Updating Preconditioners for Sequences from Compressible Flow

This contribution illustrates the application of preconditioner updates as in [2] to model problems from compressible flow, that represent a broad range of typical sequences of nonsymmetric linear systems. There, a typical technique is freezing with periodic recomputation of ILU decompositions [3]. This can be improved by updating between refactorizations. In particular, the extension to block matrices is discussed, as well as different strategies for the adaptive choice of the update and the effect of renumbering on the performance of the new method, as in [1]. This is illustrated by theoretical results. Acknowledgement: The work of the first two authors is supported by theGerman Science Foundation as part of the Sonderforschungsbereich SFB/TRTRR 30. The work of the second two authors is supported by the Pro-gram Information Society under project 1ET400300415 and by project numberKJB100300703 of the Grant Agency of the Academy of Sciences of the CzechRepublic. References[1] P. Birken, A. Meister, M. Tůma and J. Tebbens, Preconditioner updates appliedto CFD model problems, submitted to Applied numerical mathematics in 2007.[2] J. Duintjer Tebbens and M. Tůma, Efficient preconditioning of sequences of non-symmetric linear systems, to appear in SIAM J. Sci. Comput. in 2007.[3] A. Meister and J. Vömel, Efficient preconditioning of linear systems arising fromthe discretization of hyperbolic conservation laws, Adv. Comput. Math., 14 (2001),pp.49–73.