论文标题
在时间域NRBC上，用于麦克斯韦方程及其在精确模拟电磁隐形斗篷中的应用
On time-domain NRBC for Maxwell's equations and its application in accurate simulation of electromagnetic invisibility cloaks
论文作者
论文摘要
在本文中，我们介绍了针对电磁散射问题的时间域非反射边界条件（NRBC）涉及的时间卷积内核函数的分析公式。这样的精确公式本身会导致精确有效的算法用于计算NRBC以减少域名麦克斯韦系统的域中的NRBC，以$ \ mathbb r^3 $。本文的第二个目的是为电磁隐形斗篷提供新的时间域模型。与现有模型不同，它仅包含一个未知的字段，并且看似复杂的卷积可以像NRBC中的时间卷积一样有效地计算。掩盖层中的控制方程对于一般几何形状有效，例如球形或多边形层。在这里，我们旨在模拟球形隐形斗篷。我们利用径向分层的分散介质和特殊几何形状的优势，并开发出有效的矢量球形谐波（VSH） - 光谱 - 元素元素方法，以进行准确的模拟。与FDTD模拟的结果有限相比，所提出的方法在准确性和计算成本方面都是最佳的。实际上，计算时间的节省很大。
In this paper, we present analytic formulas of the temporal convolution kernel functions involved in the time-domain non-reflecting boundary condition (NRBC) for the electromagnetic scattering problems. Such exact formulas themselves lead to accurate and efficient algorithms for computing the NRBC for domain reduction of the time-domain Maxwell's system in $\mathbb R^3$. A second purpose of this paper is to derive a new time-domain model for the electromagnetic invisibility cloak. Different from the existing models, it contains only one unknown field and the seemingly complicated convolutions can be computed as efficiently as the temporal convolutions in the NRBC. The governing equation in the cloaking layer is valid for general geometry, e.g., a spherical or polygonal layer. Here, we aim at simulating the spherical invisibility cloak. We take the advantage of radially stratified dispersive media and special geometry, and develop an efficient vector spherical harmonic (VSH)-spectral-element method for its accurate simulation. Compared with limited results on FDTD simulation, the proposed method is optimal in both accuracy and computational cost. Indeed, the saving in computational time is significant.
