Abstract
In many astrophysical hydrodynamical and magnetohydrodynamical problems explicit time integration is inefficient due to the disparate time scales, or because we are looking for a steady-state. Implicit schemes can offer a viable alternative, which requires efficient solution of large linear systems. In multi-dimensional flows these linear systems cannot be solved with a direct method, so that iterative methods must be used. Since the physical problems are often advection dominated, the matrix is approximately anti-symmetric and non-diagonally dominant, thus preconditioning is necessary.
We describe a new approach, in which a GMRES type iterative method is combined with an Eisenstat implementation of a relaxed form of a modified Block Incomplete LU-decomposition as preconditioner. Parallelisation aspects of the algorithm are also discussed.
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© 1997 Springer-Verlag Berlin Heidelberg
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van der Ploeg, A., Keppens, R., Tóth, G. (1997). Block incomplete LU-preconditioners for implicit solution of advection dominated problems. In: Hertzberger, B., Sloot, P. (eds) High-Performance Computing and Networking. HPCN-Europe 1997. Lecture Notes in Computer Science, vol 1225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031614
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DOI: https://doi.org/10.1007/BFb0031614
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