Journal of Scientific Computing

, Volume 57, Issue 3, pp 670–688 | Cite as

A Spectral-Element Method for Transmission Eigenvalue Problems

  • Jing An
  • Jie ShenEmail author


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.


Spectral method Transmission eigenvalue Helmholtz equation 

Mathematics Subject Classification (1991)

78M22 78A46 65N35 35J05 41A58 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematics and ScienceXiamen UniversityXiamenChina
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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