Research

Parabolic Equation (PE) methods are frequently used to model propagation through rural environments and over bodies of water (Levy, “Parabolic Equation Methods for Electromagnetic Wave Propagation”, The Institution of Engineering and Technology, 2009). These methods come in two distinct flavors. (i) Split- Step Fourier (SSF) -based PE methods rely on spectral propagators to advance fields from one range slice to the next. Their ability to simulate wide-angle phenomena, ease of implementation, and computational efficiency oftentimes makes them the method of choice for modeling long range and non-line-of-sight phenomena. (ii) Finite Difference (FD) -based PE methods use a spatial approximation of the pseudo- spectral one-way propagator to advance fields from one range slice to the next. While they seldom compete with SSF solvers in terms of computational efficiency, they allow for accurate modeling of field interactions with complex terrain (Lee and McDaniel, "Ocean acoustics propagation by finite difference methods", Comput. Math. Applic, vol. 14, 1987; Levy, “Parabolic equation modelling of propagation over irregular terrain”, Electronics Letters, vol. 26, no. 15, 1990). SSF and FD methods have long been treated as independent solution frameworks for analyzing wave propagation.