Preconditioned Krylov Subspace Methods for Solving
Nonsymmetric Matrices from CFD Applications

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506--0046, USA


We conduct experimental study on the behavior of several preconditioned iterative methods to solve nonsymmetric matrices arising from computational fluid dynamics (CFD) applications. The preconditioned iterative methods consist of Krylov subspace accelerators and a powerful general purpose multi-level block ILU (BILUM) preconditioner. The BILUM preconditioner and an enhanced version of it are modified slightly from their original versions to precondition different Krylov subspace methods. We choose to test three popular transpose-free Krylov subspace methods: BiCGSTAB, GMRES and TFQMR. Numerical experiments using several sets of test matrices arising from various realistic CFD applications are reported.

Key words: Multi-level preconditioner, Krylov subspace methods, nonsymmetric matrices, CFD applications.

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This paper has been published in Computer Methods in Applied Mechanics and Engineering, Vol.189, No. 3, 825-840 (2000). Also Technical Report No. 280-98, Department of Computer Science, University of Kentucky, Lexington, KY, 1998. This research was supported in part by the University of Kentucky Center for Computational Sciences. This paper has been accpted for publication in Computer Methods in Applied Mechanics and Engineering.