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This paper introduces techniques based on diagonal threshold tolerance when developing multi-elimination and multi-level incomplete LU (ILUM) factorization precondi-tioners for solving general sparse linear systems. Existing heuristics solely based on the adjacency graph of the matrices have been used to nd 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 nding 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 eeciency of various heuristic strategies.

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