报告题目：An Improved Local Min-Orthogonal Method for Finding Multiple Saddle Solutions to Semilinear PDEs

报 告 人：陈先进（中国科学技术大学）

报告时间：2024年12月13日  10:30-11:30

报告地点：腾讯会议（691203563）

报告摘要：

Local Min-Orthogonal (LMO) method is an efficient numerical method to solve nonlinear elliptic equations or systems for their multiple saddle-solutions. WVith a given finite-dimensional subspace L, the LMO method can find multipile saddle solutions outside such L. In this talk, the L-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 its convergence analysis. A new step-size rule and a new local characterization on saddles are then established, based on which an improved LMO (also called LMO+) method is developed. The new method can overcome some limitations of the LMO-type method and enjoy some important advantages, such as boundedness of the iterated sequence and of its corresponding energy functional. In the end, numerical examples are presented to demonstrate the effectiveness of the new method.

报告人简介：

陈先进，德克萨斯A&M大学（美）数学博士，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., Physica D, J. Comput. Appl. Math., Comm. in Math. Sci., Numer. Meth. PDEs等知名期刊上。