Limiting accuracy of two-dimensional parabolic equation solution using split-step Fourier transform method

Abstract

Numerical solution of the wave parabolic equation on a rectangular grid is analyzed, when the method of discrete split-step Fourier transform (FT) is used to calculate the values of the field in an inhomogeneous medium at the next step in the range. The goal was to identify the limiting possibilities of the FT method itself, so studies were carried out for the case of radio wave propagation in free space. Two related problems were solved: what is the minimum value of the root-mean-square error (RMSE) of the field calculation and what should be the values of the transfer coefficients of the Fourier series harmonics and the values of the coefficients of the artificial absorbing layer (AL) both depending on the parameters of the computational scheme. It is shown that the dependence of the RMSE on the distance to the source always has the maximum. The forms of the optimal AL differ from those traditionally used primarily due to the presence of a significant imaginary component.