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Overlapping Localized Exponential Time Differencing Methods for Diffusion Problems
发布时间: 2018-04-26     21:19   【返回上一页】 发布人:Ju Lili


北京师范大学数学科学学院

 

计算数学学术报告

 

报告题目:Overlapping Localized Exponential Time Differencing Methods for Diffusion Problems

 

报告:Ju Lili 教授 University of South Carolina

 

时间地点:57  300-400  教八107

 

邀请人: 张辉

 

报告摘要:The localized exponential time differencing (ETD) based on overlapping domain decomposition has been recently introduced for extreme-scale phase field simulations of coarsening dynamics, which displays excellent parallel scalability in supercomputers. This work serves as the first step toward building a solid mathematical foundation for this approach. We study the overlapping localized ETD schemes for a model time-dependent diffusion equation discretized in space by the standard central difference. Two methods are proposed and analyzed for solving the fully discrete localized ETD systems: the first one is based on Schwarz iteration applied at each time step and involves solving stationary problems in the subdomains at each iteration, while the second one is based on the Schwarz waveform relaxation algorithm in which time-dependent subdomain problems are solved at each iteration. The convergences of the associated iterative solutions to the corresponding fully discrete localized ETD solution and to the exact semidiscrete solution are rigorously proved. Numerical experiments are also carried out to confirm theoretical results and to compare the performance of the two methods.