Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction

Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction

Year:    2014

Author:    Jing An, Jie Shen

Journal of Mathematical Study, Vol. 47 (2014), Iss. 1 : pp. 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 computing 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v47n1.14.01

Journal of Mathematical Study, Vol. 47 (2014), Iss. 1 : pp. 1–20

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

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

Author Details

Jing An

Jie Shen

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