Year: 2013
Communications in Computational Physics, Vol. 14 (2013), Iss. 3 : pp. 780–800
Abstract
Schwarz waveform relaxation (SWR) algorithm has been investigated deeply and 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 diffusion equations 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 determine a 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 than the one arising for regular problems without delay. We propose new notion to solve the min-max problem and obtain a quasi-optimized choice of the parameter, which is shown efficient to accelerate the convergence of the SWR algorithm. Numerical results are provided to validate the theoretical conclusions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.100312.071112a
Communications in Computational Physics, Vol. 14 (2013), Iss. 3 : pp. 780–800
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
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Quasi-overlapping Semi-discrete Schwarz Waveform Relaxation Algorithms: The Hyperbolic Problem
Al-Khaleel, Mohammad
Wu, Shu-Lin
Computational Methods in Applied Mathematics, Vol. 20 (2020), Iss. 3 P.397
https://doi.org/10.1515/cmam-2018-0188 [Citations: 5]