A Novel Transformation Optics-Based FDTD Algorithm for Fast Electromagnetic Analysis of Small Structures in a Large Scope
A Novel Transformation Optics-Based FDTD Algorithm for Fast Electromagnetic Analysis of Small Structures in a Large Scope
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一种基于变换光学的新型 FDTD 算法，用于大范围小型结构的快速电磁分析
DOI：
10.1109/access.2019.2938615
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发表时间：
2019
期刊：
影响因子：
3.9
通讯作者：
Qing Huo Liu
中科院分区：
文献类型：
--
作者：
Ruonan Chen;Lei Kuang;Zhengqi Zheng;Qing Huo Liu
本文提出了一种新的基于变换光学的正方形变换域时域有限差分（TO-FDTD）算法，该算法适用于大计算域中小结构的快速电磁分析。一个小的结构，可以解决与粗网格的转换区域，因为它是扩大了变换光学。对小结构不采用细网格，从而大大提高了计算效率。此外，TO-FDTD算法还可以避免时空场插值和亚网格算法的后期不稳定性。为了消除其变换区域的曲线边界引入的阶梯误差，我们提出了方形变换区域而不是圆形变换区域。我们在极坐标系中对正方形边界进行了参数化处理，使其易于实现。通过坐标变换，可以在变换区域内得到新的各向异性介电常数和磁导率。然后我们发展了一种稳定的各向异性FDTD算法来求解变换后的麦克斯韦方程组。小结构衍射和散射的数值结果表明，我们提出的TO-FDTD算法具有较高的计算效率和精度。
In this paper, we present a novel Transformation Optics based Finite-difference time-domain (TO-FDTD) algorithm with Square Transformed Region, which is suitable for fast electromagnetic analysis of small structures in a large computational domain. A small structure can be solved with coarse grids in a transformed region, since it is enlarged by transformation optics. No fine grid is applied for the small structure so that computational efficiency can be improved greatly. In addition, the TO-FDTD algorithm can also avoid time-space field interpolations and the late-time instability of the subgridding algorithm. To eliminate the staircasing errors introduced by curved boundaries of its transformed region, we propose the square transformed region instead of the circular one. We parameterize the square boundary in polar coordinates so that it is easy to be implemented. Through coordinate transformation, new anisotropic permittivity and permeability can be obtained in the transformed region. Then we develop a stable anisotropic FDTD algorithm to solve the transformed Maxwell’s Equations. Numerical results on diffraction and scattering of small structures show that our proposed TO-FDTD algorithm has high computational efficiency and accuracy.