Volume 47, Issue 1
Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction

Jing An & Jie Shen

J. Math. Study, 47 (2014), pp. 1-20.

Published online: 2014-03

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  • Abstract

An important step in estimating the index of refraction of electromagnetic scattering problems is to compute the associated transmission eigenvalue problem. We develop in this paper efficient and accurate spectral methods for computing the transmission eigenvalues associated to the electromagnetic scattering problems. We present ample numerical results to show that our methods are very effective for com- puting transmission eigenvalues (particularly for computing the smallest eigenvalue), and together with the linear sampling method, provide an efficient way to estimate the index of refraction of a non-absorbing inhomogeneous medium.

  • Keywords

spectral method index of refraction transmission eigenvalue electromagnetic scattering inverse problem.

  • AMS Subject Headings

78A45 65N35 35J05 41A58

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COPYRIGHT: © Global Science Press

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@Article{JMS-47-1, author = {}, title = {Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction}, journal = {Journal of Mathematical Study}, year = {2014}, volume = {47}, number = {1}, pages = {1--20}, abstract = {

An important step in estimating the index of refraction of electromagnetic scattering problems is to compute the associated transmission eigenvalue problem. We develop in this paper efficient and accurate spectral methods for computing the transmission eigenvalues associated to the electromagnetic scattering problems. We present ample numerical results to show that our methods are very effective for com- puting transmission eigenvalues (particularly for computing the smallest eigenvalue), and together with the linear sampling method, provide an efficient way to estimate the index of refraction of a non-absorbing inhomogeneous medium.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v47n1.14.01}, url = {http://global-sci.org/intro/article_detail/jms/9947.html} }
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