Variable Step Size Solution of Standard Parabolic Equation in Complex Environment

复杂环境下标准抛物方程变步长解法

¹ School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
² The Science and Technology on UAV Laboratory, Northwestern Polytechnical University, Xi'an 710065, China

Received: 9 October 2018

Abstract

Aiming at the problem that it is difficult to balance the accuracy and velocity of the fixed-step solution of standard parabolic equation in the study of radio wave propagation in a wide range of complex environments, a variable-step solution method of standard parabolic equation is proposed. Firstly, after deducing the relationship between the error of SSFT solution and step size, frequency and other factors; And the basic selection range of step size for SPE variable step size solution is given. Secondly, the action mechanism of different environmental factors and the requirement of changing trend for step size are expounded through simulation, and the complex environment of SPE application is classified according to the requirement of error. Finally, the method is used to simulate the characteristics of the typical complex environment. The simulation results show that the method can save up to 71.4% of the time compared with the fixed-step method of parabolic equation under the condition of ensuring the calculation accuracy. The reliability and efficiency of the proposed method are verified, and the calculation efficiency of the parabolic equation radio wave prediction can be greatly improved. Therefore, the parabolic equation method with variable step size can ensure the accuracy of calculation, reduce the memory and time required for calculation, greatly improves the efficiency of calculation, and has practical significance in the application of real-time prediction of electromagnetic wave propagation in a wide range of complex environments.

摘要

针对标准抛物方程 (standard parabolic equation，SPE) 的固定步长解法在大范围复杂环境电波传播研究中计算精度与速度难以平衡的问题，提出标准抛物方程的变步长解法。首先，在推导出SSFT解法的误差与步长、频率等因素的关系后，为SPE的变步长解法给出步长的基本选择范围；其次，在满足误差要求条件下对SPE应用的复杂环境进行等级划分，阐述了不同环境因素作用机理及变化趋势对步长要求，为不同的复杂环境等级中选择相应的步长提供依据；最后，利用该方法对典型复杂环境的电波特性进行仿真，仿真结果表明该方法在确保计算精度的情况下，相对于抛物方程的固定步长解法节省时间最高可达71.4%，验证了提出方法的可靠性与高效性，能大幅度提高抛物方程电波预测的计算效率。因此，采用可变步长的抛物方程方法能在保证计算精度的同时，减少计算所占内存及所需时间，极大地提高了计算效率，在大范围复杂环境电磁波传播实时预测应用中具有现实意义。