Limiting Accuracy of Solving the Two-Dimensional Parabolic Equation by the Split-Step Fourier Transform Method

Numerical solution of the wave parabolic equation on a rectangular grid is analyzed when the discrete split-step Fourier transform (FT) method is used to calculate the field values in an inhomogeneous medium on the next step in the range. The goal is to find out the limiting possibilities of the FT method itself, so studies have been carried out for radio wave propagation in free space only. Two related problems have been solved. First, the minimum value of the root-mean-square error (RMSE) of the calculated field has been estimated. Second, the same has been done for the transmission coefficients of the Fourier series harmonics and of the coefficients of the artificial absorbing layer (AL), which are dependent on the parameters of the computational scheme. It is shown that the dependence of the RMSE value on the distance to the source always has a maximum. The forms of the optimal ALs differ from those used conventionally primarily by the presence of a significant imaginary component.