Multilevel Preconditioners Constructed From Inverse-Based ILUs

This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. As a consequence a few strategies are developed whose goal is to achieve this feature. A number of "templates" for enabling implementations of these factorizations are presented. Numerical experiments show that the resulting ILUs offer a good compromise between robustness and efficiency.