一种新型的高阶时域有限差分方法

许杰; 徐珂; 黄志祥

doi:10.11999/JEIT190050

一种新型的高阶时域有限差分方法

doi: 10.11999/JEIT190050

安徽大学电子信息工程学院合肥 230039

基金项目: 国家自然科学基金(61722101, 61801002, 61701001, 61701003)，安徽大学物理科学与信息技术研究所开放式学科建设基金(2019AH001)

详细信息

作者简介:
许杰：男，1989年生，博士，研究方向为计算电磁学、高性能计算和时域数值算法

徐珂：男，1991年生，博士，研究方向为计算电磁学、多物理仿真和时域数值算法

黄志祥：男，1979年生，教授，博士生导师，研究方向为计算电磁学，电磁散射与逆散射

通讯作者:
黄志祥　zxhuang@ahu.edu.cn

中图分类号: O441.4
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- 文章访问数: 2450
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- PDF下载量: 107
- 被引次数: 0
出版历程
- 收稿日期: 2019-01-17
- 修回日期: 2019-08-28
- 网络出版日期: 2019-09-02
- 刊出日期: 2020-02-19

A New High Order Finite Difference Time Domain Method

College of Electronic Information Engineering, Anhui University, Hefei 230039, China

Funds: The Natural National Natural Science of China (61722101, 61801002,61701001, 61701003), The Open Fund for Discipline Construction, Institute of Physical Science and Information Technology, Anhui University (2019AH001)

摘要

摘要:
相比于传统高阶时域有限差分算法(FDTD)而言，该文提出了一种改进的高阶FDTD的优化方法，该算法基于安培环路定律，通过计算机技术寻找到一组最优的系数使得FDTD方法的全局色散误差达到最小，通过不同分辨率下的点源辐射模拟证明了该方法在较低分辨率的情况下仍然具有极低的相位误差，对于解决电大尺寸结构建模中的数值色散等问题提供了有效的解决方案。
- 时域有限差分方法 /
- 相位误差 /
- 优化算法 /
- 安培环路定律
Abstract:
Compared with the traditional high-order Finite Difference Time Domain(FDTD) Method, an improved high-order FDTD optimization method is proposed in this paper. This algorithm is based on Ampere’s law of circuits and finds a set of optimal coefficients through computer technology to minimize the global dispersion error of the FDTD method.The simulation of point source radiation with different resolutions shows that this method still has very low phase error in the case of lower resolution. It provides an effective solution to the problem of numerical dispersion in the modeling of large size structures.
- Finite Difference Time Domain(FDTD) /
- Phase error /
- Optimization algorithm /
- Ampere’s law

HTML全文

图 1 高阶FDTD方法示意图

下载: 全尺寸图片幻灯片

图 2 改进的高阶FDTD算法示意图

下载: 全尺寸图片幻灯片

图 3 不同FDTD方法下的色散曲线

下载: 全尺寸图片幻灯片

图 4 2维点源辐射模型

下载: 全尺寸图片幻灯片

图 5 不同方法下点源辐射时域图

下载: 全尺寸图片幻灯片

图 6 矩形波导示意图

下载: 全尺寸图片幻灯片

图 7 不同方法下的S21参数曲线

下载: 全尺寸图片幻灯片

表 1 部分分辨率的色散误差

R	K₁	K₂	${\varPhi _{\gamma_i} }$
5	–0.14493668	0.102073777	5.3797×10^–10
10	–0.11619507	0.073446898	9.1959×10^–14
15	–0.11180257	0.069281772	8.4433×10^–16
20	–0.11032252	0.067892310	2.2994×10^–17
25	–0.10964732	0.067260967	4.3034×10^–18
30	–0.10928263	0.066920442	1.5703×10^–19
35	–0.10906389	0.066716504	4.4814×10^–20

下载: 导出CSV

表 2 4种情况下的运行时间和占用内存对比

	FDTD 方法	运行时间(s)	占用内存(MB)	空间步长(m)	时间步长(s)
粗网格	S22	0.0356	0.1	0.100	0.16×10^–9
	S24	0.0323	0.2	0.100	0.16×10^–9
	M24	0.0329	0.7	0.100	0.16×10^–9
细网格	S22	77.3070	3.0	0.004	0.66×10^–10

下载: 导出CSV

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