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A Wavelet Approach to Robust Multilevel Solvers for Anisotropic Elliptic Problems

✍ Scribed by Andreas Rieder; Jr. Raymond O.; Wells; Xiaodong Zhou

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
784 KB
Volume
1
Category
Article
ISSN
1063-5203

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✦ Synopsis

A wavelet variation of the "Frequency decomposition multigrid method, Part I" (FDMGM) of Hackbusch [Numer. Math. 56 (1989) 229-245] is presented. The perfect reconstruction property and the multiresolution structure of wavelets yield the robustness of the additive as well as of the multiplicative version of a two-level method corresponding to any intermediate level in the FDMGM. Aspects of the robustness of the multilevel scheme are discussed. Numerical experiments confirm the theoretical results. The wavelet version of the FDMGM presented here involves wavelet packets which have been used before this primarily in signal processing. (C) 1994 Academic Press. Inc.

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## History of the problem While it is relatively easy to get estimations of upper bounds for eigerivalues of elliptic differential operators with the well-known methods of J. W. S. RAYLEIGH and W. RITZ, the estimation of lower bounds is much more complicated. Estimations of lower bounds for eigenv