电磁场2.5维时域间断有限元方法

侯毅然; 王玉恒; 王向晖; 张杰; 齐红新

doi:10.11884/HPLPB202133.210056

电磁场2.5维时域间断有限元方法

doi: 10.11884/HPLPB202133.210056

1.
华东师范大学物理与电子科学学院，上海 200241
2.
华南理工大学广东省半导体照明与信息化工程技术研究中心，广州 510641

基金项目: 国家自然科学基金项目（31600675）

详细信息

作者简介:
侯毅然（1996—），男，硕士研究生，主要从事计算电磁学研究

通讯作者:
齐红新（1974—），男，博士，主要从事计算电磁学研究

中图分类号: O441.4
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- 被引次数: 0
出版历程
- 收稿日期: 2021-02-23
- 修回日期: 2021-04-06
- 网络出版日期: 2021-05-22
- 刊出日期: 2021-07-15

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

1.
School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
2.
Guangdong Provincial Engineering Research Centre on Solid-State Lighting and Its Informationisation, South China University of Technology, Guangzhou 510641, China

摘要

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。
- 时域间断有限元 /
- 2.5D /
- FDTD /
- 电磁场分析 /
- 光纤
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%.
- discontinuous Galerkin time-domain method /
- 2.5-dimensional /
- FDTD /
- electromagnetic field analysis /
- optical fibers

HTML全文

图 1 单模光纤模型

Figure 1. Single mode fiber model

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图 2 计算区域的网格划分

Figure 2. FDTD grid and DGTD grid

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图 3 偶极子极化方向不同，观察点处电场强度分量随时间的变化关系以及误差分析

Figure 3. Relationship between electric field intensity component with time in different polarization direction of dipole source

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图 4 光子晶体光纤横截面结构及特征参数示意图

Figure 4. Calculation window of photonic crystal fiber

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图 5 相同模型、不同算法、不同网格密度、基模色散曲线对比

Figure 5. Comparison of dispersion curves of the same model, different algorithms and different mesh densities

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表 1 两种算法消耗计算资源的比较

Table 1. Comparison of two algorithms consuming computing resources

method	mesh	${\Delta _t}/fs$	memory/MB	time/s
2.5D-FDTD	625	0.094	261.5	823
2.5D-DGTD	432	0.013	227.4	217

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表 2 不同算法的有效折射率

Table 2. Fundamental effective index of different algorithms

method	mesh	result	relative error/%
2.5D-FDTD	211 600	1.428 72	0.002 8
	52 900	1.428 78	0.007 0
	13 225	1.428 84	0.011 2
2.5D-DGTD	23 720	1.428 69	0.000 7
	12 368	1.428 71	0.002 1
	5 972	1.428 71	0.002 1
3D-full-vector finite difference^[20]	14 400	1.428 68	−

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表 3 两种算法消耗计算资源的比较

Table 3. Comparison of two algorithms consuming computing resources

method	$\Delta l/{\rm{um}}$	mesh	${\Delta _{ {\rm{t} },\max} }/{\rm{fs}}$	memory/GB	time/s
2.5D-FDTD	0.047 92	211 600	0.112	1.4	22 812
	0.095 65	52 900	0.225	0.34	3 083
	0.191 67	132 25	0.451	0.07	432
2.5D-DGTD	0.106 67	23 720	0.280	0.874	5 732
	0.144 14	12 368	0.285	0.458	3 225
	0.207 79	5 972	0.360	0.229	1 394

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