Adaptive techniques for improvin g the performance of incomplete factorization p reconditioning

Abstract

Three techniques for improving the robustness and performance of incomplete factorization preconditioners for sparse systems with symmetric positive definite or mildly indefinite coefficient matrices are introduced. The primary contribution is two new block algorithms for incomplete factorization that result in an improvement in the per formance of both the preconditioner generation and the iterative solution phases. One of the algorit hms applies to matrices that have a natural block structure in their original form, and the other appl ies to matrices without natural dense blocks. Additionally, two relatively simple but highly effective heuristic strategies are introduced. These include selecting the solver based on the definiteness properties of the preconditioner and automatic selection and tuning of incomplete factorization parameters. All three techniques have adaptive components; i.e., the preconditioner-solver combination chooses parameters or algorithmic components based on the properties of the coefficient matrix and its incomplete factors. Two of the three techniques are applicable to incomplete LU factorization for unsymmetric systems as well. © 2010 Society for Industrial and Applied Mathematics.