In this thesis, we present a simple and efficient \emph{a posteriori} error estimation procedure for a discontinuous finite element method applied to scalar first-order hyperbolic problems on structured and unstructured tetrahedral meshes. We present a local error analysis to derive a discontinuous Galerkin orthogonality condition for the leading term of the discretization error and find basis functions spanning the error for several finite element spaces. We describe an implicit error estimation procedure for the leading term of the discretization error by solving a local problem on each tetrahedron. Numerical computations show that the implicit \emph{a posteriori} error estimation procedure yields accurate estimates for linear and nonlinear problems with smooth solutions. Furthermore, we show the performance of our error estimates on problems with discontinuous solutions. We investigate pointwise superconvergence properties of the discontinuous Galerkin (DG) method using enriched polynomial spaces. We study the effect of finite element spaces on the superconvergence properties of DG solutions on each class and type of tetrahedral elements. We show that, using enriched polynomial spaces, the discretization error on tetrahedral elements having one inflow face, is O(h^{p+2}) superconvergent on the three edges of the inflow face, while on elements with one inflow and one outflow faces the DG solution is O(h^{p+2}) superconvergent on the outflow face in addition to the three edges of the inflow face. Furthermore, we show that, on tetrahedral elements with two inflow faces, the DG solution is O(h^{p+2}) superconvergent on the edge shared by two of the inflow faces. On elements with two inflow and one outflow faces and on elements with three inflow faces, the DG solution is O(h^{p+2}) superconvergent on two edges of the inflow faces. We also show that using enriched polynomial spaces lead to a simpler{a posterior error estimation procedure. Finally, we extend our error analysis for the discontinuous Galerkin method applied to linear three-dimensional hyperbolic systems of conservation laws with smooth solutions. We perform a local error analysis by expanding the local error as a series and showing that its leading term is O( h^{p+1}). We further simplify the leading term and express it in terms of an optimal set of polynomials which can be used to estimate the error. / Ph. D.

This thesis introduces a representation of graphical data, progressive meshes, and its fields of usage. The main part of this work is mathematical representation of progressive meshes and the simplification algorithm, which leads to this representation. Examples of changes in progressive mesh representation are also part of this thesis, along with few examples. The result is an application that implements the calculation of the Progressive Meshes model representation

For everyday cycling, one needs to carry rainproof clothing just for the case of unexpected downpours. In the present research, we present a concept for a helmet which is automatically rainproof when the rain starts. When the sun comes out, the helmet is breathable again even before it completely dries up. This functionality is provided by active hydrogel meshes. Hydrogel meshes offer great advantages due to their ability to change the aperture size with swelling and deswelling. In our current work, we present the design and modeling steps for hydrogel-layered active meshes which use (i) swelling and deswelling in hydrated state and (ii) swelling starting from the dry state. The main goal is to close the air openings of a bicycle helmet when rain starts as an automatic rainproofing. This can be achieved through the swelling of the hydrogel pNiPAAM-co-chlorophyllin in the meshes, which leads to closing when hydrated. At the same time, the light-sensitive behavior leads to opening of the apertures under direct sun exposure, i.e. when the sun appears again after the rain. We present the steps of modeling and design using the Normalized Extended Temperature-Expansion-Model (NETEM) to perform simulations in Abaqus. The model is capable of describing both the swelling of the hydrogel under light stimulus and the volume change due to hydration. It is based on the analogy between free swelling and thermal expansion and defined for nonlinear displacements. We also discuss the fabrication process of hydrogel-layered fibers and challenges in their application and simulation. As a proof of concept for hydrogel-layered meshes, we show preliminary experimental results of a poly(acrylamide)/poly(2-acrylamido-2-methyl-1-propanesulfonic acid) (PAAm/PAMPS) hydrogel with semi-interpenetrated network (SIPN) structure and its swelling capacities on a mesh. Starting from the active hydrogel meshes as presented in the current work, the next step can be smart textiles that harness the power of hydrogels: the adaptation to combinations of stimuli - like humidity, temperature and brightness - that define environments.

[pt] Na visualização de campos escalares de dados volumétricos, o uso de seções de corte é uma técnica eficaz para se inspecionar a variação do campo no interior do domínio. A técnica de visualização consiste em mapear sobre a superfície da seção de corte um mapa de cores, o qual representa a variação do campo escalar na interseção da superfície com o volume. Este trabalho propõe um método eficiente para o mapeamento de campos escalares de malhas não estruturadas em seções de corte arbitrárias. Trata-se de um método de renderização direta (a interseção da superfície com o modelo não é extraída) que usa a GPU para garantir bom desempenho. A idéia básica do método proposto é utilizar o rasterizador da placa gráfica para gerar os fragmentos da superfície de corte e calcular a interseção de cada fragmento com o modelo em GPU. Para isso, é necessário testar a localização de cada fragmento na malha não estruturada de maneira eficiente. Como estrutura de aceleração, foram testadas três variações de grades regulares para armazenar os elementos (células) da malha, e cada elemento é representado pela lista de planos de suas faces, facilitando o teste de pertinência fragmento-elemento. Uma vez determinado o elemento que contém o fragmento, são aplicados procedimentos para interpolar o campo escalar e para identificar se o fragmento está próximo à fronteira do elemento, a fim de representar o aramado (wireframe) da malha na superfície de corte. Resultados obtidos demonstram a eficácia e a eficiência do método proposto. / [en] For the visualization of scalar fields in volume data, the use of cross sections is an effective technique to inspect the field variation inside the domain. The technique consists in mapping, on the cross section surfaces, a colormap that represents the scalar field on the surfasse-volume intersection. In this work, we propose an efficient method for mapping scalar fields of unstructured meshes on arbitrary cross sections. It is a direct-rendering method (the intersection of the surface and the model is not extracted) that uses GPU to ensure efficiency. The basic idea is to use the graphics rasterizer to generate the fragments of the cross-section surface and to compute the intersection of each fragment with the model. For this, it is necessary to test the location of each fragment with respect to the unstructured mesh in an efficient way. As acceleration data structure, we tested three variations of regular grids to store the elements (cells) of the mesh, and each elemento is represented by the list of face planes, easing the in-out test between fragments and elements. Once the element that contains the fragment is determined, it is applied procedures to interpolate the scalar field and to check if the fragment is close to the element boundary, to reveal the mesh wireframe on the surface. Achieved results demonstrate the effectiveness and the efficiency of the proposed method.

As plantas tropicais vêm ocupando uma parcela crescente do setor de floricultura, tanto no mercado nacional quanto no internacional, por apresentarem formas exuberantes e coloridas. Neste sentido, o Costus lasius Loes. tem se destacado entre as plantas ornamentais por possuir, como característica mais atraente, pequenas inflorescências amarelo-ouro e caule pouco espiralado, marcas que dão leveza à combinação de plantas de vaso. Entretanto, esta espécie é pouco pesquisada no Brasil, principalmente quanto às condições ambientais de cultivo, de nutrição e de manejo da fertirrigação. O presente trabalho tem como objetivo avaliar o efeito de diferentes malhas fotoconversoras de sombreamento e diferentes concentrações de potássio, no cultivo de Costus lasius em ambiente protegido. O experimento foi conduzido em uma área experimental do Departamento de Produção Vegetal da Escola Superior de Agricultura \"Luiz de Queiroz\", em Piracicaba, SP. Os tratamentos foram constituídos da combinação de cinco concentrações de potássio na solução de fertirrigação (40, 80, 120, 160 e 200 mg L-1), com três diferentes colorações de cobertura Chromatinet (Polysak Plastic Industries Ltd), nas cores vermelha, azul e preta, com índice de sombreamento de 50%. Foram utilizados 25 vasos \"pote 19\" por malha, em um total de 75, com um número de duas plantas por vaso, dispostos em bancadas de alumínio já disponíveis no local. Foram avaliados o crescimento das plantas, o número de folhas, de hastes e de inflorescências, as dimensões das hastes e das inflorescências, a sanidade das folhas e das inflorescências, o índice de preenchimento de vaso, a matéria fresca e seca, o índice de área foliar, o índice de estresse hídrico da cultura, o índice de clorofila e o acúmulo das concentrações de macronutrientes no tecido vegetal. O sombreamento com a malha vermelha melhorou as características de crescimento, número de folhas e aumentou a produção de massa fresca e seca de costus. A concentração de 200 mg L-1 de K+, na solução de fertirrigação, é a recomendada para aumentar a massa fresca e o maior número das inflorescências, características relevantes para a espécie Costus lasius como planta ornamental. Os maiores teores de potássio acumulados nas inflorescências do costus são proporcionados pela concentração 200 mg L-1 sobre as malhas vermelha e azul; e pela concentração 160 mg L-1 no ambiente sombreado com a malha preta. A dose de 200 mg L-1 de K+ associada a malha preta conduzem aos melhores resultados em termos de produção de hastes e inflorescências. O cultivo de costus sobre a malha azul tem maior eficiência no aproveitamento da clorofila e no processo fotossintético, indicando a camada basal das folhas como referência para esse tipo de avaliação. O IEHC apresenta grande variabilidade durante todo o ciclo e indica o ambiente de malha vermelha como o mais passível de causar estresse hídrico para as plantas na maioria dos meses estudados. / Tropical plants have been participating of a growing portion in brazilian floriculture and in international markets, because of its exuberant and colorful forms. In this sense, the Costus lasius Loes. has stood out among ornamental plants because of its more attractive characteristics: small yellow-gold inflorescences and slightly spiraled stem, attributes that give lightness to the potted plants. However, there are few studies about this species in Brazil and mainly regarding the environmental conditions of cultivation, nutrition and fertirrigation management. The goal of this work is to evaluate the effect of different photoconverters meshes and different concentrations of potassium in the cultivation of Costus lasius in greenhouse. The experiment was conducted in an experimental area of the Plant Production Department at the School of Agriculture \"Luiz de Queiroz\", in Piracicaba, SP. Treatments were composed by a combination of five potassium concentrations in the fertigation solution (40, 80, 120, 160 and 200 mg L-1) in three different meshes (Polysak Plastic Industries Ltd): red, blue and black, with shading capacity of 50%. For each meshe color twenty-five pots were used, 75 pots in total, with two plants per pot, arranged in aluminum benches already available at the place. In this experiment were evaluated the plants growth, number of leaves, stems and inflorescences, dimensions of stems and inflorescences, leaves and inflorescences health, vessel filling index, fresh and dry matter, leaf area index, crop water stress index, chlorophyll index and accumulation of macronutrients concentrations in plant tissue. The shading with the red mesh improved the growth characteristics, number of leaves and increased the production of fresh and dry mass of costus. The K+ concentration of 200 mg L-1 in the fertigation solution is recommended to increase the fresh mass and to achieve the highest number of inflorescences, which are relevant characteristics for the specie Costus lasius as ornamental plant. The highest levels of accumulated potassium in costus inflorescences are provided by the concentration of 200 mg L-1 on the red and blue meshes; and by the concentration of 160 mg L-1 in the environment shaded with the black mesh. The dose of 200 mg L-1 of K+ associated with black mesh leads to the best results in terms of stem and inflorescence production. The cultivation of costus on the blue mesh has greater efficiency in the use of chlorophyll and in the photosynthetic process, indicating the basal layer leaves as reference for this type of evaluation. The CWSI shows great variability throughout the cycle and indicates the red mesh environment as the most likely to cause hydric stress to plants in most of the months studied.

Este trabalho propõe um esquema de diferenças finitas compacta de alta ordem para resolver problemas elípticos com coeficientes variáveis em malhas composta. São apresentados a formulação matemática e a dedução do método compacto de quarta ordem aplicado à problemas elípticos bidimensionais, em malha regular e composta. Foi adotado o uso da biblioteca PETSc com os seus pré-condicionadores e métodos numéricos para resolver os sistemas lineares resultantes da discretização do problema. Por fim, testes visando verificar o código foram feitos, utilizando o método de soluções manufaturadas, para mostrar alta eficiência e acurácia do método desenvolvido. / This paper proposes a scheme of compact finite difference higher order for solve elliptic problems with variable coeficients in composite meshes. we present the mathematical formulation and the deduction of the compact method of fourth order applied to two-dimensional elliptic problems in regular and composite mesh . It was adopted using the PETSc library with its pre- conditioners and numerical methods for solving linear systems resulting from discretization of the problem. Finally , tests to verify the code were made using the method of manufactured solutions to show high eficiency and accuracy of the method developed .

Computational modeling offers better insight into a wide range of bioelectrical and biomechanical problems with improved tools for the design of medical devices and the diagnosis of pathologies. Electromagnetic modeling at low and high frequencies is particularly necessary. Modeling electromagnetic, structural, thermal, and acoustic response of the human body to different internal and external stimuli is limited by the availability of numerically efficient computational human models. This study describes the development to date of a computational full-body human model - Visible Human Project (VHP) - Female Model. Its unique feature is full compatibility both with MATLAB and specialized FEM computational software packages such as ANSYS HFSS/Maxwell 3D. This study also describes progress made to date in using the newly developed tools for segmentation. A visualization tool is implemented within MATLAB and is based on customized version of the constrained 2D Delaunay triangulation method for intersecting objects. This thesis applies a VHP - Female Model to a specific application, transcranial Direct Current Stimulation (tDCS). Transcranial Direct Current Stimulation has been beneficial in the stimulation of cortical activity and treatment of neurological disorders in humans. The placement of electrodes, which is cephalic versus extracephalic montages, is studied for optimal targeting of currents for a given functional area. Given the difficulty of obtaining in vivo measurements of current density, modeling of conventional and alternative electrode montages via the FEM has been utilized to provide insight into the tDCS montage performance. An insight into future work and potential areas of research, such as study of bone quality have been presented too.

Cette thèse propose l’étude d’une méthode numérique permettant de simuler un plasma. On considère un ensemble de particules, dont le mouvement est régi par l’équation de Vlasov, et qui est sensible aux forces électromagnétiques, qui proviennent des équations de Maxwell. La résolution numérique des équations de Vlasov-Maxwell est réalisée par une méthode Particle In Cell (PIC). La résolution des équations de Maxwell nécessite un maillage suffisamment fin afin de modéliser correctement les problémes multi-échelles que nous souhaitons traiter. Cependant, mailler finement tout le domaine de calcul a un coût. La nouveauté de cette thèse est de proposer un solveur PIC sur des maillages cartésiens localement raffinés, des maillages non conformes, afin de garantir la bonne modélisation du phénomène physique et d’éviter une trop forte pénalisation des temps de calcul.Nous utilisons une méthode Galerkin Discontinue en domaine temporelle (GDDT), qui offre l’avantage d’être d'une grande flexibilité dans le choix du maillage et qui est une méthode d’ordre élevé. Un point fondamental dans l’étude des solveurs PIC concerne le respect de la conservation de la charge. Nous proposons deux approches afin de traiter cet aspect. La première concerne les méthodes utilisant un système de Maxwell augmenté, dont la nouveauté a été de les étendre aux maillages non conformes. La seconde approche repose sur une méthode originale de pré-traitement du calcul du terme source de courant. / This thesis deals with the study of a numerical method to simulate a plasma. We consider a set of particles whose displacement is governed by the Vlasov equation and which creates an electromagnetic field thanks to Maxwell equations. The numerical resolution of the Vlasov-Maxwell system is performed by a Particle In Cell (PIC) method. The resolution of Maxwell equations needs a sufficiently fine mesh to correctly simulate the multi scaled problems that we have to face. Yet, a uniform fine mesh of the whole domain has a prohibitive cost. The novelty of this thesis is a PIC solver on locally refined Cartesian meshes : non conforming meshes, to guarantee the good modeling of the physical phenomena and to avoid too large CPU time. We use the Discontinuous Galerkin in Time Domain (DGTD) method which has the advantage of a great flexibility in the choice of the mesh and which is a high order method. A fundamental point in the study of PIC solvers is the respect of the charge conserving law. We propose two approaches to tackle this point. The first one deals with augmented Maxwell systems, that we have adapted to non conforming meshes. The second one deals with an original method of preprocessing of the calculation of the current source term.

Cette thèse porte sur la généralisation de la méthode NXFEM proposée par A. et P. Hansbo pour le problème d’interface elliptique. La modélisation et simulation numérique d’écoulements dans des domaines fracturés sont au coeur de nombreuses applications, telles que le milieu pétrolier (modélisation de réservoirs, présence de failles, propagation d’un signal, repérage de couches), l’aérospatiale (problème de chocs, de rupture), en génie civil (fissuration du béton), mais également dans la biologie cellulaire (déformation des globules rouges). En outre, de nombreux projets de recherche nécessitent le développement des méthodes robustes pour la prise en compte de singularités, ce qui fait partie des motivations et des objectifs de l'équipe Concha, ainsi que de cette thèse. Une modification de cette méthode a tout d’abord été proposée afin d’obtenir la robustesse à la fois par rapport à la géométrie du maillage coupé par l’interface et par rapport aux paramètres de diffusion. Nous nous sommes ensuite intéressés à sa généralisation à tout type de maillages 2D-3D (triangles, quadrilatères, tétraèdres, hexaèdres), et pour tout type d’éléments finis (conformes, non conformes, Galerkin discontinus) pour des interfaces planes et courbes. Les applications ont été orientées vers des problèmes d’écoulements en milieux poreux fracturés : adaptation de la méthode NXFEM à la résolution d’un modèle asymptotique de failles, à des problèmes instationnaires, de transports, ou encore à des domaines multi-fracturés. / This thesis focuses on the generalization of the NXFEM method proposed by A. and P. Hansbo for elliptic interface problem. Numerical modeling and simulation of flow in fractured media are at the heart of many applications, such as petroleum and porous media (reservoir modeling, presence of faults, signal propagation, identification of layers ...), aerospace (problems of shock, rupture), civil engineering (concrete cracking), but also in cell biology (deformation of red blood cells). In addition, many research projects require the development of robust methods for the consideration of singularities, which is one of the motivations and objectives of the Concha team and of this thesis. First a modification of this method was proposed to obtain a robust method not only with respect to the mesh-interface geometry, but also with respect to the diffusion parameters. We then looked to its generalization to any type of 2D-3D meshes (triangles, quadrilaterals, tetrahedra, hexahedra), and for any type of finites elements (conforming, nonconforming, Galerkin discontinuous) for plane and curved interfaces. The applications have been referred to the flow problems in fractured porous media : adaptation of NXFEM method to solve an asymptotic model of faults, to unsteady problems, transport problems, or to multi-fractured domains.

As plantas tropicais vêm ocupando uma parcela crescente do setor de floricultura, tanto no mercado nacional quanto no internacional, por apresentarem formas exuberantes e coloridas. Neste sentido, o Costus lasius Loes. tem se destacado entre as plantas ornamentais por possuir, como característica mais atraente, pequenas inflorescências amarelo-ouro e caule pouco espiralado, marcas que dão leveza à combinação de plantas de vaso. Entretanto, esta espécie é pouco pesquisada no Brasil, principalmente quanto às condições ambientais de cultivo, de nutrição e de manejo da fertirrigação. O presente trabalho tem como objetivo avaliar o efeito de diferentes malhas fotoconversoras de sombreamento e diferentes concentrações de potássio, no cultivo de Costus lasius em ambiente protegido. O experimento foi conduzido em uma área experimental do Departamento de Produção Vegetal da Escola Superior de Agricultura \"Luiz de Queiroz\", em Piracicaba, SP. Os tratamentos foram constituídos da combinação de cinco concentrações de potássio na solução de fertirrigação (40, 80, 120, 160 e 200 mg L-1), com três diferentes colorações de cobertura Chromatinet (Polysak Plastic Industries Ltd), nas cores vermelha, azul e preta, com índice de sombreamento de 50%. Foram utilizados 25 vasos \"pote 19\" por malha, em um total de 75, com um número de duas plantas por vaso, dispostos em bancadas de alumínio já disponíveis no local. Foram avaliados o crescimento das plantas, o número de folhas, de hastes e de inflorescências, as dimensões das hastes e das inflorescências, a sanidade das folhas e das inflorescências, o índice de preenchimento de vaso, a matéria fresca e seca, o índice de área foliar, o índice de estresse hídrico da cultura, o índice de clorofila e o acúmulo das concentrações de macronutrientes no tecido vegetal. O sombreamento com a malha vermelha melhorou as características de crescimento, número de folhas e aumentou a produção de massa fresca e seca de costus. A concentração de 200 mg L-1 de K+, na solução de fertirrigação, é a recomendada para aumentar a massa fresca e o maior número das inflorescências, características relevantes para a espécie Costus lasius como planta ornamental. Os maiores teores de potássio acumulados nas inflorescências do costus são proporcionados pela concentração 200 mg L-1 sobre as malhas vermelha e azul; e pela concentração 160 mg L-1 no ambiente sombreado com a malha preta. A dose de 200 mg L-1 de K+ associada a malha preta conduzem aos melhores resultados em termos de produção de hastes e inflorescências. O cultivo de costus sobre a malha azul tem maior eficiência no aproveitamento da clorofila e no processo fotossintético, indicando a camada basal das folhas como referência para esse tipo de avaliação. O IEHC apresenta grande variabilidade durante todo o ciclo e indica o ambiente de malha vermelha como o mais passível de causar estresse hídrico para as plantas na maioria dos meses estudados. / Tropical plants have been participating of a growing portion in brazilian floriculture and in international markets, because of its exuberant and colorful forms. In this sense, the Costus lasius Loes. has stood out among ornamental plants because of its more attractive characteristics: small yellow-gold inflorescences and slightly spiraled stem, attributes that give lightness to the potted plants. However, there are few studies about this species in Brazil and mainly regarding the environmental conditions of cultivation, nutrition and fertirrigation management. The goal of this work is to evaluate the effect of different photoconverters meshes and different concentrations of potassium in the cultivation of Costus lasius in greenhouse. The experiment was conducted in an experimental area of the Plant Production Department at the School of Agriculture \"Luiz de Queiroz\", in Piracicaba, SP. Treatments were composed by a combination of five potassium concentrations in the fertigation solution (40, 80, 120, 160 and 200 mg L-1) in three different meshes (Polysak Plastic Industries Ltd): red, blue and black, with shading capacity of 50%. For each meshe color twenty-five pots were used, 75 pots in total, with two plants per pot, arranged in aluminum benches already available at the place. In this experiment were evaluated the plants growth, number of leaves, stems and inflorescences, dimensions of stems and inflorescences, leaves and inflorescences health, vessel filling index, fresh and dry matter, leaf area index, crop water stress index, chlorophyll index and accumulation of macronutrients concentrations in plant tissue. The shading with the red mesh improved the growth characteristics, number of leaves and increased the production of fresh and dry mass of costus. The K+ concentration of 200 mg L-1 in the fertigation solution is recommended to increase the fresh mass and to achieve the highest number of inflorescences, which are relevant characteristics for the specie Costus lasius as ornamental plant. The highest levels of accumulated potassium in costus inflorescences are provided by the concentration of 200 mg L-1 on the red and blue meshes; and by the concentration of 160 mg L-1 in the environment shaded with the black mesh. The dose of 200 mg L-1 of K+ associated with black mesh leads to the best results in terms of stem and inflorescence production. The cultivation of costus on the blue mesh has greater efficiency in the use of chlorophyll and in the photosynthetic process, indicating the basal layer leaves as reference for this type of evaluation. The CWSI shows great variability throughout the cycle and indicates the red mesh environment as the most likely to cause hydric stress to plants in most of the months studied.