Approximate inverse preconditioners with adaptive dropping. (June 2015)

• Record Type: Journal Article
• Authors: Kopal, Jiří; Rozložník, Miroslav; Tůma, Miroslav
• Is Part Of: Advances in engineering software. Volume 84(2015)
• Page Start: 13
• Page End: 20
• Publication Date: 2015-06
• Subjects: Approximate inverse -- Gram–Schmidt orthogonalization -- Incomplete decomposition -- Preconditioned conjugate gradient method -- Algebraic preconditioning -- Pivoting; Computer-aided engineering -- Periodicals; Engineering -- Computer programs -- Periodicals; Engineering -- Software -- Periodicals; Periodicals; 620.0028553
• DOI: 10.1016/j.advengsoft.2015.01.006
• Languages: English
• ISSNs: 0965-9978

Abstract

Abstract: It is well-known that analysis of incomplete Cholesky and LU decompositions with a general dropping is very difficult and of limited applicability, see, for example, the results on modified decompositions (Dupont et al., 1968; Gustafsson, 1978; Bern et al., 2006) and later results based on similar concepts. This is true not only for the dropping based on magnitude of entries but it also applies to algorithms that use a prescribed sparsity pattern. This paper deals with dropping strategies for a class of AINV-type incomplete decompositions (Benzi et al., 1996) that are based on the generalized Gram–Schmidt process. Its behavior in finite precision arithmetic has been discussed in Rozložník et al. (2012). This analysis enables better understanding of the incomplete process, and the main goal of the paper is to propose a new adaptive dropping strategy and to illustrate its efficiency for problems in structural mechanics. In addition, we add a brief comparison with another approximate inverse preconditioning strategy that is based on different principles and used in engineering applications.