A Multi-Level Method for Transmission Eigenvalues of Anisotropic Media
Document Type
Article
Publication Date
12-15-2013
Department
Department of Mathematical Sciences
Abstract
In this paper, we propose a multi-level finite element method for the transmission eigenvalue problem of anisotropic media. The problem is non-standard and non-self-adjoint with important applications in inverse scattering theory. We employ a suitable finite element method to discretize the problem. The resulting generalized matrix eigenvalue problem is large, sparse and non-Hermitian. To compute the smallest real transmission eigenvalue, which is usually an interior eigenvalue, we devise a multi-level method using Arnoldi iteration. At the coarsest mesh, the eigenvalue is obtained using Arnoldi iteration with an adaptive searching technique. This value is used as the initial guess for Arnoldi iteration at the next mesh level. This procedure is then repeated until the finest mesh level. Numerical examples are presented to show the viability of the method.
Publication Title
Journal of Computational Physics
Recommended Citation
Ji, X.,
&
Sun, J.
(2013).
A Multi-Level Method for Transmission Eigenvalues of Anisotropic Media.
Journal of Computational Physics,
255, 422-435.
http://doi.org/10.1016/j.jcp.2013.08.030
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6662
Publisher's Statement
© 2013 Elsevier Inc.