Variable Step Size Technique for the Parabolic Equation in Complex Environmental Conditions

Abstract

In this paper, a variable step size method for the PE (Parabolic Equation) is proposed to solve the problem of low computational efficiency in the study of radio wave propagation at a large range of complex environments. Firstly, the relationship between the error and the step size, the frequency and other factors of the SSFT (Split-Step Fourier Transform) solution in the standard atmosphere is deduced, and then the basic selection range of the step size is given for the variable step size method. 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 PE application is classified according to the requirement of error. Finally, the electric wave characteristics of typical complex environment are advanced by the method. The simulation results show that compared with the small step method, the variable step size method of the PE can reduce the horizontal sampling point by 55.9% and the calculation time by 69.6% when the accuracy is close to the small step method, and the variable step size method is more accurate than the fixed large size step method. Therefore, the variable step size on the PE can not only ensure the accuracy of calculation, but also reduce the memory and time required, which greatly improves the reliability and efficiency. Moreover, it is suitable for solving the problem of the radio wave propagation in complex environment.INDEX TERMS Split-step Fourier transform, parabolic equation, radio wave propagation, variable step size method.