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arXiv · 1503.04741

Recursive integral method for transmission eigenvalues

Ruihao Huang·Allan A. Struthers·Jiguang Sun·Ruming Zhang
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Abstract

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this paper, we propose a recursive integral method for computing transmission eigenvalues from a finite element discretization of the continuous problem. The method, which overcomes some difficulties of existing methods, is based on eigenprojectors of compact operators. It is self-correcting, can separate nearby eigenvalues, and does not require an initial approximation based on some a priori spectral information. These features make the method well suited for the transmission eigenvalue problem whose spectrum is complicated. Numerical examples show that the method is effective and robust.

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Ruihao Huang, Allan A. Struthers, Jiguang Sun, Ruming Zhang. 2015-03-16. Recursive integral method for transmission eigenvalues. https://doi.org/10.1016/j.jcp.2016.10.001

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