Variable Step Size Solution of Standard Parabolic Equation in Complex Environment

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.