Efficient Spectral Methods for Transmission Eigenvalues and Estimation of the Index of Refraction (Journal of Mathematical Study, 2014)
An important step in estimating the index of refraction of electromagneticscattering problems is to compute the associated transmission eigenvalue problem.We develop in this paper efficient and accurate spectral methods for computing thetransmission eigenvalues associated to the electromagnetic scattering problems. Wepresent 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 theindex of refraction of a non-absorbing inhomogeneous medium.
Keywords: spectral method; index of refraction; transmission eigenvalue; electromagnetic scattering; inverse problem.