SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 871-896, January 2021.
It is critically important that engineers be able to numerically simulate the scattering of electromagnetic radiation by bounded obstacles. Additionally, that these simulations be robust and highly accurate is necessitated by many applications of great interest. High-order spectral algorithms applied to interfacial formulations can rapidly deliver high fidelity approximations with a modest number of degrees of freedom. The class of high-order perturbation of surfaces methods has proven to be particularly appropriate for these simulations, and in this contribution we consider questions of both practical implementation and rigorous analysis. For the former we generalize our recent results to utilize the uniformly well-defined impedance-impedance operators rather than the Dirichlet--Neumann operators which occasionally encounter unphysical singularities. For the latter we utilize this new formulation to establish the existence, uniqueness, and analyticity of solutions in non-resonant configurations. We also include results of numerical simulations based on an implementation of our new formulation which demonstrates its noteworthy accuracy and robustness.

中文翻译：

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通过阻抗-阻抗算子对二维局部表面等离子体共振的仿真

SIAM应用数学杂志，第81卷，第3期，第871-896页，2021年1月。
至关重要的是，工程师们必须能够通过数值模拟边界障碍物对电磁辐射的散射。另外，许多感兴趣的应用都需要使这些模拟具有鲁棒性和高度准确性。应用于界面配方的高阶光谱算法可以以适度的自由度快速提供高逼真的逼近度。事实证明，这类表面的高阶扰动方法特别适合于这些模拟，在这一贡献中，我们考虑了实际实现和严格分析的问题。对于前者，我们将最近的结果推广到使用统一定义的阻抗阻抗算符，而不是偶尔遇到非物理奇点的Dirichlet-Neumann算符。对于后者，我们利用这一新公式来建立非谐振配置中解的存在性，唯一性和解析性。我们还包括基于我们新配方实施方式的数值模拟结果，证明了其值得注意的准确性和鲁棒性。