谱元法求解Helmholtz方程透射特征值问题

戴海; 潘文峰

doi:10.21656/1000-0887.380327

谱元法求解Helmholtz方程透射特征值问题

doi: 10.21656/1000-0887.380327

戴海,
潘文峰

武汉理工大学理学院, 武汉 430070

基金项目: 中央高校基本科研业务费(2017IB014)

详细信息

作者简介:
戴海（1992—），男，硕士生（通讯作者. E-mail: 1670112042@qq.com);潘文峰(1964—)，男，教授（E-mail: pan@mail.whut.edu).

中图分类号: O175.2
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- 文章访问数: 1153
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出版历程
- 收稿日期: 2017-12-18
- 修回日期: 2018-01-18
- 刊出日期: 2018-07-15

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

School of Science, Wuhan University of Technology, Wuhan 430070, P.R.China

摘要

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.
- 透射特征值问题 /
- 二次特征值问题 /
- 谱元法 /
- Chebyshev基函数
Abstract: 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.
- transmission eigenvalue problem /
- quadratic eigenvalue problem /
- spectral element method /
- Chebyshev basis function

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参考文献(16)

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谱元法求解Helmholtz方程透射特征值问题

doi: 10.21656/1000-0887.380327

作者简介:
戴海（1992—），男，硕士生（通讯作者. E-mail: 1670112042@qq.com);潘文峰(1964—)，男，教授（E-mail: pan@mail.whut.edu).

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

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留言板

谱元法求解Helmholtz方程透射特征值问题

doi: 10.21656/1000-0887.380327

作者简介: 戴海（1992—），男，硕士生（通讯作者. E-mail: 1670112042@qq.com);潘文峰(1964—)，男，教授（E-mail: pan@mail.whut.edu).

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出版历程

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

计量

出版历程

目录

作者简介:
戴海（1992—），男，硕士生（通讯作者. E-mail: 1670112042@qq.com);潘文峰(1964—)，男，教授（E-mail: pan@mail.whut.edu).