An effective 3D leapfrog scheme for electromagnetic modelling of arbitrary shaped dielectric objects using unstructured meshes
An effective 3D leapfrog scheme for electromagnetic modelling of arbitrary shaped dielectric objects using unstructured meshes
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DOI：
10.1007/s00466-015-1216-4
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发表时间：
2015-12
影响因子：
4.1
通讯作者：
A. Gansen;M. E. Hachemi;Salim Belouettar;O. Hassan;Kenneth Morgan
中科院分区：
文献类型：
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作者：
A. Gansen;M. E. Hachemi;Salim Belouettar;O. Hassan;Kenneth Morgan
在计算电磁学中，标准 Yee 算法的优点是简单且计算成本低。然而，由于弯曲界面的阶梯表示会导致精度损失，因此它通常不是建模与任意形状物体的电磁相互作用的首选方法。对于这些问题，通常采用非结构化网格有限体积时域方法，尽管该方案不满足离散级别的无散条件。在本文中，我们推广了用于非结构化网格的标准 Yee 算法，并解决了与楼梯相关的精度损失问题，同时保留了算法的无散性性质。该方案在高质量原始 Delaunay 和双 Voronoi 网格上实现。该方法的性能在之前的工作中通过模拟自由空间中球形 3D PEC 物体的电磁波散射得到了验证。在本文中，我们使用针对界面处 Delaunay 和 Voronoi 边缘的新平均技术，展示了该方案针对有损电介质穿透问题的性能。详细解释了该方法的实施，并演示了任意形状 3D 物体的透射率和散射模拟所获得的结果的质量。
In computational electromagnetics, the advantages of the standard Yee algorithm are its simplicity and its low computational costs. However, because of the accuracy losses resulting from the staircased representation of curved interfaces, it is normally not the method of choice for modelling electromagnetic interactions with objects of arbitrary shape. For these problems, an unstructured mesh finite volume time domain method is often employed, although the scheme does not satisfy the divergence free condition at the discrete level. In this paper, we generalize the standard Yee algorithm for use on unstructured meshes and solve the problem concerning the loss of accuracy linked to staircasing, while preserving the divergence free nature of the algorithm. The scheme is implemented on high quality primal Delaunay and dual Voronoi meshes. The performance of the approach was validated in previous work by simulating the scattering of electromagnetic waves by spherical 3D PEC objects in free space. In this paper we demonstrate the performance of this scheme for penetration problems in lossy dielectrics using a new averaging technique for Delaunay and Voronoi edges at the interface. A detailed explanation of the implementation of the method, and a demonstration of the quality of the results obtained for transmittance and scattering simulations by 3D objects of arbitrary shapes, are presented.