Fourier Mode Analysis of the Multigrid Waveform Relaxation and Time-Parallel Multigrid Methods

The advent of parallel computers has led to the development of new solution algorithms for time-dependent partial differential equations. Two recently developed methods, the multigrid waveform relaxation method and the time-parallel multigrid method, have been designed to solve parabolic partial differential equations on many time-levels simultaneously. This paper compares the convergence properties of these methods, based on the results of an exponential Fourier mode analysis for a model problem