报告题目： Waveform Relaxation for Partial Differential Equations

主讲人：蒋耀林 教授

单  位：西安交通大学

时  间： 2022 年 10 月 30 日（周日）上午 10:30-11:30

地  点：腾讯会议号：311631271

报告人简介：

蒋耀林，西安交通大学教授(二级)，教育部“长江学者”特聘教授，教育部跨世纪优秀人才，国务院特殊津贴专家，西安交通大学首批领军学者，教育部(中国科协)“英才计划”数学学科导师。早年留学香港中文大学和比利时K. U. Leuven大学，1998年晋升教授和担任博士生导师。中国工业与应用数学学会常务理事(2004-2016)，陕西省工业与应用数学学会理事长(2006-2022)。从事偏微分方程高性能计算方法研究，在波形松弛、模型降阶和时空并行三类计算与应用数学方法做出学术贡献。出版学术著作5部，被科学出版社和高等教育出版社分别列为“现代数学基础丛书184辑”和“现代数学基础32辑”；发表学术期刊论文300余篇，其中包括SIAM J. (SINUM, SISC, SIMAX)，IEEE Trans.（TAC, TCAS, TCAD）国际著名SCI期刊论文260余篇。主持国家级项目12项和省重点项目1项：国家自然科学基金项目9项, 科技部项目3项, 陕西省国际合作重点项目1项。个人主页：http://yljiang.gr.xjtu.edu.cn

报告摘要：

In this talk, we apply waveform relaxation (WR) to PDEs directly at PDEs level. Compared with traditionally implementing WR to a large scale system of ODEs obtained by discretizing the spatial variables of the PDEs, the information transmission between sub-systems can be avoided and the convergence rate does not deteriorate when the mesh is refined. Picard WR at PDEs level is first presented to show the advantages of the new approach. The estimation on iteration errors and two parallelisms of the WR are analyzed. Next the approach is improved by quasi-Newton relaxation and a theoretical framework of energy estimation for the superlinear convergence of some semi-linear PDEs is developed. We then discuss the general WR at PDEs level to obtain general convergence estimates for the single and coupled PDEs. Finally in several numerical experiments, we demonstrate the comparisons of iteration errors by four WR methods. The results suggest that the really new methods achieve excellent results after very few iterations and can be highly implemented in parallel.