Quasi-Optimized Overlapping Schwarz Waveform Relaxation Algorithm for PDEs with Time-Delay (Communications in Computational Physics, 2013)
Schwarz waveform relaxation (SWR) algorithm has been investigated deeplyand widely for regular time dependent problems. But for time delay problems, complete analysis of the algorithm is rare. In this paper, by using the reaction diffusionequations with a constant discrete delay as the underlying model problem, we investigate the convergence behavior of the overlapping SWR algorithm with Robin transmission condition. The key point of using this transmission condition is to determinea free parameter as well as possible and it is shown that the best choice of the parameter is determined by the solution of a min-max problem, which is more complex thanthe one arising for regular problems without delay. We propose new notion to solvethe min-max problem and obtain a quasi-optimized choice of the parameter, which isshown efficient to accelerate the convergence of the SWR algorithm. Numerical resultsare provided to validate the theoretical conclusions.