Parabolic Equation Solution of Tropospheric Wave Propagation Using Fem

Abstract

Abstract-In this work, the parabolic equation applied on radiowave and microwave tropospheric propagation, properly manipulated, and resulting in a one-dimensional form, is solved using the Finite Element Method (FEM). The necessary vertical tropospheric profile characteristics are assigned to each mesh element, while the solution advances in small and constant range segments, each excited by the solution of the previous step. This is leading to a marching algorithm, similar to the widely used SplitStep formulation. The surface boundary conditions including the wave polarization and surface conductivity properties are directly applied to the FEM system of equations. Since the FEM system returns the total solution, a technique for the separation of the transmitted and reflected waves is also presented. This method is based on the application of the Discrete Fourier Transform (DFT) in the space domain, which allows for the separation of the existing wave components. Finally, abnormal tropospheric condition propagation is being employed to assess the method, while the results are compared to those obtained using the Advance Refractive Prediction System (AREPS v.3.03) software package.

Comparison of the signal level calculation results using numerical solution of parabolic equation with experimental data for the transhorizon paths

“…Then, step by step, using the same algorithm it is necessary to calculate the field values at all nodes of the next vertical row The parabolic equation numerical technique is commonly used to define radiowave characteristics in the line-of-sight coverage and the diffraction region [4][5][6][7][8]. For the longdistance tropospheric propagation this method is rarely used and is therefore studied a lot worse [9][10][11][12]. Thereby the problem of the calculation accuracy estimation in the transition region from the diffraction to the long-distance tropospheric propagation region and the radiowave beyondthe-horizon propagation region is arisen.…”

A Novel Wavelet-Galerkin Method for Modeling Radio Wave Propagation in Tropospheric Ducts

“…So, it takes long to solve these matrices and it also uses up too much memory. Finite Element Method (FEM) has also been employed for the solution of parabolic equation [3][4][5][6][7]. Effective boundary handling makes FEM attractive to numerical solution of partial differential equations (PDE).…”

A Novel Marching Algorithm for Radio Wave Propagation Modeling Over Rough Surfaces

“…Recently, the finite element method (FEM) has been employed for the solution of parabolic equations [2]. A linear dependence for the range variation of electromagnetic field is assumed.…”