报告人: 李会元(中国科学院软件研究所)

邀请人：王海永

报告时间：2021年4月17日(星期六)14:30-16:30

报告地点：科技楼(南楼)602室

报告题目：Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains

报告摘要：In this talk, we develop an efficient Hermite spectral-Galerkin method for nonlocal diffusion equations in unbounded domains. We show that the use of the Hermite basis can de-convolute the troublesome convolutional operations involved in the nonlocal Laplacian. As a result, the “stiffness”matrix can be fast computed and assembled via the four-point stable recursive algorithm with O(N^2) arithmetic operations. Moreover, the singular factor in a typical kernel function can be fully absorbed by the basis. With the aid of Fourier analysis, we can prove the convergence of the scheme. We demonstrate that the recursive computation of the entries of the stiffness matrix can be ex- tended to the two-dimensional nonlocal Laplacian using theisotropic Hermite functions as basis functions. We provide ample numerical results to illustrate the accuracy and efficiency of the proposed algorithms.

报告人简介：李会元，中国科学院软件研究所研究员，博士生导师。主要研究领域为偏微分方程的高精度谱方法与谱元法，特征值问题的高性能计算方法等。在SIAM J. Numer. Anal., SIAM J. Sci. Comp., Appl. Comput. Harmon. Anal., Math. Comp.等发表论文五十余篇。