An adaptive multilevel factorized sparse approximate inverse preconditioning. (November 2017)

• Record Type: Journal Article
• Authors: Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav
• Is Part Of: Advances in engineering software. Volume 113(2017)
• Page Start: 19
• Page End: 24
• Publication Date: 2017-11
• Subjects: Approximate inverse -- Gram–Schmidt orthogonalization -- Incomplete factorization -- Multilevel methods -- Preconditioned conjugate gradient method; 65F08 -- 65F25 -- 65F50; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2016.10.005
• Languages: English
• ISSNs: 0965-9978

Abstract

Highlights: New multilevel schemes for approximate inverse preconditioning were proposed. The proposed algorithms are more memory efficient than one-level methods. A new way to construct the Schur complement improves the factorization. Computational efficiency was demonstrated on several test problems. 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 U Z = I between the direct factor U and the inverse factor Z that satisfy A = U T U and A − 1 = Z Z T . The proposed strategy significantly extends and refines the approach from [1], see also [2], 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.