Aujourd'hui, dans de nombreux champs d'applications, de plus en plus de problèmes d'ingénierie demandent d'avoir une évaluation précise et efficace de quantités d'intérêt.Très souvent, ces quantités dépendent de la solution d'une équation aux dérivées partielles (EDP) paramétrée où les paramètres -- physiques ou géométriques -- sont les entrées du modèle et les quantités d'intérêt -- valeurs moyennes -- en sont les sorties.Les techniques de réduction d'ordre, notamment la méthode des bases réduites qui est la méthode utilisée tout au long de ces travaux,permettent de répondre à ces demandes.Dans cette thèse nous nous intéressons à la mise en place d'un framework en C++, supportant le calcul parallèle, permettant d'appliquer la méthode des bases réduites à des problèmes multi-physiques non-linéaires tels queles problèmes de convection naturelle (couplage fluide-thermique), ou encore la modélisation d'aimants de type résistifs à hauts champs (nous nous limitons au couplage thermo-electrique) aboutissant à une étude sur la quantification d'incertitude.La méthode des bases réduites s'appuie naturellement sur une approximation obtenue via la discrétisation élément fini du problème à traiter. Pour cela nous utilisons la librairie de calcul Feel++, spécialisée dans la résolution d'EDPs.Nous nous intéressons également aux problèmes de type multi-échelles.La particularité de ces problèmes est de manipuler un ensemble de phénomènes mettant en jeu des échelles différentes, comme c'est le cas par exemple lorsque nous considérons un écoulement en milieu poreux.La méthode des éléments finis multi-échelles permet d'avoir le comportement "global", associé aux grandes échelles, de la solution du problème sans devoir le résoudre sur les petites échelles.Nous proposons une nouvelle construction des fonctions de base élément fini multi-échelles basée sur la méthode des bases réduites. / Today, in many fields of applications, more and more engineering problems require to have an accurate and efficient evaluation of quantities of interest.Often, these quantities depend on a partial differential equation (PDE) parameterized solution -- physical or geometrical -- are the model inputs and the quantities of interest -- average values ​​-- are the outputs.The order reduction techniques, including reduced basis method which is the method used throughout this work, can meet these demands.In this thesis, we focus on the establishment of a framework in C ++ supporting parallel computing, which applies the reduced basis method to nonlinear multiphysics problems such as problems with natural convection (fluid-thermal coupling) or the high field resistive magnet modeling (we limit ourselves to thermo-electric coupling) leading to a study on the uncertainty quantification.The reduced basis method naturally relies on an approximation obtained using the finite element discretization of the problem being treated. For this, we use the Feel ++ computation library specialized in PDE resolution.We are also interested by multiscale problems.The particularity of these problems is to manipulate a set of phenomena involving different scales, as this is the case for example when we consider a flow in porous media.The multiscale finite element method allows having a "global" behavior, linked with large scales, of the problem solution without solving it on small scales.We propose a new construction of multiscale finite element basis functions based on the reduced basis method.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-01T19:28:54Z No. of bitstreams: 1 TIAGO BRASILEIRO ARAÚJO - DISSERTAÇÃO PPGCC 2016..pdf: 18742851 bytes, checksum: 92b3eefe5e78ab27784255e850871df9 (MD5) / Made available in DSpace on 2018-08-01T19:28:54Z (GMT). No. of bitstreams: 1 TIAGO BRASILEIRO ARAÚJO - DISSERTAÇÃO PPGCC 2016..pdf: 18742851 bytes, checksum: 92b3eefe5e78ab27784255e850871df9 (MD5) Previous issue date: 2016-03-07 / Atualmente, o uso de grandes ontologias em diversos domínios do conhecimento está aumentando. Uma vez que estas ontologias podem apresentar sobreposição de conteúdo, a identificação de correspondências entre seus conceitos se torna necessária. Esse processo é chamado de Matching de Ontologias (MO). Um dos maiores desafios do matching de grandes ontologias é o elevado tempo de execução e o excessivo consumo de recursos de computacionais. Assim, para melhorar a eficiência, técnicas de particionamento de ontologias e paralelismo podem ser empregadas no processo de MO. Este trabalho apresenta uma abordagem para o Matching de Ontologias baseado em Particionamento e Paralelismo (MOPP) que particiona as ontologias de entrada em subontologias e executa as comparações entre conceitos em paralelo, usando o framework MapReduce como solução programável. Embora as técnicas de paralelização possam melhorar a eficiência do processo de MO, essas técnicas apresentam problemas referentes ao desbalanceamento de carga. Por essa razão, o presente trabalho propõe ainda duas técnicas para balanceamento de carga (básica e refinada) para serem aplicadas junto à abordagem MOPP, a fim de orientar a distribuição uniforme das comparações (carga de trabalho) entre os nós de uma infraestrutura computacional. O desempenho da abordagem proposta é avaliado em diferentes cenários (diferentes tamanhos de ontologias e graus de desbalanceamento de carga) utilizando uma infraestrutura computacional e ontologias reais e sintéticas. Os resultados experimentais indicam que a abordagem MOPP é escalável e capaz de reduzir o tempo de execução do processo de MO. No que diz respeito às técnicas de balanceamento de carga, os resultados obtidos mostram que a abordagem MOPP é robusta, mesmo em cenários com elevado grau de desbalanceamento de carga, com a utilização da técnica refinada de balanceamento de carga. / Currently, the use of large ontologies in various áreas of knowledge is increasing. Since, these ontologies can present contents overlap, the identification of correspondences among their concepts is necessary. This process is called Ontologies Matching (OM). One of the major challenges of the large ontologies matching is the high execution time and the computational resources consumption. Therefore, to get the efficiency better, partition and parallel techniques can be employed in the MO process. This work presents a Partition-Parallelbased Ontology Matching (PPOM) approach which partitions the input ontologies in subontologies and executes the comparisons between concepts in parallel, using the framework MapReduce as a programmable solution. Although the parallel techniques can get the MO efficiency process better, these techniques present problems concerning to the load imbalancing. For that reason, our work has proposed two techniques to the load balancing - the basic and the fine-grained one - which are supposed to be applied together with the PPOM approach, in order to orientate the uniform distribution of the comparisons (workload) between the nodes of a computing infrastructure. The performance of the proposed approach is assessed in different settings (different sizes of ontologies and degrees of load imbalancing) using a computing infrastructure and real and synthetic ontologies. The experimental results have indicated that the PPOM approach is scalable and able to reduce the OM process execution time. Referring to the load balancing techniques, the obtained results have shown that the PPOM approach is robust, even in settings with a high load imbalancing, with the fine-grained load balancing technique.

Les méthodes en simulation numérique dans le domaine de l’ingénierie pétrolière nécessitent la résolution de systèmes linéaires creux de grande taille et non structurés. La performance des méthodes itératives utilisées pour résoudre ces systèmes représente un enjeu majeur afin de permettre de tester de nombreux scénario.Dans ces travaux, nous présentons une manière d'implémenter des méthodes itératives parallèles au dessus d’un support exécutif à base de tâches. Afin de simplifier le développement des méthodes tout en gardant un contrôle fin sur la gestion du parallélisme, nous avons proposé une API permettant d’exprimer implicitement les dépendances entre tâches : la sémantique de l'API reste séquentielle et le parallélisme est implicite.Nous avons étendu le support exécutif HARTS pour enregistrer une trace d'exécution afin de mieux exploiter les architectures NUMA, tout comme de prendre en compte un placement des tâches et des données calculé au niveau de l’API. Nous avons porté et évalué l'API sur les processeurs many-coeurs KNL en considérant les différents types de mémoires de l’architecture. Cela nous a amené à optimiser le calcul du SpMV qui limite la performance de nos applications.L'ensemble de ce travail a été évalué sur des méthodes itératives et en particulier l’une de type décomposition de domaine. Nous montrons alors la pertinence de notre API, qui nous permet d’atteindre de très bon niveaux de performances aussi bien sur architecture multi-coeurs que many-coeurs. / Numerical methods in reservoir engineering simulations lead to the resolution of unstructured, large and sparse linear systems. The performances of iterative methods employed in simulator to solve these systems are crucial in order to consider many more scenarios.In this work, we present a way to implement efficient parallel iterative methods on top of a task-based runtime system. It enables to simplify the development of methods while keeping control on parallelism management. We propose a linear algebra API which aims to implicitly express task dependencies: the semantic is sequential while the parallelism is implicit.We have extended the HARTS runtime system to monitor executions to better exploit NUMA architectures. Moreover, we implement a scheduling policy which exploits data locality for task placement. We have extended the API for KNL many-core systems while considering the various memory banks available. This work has led to the optimization of the SpMV kernel, one of the most time consuming operation in iterative methods.This work has been evaluated on iterative methods, and particularly on one method coming from domain decomposition. Hence, we demonstrate that the API enables to reach good performances on both multi-core and many-core architectures.

O objetivo deste trabalho é estudar algoritmos paralelos para a solução de problemas de Mecânica dos Sólidos, Mecânica dos Fluídos e Interação Fluido-Estrutura empregando o Método dos Elementos Finitos para uso em configurações de memória distribuída e compartilhada. Dois processos para o particionamento da estrutura de dados entre os processadores e divisão de tarefas foram desenvolvidos baseados na aplicação do método de particionamento em faixas e do método da bissecção coordenada recursiva não sobre a geometria da malha mas sim diretamente sobre o sistema de equações, através de reordenações nodais para minimização da largura da banda. Para ordenar a comunicação entre os processadores, foi desenvolvido um algoritmo simples e genérico baseado em uma ordenação circular e alternada que permite a organização eficiente dos processos mesmo em cenários nos quais cada processador precisa trocar dados com todos os demais. Os algoritmos selecionados foram todos do tipo iterativo, por sua adequabilidade ao paralelismo de memória distribuída. Foram desenvolvidos códigos paralelos para o Método dos Gradientes Conjugados utilizado em problemas de Mecânica dos Sólidos, para o esquema explícito de Taylor-Galerkin com um passo e iterações utilizado na simulação de escoamentos compressíveis em regime transônico e supersônico, para o esquema explícito de Taylor- Galerkin com 2 passos para simulação de escoamentos incompressíveis em regime subsônico e para interação fluído-estrutura usando o esquema explícito de dois passos para o fluído e o método implícito de Newmark no contexto do método de estabilização α-Generalizado para a estrutura, com acoplamento particionado. Numerosas configurações foram testadas com problemas tridimensionais utilizando elementos tetraédricos e hexaédricos em clusters temporários e permanentes, homogêneos e heterogêneos, com diferentes tamanhos de problemas, diferentes números de computadores e diferentes velocidades de rede. / Analysis and development of distributed memory parallel algorithms for the solution of Solid Mechanics, Fluid Mechanics and Fluid-Structure Interaction problems using the Finite Element Method is the main goal of this work. Two process for mesh partitioning and task division were developed, based in the Stripwise Partitioning and the Recursive Coordinate Bisection Methods, but applied not over the mesh geometry but over the resultant system of equations through a nodal ordering algorithm for system bandwidth minimization. To schedule the communication tasks in scenarios where each processor must exchange data with all others in the cluster, a simple and generic algorithm based in a circular an alternate ordering was developed. The algorithms selected to be parallelized were of iterative types due to their suitability for distributed memory parallelism. Parallel codes were developed for the Conjugate Gradient Method ( for Solid Mechanics analysis), for the explicit one-step scheme of Taylor-Galerkin method (for transonic and supersonic compressible flow analysis), for the two-step explicit scheme of Taylor-Galerkin method (for subsonic incompressible flow analysis) and for a Fluid-Structure Interaction algorithm using a coupling model based on a partitioned scheme. Explicit two-step scheme of Taylor-Galerkin were employed for the fluid and the implicit Newmark algorithm for the structure. Several configurations were tested for three-dimensional problems using tetrahedral and hexahedral elements in uniform and nonuniform clusters and grids, with several sizes of meshes, numbers of computers and network speeds.

We study the turbulent flow of a fluid over a canopy, that we model as a deformable porous medium. This porous medium is more precisely a carpet of fibres that bend under the hydrodynamic load, hence initiating a fluid-structure coupling at the scale of a fibre's height (honami). The objective of the thesis is to develop a macroscopic model of this fluid-structure interaction in order to perform numerical simulations of this process. The volume averaging method is implemented to describe the large scales of the flow and their interaction with the deformable porous medium. An hybrid approach is followed due to the non-local nature of the solid phase; While the large scales of the flow are described within an Eulerian frame by applying the method of volume averaging, a Lagrangian approach is proposed to describe the ensemble of fibres. The interface between the free-flow and the porous medium is handle with a One-Domain- Approach, which we justify with the theoretical development of a mass- and momentum- balance at the fluid/porous interface. This hybrid model is then implemented in a parallel code written in C$++$, based on a fluid- solver available from the \openfoam CFD toolbox. Some preliminary results show the ability of this approach to simulate a honami within a reasonable computational cost. Prior to implementing a macroscopic model, insight into the small-scale is required. Two specific aspects of the small-scale are therefore studied in details; The first development deals with the inertial deviation from Darcy's law. A geometrical parameter is proposed to describe the effect of inertia on Darcy's law, depending on the shape of the microstructure of the porous medium. This topological parameter is shown to efficiently characterize inertia effects on a diversity of tested microstructures. An asymptotic filtration law is then derived from the closure problem arising from the volume averaging method, proposing a new framework to understand the relationship between the effect of inertia on the macroscopic fluid-solid force and the topology of the microstructure of the porous medium. A second research axis is then investigated. As we deal with a deformable porous medium, we study the effect of the pore-scale fluid-structure interaction on the filtration law as the flow within the pores is unsteady, inducing time-dependent fluidstresses on the solid- phase. For that purpose, we implement pore-scale numerical simulations of unsteady flows within deformable pores, focusing for this preliminary study on a model porous medium. Owing to the large displacements of the solid phase, an immersed boundary approach is implemented. Two different numerical methods are compared to apply the no-slip condition at the fluid-solid interface: a diffuse interface approach and a sharp interface approach. The objective is to find the proper method to afford acceptable computational time and a good reliability of the results. The comparison allows a cross-validation of the numerical results, as the two methods compare well for our cases. This numerical campaign shows that the pore-scale deformation has a significant impact on the pressure drop at the macroscopic scale. Some fundamental issues are then discussed, such as the size of a representative computational domain or the form of macroscopic equations to describe the momentum transport within a soft deformable porous medium.

Nesta tese é apresentado um novo workflow de simulação para avaliar o desempenho do balanceamento de carga dinâmico baseado em sobre-decomposição aplicado a aplicações paralelas iterativas. Seus objetivos são realizar essa avaliação com modificações mínimas da aplicação e a baixo custo em termos de tempo e de sua necessidade de recursos computacionais. Muitas aplicações paralelas sofrem com desbalanceamento de carga dinâmico (temporal) que não pode ser tratado a nível de aplicação. Este pode ser causado por características intrínsecas da aplicação ou por fatores externos de hardware ou software. Como demonstrado nesta tese, tal desbalanceamento é encontrado mesmo em aplicações cujo código não aparenta qualquer dinamismo. Portanto, faz-se necessário utilizar mecanismo de balanceamento de carga dinâmico a nível de runtime. Este trabalho foca no balanceamento de carga dinâmico baseado em sobre-decomposição. No entanto, avaliar e ajustar o desempenho de tal técnica pode ser custoso. Isso geralmente requer modificações na aplicação e uma grande quantidade de execuções para obter resultados estatisticamente significativos com diferentes combinações de parâmetros de balanceamento de carga Além disso, para que essas medidas sejam úteis, são usualmente necessárias grandes alocações de recursos em um sistema de produção. Simulated Adaptive MPI (SAMPI), nosso workflow de simulação, emprega uma combinação de emulação sequencial e replay de rastros para reduzir os custos dessa avaliação. Tanto emulação sequencial como replay de rastros requerem um único nó computacional. Além disso, o replay demora apenas uma pequena fração do tempo de uma execução paralela real da aplicação. Adicionalmente à simulação de balanceamento de carga, foram desenvolvidas técnicas de agregação espacial e rescaling a nível de aplicação, as quais aceleram o processo de emulação. Para demonstrar os potenciais benefícios do balanceamento de carga dinâmico com sobre-decomposição, foram avaliados os ganhos de desempenho empregando essa técnica a uma aplicação iterativa paralela da área de geofísica (Ondes3D). Adaptive MPI (AMPI) foi utilizado para prover o suporte a balanceamento de carga dinâmico, resultando em ganhos de desempenho de até 36.58% em 288 cores de um cluster Essa avaliação também é usada pra ilustrar as dificuldades encontradas nesse processo, assim justificando o uso de simulação para facilitá-la. Para implementar o workflow SAMPI, foi utilizada a interface SMPI do simulador SimGrid, tanto no modo de emulação, como no de replay de rastros. Para validar esse simulador, foram comparadas execuções simuladas (SAMPI) e reais (AMPI) da aplicação Ondes3D. As simulações apresentaram uma evolução do balanceamento de carga bastante similar às execuções reais. Adicionalmente, SAMPI estimou com sucesso a melhor heurística de balanceamento de carga para os cenários testados. Além dessa validação, nesta tese é demonstrado o uso de SAMPI para exploração de parâmetros de balanceamento de carga e para planejamento de capacidade computacional. Quanto ao desempenho da simulação, estimamos que o workflow completo é capaz de simular a execução do Ondes3D com 24 combinações de parâmetros de balanceamento de carga em 5 horas para o nosso cenário de terremoto mais pesado e 3 horas para o mais leve. / In this thesis we present a novel simulation workflow to evaluate the performance of dynamic load balancing with over-decomposition applied to iterative parallel applications at low-cost. Its goals are to perform such evaluation with minimal application modification and at a low cost in terms of time and of resource requirements. Many parallel applications suffer from dynamic (temporal) load imbalance that can not be treated at the application level. It may be caused by intrinsic characteristics of the application or by external software and hardware factors. As demonstrated in this thesis, such dynamic imbalance can be found even in applications whose codes do not hint at any dynamism. Therefore, we need to rely on runtime dynamic load balancing mechanisms, such as dynamic load balancing based on over-decomposition. The problem is that evaluating and tuning the performance of such technique can be costly. This usually entails modifications to the application and a large number of executions to get statistically sound performance measurements with different load balancing parameter combinations. Moreover, useful and accurate measurements often require big resource allocations on a production cluster. Our simulation workflow, dubbed Simulated Adaptive MPI (SAMPI), employs a combined sequential emulation and trace-replay simulation approach to reduce the cost of such an evaluation Both sequential emulation and trace-replay require a single computer node. Additionally, the trace-replay simulation lasts a small fraction of the real-life parallel execution time of the application. Besides the basic SAMPI simulation, we developed spatial aggregation and applicationlevel rescaling techniques to speed-up the emulation process. To demonstrate the real-life performance benefits of dynamic load balance with over-decomposition, we evaluated the performance gains obtained by employing this technique on a iterative parallel geophysics application, called Ondes3D. Dynamic load balancing support was provided by Adaptive MPI (AMPI). This resulted in up to 36.58% performance improvement, on 288 cores of a cluster. This real-life evaluation also illustrates the difficulties found in this process, thus justifying the use of simulation. To implement the SAMPI workflow, we relied on SimGrid’s Simulated MPI (SMPI) interface in both emulation and trace-replay modes.To validate our simulator, we compared simulated (SAMPI) and real-life (AMPI) executions of Ondes3D. The simulations presented a load balance evolution very similar to real-life and were also successful in choosing the best load balancing heuristic for each scenario. Besides the validation, we demonstrate the use of SAMPI for load balancing parameter exploration and for computational capacity planning. As for the performance of the simulation itself, we roughly estimate that our full workflow can simulate the execution of Ondes3D with 24 different load balancing parameter combinations in 5 hours for our heavier earthquake scenario and in 3 hours for the lighter one.

The theme of the thesis is to make a list few fundamental modern methods which can be used in computerized physics. The thesis describes parallel computing, neural networks,genetic algorithms, fuzzy logic. Every chapter include theoretical description, simplified mathematical expression, proposals of technical solution. Applications are briefly mentioned here too. The printed matter is completed with a few simple examples. The closing part of the thesis acquired information about these methods and outlines their future development.

O objetivo deste trabalho é estudar algoritmos paralelos para a solução de problemas de Mecânica dos Sólidos, Mecânica dos Fluídos e Interação Fluido-Estrutura empregando o Método dos Elementos Finitos para uso em configurações de memória distribuída e compartilhada. Dois processos para o particionamento da estrutura de dados entre os processadores e divisão de tarefas foram desenvolvidos baseados na aplicação do método de particionamento em faixas e do método da bissecção coordenada recursiva não sobre a geometria da malha mas sim diretamente sobre o sistema de equações, através de reordenações nodais para minimização da largura da banda. Para ordenar a comunicação entre os processadores, foi desenvolvido um algoritmo simples e genérico baseado em uma ordenação circular e alternada que permite a organização eficiente dos processos mesmo em cenários nos quais cada processador precisa trocar dados com todos os demais. Os algoritmos selecionados foram todos do tipo iterativo, por sua adequabilidade ao paralelismo de memória distribuída. Foram desenvolvidos códigos paralelos para o Método dos Gradientes Conjugados utilizado em problemas de Mecânica dos Sólidos, para o esquema explícito de Taylor-Galerkin com um passo e iterações utilizado na simulação de escoamentos compressíveis em regime transônico e supersônico, para o esquema explícito de Taylor- Galerkin com 2 passos para simulação de escoamentos incompressíveis em regime subsônico e para interação fluído-estrutura usando o esquema explícito de dois passos para o fluído e o método implícito de Newmark no contexto do método de estabilização α-Generalizado para a estrutura, com acoplamento particionado. Numerosas configurações foram testadas com problemas tridimensionais utilizando elementos tetraédricos e hexaédricos em clusters temporários e permanentes, homogêneos e heterogêneos, com diferentes tamanhos de problemas, diferentes números de computadores e diferentes velocidades de rede. / Analysis and development of distributed memory parallel algorithms for the solution of Solid Mechanics, Fluid Mechanics and Fluid-Structure Interaction problems using the Finite Element Method is the main goal of this work. Two process for mesh partitioning and task division were developed, based in the Stripwise Partitioning and the Recursive Coordinate Bisection Methods, but applied not over the mesh geometry but over the resultant system of equations through a nodal ordering algorithm for system bandwidth minimization. To schedule the communication tasks in scenarios where each processor must exchange data with all others in the cluster, a simple and generic algorithm based in a circular an alternate ordering was developed. The algorithms selected to be parallelized were of iterative types due to their suitability for distributed memory parallelism. Parallel codes were developed for the Conjugate Gradient Method ( for Solid Mechanics analysis), for the explicit one-step scheme of Taylor-Galerkin method (for transonic and supersonic compressible flow analysis), for the two-step explicit scheme of Taylor-Galerkin method (for subsonic incompressible flow analysis) and for a Fluid-Structure Interaction algorithm using a coupling model based on a partitioned scheme. Explicit two-step scheme of Taylor-Galerkin were employed for the fluid and the implicit Newmark algorithm for the structure. Several configurations were tested for three-dimensional problems using tetrahedral and hexahedral elements in uniform and nonuniform clusters and grids, with several sizes of meshes, numbers of computers and network speeds.

Afin de permettre l’utilisation de hautes fréquences dans le domainedu chauffage par induction industriel, l’emploi d’inducteurs multibrins est envisagé.Or, les pertes occasionnées dans ces inducteurs peuvent être importantes etdépendent fortement de leur géométrie interne qui est complexe. Pour faciliter laconception d’inducteurs multibrins à faibles pertes, il est nécessaire d’en comprendrele comportement électromagnétique. Dans cette thèse, nous présentons ledéveloppement d’un logiciel de calcul parallèle dévolu à la modélisation électromagnétique3D d’inducteurs multibrins. Nous décrivons une méthode originale deconstruction de la géométrie des inducteurs. Ce logiciel est basé sur une méthodenumérique de type intégrale ayant l’avantage de ne pas nécessiter le maillage desespaces entre les brins. L’emploi du calcul parallèle est une des grandes forces de celogiciel. Les études réalisées montrent l’impact de la géométrie sur le comportementde ce type d’inducteur. / In order to enable to use high frequencies in the domain of the industrialinductive heating, the use of multi-wires inductors is considered. But, lossesoccurring into that inductors can be important and strongly depend on their complexinternal geometry. To facilitate the design of lossless multi-wires inductors, it isnecessary to under stand their electromagnetic behavior. In this thesis, we presentthe development of a software of parallel computation intended to the 3D electromagneticmodeling of multi-wires inductors. We describe an original method ofbuilding of the geometry of that inductors. This software is based on an integralmethod in which the meshing of spaces between the wires is unnecessary. The useof parallel computing is one of the great forces of this software. The studies werealized show the impact of the geometry on the behavior of that type of inductor.

La reconstruction tomographique à partir de données de projections est un problème inverse largement utilisé en imagerie médicale et de façon plus modeste pour le contrôle nondestructif. Avec un nombre suffisant de projections, les algorithmes analytiques permettentdes reconstructions rapides et précises. Toutefois, dans le cas d’un faible nombre de vues(imagerie faible dose) et/ou d’angle limité (contraintes spécifiques liées à l’installation), lesdonnées disponibles pour l’inversion ne sont pas complètes, le mauvais conditionnementdu problème s’accentue, et les résultats montrent des artefacts importants. Pour aborderces situations, une approche alternative consiste à discrétiser le problème de reconstruction,et à utiliser des algorithmes itératifs ou une formulation statistique du problème afinde calculer une estimation de l’objet inconnu. Ces méthodes sont classiquement basées surune discrétisation du volume en un ensemble de voxels, et fournissent des cartes 3D de ladensité de l’objet étudié. Les temps de calcul et la ressource mémoire de ces méthodesitératives sont leurs principaux points faibles. Par ailleurs, quelle que soit l’application, lesvolumes sont ensuite segmentés pour une analyse quantitative. Devant le large éventaild’outils de segmentation existant, basés sur différentes interprétations des contours et defonctionnelles à minimiser, les choix sont multiples et les résultats en dépendent.Ce travail de thèse présente une nouvelle approche de reconstruction simultanée àla segmentation des différents matériaux qui composent le volume. Le processus dereconstruction n’est plus basé sur une grille régulière de pixels (resp. voxels), mais sur unmaillage composé de triangles (resp. tétraèdres) non réguliers qui s’adaptent à la formede l’objet. Après une phase d’initialisation, la méthode se décompose en trois étapesprincipales que sont la reconstruction, la segmentation et l’adaptation du maillage, quialternent de façon itérative jusqu’à convergence. Des algorithmes itératifs de reconstructioncommunément utilisés avec une représentation conventionnelle de l’image ont étéadaptés et optimisés pour être exécutés sur des grilles irrégulières composées d’élémentstriangulaires ou tétraédriques. Pour l’étape de segmentation, deux méthodes basées surune approche paramétrique (snake) et l’autre sur une approche géométrique (level set)ont été mises en oeuvre afin de considérer des objets de différentes natures (mono- etmulti- matériaux). L’adaptation du maillage au contenu de l’image estimée est basée surles contours segmentés précédemment, pour affiner la maille au niveau des détails del’objet et la rendre plus grossière dans les zones contenant peu d’information. En finde processus, le résultat est une image classique de reconstruction tomographique enniveaux de gris, mais dont la représentation par un maillage adapté au contenu proposeidirectement une segmentation associée. Les résultats montrent que la partie adaptative dela méthode permet de représenter efficacement les objets et conduit à diminuer drastiquementla mémoire nécessaire au stockage. Dans ce contexte, une version 2D du calcul desopérateurs de reconstruction sur une architecture parallèle type GPU montre la faisabilitédu processus dans son ensemble. Une version optimisée des opérateurs 3D permet descalculs encore plus efficaces. / Tomography reconstruction from projections data is an inverse problem widely used inthe medical imaging field. With sufficiently large number of projections over the requiredangle, the FBP (filtered backprojection) algorithms allow fast and accurate reconstructions.However in the cases of limited views (lose dose imaging) and/or limited angle (specificconstrains of the setup), the data available for inversion are not complete, the problembecomes more ill-conditioned, and the results show significant artifacts. In these situations,an alternative approach of reconstruction, based on a discrete model of the problem,consists in using an iterative algorithm or a statistical modelisation of the problem to computean estimate of the unknown object. These methods are classicaly based on a volumediscretization into a set of voxels and provide 3D maps of densities. Computation time andmemory storage are their main disadvantages. Moreover, whatever the application, thevolumes are segmented for a quantitative analysis. Numerous methods of segmentationwith different interpretations of the contours and various minimized energy functionalare offered, and the results can depend on their use.This thesis presents a novel approach of tomographic reconstruction simultaneouslyto segmentation of the different materials of the object. The process of reconstruction isno more based on a regular grid of pixels (resp. voxel) but on a mesh composed of nonregular triangles (resp. tetraedra) adapted to the shape of the studied object. After aninitialization step, the method runs into three main steps: reconstruction, segmentationand adaptation of the mesh, that iteratively alternate until convergence. Iterative algorithmsof reconstruction used in a conventionnal way have been adapted and optimizedto be performed on irregular grids of triangular or tetraedric elements. For segmentation,two methods, one based on a parametric approach (snake) and the other on a geometricapproach (level set) have been implemented to consider mono and multi materials objects.The adaptation of the mesh to the content of the estimated image is based on the previoussegmented contours that makes the mesh progressively coarse from the edges to thelimits of the domain of reconstruction. At the end of the process, the result is a classicaltomographic image in gray levels, but whose representation by an adaptive mesh toits content provide a correspoonding segmentation. The results show that the methodprovides reliable reconstruction and leads to drastically decrease the memory storage. Inthis context, the operators of projection have been implemented on parallel archituecturecalled GPU. A first 2D version shows the feasability of the full process, and an optimizedversion of the 3D operators provides more efficent compoutations.