Summary
Robustness is an important requirement for multigrid methods. In Standard multigrid methods, the smoothing process is usually the most crucial component. In particular, the robustness of a multigrid method and that of the underlying smoother are closely related. ILU is generally considered to provide a particularly robust smoothing process. Although often more robust than Standard relaxation methods, ILU is not really robust in a strict sense. This can be seen by applying a corresponding multigrid method to certain “limit cases” of typical model problems.
Two possibilities are presented which substantially improve the robustness of multi-grid methods with ILU-smoothing. One is based on a modification of the ILU-decompo-sition, while the other uses alternating ILU-smoothing. A smoothing process which turns out to be robust for all kinds of anisotropic model problems is obtained by combining both techniques: the alternating modified ILU-smoothing.
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Oertel, KD., Stüben, K. (1989). Multigrid with ILU-smoothing: systematic tests and improvements. In: Hackbusch, W. (eds) Robust Multi-Grid Methods. Notes on Numerical Fluid Mechanics, vol 23. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-86200-6_17
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DOI: https://doi.org/10.1007/978-3-322-86200-6_17
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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