Efficient Hermite Spectral-Galerkin Methods for Nonlocal Diffusion Equations in Unbounded Domains

作     者：Huiyuan Li Ruiqing Liu Li-Lian Wang 

作者机构：State Key Laboratory of Computer Science/Laboratory of Parallel ComputingInstitute of SoftwareChinese Academy of SciencesBeijing 100190China University of Chinese Academy of SciencesBeijing 100190China Division of Mathematical SciencesSchool of Physical and Mathematical SciencesNanyang Technological University637371Singapore 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2022年第15卷第4期

页      面：1009-1040页

核心收录：

学科分类：0820[工学-石油与天然气工程] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：supported in part by the National Natural Science Foundation of China(Grant Nos.11871145,11971016,12131005) The research of L.-L.Wang is partially supported by Singapore MOE AcRF Tier 1(Grant RG 15/21) R.Liu would like to thank Nanyang Technological University for hosting the visit where this research topic was initialised 

主　　题：Nonlocal diffusion equation spectral-Galerkin Hermite functions correlation/convolution recurrence algorithm 

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