No description available.

No / An investigation of the surface current distribution in a normal-mode helical antenna (NMHA) is reported. This enables precise prediction of the performance of NMHAs, since traditional wire-antenna simulations ignore important details, such as non-uniform and transverse current distributions. A moment-method formulation is developed, using two-dimensional basis functions to represent the total non-uniform surface current distribution over the surface of the wire of the helix. Piecewise-sinusoidal basis functions are employed in two normal directions, with an exact kernel formulation and application of Galerkin's solution method. The numerical solution of the singular integrals associated with self-impedance terms was computed with a very low relative error. The surface current distribution was computed for different helix geometries. It was found that the axially-directed component of the current distribution around the surface of the wire was highly non-uniform and that there was also a significant circumferential current flow due to inter-turn capacitance, both effects that are overlooked by standard filamentary current representations.

No description available.

No description available.

This thesis explores the application of Radial Basis Functions (RBFs) to fluid dynamical problems. In particular, stationary Stokes and Navier-Stokes equations are solved using RBF collocation method. An existing approach from the literature, is enchanced by an additional polynomial basis and a new preconditioner. A faster method based on the partition of unity is introduced for stationary Stokes equations. Finally, a global method based on Picard linearization is introduced for stationary Navier-Stokes equations. / Denna avhandling utforskar tillämpningen av Radial Basis Functions (RBF) på dynamiska problem med vätskor. I synnerhet löses stationära Stokes och Navier-Stokes ekvationer lösas med hjälp av RBF-samlokaliseringsmetoden. En befintlig metod från litteraturen, förbättras genom en ytterligare polynombas och en ny förkonditionering. En snabbare metod baserad på enhetens partition introduceras för stationära Stokes-ekvationer. Slutligen introduceras en global metod baserad på Picard linjärisering för stationära Navier-Stokes ekvationer.

Réalisé en cotutelle avec l'Université Bordeaux 1 (France) / En synthèse d'images, le principal calcul à effectuer pour générer une image a été formalisé dans une équation appelée équation du rendu [Kajiya1986]. Cette équation est la intègre la conservation de l'\'energie dans le transport de la lumi\`ere. Elle stipule que l'énergie lumineuse renvoyée, par les objets d'une scène, dans une direction donnée est égale à la somme de l'énergie émise et réfléchie par ceux-ci. De plus, l'énergie réfléchie par un élément de surface est définie comme la convolution de l'éclairement incident avec une fonction de réflectance. Cette dernière modélise le matériau (au sens physique) de l'objet et joue le rôle d'un filtre directionnel et énergétique dans l'équation du rendu, simulant ainsi la manière dont la surface se comporte vis-à-vis d'une réflexion. Dans ce mémoire de thèse, nous introduisons de nouvelles représentations pour la fonction de réflectance ainsi que pour la représentation de l'éclairement incident. Dans la première partie de ce mémoire, nous proposons deux nouveaux modèles pour représenter la fonction de réflectance. Le premier modèle s'inscrit dans une démarche artistique et est destiné à faciliter la création et l'édition des reflets spéculaires. Son principe est de laisser l'utilisateur peindre et esquisser les caractéristiques (forme, couleur, gradient et texture) du reflet spéculaire dans un plan de dessin paramétrisé en fonction de la direction de la réflexion miroir de la lumière. Le but du second modèle est de représenter de manière compacte et efficace les mesures des matériaux isotropes. Pour ce faire, nous introduisons une nouvelle représentation à base de polynômes rationnels. Les coefficients de ces derniers sont obtenus à l'aide d'un processus d'approximation qui garantit une solution optimale au sens de la convergence. Dans la seconde partie de ce mémoire, nous introduisons une nouvelle représentation volumétrique pour l'éclairement indirect représenté directionnellement à l'aide de vecteurs d'irradiance. Nous montrons que notre représentation est compacte et robuste aux variations géométriques et qu'elle peut être utilisée comme système de cache pour du rendu temps réel ou non, ainsi que dans le cadre de la transmission progressive des données (streaming). Enfin, nous proposons deux types de modifications de l'éclairement incident afin de mettre en valeur les détails et les formes d'une surface. Le première modification consiste à perturber les directions de l'éclairement incident tandis que la seconde consiste à en modifier l'intensité. / In image synthesis, the main computation involved to generate an image is characterized by an equation named rendering equation [Kajiya1986]. This equation represents the law of energy conservation. It stipulates that the light emanating from the scene objects is the sum of the emitted energy and the reflected energy. Moreover, the reflected energy at a surface point is defined as the convolution of the incoming lighting with a reflectance function. The reflectance function models the object material and represents, in the rendering equation, a directional and energetic filter that describes the surface behavior regarding the reflection. In this thesis, we introduce new representations for the reflectance function and the incoming lighting. In the first part of this thesis, we propose two new models for the reflectance function. The first model is targeted for artists to help them create and edit highlights. Our main idea is to let the user paint and sketch highlight characteristics (shape, color, gradient and texture) in a plane parametrized by the incident lighting direction. The second model is designed to represent efficiently isotropic material data. To achieve this result, we introduce a new representation of the reflectance function that uses rational polynomials. Their coefficients are computed using a fitting process that guarantees an optimal solution regarding convergence. In the second part of this thesis, we introduce a new volumetric structure for indirect illumination that is directionally represented with irradiance vector. We show that our representation is compact and robust to geometric variations, that it can be used as caching system for interactive and offline rendering and that it can also be transmitted with streaming techniques. Finally, we introduce two modifications of the incoming lighting to improve the shape depiction of a surface. The first modification consists in warping the incoming light directions whereas the second one consists in scaling the intensity of each light source.

Construire une surface lisse d'un objet 3D est un problème important dans de nombreuses applications graphiques. En particulier, les méthodes de subdivision permettent de passer facilement d'un maillage discret à une surface continue. Un problème général résultant de la subdivision de deux maillages initialement connectés le long d'un bord est l'apparition de fissures ou de trous entre eux. Ces fissures produisent non seulement des formes indésirables, mais induisent aussi des difficultés pour les traitements ultérieurs. Il faut donc réparer ces défauts de sorte que la surface obtenue soit lisse et puisse être subdivisée ou modifiée. Nous proposons de nouvelles méthodes pour relier deux maillages avec des résolutions différentes en utilisant une transformée en ondelettes B-splines et une approximation locale ou une interpolation locale à l'aide de fonctions de base radiales (RBF). Ces procédés génèrent un maillage de connexion où la continuité est contrôlée. La résolution du maillage est ajustable pour respecter le changement de résolution entre les zones grossières et fines. En outre, nous présentons des méthodes pour combler les trous à n-côtés, et le raffinement des maillages grâce à un schéma de subdivision adaptative. Nous avons conçu, implémenté et testé les algorithmes en MatLab pour illustrer nos méthodes et montrer des résultats expérimentaux. Ces algorithmes sont mis en oeuvre sur de nombreux modèles d'objets 3D avec des formes complexes. En outre, nous avons fourni des approches différentes pour chaque problème. Ainsi, les résultats des différentes approches sont comparés et évalués afin d'exploiter les avantages et les inconvénients de ces approches. / Constructing a smooth surface of a 3D object is an important problem in many graphical applications. In particular, subdivision methods permit to pass easily from a discrete mesh to a continuous surface. A generic problem arising from subdividing two meshes initially connected along a common boundary is the occurrence of cracks or holes between them. These cracks not only produce undesired shapes, but also bring serious trouble for further mesh processing. They must be removed or filled so that the produced surface is smooth and can be further subdivided or edited. In order to remove cracks, we propose new methods for joining two meshes with different resolutions using a Lifted B-spline wavelet transform and a local approximation or radial basis function (RBF) local interpolation. These methods generate a connecting mesh where continuity is controlled from one boundary to the other and the connecting mesh can change gradually in resolution between coarse and fine areas. Additionally, we introduce methods for filling n-sided holes, and refining meshes with an adaptive subdivision scheme. We have designed, implemented, and tested the algorithms in MatLab to illustrate our proposed methods and show experimental results. These algorithms are implemented on many 3D object models with complex shapes. Additionally, we have provided some different approaches for each problem. Thus, results from the different approaches are compared and evaluated to exploit the advantages and disadvantages of these approaches.

O Método da Coordenada Geradora Hartree-Fock Polinomial (pMCG-HF), desenvolvido por R.C. Barbosa e A.B.F. da Silva [1], é uma ferramenta matemática valiosa que permite gerar funções de base (também conhecidas como conjuntos de base). As funções de base geradas por este método têm um bom comportamento e são capazes de calcular valores precisos de propriedades eletrônicas moleculares. Porém, depois de gerar funções de base do hidrogênio até o flúor [2], fez-se necessário a adição de expoentes à função de base, correspondentes a cada átomo, para melhor adaptação à realização dos cálculos moleculares. Estas funções adicionais são o que chamamos de funções de polarização. A adição de funções de polarização, através de otimização computacional, é muito custosa, deste modo o desenvolvimento de uma regra de polarização para se esquivar desta otimização é de grande importância e por isso se transforma na beleza e no objetivo deste trabalho. Portanto, nesta dissertação, estudar-se-á um procedimento para escolher funções de polarização que reduza drasticamente o tempo computacional, no sentido de permitir uma seleção, mais simples, de expoentes da própria função de base primitiva para serem usadas nas funções de polarização p, d, f, g, etc. para a obtenção de propriedades moleculares calculadas através de métodos químico-quânticos / The polynomial generate coordinate method pGCM developed by R.C. Barbosa and A.B.F. da Silva [1] is an remarkble mathematic tool for the generation of basis functions (also known as basis sets). The basis sets generated from this method have a good behavior and are able to produce accurate values for electronic molecular properties. In fact, after generating a basis set [2] we need to add a set of exponent functions in order to better adequate a basis set to perform molecular calculations. These sets of additional functions are called polarizations functions. This work provides a methodology where the polarization functions are obtained from the initial basis set (the primitive set) without optimizing them separately by using optimization algorithms that are, computationally speaking, very costly. This procedure reduces drastically the computational time used to find polarization functions to be used in molecular quantum chemical calculations. Our methodology permits to choose the polarization functions directly from the primitive orbital exponents of each atomic symmetry s, p, d, f etc. in a very simple manner. The finding of polarization functions using our methodology was performed with several quantum chemical methods.

In this dissertation, a Method of Moments (MoM) Volume Integral Equation (VIE)-based modeling approach suitable for a patch or slot antenna on a thin finite dielectric substrate is developed and validated. Two new key features of this method are the use of proper dielectric basis functions and proper VIE conditioning, close to the metal surface, where the surface boundary condition of the zero tangential-component must be extended into adjacent tetrahedra. The extended boundary condition is the exact result for the piecewise-constant dielectric basis functions. The latter operation allows one to achieve a good accuracy with one layer of tetrahedra for a thin dielectric substrate and thereby greatly reduces computational cost. The use of low-order basis functions also implies the use of low-order integration schemes and faster filling of the impedance matrix. For some common patch/slot antennas, the VIE-based modeling approach is found to give an error of about 1% or less in the resonant frequency for one-layer tetrahedral meshes with a relatively small number of unknowns. This error is obtained by comparison with fine finite- element method (FEM) simulations, or with measurements, or with the analytical mode matching approach. Hence it is competitive with both the method of moments surface integral equation approach and with the FEM approach for the printed antennas on thin dielectric substrates. Along with the MoM development, the dissertation also presents the models and design procedures for a number of practical antenna configurations. They in particular include: i. a compact linearly polarized broadband planar inverted-F antenna (PIFA); ii. a circularly polarized turnstile bowtie antenna. Both the antennas are designed to operate in the low UHF band and used for indoor positioning/indoor geolocation.

Made available in DSpace on 2016-12-23T14:08:09Z (GMT). No. of bitstreams: 1 Parte Inicial.pdf: 580643 bytes, checksum: 1783483d80317ac5307ad55e7cbdb752 (MD5) Previous issue date: 2013-03-25 / O propósito da pesquisa aqui elaborada é mostrar a viabilidade da aplicação de Funções de Base Radial de Suporte Compacto (FBRSC) no processo de aproximação direta do núcleo da ação de domínio através de integração de contorno. Essa formulação utilizada no tratamento da integral de domínio é denominada como (Método dos Elementos de Contorno com Integração Direta de Contorno) MECIC. Com o intuito de se avaliar a efetividade das FBRSC como funções de interpolação, serão realizados diversos testes numéricos, onde se deseja calcular o volume de superfícies. Então, serão realizados testes bidimensionais de aproximação, variando-se o suporte das FBRSCs, a fim de analisar o comportamento dessas funções. Depois de verificar a efetividade e a precisão das FBRSCs no processo de interpolação, desenvolvem-se programas, no ambiente do Método dos Elementos de Contorno (MEC), para a solução de problemas governados pela Equação de Poisson com a Formulação MECIC associada ao conceito de interpolação com FBRSC com suporte devidamente otimizados. A aferição das soluções numéricas obtidas se dá a partir da comparação com as suas respectivas soluções analíticas, facilmente encontradas na literatura especializada. Assim, possibilita-se estimar o erro relativo e então a eficácia da Formulação MECIC com FBRSC. Uma vez comprovado a sua eficácia, a Formulação MECIC com FBRSC é testada também com o esquema de interpolação com ajuste de pontos. Durante todo o desenvolvimento, atenta-se para a importância do custo computacional da formulação, a partir da geração de tabelas com o tempo de processamento dos programas implementados no MEC. Dessa forma, avalia-se qualitativamente o desempenho das FBRSC na Formulação MECIC, visando futuras aplicações na área de propagação de ondas sísmicas / The purpose of this research is to show the viability of application of Compactly Supported Radial Basis Function (CSRBF) in the process of direct approximation of the core of the domain action through boundary integration. This formulation is termed as (Boundary Elements Method with Directs Boundary Integration) MECIC, and is used in the treatment of the domain integration. By evaluating the effectiveness of CSRBF as interpolation functions, it performed several numerical tests to calculate the volume of surfaces. Also; by varying the support of CSRBFs, it performed two-dimensional approximation tests to examine the behavior of these functions. After verifying the effectiveness and accuracy of CSRBFs in the interpolation process, it developed computational programs to solve physical problems using the MECIC formulation, which is governed by Poisson s Equation. That formulation is associated with the concept of CSRBF in which the support is properly optimized. The calibration of the numerical solutions is given by the confrontation with their respective analytical solutions, easily found in the specialized literature. In this way, it is possible to estimate the relative error and the effectiveness of the MECIC formulation in association with the CSRBF concept. It is tested also with the curve fitting interpolation scheme. Owing the importance of the computational cost of that formulation, it is generated several time tables showing the processing time of those Boundary Elements Method computational programs. Therefore; aiming future applications in the seismic propagation wave area, it was finally evaluated the qualitative performance of the CSRBF in MECIC s formulation