On the inverse scattering from anisotropic periodic layers and transmission eigenvalues
On the inverse scattering from anisotropic periodic layers and transmission eigenvalues
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DOI：
10.1080/00036811.2020.1836349
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发表时间：
2019-08
影响因子：
1.1
通讯作者：
I. Harris;Dinh-Liem Nguyen;J. Sands;TrungDung Truong
中科院分区：
文献类型：
--
作者：
I. Harris;Dinh-Liem Nguyen;J. Sands;TrungDung Truong
本文研究了各向异性周期层的逆散射和透射本征值。对于逆散射问题，我们研究了由近场散射数据重构周期性介质层形状的因式分解方法。该方法提供了一种快速的数值算法，以及一个独特的决定的散射体的形状重建。我们提出了一个严格的理由和数值例子的因式分解方法。散射中的透射本征值问题近年来引起了人们的广泛关注。透射本征值可以从散射数据中确定，并且它们可以提供关于散射体的材料参数的信息。本文建立了各向异性周期层散射的内透射本征值问题，并证明了存在无穷多个透射本征值。
ABSTRACT This paper is concerned with the inverse scattering and the transmission eigenvalues for anisotropic periodic layers. For the inverse scattering problem, we study the Factorization method for shape reconstruction of the periodic layers from near field scattering data. This method provides a fast numerical algorithm as well as a unique determination for the shape reconstruction of the scatterer. We present a rigorous justification and numerical examples for the factorization method. The transmission eigenvalue problem in scattering have recently attracted a lot of attentions. Transmission eigenvalues can be determined from scattering data and they can provide information about the material parameters of the scatterers. In this paper, we formulate the interior transmission eigenvalue problem and prove the existence of infinitely many transmission eigenvalues for the scattering from anisotropic periodic layers.