Aplicação do método de Galerkin descontínuo para a análise de guias fotônicos

Orientador: Hugo Enrique Hernández FigueroaDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Um novo método de onda completo para realizar a análise modal em guias de onda é introduzido nesta dissertação. A ideia central por trás do método é baseada na discretização da equação de onda vetorial com o Método de Galerkin Descontínuo com Penalidade Interior (IPDG, do inglês Interior Penalty Discontinuous Galerkin). Com uma função de penalidade apropriada, um método de alta precisão e sem modos espúrios é obtido. A eficiência do método proposto é provada em vários guias de onda, incluindo complicados guias de ondas ópticos com modos vazantes e também em guias de onda plasmônicos. Os resultados foram comparados com os métodos do estado-da-arte descritos na literatura. Também é discutida a importância dessa nova abordagem. Além disso, os resultados indicam que o método é mais preciso do que abordagens anteriores baseadas em Elementos Finitos. As principais contribuições deste trabalho são: foi desenvolvido um novo método robusto e de alta precisão para a análise de guias de ondas arbitrários, uma nova função de penalidade para o IPDG foi proposta e aplicações práticas do método proposto são apresentadas. Adicionalmente, no apêndice é apresentado uma aplicação da análise modal em simulação eletromagnética 3D com um método de Galerkin DescontínuoAbstract: A novel full-wave method to perform mode analysis on waveguides is introduced in this dissertation. The core of the method is based on an Interior Penalty Discontinuous Galerkin (IPDG) discretization of the vector wave equation. With an appropriate penalty function a spurious-free and high accuracy method is achieved. The efficiency of the proposed method was proved in several waveguides, including intricate optical waveguides with leaky modes and also on plasmonic waveguides. The obtained results were compared with the state-of-the-art mode solvers described in the literature. Also, a discussion on the importance of this new approach is presented. Moreover, the results indicate that the proposed method is more accurate than the previous approaches based on Finite Elements Methods. The main contributions of this work are: the development of a novel robust and accurate method for the analysis of arbitrary waveguides, a new penalty function for the IPDG was proposed and practical applications of the methods are discussed. In addition, in the appendix an application of modal analysis on 3D electromagnetic simulations with a Discontinuous Galerkin method is detailedMestradoTelecomunicações e TelemáticaMestre em Engenharia ElétricaCAPE

Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM

This paper proposes a novel adaptive higher-order nite element (hp-FEM) method for solving elliptic eigenvalue problems, where n eigenpairs are calculated simultaneously, but on individual higher-order nite element meshes. The meshes are automatically hp-rened independently of each other, with the goal to use an optimal mesh sequence for each eigenfunction. The method and the adaptive algorithm are described in detail. Numerical examples clearly demonstrate the superiority of the novel method over the standard approach where all eigenfunctions are approximated on the same nite element mesh

Schnelle Löser für Partielle Differentialgleichungen

The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch (Leipzig), and Gabriel Wittum (Frankfurt am Main), was held May 22nd–May 28th, 2011. This meeting was well attended by 54 participants with broad geographic representation from 7 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Gratings: Theory and Numeric Applications

International audienceThe book containes 11 chapters written by an international team of specialist in electromagnetic theory, numerical methods for modelling of light diffraction by periodic structures having one-, two-, or three-dimensional periodicity, and aiming numerous applications in many classical domains like optical engineering, spectroscopy, and optical telecommunications, together with newly born fields such as photonics, plasmonics, photovoltaics, metamaterials studies, cloaking, negative refraction, and super-lensing. Each chapter presents in detail a specific theoretical method aiming to a direct numerical application by university and industrial researchers and engineers