报告题目： An LMO+ Method for Finding Multiple Unstable Solutions to Semilinear PDEs

报告人：陈先进 博士 中国科学技术大学

报告时间：2022年7月22日（星期五） 10:00-11:00

报告地点：腾讯会议：246-459-831

校内联系人：张旭平 副教授  联系电话：84708351-8025

报告摘要： As a generalization of the local Minimax (LMM) method, the Local Min-Orthogonal (LMO) method is one of the efficient numerical methods to solve multiple-solution problems in nonlinear elliptic equations or systems. Specifically, with a given finite-dimensional closed subspace L, the LMO method can numerically find multiple unstable solutions (i.e.,saddles) outside such L. In this talk, the L-⊥ selection, the separation condition and the continuity condition used in the framework of the LMO method are successively improved or weakened so that they are not only closer to the real algorithm's implementation but also able to improve the relevant analysis. A new step-size rule and a new local characterization on saddles are then established, based on which an LMO+ method is developed. Some new properties of the LMO/LMO+ method are also explored. In the end, numerical examples conform the effectiveness of the LMO+ method.

报告人简介：陈先进，美国德克萨斯A&M大学（Texas A&M University）数学博士，美国明尼苏达大学应用数学研究所博士后，现任教于中国科学技术大学。目前主要从事非线性偏微分方程(组)不稳定多解的分析与计算方面的研究，并在该领域取得了一些原创性的研究成果，成果发表在Math. Comp., J. Sci. Comput., Appl. Numer. Math., J. Comput. Appl. Math., Numer. Meth. Partial Differential Equations 等知名期刊上。