Approximate inverse preconditioners with adaptive dropping

作者：Kopal Jiri^*; Rozloznik Miroslav; Tuma Miroslav

来源：Advances in Engineering Software, 2015, 84: 13-20.

DOI：10.1016/j.advengsoft.2015.01.006

• Approximate inverse
• Gram-Schmidt orthogonalization
• Incomplete decomposition
• Preconditioned conjugate gradient method
• Algebraic preconditioning
• Pivoting

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 Rozloinik 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.

• 出版日期2015-6