On SOR Waveform Relaxation Methods

Creators: Janssen, Jan; Vandewalle, Stefan

Abstract

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 scalar 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.

Additional Information

©1997 Society for Industrial and Applied Mathematics. Reprinted with permission. Received by the editors November 1, 1995; accepted for publication (in revised form) July 18, 1996. This text presents research results of the Belgian Incentive Program "Information Technology" - Computer Science of the Future, initiated by the Belgian State - Prime Minister's Service - Federal Office for Scientific, Technical and Cultural Affairs. The scientific responsibility is assumed by its authors. This work was supported in part by the NSF under Cooperative Agreement CCR-9120008. The authors would like to thank Min Hu, Ken Jackson, Andrew Lumsdaine, Ulla Miekkala, and Mark W. Reichelt for many helpful discussions and an anonymous referee for several suggestions which substantially improved the quality and structure of the paper.

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