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Afin de surmonter les difficultés de la méthode des éléments finis (MEF) liées à la forte dépendance de la solution au maillage, des méthodes sans maillage ont été développées durant les 20 dernières années. Ces techniques ont l’avantage de procurer des approximations très régulières, capables de répondre de manière plus satisfaisante aux exigences croissantes des applications. Cependant, certaines caractéristiques intrinsèques à la plupart de ces approches rendent leur mise en œuvre difficile : souvent des techniques supplémentaires spécifiques doivent être mises en place pour imposer les conditions aux limites et traiter les discontinuités physiques. Récemment, la méthode des éléments naturels (MEN) est apparue, se basant sur les concepts de diagramme de Voronoï et de voisins naturels. C’est une approche capable d’associer les avantages d’une approximation très régulière propre aux méthodes sans maillage et une mise en œuvre quasiment identique à la MEF. Cette thèse porte sur l’étude et le développement de la MEN dédiée aux applications du génie électrique. Le but principal de ce travail exploratoire est l’étude des limitations ainsi que des avantages et du potentiel de la MEN et ses concepts sous-jacents. Les analyses de performances de la méthode sont présentées. Sur les points ouverts tels que l’intégration numérique, la montée en ordre et l’interpolation vectorielle, des développements originaux sont proposés. / In order to overcome the limitations related to the finite element method’s (FEM) narrow dependency of the solution on the mesh, meshless or meshfree methods were developed over the last 20 years. These techniques present the advantage of yielding very smooth approximations, being able to respond more adequately to the increasing demands of applications. However, some intrinsic features of most of these approaches make the implementation difficult, often requiring additional specific techniques for the imposition of the boundary conditions and the treatment of physical discontinuities. Recently, the natural element method (NEM) was developed. This approach, based on the Voronoi diagram and the “natural neighbors” concepts, combines the advantages of very smooth approximations and a FEM-like implementation. This thesis focuses on the study and development of the NEM, dedicated to electrical engineering applications. The main purpose of this exploratory work is the study of the limitations, benefits and the potential of the NEM and its underlying concepts. Several analyses of NEM’s performance are presented. As far as the numerical integration, higher order approximations and the vector interpolation are concerned, original developments are proposed.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-21T19:02:46Z No. of bitstreams: 2 Dissertação - Alcione Borges Purcina - 2016.pdf: 4973424 bytes, checksum: b35ba030a2a1888c5554daaa45f886e4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T20:22:01Z (GMT) No. of bitstreams: 2 Dissertação - Alcione Borges Purcina - 2016.pdf: 4973424 bytes, checksum: b35ba030a2a1888c5554daaa45f886e4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-07T20:22:01Z (GMT). No. of bitstreams: 2 Dissertação - Alcione Borges Purcina - 2016.pdf: 4973424 bytes, checksum: b35ba030a2a1888c5554daaa45f886e4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-09 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / In the last years, there is a growing interest in the study of nonlinear phenomena that because with the modernization of the structures and employment of innovative and more flexible materials, the nonlinearities become more evident. In that sense, this work aims to study the behavior of a mechanical system with two degrees of freedom with non-linear characteristics in primary resonance. The structure consists of the main system connected to a secondary system to act as a Nonlinear Dynamic Vibration Absorber, which partially or fully absorbs the vibrational energy of the system. The numerical solutions of the problem are obtained using the Runge-Kutta methods of 4th order and approximate analytical solutions are obtained using the Multiple Scales Method, and then it turns out how close can be closer to the numerical solutions. Through the mentioned disturbance method, too, it is determined the answers for the ordinary differential equations of the first order, which describe the modulation amplitudes and phases. Thus, the solution in steady state and the stability are studied using the frequency response. Furthermore, the behavior of the main system and the absorber are investigated through numerical simulations, such as responses in the time domain, phase planes and Poincaré map; which show that the system displays periodic movements, quasi-periodic and chaotic. / Nos últimos anos, é crescente o interesse pelo estudo dos fenômenos não lineares, isso porque com a modernização das estruturas e o emprego de materiais inovadores e mais flexíveis, as não linearidades tornaram-se mais evidentes. Nesse sentido, este trabalho tem por objetivo estudar o comportamento de um sistema mecânico de 2 graus de liberdade com características não lineares, em ressonância primária. A estrutura consiste do sistema principal conectado a um sistema secundário que atuará como um Absorvedor Dinâmico de Vibração não linear que, por sua vez, absorve parcial ou totalmente a energia vibratória do sistema. As soluções numéricas do problema são obtidas utilizando o Método de Runge-Kutta de 4ª ordem e as soluções analíticas aproximadas, são obtidas utilizando o Método das Múltiplas Escalas, para então verificar o quão próximas tais soluções conseguem aproximar-se das soluções numéricas. Através do Método de Perturbação mencionado, também, são determinadas as respostas para as equações diferenciais ordinárias de primeira ordem, que descrevem a modulação das amplitudes e fases. Sendo assim, a solução em regime permanente e sua estabilidade são estudadas utilizando a curva resposta de frequência. Além disso, o comportamento do sistema principal e do absorvedor são investigados através de simulações numéricas, tais como: respostas no domínio do tempo, os planos de fase e os seções de Poincaré; as quais evidenciam que o sistema exibe movimentos periódicos, quase-periódicos e caótico.

La striction diffuse et localisée sont des phénomènes précurseurs à la rupture ductile et représentent l'une des principales causes de rebut des pièces métalliques au cours de leur mise en forme. La mise en œuvre d'outils théoriques et numériques capables de prédire l'apparition de ces défauts s'avère nécessaire pour des raisons économiques et environnementales. Ces outils nécessitent en partie l'intégration d'un modèle de comportement adéquat permettant de reproduire les phénomènes physiques mis en jeu. Un tel modèle de comportement est ensuite couplé à un indicateur d'instabilité plastique offrant la possibilité de prédire de manière fiable les phénomènes de striction diffuse et localisée. Dans ce travail de thèse, nous avons considéré certains modèles d'endommagement micromécaniques basés sur l'approche de Gurson, et qui ont été couplés à différents critères d'instabilités plastiques reposant sur l'Analyse de Bifurcation. L'implantation numérique des modèles retenus a été réalisée dans le code de calcul par éléments finis Abaqus/Standard. En ce qui concerne les modèles d'endommagement, plusieurs schémas d'intégrations ont été testés afin d'analyser leur performance et leur robustesse lorsque le comportement présente un effet adoucissant. L'approche combinant le modèle de comportement et les critères de striction a été utilisée pour prédire les limites de formabilité en striction diffuse et localisée de plusieurs matériaux métalliques. Les résultats obtenus ont permis de dresser une hiérarchisation théorique et numérique des critères de striction utilisés. / Diffuse and localized necking are precursors to ductile fracture, and represent one of the main causes of metal parts rejection during forming operations. The implementation of theoretical and computational tools to predict the occurrence of these defects turns out to be necessary for economic and environmental reasons. These tools require in part the introduction of an appropriate behavior model in order to reproduce the physical phenomena involved during forming operations. Such a behavior model is then coupled to a plastic instability indicator providing the ability to reliably predict diffuse and localized necking. In the present work, we considered a micromechanical damage models based on Gurson's approach, which were coupled to different plastic instabilities criteria, based on Bifurcation Analysis. The numerical implementation of these models was carried within the implicit finite element code Abaqus/Standard. With regard to the damage models, several integration schemes were tested to analyze their performance and robustness when the behavior exhibits softening effect. The approach combining the Gurson's damage model and necking criteria has been applied for the prediction of formability limits of several metallic materials. The obtained results allowed establishing a theoretical and numerical classification between the necking criteria used in this work.

This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.

The K-distribution method is a fast approximative method used for calculating thermal infrared radiative transfer in the atmosphere, as opposed to the traditional Line-by-line method, which is precise, but very time-costly. Here we consider the atmosphere to consist of homogeneous and plane-parallel layers in local thermal equilibrium. This lets us use efficient upwards recursion for calculating the thermal infrared radiative transfer and ultimately the outgoing irradiance at the top of the atmosphere. Our specific implementation of the K-distribution method revolves around changing the integration space from the wavenumber domain to the g domain by employing Gauss-Legendre quadrature in two steps. The method is implemented in MATLAB and is shown to be several thousand times faster than the traditional Line-by-line method, with the relative error being only 3 % for the outgoing irradiance at the top of the atmosphere.

Les critères de substitution peuvent être utilisés à la place du critère de jugement le plus pertinent pour évaluer l'efficacité d'un nouveau traitement. Dans un contexte de méta-analyse, l'approche classique pour la validation d'un critère de substitution est basée sur une stratégie d'analyse en deux étapes. Pour des critères de jugement à temps d’évènements, cette approche est souvent sujette à des problèmes d'estimations. Nous proposons une approche de validation en une étape s'appuyant sur des modèles conjoints à fragilités et à copules. Ces modèles incluent à la fois des effets aléatoires au niveau essai et au niveau individuel ou des fonctions de copule. Nous considérons des fonctions de risque de base non paramétriquesà l'aide des splines. Les paramètres des modèles et les fonctions de risque de base ont été estimés par une méthode semi-paramétrique, par maximisation de la vraisemblance marginale pénalisée, considérant différentes méthodes d'intégration numérique. La validation des critères de substitution à la fois au niveau individuel et au niveau essai a été faite à partir du tau de Kendall et du coefficient de détermination. Les études de simulation ont été faites pour évaluer les performances de nos modèles. Les modèles ont été appliqués aux données individuelles issues des méta-analyses sur le cancer afin de rechercher de potentiels critères de substitution à la survie globale. Les modèles étaient assez robustes avec réduction des problèmes de convergence et d'estimation rencontrés dans l'approche en deux étapes. Nous avons développé un package R convivial implémentant les nouveaux modèles. / Surrogate endpoint can be used instead of the most relevant clinical endpointto assess the efficiency of a new treatment. In a meta-analysis framework, the classical approach for the validation of surrogate endpoint is based on a two-step analysis. For failure time endpoints, this approach often raises estimation issues.We propose a one-step validation approach based on a joint frailty and a joint frailty-copula model.The models include both trial-level and individual-level random effects or copula functions. We chose a non-parametric form of the baseline hazard functions using splines. We estimated parameters and hazard functions using a semi-parametric penalized marginal likelihood method, considering various numerical integration methods. Both individual level and trial level surrogacy were evaluated using Kendall's tau and coefficient of determination. The performance of the estimators was evaluated using simulation studies. The models were applied to individual patient data meta-analyses in cancer clinical trials for assesing potentiel surrogate endpoint to overall survival.The models were quite robust with a reduction of convergence and model estimation issues encountered in the two-step approach.We developed a user friendly R package implementing the models.