谱元法求解Helmholtz方程透射特征值问题  

A Spectral Element Method for Transmission Eigenvalue Problems of the Helmholtz Equation

作　　者：戴海 潘文峰[1] DAI Hai;PAN Wenfeng(School of Science,Wuhan University of Technology,Wuhan 430070,P.R.China)

机构地区：[1]武汉理工大学理学院,武汉430070

出　　处：《应用数学和力学》2018年第7期833-840,共8页Applied Mathematics and Mechanics

基　　金：中央高校基本科研业务费(2017IB014)

摘　　要：研究了Helmholtz方程透射特征值问题,提出一种Chebyshev谱元法求解,该方法兼具了有限元法处理边界及区域的灵活性和谱方法的快速收敛特性.运用加权余量原理,得到了Chebyshev谱元法用于透射特征值问题的基本理论以及数学公式,将原问题转化为二次特征值问题.最后通过数值实验算例验证了Chebyshev谱元法的有效性.A Chebyshev spectral element method for the transmission eigenvalue problems of the Helmholtz equation was proposed,which combined the flexibility of the finite element method to deal with the boundary and region and the fast convergence of the spectral method. By means of the principle of weighted residuals,the basic theory and mathematical formulae of the Chebyshev spectral element method for transmission eigenvalue problems were obtained. The original problem was transformed into quadratic eigenvalue problems. Furthermore,several numerical examples were given to illustrate the effectiveness of the proposed method.

关 键 词：透射特征值问题 二次特征值问题 谱元法 Chebyshev基函数 

分 类 号：O175.2[理学—数学]