Title: Acceleration of a Schwarz waveform relaxation method for parabolic problems

Authors: M. Garbey

Addresses: Department of Computer Science, University of Houston, Houston, TX 77204, USA

Abstract: In this paper we generalise the Aitken-like acceleration method of the additive Schwarz algorithm for elliptic problems to the additive Schwarz waveform relaxation (ASWR) for parabolic problems. The domain decomposition is in space and time. We show that our technique: 1) is a direct solver that requires at most four solves per subdomain in the case of a one space dimension linear parabolic problem with time independent coefficients; 2) can be applied easily to multidimensional problems, provided that the operator is separable in space; 3) is an efficient iterative procedure for parabolic problems that are weak non-linear perturbations of linear operators with time independent coefficients; 4) provides a rigorous framework to optimise the parallel implementation on a slow network of computers.

Keywords: PDE; partial differential equations; parabolic problems; domain decomposition; parallel algorithms; acceleration technique; elliptic problems; additive Schwarz waveform relaxation; optimisation; parallel implementation; computer networks.

DOI: 10.1504/IJMMNO.2010.031748

International Journal of Mathematical Modelling and Numerical Optimisation, 2010 Vol.1 No.3, pp.185 - 212

Published online: 22 Feb 2010 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article