Laboratory for High Performance Scientific Computing and Computer Simulation

Department of Computer Science

University of Kentucky

Lexington, KY 40506-0046

A two step combined stable preconditioning strategy is proposed to construct stable and accurate incomplete LU (ILU) factorization of indefinite sparse matrices arising from CFD applications. This preconditioning procedure is divided into two steps, and each step is a factorization of a shifted matrix with a parameter factor. Studies and experiments are conducted to show how this combined factorization approach enhances the stability of ILU factorization. The results indicate that this two step combined preconditioner can be computed with high accuracy by allowing liberal amounts of fill-in. Numeral experiments are used to compare this strategy with the standard ILU preconditioning techniques, which shows the new strategy is more robust on a set of difficult CFD test problems.

**Acknowledgment:** This research work was supported in part by the U.S.
National Science Foundation under grants CCR-9902022, CCR-9988165,
CCR-0092532, in part by the U.S. Department of Energy under grant
DE-FG02-02ER45961, in part by the Japanese Research
Organization for Information Science and Technology, and in
part by the University of Kentucky Research Committee.