Silva, José Patrocínio daSilva, Paulo César Linhares da2019-08-192019-08-192019-05-24SILVA, Paulo César Linhares da. Aplicação das Wavelets de Daubechies em conjunto com o método de propagação vetorial de feixes na análise de estruturas fotônicas. 2019. 120f. Tese (Doutorado em Engenharia Elétrica e de Computação) - Centro de Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, 2019.https://repositorio.ufrn.br/jspui/handle/123456789/27573In the Finite Element Method (FEM), the elements are connected by points, which are called nodes or nodal points. The set of elements and nodes, local and global, is known as mesh. In this case, what is subdivided into the mesh is the geometry of the structure to be analyzed. In order to analyze the physical behavior of the structure, we use mathematical equations that do not have an exact solution, but can be approximated numerically. The precision of the FEM depends on the number of nodes, the number of elements and the size and types of elements that make up the mesh. That is, the smaller the size of the element and the greater the number of them in a given mesh, the greater the precision in the results of the analysis. In this context, the computer simulation software has been evolving and seeks to improve the analyzes addressed by the FEM, improving the choice of types and the generation of the mesh, leading to a good performance of the modeling techniques. In this work, the search is for a better performance of FEM, when applied in conjunction with other techniques, to simulate the propagation of electromagnetic waves in dielectric waveguides. For this, we used the Daubechies wavelet as a mathematical tool to obtain the coefficients of the elementary matrices, which arise in the analysis, due to the geometry of the elements that form the mesh. Therefore, the proposal is to develop a Daubechies base to be used in conjunction with the Vector Beam Propagation Method (VBPM), in the analysis of the electromagnetic propagation in guided media. The VBPM uses as a numerical basis the FEM and the method of the propagation of light beams in optical structures. In order to reach the main objective of this work, a moment-generating function was developed to generate functions of type x k , starting from a base of wavelets. The function x k was expressed by means of a Daubechies wavelet base which gave rise to the elementary matrices of the VBPM, also known as base functions. To verify the accuracy of the VBPM with the new set of base functions, wave propagation was analyzed in a weak electromagnetic coupling dielectric guide and the transfer of energy between a photonic crystal optical fiber and a conventional optical fiber.Acesso AbertoDaubechiesWaveletsVBPMFEMdoctoralThesisCNPQ::ENGENHARIAS::ENGENHARIA ELETRICA