A Rigorous Numerical Analysis of the Transformed Field Expansion Method for Diffraction by Periodic, Layered Structures
A Rigorous Numerical Analysis of the Transformed Field Expansion Method for Diffraction by Periodic, Layered Structures
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DOI：
10.1137/20m131374x
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发表时间：
2021-01
期刊：
影响因子：
--
通讯作者：
Youngjoon Hong;D. Nicholls
中科院分区：
文献类型：
--
作者：
Youngjoon Hong;D. Nicholls
边界摄动法由于其能够以稳定、鲁棒和高精度的方式模拟应用感兴趣的微分方程的解，近年来受到了相当大的关注。在这方面的贡献，我们研究了严格的数值分析，最近提出的高阶扰动的表面方法的电磁波散射的双层，周期性介质中的横向电极化。所讨论的算法是一种变换场展开法，它是用傅立叶-Legendre-Galerkin，泰勒级数方法离散的。我们不仅证明了解的存在性和唯一性结果，而且还证明了我们的方案的解以高阶谱精度收敛于这些解的定理。
Boundary perturbation methods have received considerable attention in recent years due to their ability to simulate solutions of differential equations of applied interest in a stable, robust, and highly accurate fashion. In this contribution we study the rigorous numerical analysis of a recently proposed high-order perturbation of surfaces method for scattering of electromagnetic waves by a doubly layered, periodic medium in transverse electric polarization. The algorithm in question is a transformed field expansion method which is discretized with a Fourier--Legendre-Galerkin, Taylor series approach. We prove not only results on existence and uniqueness of solutions but also theorems indicating that solutions of our scheme converge to these solutions with high-order spectral accuracy.