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Li, Tiexiang; Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Jenn-Nan

On the transmission eigenvalue problem for the acoustic equation with a negative index of refraction and a practical numerical reconstruction method. (English) Zbl 1401.78010

Inverse Probl. Imaging 12, No. 4, 1033-1054 (2018).
The paper under review deals with two-dimensional Maxwell equations with transverse magnetic mode in pseudo-chiral media. The analysis is carried out on the acoustic equation with a negative index of refraction. The authors are first concerned with the transmission eigenvalue problem for this equation. By the continuous finite element method, the reduced equation is discretized and the analysis is transformed to a quadratic eigenvalue problem by deflating all nonphysical zeros. Next, the authors establish a numerical method to reconstruct the support of the inhomogeneity by the near-field measurements. The truncated singular value decomposition is proposed to solve the ill-posed near-field integral equation, at one wave number which is not a transmission eigenvalue. This method produces different jumps for the sampling points inside and outside the support. Some numerical simulations illustrate some of the results established in this paper.
Reviewer: Teodora-Liliana Rădulescu (Craiova)

Cited in 5 Documents

MSC:

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35R30 Inverse problems for PDEs
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
35P15 Estimates of eigenvalues in context of PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
76Q05 Hydro- and aero-acoustics
65F20 Numerical solutions to overdetermined systems, pseudoinverses

Keywords:

two-dimensional transmission eigenvalue problem; pseudo-chiral model; transverse magnetic mode; linear sampling method; singular value decomposition

Software:

Algorithm 922
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References:

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