Método da equação parabólica no domínio do tempo (TDPE) aplicado a predição e análise da propagação em terrenos irregulares

Abstract

In this work the Time Domain Parabolic Equation (TDPE) method is applied to analyze the propagation in two dimensions, in the paraxial direction x and height z, of the electromagnetic field with grazing incidence and vertical polarization, over smoothly irregularreliefprofiles.ThetimedomainapproximationstoNAPE(NarrowAngleParabolic Equation) and WAPE (Wide Angle Parabolic Equation) are presented, for homogeneous atmosphere propagation and soil impedance boundary conditions, considering that there is no variation of the electrical permittivity in the direction y, perpendicular to the plane of incidence. To limit the upper computational domain an absorbent layer described by the Hanning window is used. The discretized forms of the equations for NAPE are presented and a new formulation is proposed for WAPE discretization. The numerical solution of the TDPE is based on the approximations of the finite differences to partial derivatives with the Crank-Nicolson method, which results in systems of tridiagonal equations solved using the Thomas algorithm. The computational implementation was performed in MatlabR. The results obtained allow the analysis of propagation over time, the prediction of the received signal and energies of the transmitted and received signals. The signals received from the TDPE-NAPE are compared with the Electric Field Integral Equation (TD-EFIE) and Magnetic (TD-MFIE) and Uniform Theory of Diffraction (TD-UTD) methods, being that the TDPE-NAPE presented better times simulations.