Computation of Transmission Eigenvalues for Elastic Waves
Abstract
The goal of this paper is to develop numerical methods computing a few smallest elasticity transmission eigenvalues, which are of practical importance in inverse scattering theory. The problem is challenging since it is nonlinear, non-self-adjoint, and of fourth order. We construct a nonlinear function whose values are generalized eigenvalues of a series of self-adjoint fourth order problems. The roots of the function are the transmission eigenvalues. Using an -conforming finite element for the self-adjoint fourth order eigenvalue problems, we employ a secant method to compute the roots of the nonlinear function. The convergence of the proposed method is proved. In addition, a mixed finite element method is developed for the purpose of verification. Numerical examples are presented to verify the theory and demonstrate the effectiveness of the two methods.
Cite
@article{arxiv.1802.03687,
title = {Computation of Transmission Eigenvalues for Elastic Waves},
author = {Xia Ji and Peijun Li and Jiguang Sun},
journal= {arXiv preprint arXiv:1802.03687},
year = {2018}
}