L'objectif de ce travail est d'identifier les paramètres inertiels segmentaires humains, c’est-à-dire la masse, la position du centre de masse et la matrice d’inertie de ces segments. Ces paramètres, au nombre de dix par segment, constituent une donnée d'entrée indispensable aux calculs de dynamique inverse utilisés dans les études de biomécanique. Bien qu'il existe des méthodes pour avoir accès à ces paramètres par le biais de tables anthropométriques ou le calcul des volumes segmentaires, l'identification apparaît nécessaire dès lors que les sujets étudiés sont atypiques (handicapés physiques, femmes enceintes, sportifs présentant des hypertrophies musculaires). L'originalité de ce travail est de proposer une approche mixte dans l'écriture du problème d'identification combinant une formulation vectorielle et matricielle des équations du mouvement d’un système poly-articulé supposé rigide, qui ont déjà été établies au sein de l'équipe dans les travaux de thèse de Tony Monnet. La première permet d’identifier les masses et les centres de masse segmentaires. La deuxième permet d’identifier, elle, les matrices d’inertie segmentaires. Les paramètres d’entrée de cette méthode d’identification sont les matrices rotations segmentaires, leurs dérivées secondes, les accélérations segmentaires, ainsi que le torseur externe. Si ce dernier est directement mesuré par une plateforme de force, les autres grandeurs sont obtenues après des opérations sur la mesure de la cinématique segmentaire du sujet obtenue par un système opto-électronique. Ce système mesurant la cinématique du sujet grâce à des marqueurs cutanés, cette cinématique diffère de la cinématique théorique obtenue si les segments sont rigides, du fait des mouvements des masses molles. Ce travail a donc porté sur le calcul d’une matrice rotation optimale, basée sur une transformation matérielle décrivant le mouvement segmentaire.De plus les mouvements des masses molles ainsi que les instruments de mesure induisent un bruit dans les signaux cinématiques. Du fait de la double dérivation de ces signaux pour le calcul des accélérations segmentaires et des dérivées secondes des matrices rotations, ce bruit devient prépondérant sur le signal porteur. Ce travail a donc également porté sur le filtrage à effectuer pour atténuer ces bruits. Cinq filtres utilisés dans la littérature (filtre de Butterworth, lissage de Savitsky-Golay, moyenne glissante, lissage par spline et analyse spectrale) ont été implémentés et leurs effets sur les paramètres inertiels identifiés ont été comparés. Les résultats montrent que les paramètres identifiés avec la méthode vectorielle ne nécessitent pas de traitement. L’identification des matrices d’inertie nécessite, elle, un traitement et le lissage optimal est obtenu avec le moyenne glissante.Enfin, une modélisation du membre supérieur par une chaîne cinématique a également été implémentée afin de rigidifier la cinématique acquise. Les premiers résultats ne sont pas satisfaisants mais le modèle retenu peut être affiné avant de conclure sur l’intérêt de cette modélisation pour l’identification des paramètres inertiels. Finalement, l’approche mixte développée permet l'identification des dix paramètres inertiels des segments du corps humain. La méthode a été validée en identifiant les paramètres inertiels des segments constituant le membre supérieur de dix huit sujets. Les paramètres obtenus ont ensuite été comparés à ceux issus d’une table anthropométrique. Les résultats montrent que les paramètres identifiés sont très proches de ceux estimés. Cela montre donc que l’identification des paramètres inertiels est fiable et permet d’avoir accès aux paramètres inertiels de sujets atypiques, pour qui les tables anthropométriques ne sont pas disponibles. / The aim of this thesis is the identification of body segment inertial parameters (BSIP), i.e. the segment mass, center of mass location and inertia tensor. Those ten parameters per segment are a mandatory input for inverse kinetics methods which are widely used in biomechanics studies. Despite the fact that methods exist to estimate them from anthropometric tables or segment volumes measurements, identification is useful when subjects are atypical (such as disabled people, pregnant women or athletes with muscular hypertrophies). The originality of this work is to use a mixed approach to write the identification problem, combining a vectorial and a matrix formulations of rigid multi-body motion equations, based on previous work did in the RoBioSS axis by Tony Monnet during his PhD. The first one permit to identify segmental masses and center of mass locations. The second one identifies segmental inertia tensors.Inputs of identification algorithm are rotation matrices, their second derivatives, segmental accelerations, and external torsor. Even though this external torsor is directly measured with a force plate, the others inputs are derived from kinematics measurements performed by an optoelectronical device. This device measures kinematics with skin mounted markers tracked by cameras, and the obtained kinematics deviate from the theoretical kinematics of rigid bodies, because of the soft tissues artefacts. In order to deal with these artefacts an optimal rotation matrix computation, based on material transformation, has been performed.Also, noise appears during measurement because of the soft tissues artefacts and the measure device. When double numerical derivatives are applied, this noise becomes greater than the carrier signal. In order to deal with it, five filters, i.e. Butterworth filter, Savitsky-Golay smoothing, sliding average window, spline smoothing and singular spectrum analysis, taken from literature have been implemented and compared. Results show that BSIP identify from vectorial formulation didn’t need any filtering. On the other hand, inertia tensors identification needed smoothed inputs and the best way to smooth them was the sliding average window.Finally, a kinematic chain model of the upper limb has been implemented to rigidify the kinematics. Preliminary results aren’t satisfying but the chain model can be improved before assuming kinematic chain aren’t well suited to enhance BSIP identification. Ultimately, the developed mixed approach has been validated by upper limb inertial parameters identification of eighteen subjects. Identified inertial parameters have also been compared with ones estimated with an anthropometric table. The conclusion is that the identified parameters were very close to the estimated ones, which shows that identification will be reliable to estimate inertial parameters of atypical subjects for whom anthropometric tables aren’t available.

Cette thèse comporte deux volets indépendants mais tous deux motivés par la modélisation mathématique et la simulation numérique de procédés photovoltaïques. La Partie I traite de systèmes d’équations aux dérivées partielles de diffusion croisée, modélisant l’évolution de concentrations ou de fractions volumiques de plusieurs espèces chimiques ou biologiques. Nous présentons dans le chapitre 1 une introduction succincte aux résultats mathématiques connus sur ces systèmes lorsqu’ils sont définis sur des domaines fixes. Nous présentons dans le chapitre 2 un système unidimensionnel que nous avons introduit pour modéliser l’évolution des fractions volumiques des différentes espèces chimiques intervenant dans le procédé de déposition physique en phase vapeur (PVD) utilisé pour la fabrication de cellules solaires à couches minces. Dans ce procédé, un échantillon est introduit dans un four à très haute température où sont injectées les différentes espèces chimiques sous forme gazeuse, si bien que des atomes se déposent petit à petit sur l’échantillon, formant une couche mince qui grandit au fur et à mesure du procédé. Dans ce modèle sont pris en compte à la fois l’évolution de la surface du film solide au cours du procédé et l’évolution des fractions volumiques locales au sein de ce film, ce qui aboutit à un système de diffusion croisée défini sur un domaine dépendant du temps. En utilisant une méthode récente basée sur l’entropie, nous montrons l’existence de solutions faibles à ce système et nous étudions leur comportement asymptotique dans le cas où les flux extérieurs imposés à la surface du film sont supposés constants. De plus, nous prouvons l’existence d’une solution à un problème d’optimisation sur les flux extérieurs. Nous présentons dans le chapitre 3comment ce modèle a été adapté et calibré sur des données expérimentales. La Partie II est consacrée à des questions reliées au calcul de la structure électronique de matériaux cristallins. Nous rappelons dans le chapitre 4 certains résultats classiques relatifs à la décomposition spectrale d’opérateurs de Schrödinger périodiques. Dans le chapitre 5, nous tentons de répondre à la question suivante : est-il possible de déterminer un potentiel périodique tel que les premières bandes d’énergie de l’opérateur de Schrödinger associé soient aussi proches que possible de certaines fonctions cibles ?Nous montrons théoriquement que la réponse à cette question est positive lorsque l’on considère la première bande de l’opérateur et des potentiels unidimensionnels appartenant à un espace de mesures périodiques bornées inférieurement en un certain sens. Nous proposons également une méthode adaptative pour accélérer la procédure numérique de résolution du problème d’optimisation. Enfin, le chapitre 6 traite d’un algorithme glouton pour la compression de fonctions de Wannier en exploitant leurs symétries. Cette compression permet, entre autres, d’obtenir des expressions analytiques pour certains coefficients de tight-binding intervenant dans la modélisation de matériaux 2D / This thesis includes two independent parts, both motivated by mathematical modeling and numerical simulation of photovoltaic devices. Part I deals with cross-diffusion systems of partial differential equations, modeling the evolution of concentrations or volume fractions of several chemical or biological species. We present in Chapter 1 a succinct introduction to the existing mathematical results about these systems when they are defined on fixed domains. We present in Chapter 2 a one-dimensional system that we introduced to model the evolution of the volume fractions of the different chemical species involved in the physical vapor deposition process (PVD) used in the production of thin film solar cells. In this process, a sample is introduced into a very high temperature oven where the different chemical species are injected in gaseous form, so that atoms are gradually deposited on the sample, forming a growing thin film. In this model, both the evolution of the film surface during the process and the evolution of the local volume fractions within this film are taken into account, resulting in a cross-diffusion system defined on a time dependent domain. Using a recent method based on entropy estimates, we show the existence of weak solutions to this system and study their asymptotic behavior when the external fluxes are assumed to be constant. Moreover, we prove the existence of a solution to an optimization problem set on the external fluxes. We present in Chapter3 how was this model adapted and calibrated on experimental data. Part II is devoted to some issues related to the calculation of the electronic structure of crystalline materials. We recall in Chapter 4 some classical results about the spectral decomposition of periodic Schrödinger operators. In text of Chapter 5, we try to answer the following question: is it possible to determine a periodic potential such that the first energy bands of the associated periodic Schrödinger operator are as close as possible to certain target functions? We theoretically show that the answer to this question is positive when we consider the first energy band of the operator and one-dimensional potentials belonging to a space of periodic measures that are lower bounded in certain ness. We also propose an adaptive method to accelerate the numerical optimization procedure. Finally, Chapter 6 deals with a greedy algorithm for the compression of Wannier functions into Gaussian-polynomial functions exploiting their symmetries. This compression allows, among other things, to obtain closed expressions for certain tight-binding coefficients involved in the modeling of 2D materials

Les travaux réalisés au cours de cette thèse s'intéressent à l'origine et à la formation des satellites naturels réguliers de Mars et Jupiter qui sont les cibles de futures missions d'exploration spatiale dédiées à leur caractérisation. Le cas controversé de l'origine de Phobos et Deimos, les lunes de Mars, est adressé et il est montré que leur formation à la suite d'un impact géant permettrait de réconcilier leurs propriétés orbitales et physiques. Concernant les satellites galiléens orbitant Jupiter, il est montré que dans le contexte classiquement utilisé de leur formation, la croissance des lunes a certainement procédé par l'accrétion de grains de poussières, un processus appelé "pebble accretion", plutôt que par celle de corps plus grands comme il est typiquement considéré. Des propriétés intéressantes, ainsi que d'autres plus problématiques, de la croissance des lunes galiléennes par "pebble accretion" sont dérivées. Dans un second temps, le transport de solides nécessaires à l'assemblage des lunes galiléennes dans le disque circum-jovien est étudié dans le contexte des récentes théories de formation des planètes géantes. Nous montrons que la vision classique selon laquelle le gaz accrété par Jupiter transporte assez de solides pour former ses lunes est probablement erronée. Il est proposé que, aidée par la formation de Saturne, Jupiter a pu capturer dans son disque assez de planétésimaux pour assembler les satellites galiléens. Contrairement aux précédents scénarios, le cadre proposé prédit que des analogues aux satellites galiléens ne se forment pas autour de toutes les planètes géantes / This thesis aims at better understanding the origin and formation of the martian moons, Phobos and Deimos, and the major jovian satellites known as the galilean moons, each of these systems being the target of future space exploration missions dedicated to their characterization. We address the puzzling origin of Phobos and Deimos and show that their formation following a giant impact could allow to account for both their orbital and physical properties. As regards the galilean moons, we argue that their growth would likely proceed through the accretion of small dust grains, a process known as pebble accretion, rather than through the accretion of larger satellitesimals within the typical framework assumed for their formation. We derive some interesting properties as well as some drawbacks of pebble accretion in the galilean system. Then, the delivery of solid material from the protoplanetary disk to the circum-jovian disk is investigated in light of recent developments of the theory of giant planets' formation. It is shown that the classic view that the gas accreted by Jupiter transports enough solids to build many galilean-like satellites is likely to be erroneous and some other mechanism must have taken place to account for the presence of the massive galilean moons. It is proposed that, with the help of Saturn's formation, Jupiter could have captured within its disk enough planetesimals on initially heliocentric orbits to build the galilean moons. Unlike previous scenarios, the proposed framework predicts that the presence of galilean analogues would not be ubiquitous around extrasolar giant planets

[pt] Este trabalho tem como objetivo apresentar uma alternativa para se analisar e avaliar opções sobre DI Futuro. Para tanto, faremos uso da teoria clássica sobre derivativos, e em particular, do modelo sugerido por Black [2] para a avaliação de opções sobre futuros de commodities. O contrato em questão, não possui solução analítica devido ao comportamento não linear do seu pay- off. A teoria define que a equação diferencial que descreve o comportamento do preço do ativo é função do ativo objeto. Neste trabalho, algumas simplificações foram assumidas, face a não adoção de um modelo estocástico que determine o comportamento futuro da taxa livre de risco, neste caso definida como um parâmetro determinístico do modelo. É fato de que tal simplificação não invalida os resultados, pelo contrário, McConnell e Schwartz [17] mostram que a relação custo benefício em se adotar modelos mais sofisticados não compensa frente aos resultados obtidos quando praticidade e ganhos são comparados. De posse da equação diferencial que governa o comportamento do preço do derivativo, se faz presente a necessidade de se usar um procedimento numérico - Método de Diferenças Finitas Explícito (MDFE). / [en] The main objective of this paper is to describe an alternative model to value Brazilian DI Future option. And so, we will make use of the classical derivatives theory, in particular, to the model introduced by Black for options on commodities future contracts. For such instrument, the analytical solution is not possible to be obtained due to the non-linear formulation of the pay-off (Risk Neutral Valuation). The theory defines the differential equation that describes the asset price behavior, in this case the financial operation agreed, as function of the underlying variables that govern its behavior. In the present work some simplifications had been carried through, regarding the non-adoption of a stochastic model to represent the future behavior of the risk-free rate, being defined as a deterministic parameter in the model. One must bear in mind that such simplification does not invalidate the results; on the contrary, McConnell e Schwartz [17] shows that the trade-off between the practicability and the profit in term of the results makes questionable the use of the more sophisticated model. Having the differential equation that governs the behavior of the derivative contract price, a numerical procedure is carried out - Explicit Finite Differences Method (EFDM).

Nesta dissertação nós revisamos aspectos gerais de teorias de gauge, os princípios da formulação de rede da cromodinâmica quântica (QCD) e algumas propriedades de quarkônios pesados, i.e. estados ligados de um quark pesado e seu antiquark. Como um exemplo de simulações de Monte Carlo de modelos de rede, apresentamos aplicações nos casos do oscilador harmônico e teorias de gauge SU(2). Nós estudamos o efeito de incorporar o propagador de gluon de simulações na rede em um modelo de potencial para a descrição do quarkônio, no caso do botômomio e do charmônio. Nós usamos em ambos os casos uma abordagem numérica para calcular as massas dos estados de quarkônio. O espectro resultante é comparado em ambos os casos com cálculos usando o potencial de Coulomb mais linear (ou potencial Cornell). / In this dissertation we review general aspects of gauge theories, the principles of the lattice formulation of quantum chromodynamics (QCD) and some properties of heavy quarkonia, i.e. bound states of a heavy quark and its antiquark. As an illustration of Monte Carlo simulations of lattice models, we present applications in the case of the harmonic oscillator and SU(2) gauge theory. We study the effect of incorporating the gluon propagator from lattice simulations into a potential model for the description of quarkonium, in the case of bottomonium and charmonium. We use a numerical approach to evaluate masses of quarkonium states. The resulting spectrum is compared in both cases to calculations using the Coulomb plus linear (or Cornell) potential.

A Técnica do Super-Passo pode melhorar significantemente a performance do Método de Euler Explícito, reduzindo a restrição existente ao passo no tempo. A técnica é descrita para a equação do calor linear. É mostrada a simplicidade de sua implementação para o caso do Método de Euler Explícito. A perfomance da Técnica do Super-Passo é comparada aos Métodos de Euler Explícito e Implícito, e Crank-Nicolson. Os resultados obtidos sugerem que o Super-Passo pode melhorar a eficiência do Método de Euler Explícito em aproximadamente uma ordem de grandeza reduzindo o tempo de processamento, enquanto que o erro produzido pela Técnica do Super-Passo é comparável ao produzido pelo Método de Euler Implícito. / The Super-Time-Stepping Technique can significantly increase the performance of the Explícit Euler Method, reducing the existing tie step restriction. The Techinique is described for a linear heat equation. The simplicity of this implementation for the case of the Explícit Euler Method is shown. The perfomance of the Technique of the Super-Time-Stepping is compared to Explicit and Implicit Euler, and Crank-Nicolson Methods. The obtained results suggest that the Technique of the Super-Time-Stepping potentially increases the efficiency of the Explicit Euler Method by 2 factor of 3 regarding the processing time, while the error produced is comparable to that produced by the Implicit Euler Method.

Este trabalho apresenta um estudo do comportamento de pilares de aço em situação de incêndio, abordado desde um ponto de vista numérico. Foram realizadas cerca de meio milhar de modelagens, utilizando o programa Vulcan e códigos desenvolvidos pelo autor deste trabalho, considerando-se análise não-linear geométrica e do material, a curva temperatura-tempo ISO 834, variação das propriedades termo-mecânicas de 4 tipos de aço, para vários perfis britânicos e brasileiros. Foi estudado o efeito da dilatação térmica em pilares com restrição aos deslocamentos axiais. Foi feita uma análise paramétrica em base a um modelo constituído por um pilar e uma mola axial em uma das suas extremidades. Foram construídas curvas para determinação da temperatura crítica a partir das normas Eurocódigo 3 Parte 1-2:2005 e ANSI/AISC 360-05 que são a base de modificações que serão apresentadas nas futuras ABNT/NBR 14323 e ABNT/NBR 8800. / This work presents studies about steel columns in fire situation with a numerical focus. The program Vulcan and some codes in Matlab developed by the author of this work were used for the modeling of more than half thousand models. The numerical models were solved considering geometric and material non-linearity, ISO 834 temperature-time curve, thermo-mechanical variation on 4 different steels, for some European and Brazilian typical cross sections. The effect of axial restrain for thermal dilatation on steel columns was studied. A parametric analysis based on a model using springs was made. Some curves for critical temperature determination were designed based on calculations using Eurocode 3 Part 1-2:2005 and ANSI/AISC 360-05, those International Standards are the base for the studies on preparing the new Brazilian Standards ABNT/NBR 14323 and ABNT/NBR 8800.

Flexible pipes are used in the offshore oil production to transport fluid and gas from the sea bead to the floating stations, and vice versa. These pipes have several concentric layers, of different materials, geometries and structural functions, since they are exposed to adverse operating environments, subjected to high internal and external pressures, high axial stresses and a series of dynamic loads. The local analysis is an important stage of a flexible pipe design and it consists on determining the stresses and strains distributions along the layers of the pipe. Multipurpose finite element packages are commonly used in the local analysis of flexible pipes, but they possess many limitations due to its generic nature, varying from the absence of specific tools for model creation to heavy restrictions of the number of degrees-of-freedom to make computational processing feasible. At the Polytechnic School of the University of São Paulo, within a research line in progress, several finite macroelements were formulated specifically for structural analysis of flexible pipes, taking into account their particularities, such as geometric patterns and layers assemblage. However, the numerical tools that implement these elements present very high memory and processing consumptions, limiting its usage for large-scale models. Therefore, this work has been motivated by memory and processing limitations of finite element structural analysis of flexible pipes for offshore applications. In this context, the Element-by-Element method, which does not require the global stiffness matrix, was chosen for its potential in memory reduction and processing capabilities, given its scalability and ease of parallelization. After an extensive literature review on numerical methods regarding the EBE method, it was chosen the Element-by-Element Diagonal Preconditioned Conjugate Gradient Method (EBE-PCG) algorithm. Aiming higher computational performance, the finite macroelements formulated by (PROVASI, 2013) were converted to the C++ language, implemented and parallelized in a new analysis tool, named as PipeFEM. The diagonal preconditioned EBE-PCG algorithm was implemented and parallelized with OpenMP. The scalability of the PCG algorithm is directly influenced by the efficiency of the matrix-vector product, an operation that, in the element-by-element method, is computed in a local basis with the blocks that comprise the model, and that requires synchronization techniques when performed in parallel. Four different synchronization strategies were developed, being the one based on geometric- and mesh- based mappings the most efficient of them. Numerical experiments showed a reduction of almost 92% in the EBE-PCG solution time of the parallelized version in comparison to the sequential one. In order to compare the efficiency of PipeFEM with the well-established finite element package ANSYS, a simplified flexible pipe was modeled in both software. PipeFEM was approximately 82 times faster than ANSYS to solve the problem, spending 24.27 seconds against 33 minutes and 18 seconds. In addition to this, PipeFEM required much less memory, 61.8MB against 6.8GB in ANSYS. In comparison to the dense version of MacroFEM, a reduction of more than three orders of magnitude was achieved in memory consumption. Despite the low the rate of convergence presented by the diagonal preconditioner, the implementation is very efficient in computational terms. Therefore, the objectives of this work were fulfilled with the development and application of the EBE method, allowing a reduction of memory and simulation costs. / Tubos flexíveis são utilizados na produção offshore de petróleo para o transporte de fluidos e gás natural das estruturas submersas até as estações flutuantes, e vice-versa. Estes tubos possuem diversas camadas concêntricas, de diferentes materiais, geometrias e funções estruturais, pois são expostos a ambientes adversos de operação, nos quais são submetidos à elevadas pressões internas e externas, elevados carregamentos e tensões axiais, além de uma série de carregamentos dinâmicos. A análise local é uma etapa importante do dimensionamento de um tubo flexível e consiste em determinar as distribuições de tensões e deformações ao longo das camadas do tubo. Pacotes multiuso de elementos finitos são comumente utilizados na análise local de tubos flexíveis, mas, devido as suas naturezas genéricas, possuem limitações que variam desde a ausência de ferramentas específicas para a criação de modelos até restrições pesadas no número total de graus de liberdade para tornar exequível o processo computacional. Na Escola Politécnica da Universidade de São Paulo, dentro de uma linha de pesquisa em andamento, diversos macroelementos finitos foram formulados especificamente para a análise estrutural de tubos flexíveis, levando em consideração as suas particularidades, como por exemplo padrões de geometrias e de montagem de camadas. Entretanto, a ferramenta numérica que implementa esses elementos apresenta elevado consumo de memória e de processamento, o que limita o seu uso para modelos de grande escala. Portanto, este trabalho foi motivado por limitações de memória e processamento em análises estruturais com o método dos elementos finitos para tubos flexíveis de aplicações offshore. Neste contexto, o método elemento-a-elemento, caracterizado pela eliminação da matriz global de rigidez, foi escolhido devido ao seu potencial de redução de consumo de memória e às suas capacidades de processamento, dada a sua escalabilidade e facilidade de paralelização. Após uma extensa revisão bibliográfica em métodos numéricos a respeito do método EBE, foi escolhido a versão diagonalmente precondicionada do método do gradiente conjugado (EBE-PCG). Com o intuito de se obter maior performance computacional, os macroelementos finitos formulados por (PROVASI, 2013) foram convertidos para a linguagem C++, paralelizados e implementado em uma nova ferramenta de análise chamada de PipeFEM, totalmente escrita em C++ e que explora paralelismo em todos as etapas. O algoritmo EBE-PCG foi implementado e paralelizado com OpenMP. A escalabilidade do algoritmo PCG é diretamente influenciada pela eficiência do produto entre matriz e vetor, uma operação que no método elemento-a-elemento é calculada na base local com os blocos que compõem o modelo, o que requer técnicas de sincronização quando realizada de modo paralelo. Quatro diferentes estratégias de sincronização foram desenvolvidas, sendo a mais eficiente delas a que utilizada mapeamentos baseados em características da geometria e malha. Experimentos numéricos mostraram uma redução de quase 92% no tempo de simulação do algoritmo PCG da versão paralelizada em relação à sequencial. De modo a comparar a eficiência do PipeFEM com o pacote bem estabelecido de elementos finitos, ANSYS, um tubo simplificado foi modelado em ambos os programas. PipeFEM foi aproximadamente 82 vezes mais rápido do que o ANSYS, gastando 24.27 segundos contra 33 minutos e 18 segundos. Além disso, PipeFEM consumiu muito menos memória, 61.8MB contra 6.8GB in ANSYS. Em comparação com a versão densa do MacroFEM, uma redução superior a três ordens de grandeza no consum e de memória foi obtida. Assim, apesar da baixa taxa de convergência apresentada pelo precondicionador diagonal, a implementação está muito eficiente em termos computacionais. Portanto, os objetivos deste trabalho foram alcançados com o desenvolvimento e aplicação do método EBE, o que permitiu uma redução considerável dos custos de simulação e memória.

Submitted by Maria Cristina (library@lncc.br) on 2017-08-14T19:07:20Z No. of bitstreams: 1 Tese-AlanAmad.pdf: 11294057 bytes, checksum: cadab8a6da3988a5a62791507562b196 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2017-08-14T19:07:34Z (GMT) No. of bitstreams: 1 Tese-AlanAmad.pdf: 11294057 bytes, checksum: cadab8a6da3988a5a62791507562b196 (MD5) / Made available in DSpace on 2017-08-14T19:07:45Z (GMT). No. of bitstreams: 1 Tese-AlanAmad.pdf: 11294057 bytes, checksum: cadab8a6da3988a5a62791507562b196 (MD5) Previous issue date: 2016-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Capes) / Wave propagation modeling is a challenging problem with many important practical applications in engineering and applied sciences. These applications include the modeling in acoustic, scattering, vibration, structural dynamic response, earthquake, seismic, electromagnetism, photonic, and so on. In fluid-structure modeling, the applications include, for example, simulations in aircraft, rockets, turbines, marine structures, storage tanks, dams, suspension bridges and noise reduction. Our interest is the development of numerical methods to accurately solving time-harmonic wave problems. In this thesis, we propose finite difference and finite element methods to solve the acoustic and elastic problems and a coupled acoustic fluid-structure problem. We also develop a numerical model to simulate hyperthermia therapy, based on topological derivatives and on a stabilized hybrid method. / Modelagem em propagação de ondas é um problema desafiador, com muitas aplicações práticas importantes em engenharia e ciências aplicadas. Estas aplicações incluem a modelagem em acústica, dispersão, vibração, resposta dinâmica estrutural, terremoto, sísmica, eletromagnetismo, fotônica, e assim por diante. Em modelagem de fluido-estrutura, as aplicações incluem simulações em aviões, foguetes, turbinas, estruturas marítimas, tanques de armazenamento, barragens e pontes suspensas, redução de ruído, por exemplo. Nosso interesse é o desenvolvimento de métodos numéricos para resolver precisamente problemas de ondas harmônicas no tempo. Nesta tese consideramos métodos de diferenças finitas e elementos finitos para resolver problemas acústicos e elásticos e um problema acoplado de fluido-estrutura acústica. Também desenvolvemos um modelo numérico para simular terapia por hipertermia, baseado em derivadas topológicas e um método híbrido estabilizado.

In this thesis we study methods for solving the neutron transport equation (or linear Boltzmann equation). This is an integro-differential equation that describes the behaviour of neutrons during a nuclear fission reaction. Applications of this equation include modelling behaviour within nuclear reactors and the design of shielding around x-ray facilities in hospitals. Improvements in existing modelling techniques are an important way to address environmental and safety concerns of nuclear reactors, and also the safety of people working with or near radiation. The neutron transport equation typically has seven independent variables, however to facilitate rigorous mathematical analysis we consider the monoenergetic, steady-state equation without fission, and with isotropic interactions and isotropic source. Due to its high dimension, the equation is usually solved iteratively and we begin by considering a fundamental iterative method known as source iteration. We prove that the method converges assuming piecewise smooth material data, a result that is not present in the literature. We also improve upon known bounds on the rate of convergence assuming constant material data. We conclude by numerically verifying this new theory. We move on to consider the use of a specific, well-known diffusion equation to approximate the solution to the neutron transport equation. We provide a thorough presentation of its derivation (along with suitable boundary conditions) using an asymptotic expansion and matching procedure, a method originally presented by Habetler and Matkowsky in 1975. Next we state the method of diffusion synthetic acceleration (DSA) for which the diffusion approximation is instrumental. From there we move on to explore a new method of seeing the link between the diffusion and transport equations through the use of a block operator argument. Finally we consider domain decomposition algorithms for solving the neutron transport equation. Such methods have great potential for parallelisation and for the local application of different solution methods. A motivation for this work was to build an algorithm applying DSA only to regions of the domain where it is required. We give two very different domain decomposed source iteration algorithms, and we prove the convergence of both of these algorithms. This work provides a rigorous mathematical foundation for further development and exploration in this area. We conclude with numerical results to illustrate the new convergence theory, but also solve a physically-motivated problem using hybrid source iteration/ DSA algorithms and see significant reductions in the required computation time.