A spectral projection method for transmission eigenvalues
Document Type
Article
Publication Date
8-2016
Department
Department of Mathematical Sciences
Abstract
We consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which leads to a generalized matrix eigenvalue problem. We propose a novel method based on the spectral projection. The method probes a given region on the complex plane using contour integrals and decides whether the region contains eigenvalue(s) or not. It is particularly suitable to test whether zero is an eigenvalue of the generalized eigenvalue problem, which in turn implies that the associated wavenumber is a transmission eigenvalue. Effectiveness and efficiency of the new method are demonstrated by numerical examples.
Publication Title
Science China Mathematics
Recommended Citation
Zeng, F.,
Sun, J.,
&
Xu, L.
(2016).
A spectral projection method for transmission eigenvalues.
Science China Mathematics,
59(8), 1613-1622.
http://doi.org/10.1007/s11425-016-0289-8
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5043