Overlapping Schwarz waveform relaxation method for the solution of the convection-diffusion equation

Abstract

In this article we study the convergence of the overlapping Schwarz wave form relaxation method for solving the convection-diffusion equation over multi-overlapped subdomains. It is shown that the method converges linearly and superlinearly over long and short time intervals, and the convergence depends on the size of the overlap. Numerical results are presented from solving specific types of model problems to demonstrate the convergence and the role of the size of the overlap.