General numerical solution of integral equation for long-range low-frequency groundwave propagation over irregular terrain

The flexibility of the integral equation (IE) method is limited by the available numerical solutions with uniform-grid schemes. In this paper, a general numerical solution of the IE is presented to predict long-range low-frequency (LF) groundwave propagation over irregular terrain. The general numerical solution is re-derived with the aid of Legendre–Gauss quadrature and interpolation quadrature. The great advantage of the resulting algorithm is that it can freely use non-uniform grid sizes in the computation area without loss of accuracy. Numerical results in two surface types, including triangular mountain and actual terrain are used to demonstrate the performance of the presented algorithm. Furthermore, it is ascertained that the non-physical perturbations at long propagation ranges in the IE predictions are caused by the inherent uniform-grid schemes of the numerical solution rather than the several approximations in the derivation of the IE form.