椭圆特征值问题的局部径向基函数差分法  

Local RBF-FD Method for the Elliptic Eigenvalue Problem

作　　者：张毅 冯新龙[1] ZHANG Yi;FENG Xin-long(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《工程数学学报》2020年第5期631-641,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11671345);新疆自然科学基金(2016D01C071;2016D01C058).

摘　　要：本文介绍椭圆特征值问题的局部径向基函数差分法.这种方法的主要思想是人为选取各插值节点所对应的影响区域,只考虑影响区域内插值点对该插值节点的影响,忽略影响区域外插值点的影响.这种局部化方法在损失一定计算精度的同时离散得到稀疏矩阵,从而使算法能应用于计算大规模插值节点科学计算.通过数值实验,研究了节点分部,插值点数以及形状参数对该特征值问题计算结果的影响,并选用三种径向基函数进行计算比较.数值结果和解析解非常吻合.This paper is concerned with the application of the local RBF-FD method for the elliptic eigenvalue problem.The main idea of this method is to select the influential region corresponding to each interpolation node artificially and consider only the influence of the interpolation point in the region on the interpolation node,ignoring the influence of the nodes outside the region.This localization method obtains sparse matrices while losing a certain degree of computational accuracy,so that the algorithm can be applied to the computation of large-scale interpolation node scientific calculations.Through numerical experiments,we study the influence of node layouts,interpolation points,and the shape parameter on the calculation result of the eigenvalue problem,and using three radial basis functions to calculate and compare.The results obtained from the experiments are in good agreement with the analytical solutions to the problem.

关 键 词：椭圆特征值问题 径向基函数 径向基函数差分法 形状参数 

分 类 号：O241.82[理学—计算数学]