Summary
This paper consists of two parts. In the first part, a partially successful attempt is made to extend multigrid theory to the case of a discontinuous coefficient, and an open problem is formulated. In the second part a non-recursive formulation of the fundamental multigrid algorithm is presented that contains only one goto Statement, and is better structured than the usual formulation.
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References
WESSELING, P.: “Finite volume multigrid”. In: S.F. MacCormick (ed.), Proceedings, Third Copper Mountain Conference on Multigrid Methods, April 1987. To appear, 1988.
WESSELING, P.: “Cell-centered multigrid for interface Problems”. To appear in J. Comp. Phys.
ALCOUFFE, R.E., BRANDT, A., DENDY Jr., J.E., PAINTER, J.W.: “The multigrid method for the diffusion equation with strongly discontinuous coefficients”, SIAM J. Sci. Stat. Comp., 2 (1981) pp. 430–454.
DENDY Jr., J.E.: “Black box multigrid”, J. Comp. Phys., 48 (1982) pp. 366–386.
DENDY Jr., J.E.: “Black box multigrid for nonsymmetric Problems”, Appl. Math. Comp., 13 (1983) pp. 261–283.
KETTLER, R., MEIJERINK, J.A.: “A multigrid method and a combined multigrid-conjugate gradient method for elliptic Problems with strongly discontinuous coefficients in general domains”, Shell Publ. 604, 1981, KSEPL, Rijswijk, The Netherlands.
KETTLER, R.: “Analysis and comparison of relaxation schemes in robust multigrid and preconditioned conjugate gradient methods”, in [9], pp. 502–534.
KETTLER, R.: “Linear multigrid Solution methods in numerical reservoir Simulation”, Ph.D. Thesis, University of Technology, Dept. of Math, and Inf., P.O. Box 356, 2600 AJ Delft, The Netherlands.
HACKBUSCH, W., TROTTENBERG, U. (eds.): “Multigrid methods”, Proc., Köln-Porz, Lecture Notes in Mathematics 960, Springer-Verlag, Berlin, 1982.
HACKBUSCH, W.: “Multi-grid methods and applications”, Springer-Verlag, Berlin, 1985.
BRANDT, A.: “Multi-level adaptive Solutions to boundary-value Problems”, Math. Comp., 31 (1977) pp. 333–390.
STÜBEN, K., TROTTENBERG, U.: “Multigrid methods: fundamental algorithms, model problem analysis and applications”, in [9], pp. 1–176.
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Wesseling, P. (1989). Two Remarks on Multigrid Methods. 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_19
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DOI: https://doi.org/10.1007/978-3-322-86200-6_19
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08097-6
Online ISBN: 978-3-322-86200-6
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