A novel stable, accurate and fast numerical method based on triangular meshing and space transformations for electrodynamics problems with arbitrary boundaries is developed. Using transformation optics it is possible to convert non uniform domains into uniform rectangular ones allowing Maxwell’s Equations to be solved quickly and simply using a modified finite difference time domain (FDTD) algorithm. A novel averaging method is presented to ensure the stability and accuracy of our algorithm when dealing with anisotropic and inhomogeneous materials in the transformed space. Finally we demonstrate the advantages of the present technique compared with conventional FDTD and transformation optics FDTD through a couple of scattering problems. These show that this method is more than one thousand times faster than classical FDTD in the presence of curved boundaries.

中文翻译：

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应用空间曲率的三角网格新型时域电磁仿真

提出了一种基于三角形网格划分和空间变换的新颖，稳定，快速的数值方法，用于求解具有任意边界的电动力学问题。使用变换光学器件，可以将非均匀区域转换为均匀矩形区域，从而可以快速简便地使用改进的有限差分时域（FDTD）算法求解麦克斯韦方程组。提出了一种新颖的平均方法，以确保我们的算法在处理变换空间中的各向异性和非均质材料时的稳定性和准确性。最后，我们通过一些散射问题证明了与传统FDTD和变换光学器件FDTD相比，本技术的优势。