Jiří Kopal, Miroslav Rozložník, Miroslav Tůma
• authors from KNM: Tůma Miroslav

Abstract

This paper deals with adaptively preconditioned iterative methods for solving large and sparse systems of linear equations. In particular, the paper discusses preconditioning where adaptive dropping reflects the quality of preserving the relation UZ = I between the direct factor U and the inverse factor Z. The proposed strategy significantly extends and refines the previous approach by the same author team by using a specific multilevel framework. Numerical experiments with two levels demonstrate that the new preconditioning strategy is very promising. Namely, we show a surprising fact that in our approach the Schur complement is better to form in a more sophisticated way than by a standard sparse matrix-matrix multiplication.