A Two Step Combined Stable Preconditioning Strategy for
Incomplete LU Factorization of CFD Matrices

Li Wang and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA


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.

Key words: Preconditioning, sparse matrix, incomplete LU factorization, shifted incomplete factorization

Mathematics Subject Classification: 65F10, 65F50, 65N55, 65Y05.

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This paper (its revised version) has been published in Applied Mathematics and Computation, Vol. 144, No. 1, pp. 75-87 (2003).

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.