language: en

On the Robustness of the Damped V -cycle of the Wavelet Frequency Decomposition Multigrid Method

Andreas Rieder 1,2 Xiaodong Zhou 1
December 15, 1993

Abstract The V -cycle of the wavelet variation of the "Frequency decomposition multigrid method" of Hackbusch [Numer. Math., 56, pp. 229-245, 1989] is considered. It is shown that its convergence speed is not affected by the presence of anisotropy provided that the corresponding coarse grid correction is damped sufficiently strong. Our analysis is based on properties of wavelet packets which are supplied and proved. Numerical approximations to the speed of convergence illustrate the theoretical results.

Key words: wavelets, wavelet packets, robust multilevel methods, V -cycle Subject classification: AMS(MOS) 65F10, 65N30

[1 supported partially by AFOSR under grant number 90-0334 which was funded by DARPA partially supported by a Feodor Lynen-Fellowship of the Alexander von Humboldt Foundation]