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Cássio Gonçalves do Regohttp://lattes.cnpq.br/4951179285879076Gláucio Lopes RamosClaudio Garcia BatistaFernando Jose da Silva Moreirahttp://lattes.cnpq.br/0454517457113247Nayara Ferreira Lessa2023-06-02T16:39:39Z2023-06-02T16:39:39Z2019-02-27http://hdl.handle.net/1843/54381Neste trabalho é aplicado o método da Equação Parabólica no Domínio do Tempo (TDPE) para análise da propagação em duas dimensões, na direção paraxial x e altura z, do campo eletromagnético com incidência rasante e polarização vertical, sobre perfis de relevo suavemente irregulares. São apresentadas as aproximações para NAPE (Narrow Angle Parabolic Equation) e WAPE (Wide Angle Parabolic Equation) no domínio do tempo, para a propagação em atmosfera homogênea e as condições de contorno de impedância do solo, considerando que não há variação da permissividade elétrica na direção y, perpendicular ao plano de incidência. Para limitar o domínio computacional superior é utilizada uma camada absorvente descrita pela janela de Hanning. As formas discretizadas das equações para NAPE são apresentadas e é proposta uma nova formulação para a discretização da WAPE. A solução numérica da TDPE é baseada nas aproximações das derivadas parciais por diferencias finitas com o método de CrankNicolson,queresultaemsistemasdeequaçõestridiagonaisresolvidasutilizandooalgoritmo de Thomas. A implementação computacional foi realizada no MatlabR. Os resultados obtidos possibilitam a análise da propagação com o passar do tempo, a predição do sinal recebido e energias dos sinais transmitido e recebido. Os sinais recebidos da TDPE-NAPE são comparados com métodos das Equações Integrais do Campo Elétrico (TD-EFIE) e Magnético (TD-MFIE) e a Teoria Uniforme da Difração (TD-UTD), sendo que a TDPE-NAPE apresentou melhores tempos nas simulações.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.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorporUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em Engenharia ElétricaUFMGBrasilENG - DEPARTAMENTO DE ENGENHARIA ELÉTRICAhttp://creativecommons.org/licenses/by-nc-nd/3.0/pt/info:eu-repo/semantics/openAccessEngenharia elétricaDiferenças finitasEquação parabólica no domínio do tempo (TDPE)Propagação eletromagnéticaNAPEWAPEDiferenças finitasCrank-Nicolson (CN)Algoritmo de ThomasMétodo da equação parabólica no domínio do tempo (TDPE) aplicado a predição e análise da propagação em terrenos irregularesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALNAYARA FERREIRA LESSA-M.pdfNAYARA FERREIRA LESSA-M.pdfapplication/pdf2070545https://repositorio.ufmg.br/bitstream/1843/54381/1/NAYARA%20FERREIRA%20LESSA-M.pdfbad94940c9e7c1d5c1558850d0704146MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufmg.br/bitstream/1843/54381/2/license_rdfcfd6801dba008cb6adbd9838b81582abMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/54381/3/license.txtcda590c95a0b51b4d15f60c9642ca272MD531843/543812023-06-02 13:39:39.594oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-06-02T16:39:39Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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