Abstract
A robust and efficient MG (Multigrid) method should incorporate both suitable transitions between fine and coarse grids and a good smoothing method.
In a recent paper, we presented an MG method based on incomplete Gauss elimination / continuity interpolation to cope with strong inhomogeneities and general domains. Further acceleration has been achieved by using the MG method as preconditioning for CG, the result being called MGCG. In addition, a robust smoothing method is required for problems with strong anisotropies.
In this paper, several Gauss-Seidel and incomplete LU relaxation schemes are more extensively compared with respect to their smoothing factors and efficiencies. Besides, the practical behaviour of some of these schemes is compared for three iterative methods (MG, MGCG and ICCG) and two difficult test problems (according to Stone and Kershaw).
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Kettler, R. (1982). Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods. Lecture Notes in Mathematics, vol 960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069941
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DOI: https://doi.org/10.1007/BFb0069941
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