薄层的不定常电磁散射
Time-dependent electromagnetic scattering from thin layers
摘要：
利用广义阻抗边界条件描述了表面薄层中存在波-物相互作用的障碍物对电磁波的散射，提供了有效的近似模型。特别地，这包括围绕完美导体的薄涂层和高导电材料的集肤效应。在这项工作中采取的方法是推导，分析和离散化的系统的不定常边界积分方程，确定的切向轨迹的散射电场和磁场。在熟悉的第二步中，在外部域中通过表示公式来评估场，该表示公式使用麦克斯韦方程组的不定常势算子。对不定常边界积分方程在时间上采用基于Runge-Kutta的卷积求积法离散，在空间上采用Raviart-Thomas边界元离散。使用频率显式的边界从适定性分析这里给出连同已知的近似性质的数值方法，充分的离散化被证明是稳定的和收敛的，与明确给定的速率的情况下，充分的正则性。采用相同的基于Runge-Kutta的卷积求积离散的不定常表示公式，获得的最佳阶的收敛远离散射边界，而减少发生的边界附近。数值实验验证了理论结果。
英文摘要：
The scattering of electromagnetic waves from obstacles with wave-material interaction in thin layers on the surface is described by generalized impedance boundary conditions, which provide effective approximate models. In particular, this includes a thin coating around a perfect conductor and the skin effect of a highly conducting material. The approach taken in this work is to derive, analyse and discretize a system of time-dependent boundary integral equations that determines the tangential traces of the scattered electric and magnetic fields. In a familiar second step, the fields are evaluated in the exterior domain by a representation formula, which uses the time-dependent potential operators of Maxwell's equations. The time-dependent boundary integral equationis discretized with Runge--Kutta based convolution quadrature in time and Raviart--Thomas boundary elements in space. Using the frequency-explicit bounds from the well-posedness analysis given here together with known approximation properties of the numerical methods, the full discretization is proved to be stable and convergent, with explicitly given rates in the case of sufficient regularity. Taking the same Runge--Kutta based convolution quadrature for discretizing the time-dependent representation formulas, the optimal order of convergence is obtained away from the scattering boundary, whereas an order reduction occurs close to the boundary. The theoretical results are illustrated by numerical experiments.
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