Seminars on Numerical Algorithms, Analyses, and Applications：Local minimax method for the solution of saddle point of semilinear partial differential equations

：谢资清（湖南师范大学）
：2023-08-15 16:30
：海韵园实验楼105报告厅

报 告 人：谢资清（湖南师范大学）

时  间：2023年8月15日16:30

地  点：海韵园实验楼105报告厅

内容摘要:

In this report we will systematically introduce the monotonic and non-monotonic local minima-max methods (LMM) and the algorithm framework for the saddle point calculation problem of semilinear partial differential equations with variational structure. Among them, the monotonic LMM is based on three standardized non-exact search strategies of Armijo, Goldstein and (strong) Wolf-Powell respectively, and the selection of the descending direction can be extended from the steepest descending direction to a more general descending direction, thus making it possible to accelerate the algorithm. Non-monotonic LMM is based on BB step size and Zhang-Hager non-monotonic search strategy. Numerical results show that this method can greatly improve the algorithm efficiency of LMM. Our work overcomes the inherent difficulties of nonlinear, non-convex, multiple solutions and instability in the saddle point calculation of semi-linear partial differential equations, and rigorously proves the feasibility and large-scale convergence of the method. As an application of LMM, which is used to calculate the saddle point solution of a class of semi-linear singularly perturbed Neumann problems, we found and accurately characterized the corresponding critical perturbation value.

个人简介：

谢资清，教授、博士生导师，计算与随机数学教育部重点实验室主任，湖南师范大学副校长，十三届全国人大代表，十四届全国政协委员。主要从事计算数学与应用数学的研究工作。现任湖南省数学会副理事长兼任湖南省高中数学奥林匹克竞委会主任。博士毕业于中国科学院应用数学研究所。曾分别以第一完成人身份获湖南省自然科学奖一等奖和湖南省教学成果奖一等奖。曾入选教育部新世纪优秀人才支持计划，并获批为享受国务院政府特殊津贴专家。在SIAM J. Sci. Comput., SIAM J. Numer. Anal., Math. Comput., J. Comp. Phys.等期刊发表论文80余篇。曾多次应邀访问美国、瑞典、挪威、德国、日本、新加坡、香港等国家和地区的知名大学。

 

联系人：陈黄鑫