Wavelet approach to robust multilevel solvers for anisotropic elliptic problems

Abstract

A wavelet variation of the “Frequency decomposition multigrid method, Part I” (FDMGM) of Hackbusch 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. © 1994 Academic Press, Inc.