电磁场2.5维时域间断有限元方法

2.5-D discontinuous Galerkin time-domain method for Maxwell equations

  • 摘要: 介质沿空间固定方向均匀分布的结构在电磁导波器件中有十分广泛的应用,对这类器件的分析通常被称为2.5D电磁问题。利用器件在固定方向介质分布均匀的特点,将电磁场量沿该方向进行空间傅里叶变换,可以把对三维问题的分析转化为两维问题求解,从而极大地减小计算开销。针对传统基于差分的2.5D电磁场算法在弯曲形状逼近上有阶梯误差的缺陷,本文提出了基于三角形网格的2.5D时域间断有限元方法(DGTD),并用它模拟了电偶极子与光纤的耦合效率和光子晶体光纤的色散特性。与基于规则网格的2.5D差分方法进行对比。结果表明,文中建立的2.5D DGTD方法对弯曲形状的模拟更加逼真,计算内存占用最大减少10.4%,计算精度最大相差0.011%,计算时间缩短74.9%,计算效率提高。

     

    Abstract: In this work, a 2.5-dimensional discontinuous Galerkin time-domain(2.5D-DGTD) method with perfectly matched layer is proposed as a flexible tool to solve accurately electromagnetic problems in which media are homogeneous in one direction. Two numerical examples are simulated to demonstrate the advantages of the proposed method, which are the coupling between an electric dipole and optical fiber, and the analysis of dispersion characteristics of a photonic crystal fiber. The method is compare with the traditional 2.5-dimensional finite-difference time-domain method. The results show that the 2.5D-DGTD method is more realistic, especially for the simulation of curved shapes, where compared the calculation memory is reduced by 10.4%, the calculation accuracy differs by 0.011%, the calculation time is shortened, and the calculation efficiency is increased by 74.9%.

     

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