Optimal Control of the Convergence Rate of Schwarz Waveform Relaxation Algorithms

Abstract

In this study we present a non-overlapping Schwarz waveform relaxation method applied to the one dimensional unsteady diffusion equation. We derive efficient interface conditions using an optimal control approach once the problem is discretized. Those conditions are compared to the usual optimized conditions derived at the PDE level by solving a min-max problem. The performance of the proposed methodology is illustrated by numerical experiments. © Springer-Verlag Berlin Heidelberg 2013.