Quasi-optimized Schwarz methods for reaction diffusion equations with time delay

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Wu, Shu-Lin¹  Huang, Cheng-Ming² 

[1] Sichuan Univ Sci & Engn, Sch Sci, Zigong 643000, Sichuan, Peoples R China

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

关键词: Schwarz waveform relaxation;    Reaction diffusion equations;    Time delay;    Optimization;   

DOI  :  10.1016/j.jmaa.2011.06.052

来源: Elsevier

【 摘 要 】

In this paper, we investigate the convergence behavior of the Schwarz waveform relaxation (SWR) algorithms for solving PDEs with time delay. We choose the reaction diffusion equations with a constant time delay as the underlying model problem and try to derive optimized transmission conditions of Robin type. To this end, we propose a new method to get quasi-optimized parameter involved in the transmission conditions and it is shown that this method is essentially different from the existing ones. Moreover, when the situation is reduced into the heat equations with a constant delay, we show that this method results in a more efficient quasi-optimized parameter. Numerical results are provided to validate our theoretical results. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free