New Estimates of the Contraction Number of V-cycle Multi-Grid with Applications to Anisotropic Equations
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.
Unable to display preview. Download preview PDF.
- [MMB87]J. Mandel, S. McCormick, and R. Bank. Variational multigrid theory. In S. McCormick, editor, Multigrid Methods ,chapter 5. SIAM, Philadelphia, 1987.Google Scholar
- [ST82]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.Google Scholar
- [Ste91]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.Google Scholar
- [Ste92]R.P. Stevenson. Sharp estimates of the multi-grid contraction number including the V-cycle. In preparation, 1992.Google Scholar