强激光与粒子束, 2020, 32 (3): 033202, 网络出版: 2020-03-19
传输线方程的高精度龙格?库塔数值求解方法 下载: 600次
High-precision Runge-Kutta method for transmission line equation
摘要
提出了一种求解传输线方程的高精度龙格-库塔(RK)方法。此方法在空间上采取高阶泰勒展开,提高了对空间微分的近似精度,减少了数值色散所带来的误差。与传统的时域有限差分法(FDTD)方法相比,在每波长采样数相同时,RK方法的计算精度更高。同时,根据Taylor模型,对外界平面波激励源进行离散,成功利用RK方法对外部场激励传输线进行求解,扩大了龙格?库塔方法在求解传输线方程时的应用范围。通过编程对平面波辐照下无限大地平面上的单导体与双导体的算例分别应用FDTD方法与RK方法进行了计算,验证了RK方法的正确性。结果表明同等计算条件下RK方法的计算精度更高。
Abstract
This paper presents a high-precision Runge-Kutta (RK) method for solving transmission line equations. This method adopts high-order Taylor expansion in space, which improves the approximation accuracy of spatial differentiation. Compared with the traditional finite element time-domain method, when the number of samples per wavelength is the same, RK method has higher precision. At the same time, according to the Taylor model, researchers use RK method to solve transmission line equation in the external field excitation. The correctness and high precision of the RK method are verified by numerical examples of our study.
王旭桐, 周辉, 马良, 程引会, 李进玺, 刘逸飞, 赵墨, 郭景海, 王文兵. 传输线方程的高精度龙格?库塔数值求解方法[J]. 强激光与粒子束, 2020, 32(3): 033202. Xutong Wang, Hui Zhou, Liang Ma, Yinhui Cheng, Jinxi Li, Yifei Liu, Mo Zhao, Jinghai Guo, Wenbing Wang. High-precision Runge-Kutta method for transmission line equation[J]. High Power Laser and Particle Beams, 2020, 32(3): 033202.