Diagonal threshold techniques in robust multi-level ILU preconditioners for general sparse linear systems

This paper introduces techniques based on diagonal threshold tolerance when developing multi-elimination and multi-level incomplete LU (ILUM) factoriz ation preconditioners for solving general sparse linear systems. Existing h euristics solely based on the adjacency graph of the matrices have been use d to find independent sets and are not robust for matrices arising from cer tain applications in which the matrices may have small or zero diagonals. N ew heuristic strategies based on the adjacency graph and the diagonal value s of the matrices for finding independent sets are introduced. Analytical b ounds for the factorization and preconditioned errors are obtained for the case of a two-level analysis. These bounds provide useful information in de signing robust ILUM preconditioners. Extensive numerical experiments are co nducted in order to compare robustness and efficiency of various heuristic strategies. Copyright (C) 1999 John Wiley & Sons, Ltd.