A two step combined preconditioning strategy is proposed to construct stable and accurate incomplete LU factorization of indefinite matrices arising from CFD applications. This preconditioning procedure is divided into two steps, each step is a factorization of a shifted matrix. Numeral experiments show that a preconditioner can be computed with high accuracy and low fill-in, and that the new strategy is robust on some difficult CFD test problems.
Mathematics Subject Classification: 65F10, 65F50, 65N55, 65Y05.
Technical Report 334-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002. This research was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, and 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 & Technology, and in part by the University of Kentucky Research Committee.