基于MATLAB的电磁场有限差分法的数值分析

曲靖师范学院学报 ›› 2023, Vol. 42 ›› Issue (3): 9-14.

基于MATLAB的电磁场有限差分法的数值分析

朱永芳

安徽三联学院基础部,安徽合肥 230601

收稿日期:2022-12-12 出版日期:2023-05-26 发布日期:2023-06-30
作者简介:朱永芳,安徽三联学院基础部讲师,主要从事应用数学研究.
基金资助:
安徽省高校自然科学研究项目“几类泛函微分方程稳定性的研究”(KJ2021A1175);安徽三联学院校级科研项目“关于一类SEIQR传染病模型的研究”(KJZD2022011).

Numerical Analysis of Finite Difference Method of Electromagnetic Fields Based on MATLAB

ZHU Yongfang

Department of Elementary Courses, Anhui Sanlian University , Hefei Anhui 230601, China

Received:2022-12-12 Published:2023-05-26 Online:2023-06-30

摘要/Abstract

摘要： 采用FDTD方法,通过MATLAB软件对二维电磁场进行仿真,对电磁场有限差分法的数值进行分析. 结果表明:FDTD法适合用于计算复杂电磁场数值,矩形无限长槽模型和二维正方形静电场模型都可进行简单电磁场域计算,数值分析显示,矩形无限长槽模型迭代次数为213,二维正方形静电场模型迭代次数为62. 电场强度大小从图中线密集程度可反映出来,超松弛法、简单迭代法求解结果和设置的网格数有关. 当网格区域值不均时,场的变化不能通过差分格式反映出来. 使用麦克斯韦方程组积分形式可将网格内场变化信息能反映出来,得到的差分方程更准确.

关键词: MATLAB软件, 有限差分法, 电磁场, 数值分析

Abstract: The FDTD method is used to simulate the two-dimensional electromagnetic field through MATLAB software, and the numerical value of the electromagnetic field finite difference method is analyzed. The results show that the FDTD method is suitable for calculating the complex electromagnetic field values. Both the rectangular infinite slot model and the two-dimensional square electrostatic field model can be used for simple electromagnetic field calculation. The numerical analysis shows that the number of iterations of the rectangular infinite slot model is 213.The iteration number of two-dimensional square electrostatic field model is 62. The intensity of the electric field can be reflected from the density of the lines in the figure. The solution results of the over-relaxation method and the simple iteration method are related to the number of grids set. When the grid area values are uneven, the field changes cannot be reflected by the difference scheme. The integral form of Maxwell equations can reflect the change information of the field in the grid, and the difference equation obtained is more accurate.

Key words: MATLAB software, finite difference method, electromagnetic field, numerical analysis

中图分类号:

O175
TM15

朱永芳. 基于MATLAB的电磁场有限差分法的数值分析[J]. 曲靖师范学院学报, 2023, 42(3): 9-14.

ZHU Yongfang. Numerical Analysis of Finite Difference Method of Electromagnetic Fields Based on MATLAB[J]. Journal of Qujing Normal University, 2023, 42(3): 9-14.

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