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Diagonal threshold techniques in robust multi‐level ILU preconditioners for general sparse linear systems
Author(s) -
Saad Yousef,
Zhang Jun
Publication year - 1999
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199906)6:4<257::aid-nla157>3.0.co;2-#
Subject(s) - mathematics , diagonal , preconditioner , linear system , algorithm , mathematical analysis , geometry
This paper introduces techniques based on diagonal threshold tolerance when developing multi‐elimination and multi‐level incomplete LU (ILUM) factorization preconditioners for solving general sparse linear systems. Existing heuristics solely based on the adjacency graph of the matrices have been used to find independent sets and are not robust for matrices arising from certain applications in which the matrices may have small or zero diagonals. New heuristic strategies based on the adjacency graph and the diagonal values of the matrices for finding independent sets are introduced. Analytical bounds for the factorization and preconditioned errors are obtained for the case of a two‐level analysis. These bounds provide useful information in designing robust ILUM preconditioners. Extensive numerical experiments are conducted in order to compare robustness and efficiency of various heuristic strategies. Copyright © 1999 John Wiley & Sons, Ltd.