SIAM Journal on Numerical Analysis, Volume 59, Issue 1, Page 456-476, January 2021.
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.

中文翻译：

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周期性分层结构衍射场变换方法的严格数值分析

SIAM数值分析学报，第59卷，第1期，第456-476页，2021年1月。
边界摄动法由于具有以稳定，鲁棒和高度精确的方式模拟应用感兴趣的微分方程解的能力，因此近年来受到了相当大的关注。在这项贡献中，我们研究了最近提出的表面高阶扰动方法的严格数值分析，该方法用于在横向极化中通过双层周期性介质散射电磁波。所讨论的算法是一种变换的场扩展方法，通过傅里叶-勒根德勒-加勒金，泰勒级数方法离散化。我们不仅证明了解的存在性和唯一性的结果，而且证明了表明该方案的解以高阶谱精度收敛到这些解的定理。