Multigrid Waveform Relaxation for Anisotropic Partial Differential Equations

Multigrid waveform relaxation provides fast iterative methods for the solution of time-dependent partial differential equations. In this paper we consider anisotropic problems and extend multigrid methods developed for the stationary elliptic case to waveform relaxation methods for the time-dependent parabolic case. We study line-relaxation, semicoarsening and multiple semicoarsening multilevel methods. A two-grid Fourier–Laplace analysis is used to estimate the convergence of these methods for the rotated anisotropic diffusion equation. We treat both continuous time and discrete time algorithms. The results of the analysis are confirmed by numerical experiments.