Design of Unequal Intervals for Split-Step Parabolic Equation and Mirror Kirchhoff Approximation in Three-Dimensional Environment

The split-step parabolic equation (SSPE) and the mirror Kirchhoff approximation (MKA) are fast methods for predicting the shadowing effect at millimeter waves (mmWaves). This letter proposes an algorithm for designing unequal intervals for an arbitrarily shaped scatterer in a three dimensional (3D) environment, aiming to reduce computational time. The 3D SSPE/MKA with proposed unequal intervals is validated for the scattering problem of a lossy dielectric sphere at mmWaves (40 GHz–100 GHz). The results show that the proposed method achieves good accuracy with a lowroot-mean-square error of less than 1 dB compared to the exact solution. In addition, the results show that the proposed method outperforms the conventional equal interval in terms of fast calculation speed by approximation 21%–51%.