Abstract
In this paper we refine the V-cycle multi-grid convergence proofs of Hackbusch and Wittum. We obtain a sharper bound for the contraction number. With this new bound we are able to prove robustness of the V-cycle applied to anisotropic equations when a suitable smoother is used. For a model problem we give some quantitative results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Hackbusch. Multi-Grid Methods and Applications. Springer-Verlag, Berlin, 1985.
W. Hackbusch. Iterative Lösung großer schwachbesetzter Gleichungssysteme. B.G. Teubner, Stuttgart, 1991.
J. Mandel, S. McCormick, and R. Bank. Variational multigrid theory. In S. McCormick, editor, Multigrid Methods ,chapter 5. SIAM, Philadelphia, 1987.
K. Stüben and U. Trottenberg. Multigrid methods: Fundamental algorithms, model problem analysis and applications. In Hackbusch W. and U. Trottenberg, editors, Multigrid Methods ,Proceedings, Köln-Porz 1981, pages 1–176, Berlin, 1982. Lecture Notes in Mathematics 960, Springer-Verlag.
R.P. Stevenson. On the robustness of multi-grid applied to anisotropic equations: Smoothing- and approximation-properties. Preprint 685, University of Utrecht, September 1991. Submitted to Numerische Mathematik.
R.P. Stevenson. Sharp estimates of the multi-grid contraction number including the V-cycle. In preparation, 1992.
G. Witturn. Linear iterations as smoothers in multigrid methods: Theory with applications to incomplete decompositions. IMPACT Comput. Sci. Eng. ,1:180-215, 1989.
G. Wittum. On the robustness of ILU smoothing. SIAM J. Sci. Stat. Comput. ,10 (4): 699–717, July 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Stevenson, R. (1993). New Estimates of the Contraction Number of V-cycle Multi-Grid with Applications to Anisotropic Equations. In: Hackbusch, W., Wittum, G. (eds) Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications. Notes on Numerical Fluid Mechanics (NNFM), vol 29. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85732-3_17
Download citation
DOI: https://doi.org/10.1007/978-3-322-85732-3_17
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07641-2
Online ISBN: 978-3-322-85732-3
eBook Packages: Springer Book Archive