Made available in DSpace on 2016-12-23T14:08:15Z (GMT). No. of bitstreams: 1 Atila Lupim Cruz.pdf: 1394501 bytes, checksum: 0954b2c5b1fdcb864ee81cef7d14e9e5 (MD5) Previous issue date: 2012-10-19 / A pesquisa envolvida na presente dissertação se baseou no uso de funções de base radial para gerar uma nova formulação integral, que interpola diretamente o termo não homogêneo da equação diferencial de governo, no contexto do Método dos Elementos de Contorno (MEC). Emprega-se o uso de funções primitivas das funções de interpolação originais no núcleo da integral de domínio, permitindo a transformação desta última numa integral de contorno, evitando assim a discretização do domínio por meio de células, semelhante ao realizado na Dupla Reciprocidade. Para melhor avaliação das potencialidades da formulação, os testes numéricos apresentados abordaram apenas a solução de problemas governados pela Equação de Poisson. Os problemas escolhidos dentro desta categoria possuem solução analítica, o que permitiu aferir com mais rigor a precisão dos resultados. Para melhor balizamento da eficiência da formulação proposta, todos os problemas abordados também foram resolvidos pela formulação com Dupla Reciprocidade. O custo computacional dispendido para cada uma dessas formulações também foi comparado. Para ambas as formulações também foram testados esquemas de ajuste da interpolação realizada, visando avaliar seus efeitos na precisão dos resultados e também propositando obter economia computacional em futuras aplicações em simulações na área de propagações de ondas / This research was based on the use of radial basis functions to generate a new integral formulation that interpolates directly the domain action, related to the inhomogeneous term of the governing differential equation, using the Boundary Element Method (BEM). The use of primitive functions of the original interpolation functions in the kernel of the inhomogeneous integral is proposed, allowing its transformation into a boundary integral, thus avoiding the domain discretization through cells, similar to that conducted in the Dual Reciprocity. To better evaluation of the capability of the proposed formulation, the numerical tests presented only solved problems governed by the Poisson Equation. Test problems chosen have known analytical solution, which allowed a better evaluation of the numerical accuracy. To better check the efficiency of the proposed formulation, all the problems were also solved by the Dual Reciprocity Boundary Element Formulation. The computational cost expended for each of these formulations was also compared. Fitting interpolation schemes for both formulations were also tested in order to evaluate their effects on the accuracy of the results and also looking for economy in future computational applications related to wave propagation problems

In this work, a numerical approach based on meshless methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and differentiation matrices easily by using scattered data points. We derive expressions for such matrices for the Laplace-Beltrami operator via so-called Reilly’s formulas and use them to solve the respective eigenvalue problem. Numerical studies of proposed methods are performed in order to demonstrate convergence on simple examples of one-dimensional curves and two-dimensional surfaces.

In this paper, we use the newly developed method of particular solution (MPS) and one-stage method of fundamental solution (MFS-MPS) for solving partial differential equation (PDE). In the 1-D Poisson equation, we prove the solution of MFS-MPS is converge to Spectral Collocation Method using Polynomial, and show that the numerical solution similar to those of using the method of particular solution (MPS), Kansa's method, and Spectral Collocation Method using Polynomial (SCMP). In 2-D, we also test these results for the Poisson equation and find the error behaviors.

The Method of Moments (MoM) has been used extensively to solve electromagnetic problems. Its popularity is largely attributed to its adaptability to structures with various shapes and success in predicting the equivalent induced currents accurately. However, due to its dense matrix, especially for large structures, the MoM suffers from long matrix solution time and large storage requirement. In this thesis it is shown that use of wavelet basis functions result in a MoM matrix which is sparser than the one obtained by using traditional basis functions. A new wavelet system, different from the ones found in literature, is proposed. Stabilized Bi-Conjugate Gradient Method which is an iterative matrix solution method is utilized to solve the resulting sparse matrix equation. Both a one-dimensional problem with a microstrip line example and a two-dimensional problem with a rectangular patch antenna example are studied and the results are compared.

Les problèmes de diffusion de particules, à deux et à trois corps, ont une importance cruciale en physique atomique, car ils servent à décrire différents processus de collisions. Actuellement, le cas de deux corps peut être résolu avec une précision numérique désirée. Les problèmes de diffusion à trois particules chargées sont connus pour être bien plus difficiles mais une déclaration similaire peut être affirmée. L’objectif de ce travail est de contribuer, d’un point de vue analytique, à la compréhension des processus de diffusion Coulombiens à trois corps. Ceci a non seulement un intérêt fondamental, mais est également utile pour mieux maîtriser les approches numériques en cours d’élaboration au sein de la communauté de collisions atomiques. Pour atteindre cet objectif, nous proposons d’approcher la solution du problème avec des développements en séries sur des ensembles de fonctions appropriées et possédant une expression analytique. Nous avons ainsi développé un nombre d’outils mathématiques faisant intervenir des fonctions Coulombiennes, des équations différentielles de second ordre homogènes et non-homogènes, et des fonctions hypergéométriques à une et à deux variables / Two and three-body scattering problems are of crucial relevance in atomic physics as they allow to describe different atomic collision processes. Nowadays, the two-body cases can be solved with any degree of numerical accuracy. Scattering problem involving three charged particles are notoriously difficult but something similar -- though to a lesser extent -- can be stated. The aim of this work is to contribute to the understanding of three-body Coulomb scattering problems from an analytical point of view. This is not only of fundamental interest, it is also useful to better master numerical approaches that are being developed within the collision community. To achieve this aim we propose to approximate scattering solutions with expansions on sets of appropriate functions having closed form. In so doing, we develop a number of related mathematical tools involving Coulomb functions, homogeneous and non-homogeneous second order differential equations, and hypergeometric functions in one and two variables

Made available in DSpace on 2014-12-17T14:56:03Z (GMT). No. of bitstreams: 1 OsmarADJ.pdf: 1159660 bytes, checksum: 65307a903dfe1a1f71297194d1c7e2a5 (MD5) Previous issue date: 2004-12-22 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / This dissertation presents a new proposal for the Direction of Arrival (DOA) detection problem for more than one signal inciding simultaneously on an antennas array with linear or planar geometry by using intelligent algorithms. The DOA estimator is developed by using techniques of Conventional Beam-forming (CBF), Blind Source Separation (BSS), and the neural estimator MRBF (Modular Structure of Radial Basis Functions). The developed MRBF estimator has its capacity extended due to the interaction with the BSS technique. The BSS makes an estimation of the steering vectors of the multiple plane waves that reach the array in the same frequency, that means, obtains to separate mixed signals without information a priori. The technique developed in this work makes possible to identify the multiple sources directions and to identify and to exclude interference sources / Esta disserta??o apresenta uma nova proposta para os problemas de detec??o de dire??o de chegada para mais de um sinal incidindo simultaneamente sobre um arranjo de antenas de geometria planar ou linear empregando algoritmos inteligentes. O estimador de DOA ? desenvolvido utilizando as t?cnicas de Conforma??o de Feixes Digital Convencional (CBF - Conventional Beamforming), de Separa??o Cega de Fontes (BSS {Blind Source Separation) e o estimador neural MRBF (Modular Structure of Radial Basis Functions). O estimador MRBF desenvolvido tem sua capacidade ampliada gra?as ?a intera??o com a t?cnica BSS, a qual faz uma estima??o dos vetores de guiamento das m?ltiplas ondas planas que alcan?am o arranjo na mesma freq??ncia, isto ?, consegue separar sinais misturados sem informa??es a priori. A t?cnica desenvolvida neste trabalho possibilita identificar a dire??o de m?ltiplas fontes e identificar e excluir as fontes de interfer?ncia

Orientadores: Wagner Caradori do Amaral, Ricardo Jose Gabrielli Barreto Campello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-04T02:57:58Z (GMT). No. of bitstreams: 1 Rosa_Alexda_M.pdf: 896715 bytes, checksum: 1baf3dbaef2a1280f09feabed84d996c (MD5) Previous issue date: 2005 / Resumo: Este trabalho analisa a modelagem de sistemas nao-lineares utilizando modelos de Wiener/Volterra com funcoes ortonormais de Kautz. Os modelos de Volterra sao uma generalizacao do modelo resposta ao impulso para a descricao de sistemas naolineares. Esses modelos necessitam de um numero consideravel de termos para a representacao dos kernels de Volterra. Essa complexidade pode ser reduzida utilizando-se uma representacao do tipo Wiener/Volterra, em que os kernels sao desenvolvidos utilizando uma base de funcoes ortonormais. Sao discutidos aspectos da selecao dos parametros livres (polos) que caracterizam essas funcoes, particularmente a selecao otima dos polos complexos das funcoes de Kautz. Este problema e resolvido minimizando-se o limitante superior do erro que surge a partir da aproximação truncada dos kernels de Volterra usando-se as funcoes de Kautz. Obtem-se a solu¸cao analitica para a escolha otima de um dos parametros relacionados com o polo de Kautz, sendo os resultados validos para modelos Wiener/Volterra de qualquer ordem. Apresentam-se ainda resultados de simulacoes que ilustram a metodologia apresentada, bem como a modelagem de um sistema de levitacao magnetica / Abstract: This work investigates the modelling of nonlinear systems using the Wiener/Volterra models with Kautz orthonormal functions. The Volterra models constitute a generalization of the impulse response model to describe nonlinear systems. Such models require a large number of terms for representing the Volterra kernels. However, this complexity can be reduced by using Wiener/Volterra models, in which the kernels are expanded using an orthonormal basis functions. Aspects about selection of the free parameters (poles) characterizing theses functions are discussed, in particular the optimal selection of the complex poles of the Kautz functions. This problem is solved by minimizing the upper bound of the error arising from the truncated approximation of Volterra kernels using Kautz functions. An analytical solution for the optimal choice of one of the parameters related to the Kautz pole is thus obtained, with the results valid for any-order Wiener/Volterra models. Simulations that illustrate the methodology described above are presented. Also, the modelling of a magnetic levitation system is discussed. / Mestrado / Engenharia / Mestre em Engenharia Elétrica

Microsized hexagonal gallium nitride pyramids show promise as next generation Light Emitting Diodes (LEDs) due to certain quantum properties within the pyramids. One metric for evaluating the efficiency of a LED device is by studying its Light Extraction Efficiency (LEE). To calculate the LEE for different pyramid designs, simulations can be performed using the FDTD method. Maximizing the LEE is treated as a black-box optimization problem with an interpolation method that utilizes radial basis functions. A simple heuristic is implemented and tested for various pyramid parameters. The LEE is shown to be highly dependent on the pyramid size, the source position and the polarization. Under certain circumstances, a LEE over 17% is found above the pyramid. The results are however in some situations very sensitive to the simulation parameters, leading to results not converging properly. Establishing convergence for all simulation evaluations must be done with further care. The results imply a high LEE for the pyramids is possible, which motivates the need for further research.

In this paper the obstacle description with Radial Basis Functions for contact problems in three dimensional elasticity will be done. A short Introduction of the idea of Radial Basis Functions will be followed by the usage of Radial Basis Functions for approximation of isosurfaces. Then these isosurfaces are used for the obstacle-description in three dimensional elasticity contact problems. In the last part some computational examples will be shown.

Model-based black-box optimization is a topic that has been intensively studied both in academia and industry. Especially real-world optimization tasks are often characterized by expensive or time-demanding objective functions for which statistical models can save resources or speed-up the optimization. Each of three parts of the thesis concerns one such model: first, copulas are used instead of a graphical model in estimation of distribution algorithms, second, RBF networks serve as surrogate models in mixed-variable genetic algorithms, and third, Gaussian processes are employed in Bayesian optimization algorithms as a sampling model and in the Covariance matrix adaptation Evolutionary strategy (CMA-ES) as a surrogate model. The last combination, described in the core part of the thesis, resulted in the Doubly trained surrogate CMA-ES (DTS-CMA-ES). This algorithm uses the uncertainty prediction of a Gaussian process for selecting only a part of the CMA-ES population for evaluation with the expensive objective function while the mean prediction is used for the rest. The DTS-CMA-ES improves upon the state-of-the-art surrogate continuous optimizers in several benchmark tests.