告题目： Asymptotic analysis and numerical method for singularly perturbed eigenvalue problems

报告人： 黄忠亿 教授 （清华大学）

时间：2025年10月25日(星期六)10:00-11:00

地点：数学院425

摘要：

We study the asymptotic analysis and numerical method for singularly perturbed eigenvalue problems (SPEPs), which arises in describing the semiclassical limit of the spectrum for the Schrödinger operator. We first make a close asymptotic analysis of

the SPEP and prove that, for piecewise smooth potential functions , the eigenvalues converge to the minimum value of the potential functions, and the eigenfunctions are concentrated in the immediate vicinity of the minimal points of the potential functions as ε→0. Then we propose some new schemes based on the tailored finite point method (TFPM) for numerical solutions of SPEPs with higher accuracy. Our numerical examples verify our theory and show the feasibility and efficiency of our TFPM.

报告人简介：

黄忠亿， 清华大学数学科学系长聘教授、 博士生导师， 一直从事计算数学与科学工程计算方面的研究，2013 年获优秀青年基金资助，2020 年获国家杰出青年基金资助。