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Approximate Inverse Preconditioners with Adaptive Dropping
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SYSNO ASEP 0438752 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Approximate Inverse Preconditioners with Adaptive Dropping Author(s) Kopal, J. (CZ)
Rozložník, Miroslav (UIVT-O) SAI, RID, ORCID
Tůma, Miroslav (UIVT-O) SAI, RID, ORCIDSource Title Advances in Engineering Software. - : Elsevier - ISSN 0965-9978
Roč. 84, June (2015), s. 13-20Number of pages 8 s. Language eng - English Country NL - Netherlands Keywords approximate inverse ; Gram-Schmidt orthogonalization ; incomplete decomposition ; preconditioned conjugate gradient method ; algebraic preconditioning ; pivoting Subject RIV BA - General Mathematics R&D Projects GAP108/11/0853 GA ČR - Czech Science Foundation (CSF) GA13-06684S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000353008100003 EID SCOPUS 84925428056 DOI https://doi.org/10.1016/j.advengsoft.2015.01.006 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2015
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