AbstractThis work provides an introduction to one of the most widely used advanced methods for wave propagation modeling, the Parabolic Equation (PE) method, with emphasis on its application to tropospheric radio propagation in coastal and maritime regions. The assumptions of the derivation, the advantages and drawbacks of the PE, the numerical methods for solving it, and the boundary and initial conditions for its application to the tropospheric propagation problem are briefly discussed. More details are given for the split-step Fourier-transform (SSF) solution of the PE. The environmental input to the PE, the methods for tropospheric refractivity profiling, their accuracy, limitations, and the average refractivity modeling are also summarized. The reported results illustrate the application of finite element (FE) based and SSF-based solutions of the PE for one of the most difficult to treat propagation mechanisms, yet of great significance for the performance of radars and communications links working in coastal and maritime zones — the tropospheric ducting mechanism. Recent achievements, some unresolved issues and ongoing developments related to further improvements of the PE method application to the propagation channel modeling in sea environment are highlighted.
The detonation wave propagation modeling in a cylindrical channel
