Fast Computation of the Nonlocal Boundary Condition in Finite Difference Parabolic Equation Radiowave Propagation Simulations

Finite difference parabolic equation method (FD-PEM) codes using a nonlocal boundary condition to model radiowave propagation over electrically large domains, require the computation of time consuming spatial convolution integrals. For the first time, we propose the use of recursive convolution (RC) with vector fitting (VF) to reduce this computational burden. RC is based on the ability to express functions as a sum of exponential terms. This is achieved using the VF method. Details of the RC formulation applied in a two-dimensional (2D) Wide-angle FD-PEM (WA-FD-PEM) are presented together with 2D simulations which demonstrate the computational speed and accuracy of the synthesized RC-WA-FD-PEM code.