报 告 人：李会元 中国科学院软件研究所研究员，博士生导师
报告题目：Spectral/Spectral Element Methods for the Schrodinger Equation with anInverse Square Potential
报告时间：2015年7月1日（周三）下午4:30-5:30
报告地点：静远楼1508学术报告厅
Abstract:In the talk, wepropose some spectral/spectral element methods for the eigenvalue problem of the Schrodinger equation with an inverse square potential. This eigenvalue problems is of importance in quantum mechanics. The inverse square potential generally causes strong singularities in some of the eigenfunctions such that the classic spectral methods fail and have a limited accuracy. Firstly, two efficient spectral methods with an exponential convergence rate are proposed for the Schrodinger equation on a unit ball (in an arbitrary high dimension)and an arbitrary sector. An analysis is then given to explain how our methods work. A mortar spectral element method is also developed for the Schrodinger equation in other geometries. Numerical experiments show that our spectral/spectralelement methods are perfectly competent not only for problems with an inversesquare potential, but also for those with a singularity caused by reentrantcorners.
李会元教授个人简介：
李会元，中国科学院软件研究所研究员，博士生导师。主要研究领域为大型异构系统下的高性能科学计算与数学软件，数值PDE的谱方法与谱元素方法，特征值问题的高性能计算方法等. 在国际著名期刊SIAM J. Numer. Anal., Math. Comp., J.of Sci.Comp.等上发表论文三十余篇，主持多项国家自然科学基金面上项目.