Computation of interior elastic transmission eigenvalues using a conforming finite element and the secant method

Authors

Xia Ji, Chinese Academy of Sciences
Peijun Li, Purdue University
Jiguang Sun, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

2-2020

Department

Department of Mathematical Sciences

Abstract

The interior elastic transmission eigenvalue problem, arising from the inverse scattering theory of non-homogeneous elastic media, is nonlinear, non-self-adjoint and of fourth order. This paper proposes a numerical method to compute real elastic transmission eigenvalues. To avoid treating the non-self-adjoint operator, an auxiliary nonlinear function is constructed. The values of the function are generalized eigenvalues of a series of self-adjoint fourth order problems. The roots of the function are the transmission eigenvalues. The self-adjoint fourth order problems are computed using the H²-conforming Argyris element. The secant method is employed to search the roots of the nonlinear function. The convergence of the proposed method is proved.

Publication Title

Results in Applied Mathematics

Recommended Citation

Ji, X., Li, P., & Sun, J. (2020). Computation of interior elastic transmission eigenvalues using a conforming finite element and the secant method. Results in Applied Mathematics, 5. http://doi.org/10.1016/j.rinam.2019.100083
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1524