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A Spectral-Element Method for Transmission Eigenvalue Problems

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Science, Xiamen University, Xiamen, 361005, China

    Jing An & Jie Shen

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Jie Shen

Authors
  1. Jing An
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  2. Jie Shen
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Corresponding author

Correspondence to Jie Shen.

Additional information

The work of J. Shen partially supported by AFOSR grant FA9550-11-1-0328 and NFS grant DMS-1217066.

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An, J., Shen, J. A Spectral-Element Method for Transmission Eigenvalue Problems. J Sci Comput 57, 670–688 (2013). https://doi.org/10.1007/s10915-013-9720-1

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  • DOI: https://doi.org/10.1007/s10915-013-9720-1

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