正多边形区域上Laplace算子特征值的非结构网络谱元法  

An Unstructured Spectral Element Method for the Laplace Eigenvalue Problem on Regular Polygons

作　　者：文永松 庞一成[1] 张俊[1] 朱淑娟 Wen Yongsong;Pang Yicheng;Zhang Jun;Zhu Shujuan(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数学与统计学院,贵州贵阳550025

出　　处：《南京师大学报（自然科学版）》2018年第1期26-29,共4页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：贵州省教育厅自然科学研究项目(KY字[2016]170);贵州省教育厅自然科学研究项目(KY[2015]482);贵州省科学技术基金(J[2015]2026)

摘　　要：采用高精度的混合三角形、四边形单元剖分求解任意正多边形区域上的Laplace算子的特征值.由Legendre多项式线性组合构造内部单元的基函数和边界基函数.首先,给出特征值的误差估计和算法实现.然后,测试数值算例的精度,以验证理论结果,表明方法的有效性及正确性.In this paper,we use an unstructured spectral element method which mixed triangularand quadrangle for the Laplace eigenvalue problem on the regular polygon domain.We construct the basis functions by combing with the Legendre polynomials for the interior element and boundary.The convergence of the eigenvalue and numerical implement are also given.Finally,a series of numerical examples are provided to support the theoretical results and demonstrate the accuracy and efficiency of this methods.

关 键 词：LAPLACE算子 特征值问题 非结构网络谱元法 

分 类 号：O241.82[理学—计算数学]