Approximate Inverse Preconditioners with Adaptive Dropping

0438752 - ÚI 2015 RIV NL eng J - Journal Article
Kopal, J. - Rozložník, Miroslav - Tůma, Miroslav
Approximate Inverse Preconditioners with Adaptive Dropping.
Advances in Engineering Software. Roč. 84, June (2015), s. 13-20. ISSN 0965-9978. E-ISSN 1873-5339
R&D Projects: GA ČR(CZ) GAP108/11/0853; GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : approximate inverse * Gram-Schmidt orthogonalization * incomplete decomposition * preconditioned conjugate gradient method * algebraic preconditioning * pivoting
Subject RIV: BA - General Mathematics
Impact factor: 1.673, year: 2015

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.
Permanent Link: http://hdl.handle.net/11104/0242122