Quasi-Optimized Overlapping Schwarz Waveform Relaxation Algorithm for PDEs with Time-Delay

作     者：Shu-Lin Wu Ting-Zhu Huang 

作者机构：School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduSichuan 610054China School of ScienceSichuan University of Science and EngineeringZigongSichuan 643000China 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2013年第14卷第8期

页      面：780-800页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the NSF of China(11226312,91130003) the NSF of Sichuan University of Science and Engineering(2012XJKRL005) the Opening Fund of Artificial Intelligence Key Laboratory of Sichuan Province(2011RZY04) the Chinese Universities Specialized Research Fund for the Doctoral Program(20110185110020) 

主　　题：Schwarz method waveform relaxation time delay min-max problem 

摘      要：Schwarzwaveformrelaxation(SWR)algorithmhas been investigated deeply and widely for regular time dependent *** for time delay problems,complete analysis of the algorithm is *** 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 *** key point of using this transmission condition is to determine a free parameter as better 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 *** 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 *** results are provided to validate the theoretical conclusions.