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.

摘要

本文关注各向异性周期性层的逆散射和透射特征值。对于逆散射问题，我们研究了从近场散射数据中重构周期性层形状的因子分解方法。该方法为散射体的形状重建提供了一种快速的数值算法以及独特的确定方法。我们为分解方法提供了严格的理由和数值示例。散射中的传输特征值问题最近引起了很多关注。透射特征值可以从散射数据中确定，它们可以提供有关散射体材料参数的信息。在本文中，