Simple approximation of the discrete Green's function in the frequency domain for the numerical solution of the parabolic equation

Abstract: A problem of calculation of electromagnetic field parameters by means of numerical solution of the parabolic equation using the discrete Fourier transform method with splitting is considered. The exact values of the transmission coefficients of the plane wave segments from the radiation source to a distance x in a homogeneous medium (discrete Green's function for the spectral region) are determined and the nature of their dependence on the transverse size of the rectangular region is described. A simple exponential approximation of the distance dependence for these coefficients for the near zone is proposed, the use of this approximation does not change the conventional calculation algorithm but significantly increases its accuracy.

Keywords: radio wave propagation, parabolic equation, discrete fourier transform method