On the robustness of the dampedV-cycle of the wavelet frequency decomposition multigrid method

Abstract

The dampedV-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 the convergence speed under sufficient damping is not affected by the presence of anisotropy but still depends on the number of levels. 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.