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

Jing An and Jie Shen


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

Full Article 105 140
  • 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.

  • History

Submitted: 2014-03

Accepted: 2019-02

Published online: 2014-03

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