A Spectral-Element Method for Transmission Eigenvalue Problems

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• 作者：Jing An (1)
  Jie Shen (1) (2)
  
• 关键词：Spectral method ; Transmission eigenvalue ; Helmholtz equation ; 78M22 ; 78A46 ; 65N35 ; 35J05 ; 41A58
• 刊名：Journal of Scientific Computing
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：57
• 期：3
• 页码：670-688
• 全文大小：
• 作者单位：Jing An (1)
  Jie Shen (1) (2)
  
  1. School of Mathematics and Science, Xiamen University, Xiamen, 361005, China
  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA
  
• ISSN：1573-7691

文摘

We develop an efficient spectral-element method for computing the transmission eigenvalues in two-dimensional radially stratified media. Our method is based on a dimension reduction approach which reduces the problem to a sequence of one-dimensional eigenvalue problems that can be efficiently solved by a spectral-element method. We provide an error analysis which shows that the convergence rate of the eigenvalues is twice that of the eigenfunctions in energy norm. We present ample numerical results to show that the method convergences exponentially fast for piecewise stratified media, and is very effective, particularly for computing the few smallest eigenvalues.