On SOR waveform relaxation methods

Waveform relaxation is a numerical method for solving large-scale systems of ordinary differential equations on parallel computers. It differs from standard iterative methods in that it computes the solution on many time levels or along a continuous time interval simultaneously. This paper deals with the acceleration of the standard waveform relaxation method by successive overrelaxation (SOR) techniques. In particular, different SOR acceleration schemes, based on multiplication with a scaler parameter or convolution with a time-dependent function, are described and theoretically analyzed. The theory is applied to a one-dimensional and two-dimensional model problem and checked against results obtained by numerical experiments.