FINITE ELEMENT/HOLOMORPHIC OPERATOR FUNCTION METHOD FOR THE TRANSMISSION EIGENVALUE PROBLEM

被引:9
|
作者
Gong, Bo [1 ]
Sun, Jiguang [2 ]
Turner, Tiara [3 ]
Zheng, Chunxiong [4 ,5 ]
机构
[1] Beijing Univ Technol, Beijing 100124, Peoples R China
[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA
[3] Univ Maryland Eastern Shore, Dept Math & Comp Sci, Princess Anne, MD 21853 USA
[4] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
[5] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
关键词
APPROXIMATION;
D O I
10.1090/mcom/3767
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media. It plays a key role in the unique determination of inhomogeneous media. Furthermore, transmission eigenvalues can be reconstructed from the scattering data and used to estimate the material properties of the unknown object. The problem is posted as a system of two second order partial differential equations and is nonlinear and non-selfadjoint. It is challenging to develop effective numerical methods. In this paper, we formulate the transmission eigenvalue problem as the eigenvalue problem of a holomorphic operator function. The Lagrange finite elements are used for the discretization and the convergence is proved using the abstract approximation theory for holomorphic Fredholm operator functions. The spectral indicator method is employed to compute the eigenvalues. Numerical examples are presented to validate the proposed method.
引用
收藏
页码:2517 / 2537
页数:21
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