边界场公式用于介电散射体和涂层导体的瞬态电磁散射
Boundary-field formulation for transient electromagnetic scattering by dielectric scatterers and coated conductors
AI总结：
针对介电散射体和涂层导体的瞬态电磁散射，提出边界场方程方法，在拉普拉斯域转化为等效边值问题，证明了弱解的存在唯一稳定性，并导出时域正则性估计和数值误差估计。
摘要：
我们研究了当入射电磁波照射到嵌入无限空间中的介电散射体或涂层导体时产生的瞬态散射场和透射场。通过应用边界场方程方法，我们利用散射体内部的电场方程和自由空间中散射电场的边界积分方程组，在拉普拉斯域中重新表述该问题。为了分析这个非局部边界问题，我们将其替换为等效的边值问题。在适当的函数空间中，针对拉普拉斯变换变量，建立了等效边值问题弱解的存在性、唯一性和稳定性。稳定性界被转换为时域估计，这些估计根据问题数据的正则性确定了解的正则性。这些估计可以很容易地转换为时间演化的卷积求积数值离散化的误差估计。
英文摘要：
We examine the transient scattered and transmitted fields generated when an incident electromagnetic wave impinges on a dielectric scatterer or a coated conductor embedded in an infinite space. By applying a boundary-field equation method, we reformulate the problem in the Laplace domain using the electric field equation inside the scatterer and a system of boundary integral equations for the scattered electric field in free space. To analyze this nonlocal boundary problem, we replace it by an equivalent boundary value problem. Existence, uniqueness and stability of the weak solution to the equivalent BVP are established in appropriate function spaces in terms of the Laplace transformed variable. The stability bounds are translated into time-domain estimates which determine the regularity of the solution in terms of the regularity of the problem data. These estimates can be easily converted into error estimates for a numerical discretization on the convolution quadrature for time evolution.
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