Waveform Relaxation with Overlapping Splittings

Abstract

In this paper, an extension of the waveform relaxation algorithm for solving large systems of ordinary differential equations is presented. The waveform relaxation algorithm is well suited for parallel computation because it decomposes the solution space into several disjoint subspaces. Allowing the subspaces to overlap, i.e., dropping the assumption of disjointedness, an extension of this algorithm is obtained. This new algorithm, the so-called multisplitting algorithm, is also well suited for parallel computation. As numerical examples demonstrate, this overlapping of the subsystems heavily reduces the computation time.