Estruturas de dados (ED) topológicas oferecem diversas vantagens quando se deseja executarumadeformação sobreumamalha. Essas EDs permitem movimentar os nós da malha sem modificar sua topologia, são relativamente simples de seremimplementadas e também são passíveis de serem incorporadas a um ciclo simulação/deformação de forma completamente automática e eficiente. O primeiro objetivo deste trabalho é a concepção de uma ED topológica para representação de malhas elásticas. Tais malhas podem ser do tipo superficial ou volumétrica, e ainda simples ou mista. Para melhor desempenho, confiabilidade e menor consumo de memória, deseja-se que a ED seja implícita quanto à representação de componentes incidentes e adjacentes dos elementos presentes na malha. Outro objetivo deste trabalho é abordar o problema de geração de malhas em domínios arbitrários definidos por uma função implícita. O método proposto é uma extensão do algoritmo de Partição da Unidade Implícita (PUI). Para isso, o método proposto é baseado numa abordagem de preenchimento de superfícies. Este método proposto gera adaptativamente tetraedros em diferentes níveis de refinamento de acordo com o nível de detalhe presente na região do domínio. Diferentemente de trabalhos anteriores, esta característica é feita naturalmente sem necessitar de uma estrutura auxiliar. Para este fim, usa-se uma estrutura algébrica chamada de triangulação Ja1 que é capaz de lidar com tais refinamentos. Além do mais, a triangulação Ja1 permite que se percorra a estrutura simplesmente através de regras algébricas que é uma outra vantagem do método proposto / Topological data Structures (DS) oer several advantages when performing a deformation on a mesh. These DSs allow movement throughout the mesh without modifying its topology, are relatively simple to implement, and there is always the possibility of merging it to simulation/deformation cycle on a completely automatic and ecient form. The main goal of this work is to design and implement a topological DS to represent elastic meshes. These meshes can be either of surface or volume kind, and even simple or mixed. For better performance, more reliability and lower memory consumption, it is necessary that the DSs allow the representation of incident and adjacent components of a given element to be implicit. The second objective to this work is to tackle the problem of mesh generation on arbitrary domains defined by implicit functions. The proposed method is an extension to the algorithm of Partition of Unity Implicits (PUI). For this the proposed method is based on an isosurface stung approach. It adaptively generates the tetrahedra in dierent levels of refinement accordingly to the level of detail presented by the regions of the domain. Dierently to previous work, this feature is done naturally without the aid of an auxiliary data structure. To this end, we use an algebraic structure, named Ja1 triangulation, which is capable of dealing with such refinements. In addition, the Ja1 triangulation permits traversing through the mesh by simply using algebraic rules which is another advantage to the proposed method

Dois métodos distintos são descritos e implementados. O primeiro método, proposto por Ruppert, possui garantias teóricas de qualidade quando a fronteira do domínio obedece certas restrições. O segundo método, proposto por Persson, possibilita um maior controle na densidade dos elementos que discretizam o domínio. As vantagens, desvantagens e particularidades de cada um dos métodos são descritas e detalhadas / Two distinct methods are described and implemented. The first method, proposed by Ruppert, has theoretical guarantees on the quality of elements when the domain boundaries respect certain restrictions. The second method, proposed by Persson, makes it possible to have greater control over the density of the elements that make up the domain. The advantages, disadvantages and specific points about each method are described and detailed

Triangle-mesh modeling, as one of the approaches for representing images based on nonuniform sampling, has become quite popular and beneficial in many applications. In this thesis, image representation using triangle-mesh models and its application in image scaling are studied. Consequently, two new methods, namely, the SEMMG and MIS methods are proposed, where each solves a different problem. In particular, the SEMMG method is proposed to address the problem of image representation by producing effective mesh models that are used for representing grayscale images, by minimizing squared error. The MIS method is proposed to address the image-scaling problem for grayscale images that are approximately piecewise-smooth, using triangle-mesh models. The SEMMG method, which is proposed for addressing the mesh-generation problem, is developed based on an earlier work, which uses a greedy-point-insertion (GPI) approach to generate a mesh model with explicit representation of discontinuities (ERD). After in-depth analyses of two existing methods for generating the ERD models, several weaknesses are identified and specifically addressed to improve the quality of the generated models, leading to the proposal of the SEMMG method. The performance of the SEMMG method is then evaluated by comparing the quality of the meshes it produces with those obtained by eight other competing methods, namely, the error-diffusion (ED) method of Yang, the modified Garland-Heckbert (MGH) method, the ERDED and ERDGPI methods of Tu and Adams, the Garcia-Vintimilla-Sappa (GVS) method, the hybrid wavelet triangulation (HWT) method of Phichet, the binary space partition (BSP) method of Sarkis, and the adaptive triangular meshes (ATM) method of Liu. For this evaluation, the error between the original and reconstructed images, obtained from each method under comparison, is measured in terms of the PSNR. Moreover, in the case of the competing methods whose implementations are available, the subjective quality is compared in addition to the PSNR. Evaluation results show that the reconstructed images obtained from the SEMMG method are better than those obtained by the competing methods in terms of both PSNR and subjective quality. More specifically, in the case of the methods with implementations, the results collected from 350 test cases show that the SEMMG method outperforms the ED, MGH, ERDED, and ERDGPI schemes in approximately 100%, 89%, 99%, and 85% of cases, respectively. Moreover, in the case of the methods without implementations, we show that the PSNR of the reconstructed images produced by the SEMMG method are on average 3.85, 0.75, 2, and 1.10 dB higher than those obtained by the GVS, HWT, BSP, and ATM methods, respectively. Furthermore, for a given PSNR, the SEMMG method is shown to produce much smaller meshes compared to those obtained by the GVS and BSP methods, with approximately 65% to 80% fewer vertices and 10% to 60% fewer triangles, respectively. Therefore, the SEMMG method is shown to be capable of producing triangular meshes of higher quality and smaller sizes (i.e., number of vertices or triangles) which can be effectively used for image representation. Besides the superior image approximations achieved with the SEMMG method, this work also makes contributions by addressing the problem of image scaling. For this purpose, the application of triangle-mesh mesh models in image scaling is studied. Some of the mesh-based image-scaling approaches proposed to date employ mesh models that are associated with an approximating function that is continuous everywhere, which inevitably yields edge blurring in the process of image scaling. Moreover, other mesh-based image-scaling approaches that employ approximating functions with discontinuities are often based on mesh simplification where the method starts with an extremely large initial mesh, leading to a very slow mesh generation with high memory cost. In this thesis, however, we propose a new mesh-based image-scaling (MIS) method which firstly employs an approximating function with selected discontinuities to better maintain the sharpness at the edges. Secondly, unlike most of the other discontinuity-preserving mesh-based methods, the proposed MIS method is not based on mesh simplification. Instead, our MIS method employs a mesh-refinement scheme, where it starts from a very simple mesh and iteratively refines the mesh to reach a desirable size. For developing the MIS method, the performance of our SEMMG method, which is proposed for image representation, is examined in the application of image scaling. Although the SEMMG method is not designed for solving the problem of image scaling, examining its performance in this application helps to better understand potential shortcomings of using a mesh generator in image scaling. Through this examination, several shortcomings are found and different techniques are devised to address them. By applying these techniques, a new effective mesh-generation method called MISMG is developed that can be used for image scaling. The MISMG method is then combined with a scaling transformation and a subdivision-based model-rasterization algorithm, yielding the proposed MIS method for scaling grayscale images that are approximately piecewise-smooth. The performance of our MIS method is then evaluated by comparing the quality of the scaled images it produces with those obtained from five well-known raster-based methods, namely, bilinear interpolation, bicubic interpolation of Keys, the directional cubic convolution interpolation (DCCI) method of Zhou et al., the new edge-directed image interpolation (NEDI) method of Li and Orchard, and the recent method of super-resolution using convolutional neural networks (SRCNN) by Dong et al.. Since our main goal is to produce scaled images of higher subjective quality with the least amount of edge blurring, the quality of the scaled images are first compared through a subjective evaluation followed by some objective evaluations. The results of the subjective evaluation show that the proposed MIS method was ranked best overall in almost 67\% of the cases, with the best average rank of 2 out of 6, among 380 collected rankings with 20 images and 19 participants. Moreover, visual inspections on the scaled images obtained with different methods show that the proposed MIS method produces scaled images of better quality with more accurate and sharper edges. Furthermore, in the case of the mesh-based image-scaling methods, where no implementation is available, the MIS method is conceptually compared, using theoretical analysis, to two mesh-based methods, namely, the subdivision-based image-representation (SBIR) method of Liao et al. and the curvilinear feature driven image-representation (CFDIR) method of Zhou et al.. / Graduate

Apresenta-se um pré-processador para análise de pavimentos de edifícios via método dos elementos finitos desenvolvido como um aplicativo do ambiente Windows. O programa é interativo, permitindo identificar problemas de imediato na criação do modelo a ser estudado. Possui recursos gráficos básicos para a definição geométrica da estrutura. A saída de dados é programável para que o pré-processador não se prenda a um só programa de cálculo. Assim, os mesmos dados de uma estrutura podem ser analisados por diferentes programas de cálculo o que possibilita a escolha do programa mais adequado, dependendo do tipo de análise desejado. O aplicativo tem recursos para definir elementos finitos de barra e placa. Como o número desses elementos normalmente é grande, eles são gerados de uma forma automatizada. / lt is presenting a Windows preprocessar for building slab analysis by Finite Element Method. lt is an interactive program, allowing problems to be identified while the model is generated. It has graphical resources to define the structure. The program output is defined by the user; therefore it is possible to use the preprocessar with many other finite element programs. This allows the engineer to choose the appropriate program depending on the kind of analysis is wanted. The program can define frame and shell finite elements. As slabs usually need large numbers of these elements to be properly analyzed, they are generated using automatic meshing.

Mesh generation is a fundamental precursor to finite element implementations for solution of partial differential equations in engineering and science. This dissertation advances the field in three distinct but coupled areas. A robust and fast three dimensional mesh generator for arbitrarily shaped geometries was developed. It deploys nodes throughout the domain based upon user-specified mesh density requirements. The system is integer and pixel based which eliminates round off errors, substantial memory requirements and cpu intensive calculations. Linked, but fully detachable, to the mesh generation system is a physical boundary recovery routine. Frequently, the original boundary topology is required for specific boundary condition applications or multiple material constraints. Historically, this boundary preservation was not available. An algorithm was developed, refined and optimized that recovers the original boundaries, internal and external, with fidelity. Finally, a node repositioning algorithm was developed that maximizes the minimum solid angle of tetrahedral meshes. The highly coveted 2D Delaunay property that maximizes the minimum interior angle of a triangle mesh does not extend to its 3D counterpart, to maximize the minimum solid angle of a tetrahedron mesh. As a consequence, 3D Delaunay created meshes have unacceptable sliver tetrahedral elements albeit composed of 4 high quality triangle sides. These compromised elements are virtually unavoidable and can foil an otherwise intact mesh. The numerical optimization routine developed takes any preexisting tetrahedral mesh and repositions the nodes without changing the mesh topology so that the minimum solid angle of the tetrahedrons is maximized. The overall quality enhancement of the volume mesh might be small, depending upon the initial mesh. However, highly distorted elements that create ill-conditioned global matrices and foil a finite element solver are enhanced significantly.

Este trabalho apresenta um estudo sobre segmentação de volumes médicos e uma solução para se obter malhas poligonais de pacientes específicos para uso em simulações de cirurgia. Malhas de pacientes específicos são importantes para planejamento de intervenções cirúrgicas e permitem uma melhor visualização de condições patológicas em um paciente, coisa não obtível em malhas geradas artisticamente. Nós analisamos quais são os fatores complicantes para se obter estas malhas de um paciente específico usando apenas imagens médicas obtidas em exames padrões. Para isso, nós revisamos diversos métodos existentes para segmentação de volumes médicos. Isso nos levou a definir os problemas com as técnicas existentes, e a desenvolver um método que não sofra destes problemas, utilizando pouca interação humana e não tendo dependências de mais dados que não o exame do paciente. Nosso alvo para obter malhas especificas foram órgãos de tecido mole, que são um caso especialmente complicado da área, graças a várias questões relacionadas às imagens médicas e à anatomia humana. Atacamos esse problema aplicando modificações geométricas em malhas especiais, que deformam até atingir a forma dos órgãos que se deseja segmentar. Os resultados mostram que nossa técnica conseguiu obter malhas específicas de pacientes a partir de volumes médicos com qualidade superior a de outros algoritmos de mesma classe. Graças a simplicidade do método desenvolvido, nossos resultados são facilmente implementáveis e reproduzidos. / This work presents a study about medical-volume segmentation and a solution to generate patient-specific meshes to use in patient-specific surgery simulations. Patientspecific meshes are useful assets for surgery planning and to allow better visualization of certain pathological conditions of a given patient, which are not obtainable by artistically designed meshes. We analyzed what are the complications to obtain a patient-specific mesh using only standard medical imagery exams. For that, we reviewed several medical volume segmentation techniques. It led us to define the problems within the existing techniques and to develop a method that does not suffer from these problems, with the least possible user interaction or relying on any other data other then the patient exam. Our target for obtaining specific meshes were soft tissue organs, which are a specially complicated case due to various issues related to the medical images and human anatomy. This is accomplished by geometrical operations over special meshes that deform until achieving the shape of the desired organ. Results show that our technique was able to obtain patient-specific meshes from medical images with superior quality than algorithms of the same class. Thanks to the simplicity of the developed approach, its also easy to implement and to reproduce our obtained results.

Cette thèse pose les fondations du modèle « the Second-generation Louvain-la-Neuve Ice-ocean Model » (SLIM) qui est basé sur la méthode des éléments finis et les maillages non-structurés. Ce modèle fait partie d'une seconde génération de modèles numériques de circulation marine ou océanique. Notre travail a principalement porté sur les aspects géométriques liés à l'utilisation des maillages non-structurés. Nous avons implémenté un algorithme de triangulation qui génère automatiquement des maillages anisotropes non-structurés sur le plan et la sphère et nous avons défini des stratégies de raffinement de maillage adaptées aux applications marines. Ces stratégies orchestrent la distribution de la taille et de la forme des éléments du maillage afin d'optimiser la précision et le coût en temps de calcul du nouveau modèle. Nous avons aussi abordé l'interpolation contrainte de champs scalaires et vectoriels d'un premier maillage vers un second. L'utilisation conjointe de ces trois outils combinée avec un estimateur d'erreur a posteriori permettra l'adaptation dynamique de maillages au cours de simulations transitoires. Finalement, nous avons bâti les outils géométriques nécessaires à l'écriture d'une formulation discrète des équations de la dynamique des fluides géophysiques sur la sphère. Basée sur un système de coordonnées curvilignes propre à chaque élément du maillage, cette approche originale ne possède aucune des difficultés mathématiques et numériques liées aux singularités des pôles et auxquelles les modèles de la première génération n'ont pu apporter de solution entièrement satisfaisante.

Cette thèse pose les fondations du modèle « the Second-generation Louvain-la-Neuve Ice-ocean Model » (SLIM) qui est basé sur la méthode des éléments finis et les maillages non-structurés. Ce modèle fait partie d'une seconde génération de modèles numériques de circulation marine ou océanique. Notre travail a principalement porté sur les aspects géométriques liés à l'utilisation des maillages non-structurés. Nous avons implémenté un algorithme de triangulation qui génère automatiquement des maillages anisotropes non-structurés sur le plan et la sphère et nous avons défini des stratégies de raffinement de maillage adaptées aux applications marines. Ces stratégies orchestrent la distribution de la taille et de la forme des éléments du maillage afin d'optimiser la précision et le coût en temps de calcul du nouveau modèle. Nous avons aussi abordé l'interpolation contrainte de champs scalaires et vectoriels d'un premier maillage vers un second. L'utilisation conjointe de ces trois outils combinée avec un estimateur d'erreur a posteriori permettra l'adaptation dynamique de maillages au cours de simulations transitoires. Finalement, nous avons bâti les outils géométriques nécessaires à l'écriture d'une formulation discrète des équations de la dynamique des fluides géophysiques sur la sphère. Basée sur un système de coordonnées curvilignes propre à chaque élément du maillage, cette approche originale ne possède aucune des difficultés mathématiques et numériques liées aux singularités des pôles et auxquelles les modèles de la première génération n'ont pu apporter de solution entièrement satisfaisante.

The main objective of this thesis aims at developing a new generation of software products, in order to obtain a fully automatic simulator predicting the entire Czochralski process while handling correctly the switches between the different growth stages. First of all, new efficient, robust and high-quality automatic mesh generation algorithms with enough flexibility for any complex geometry were implemented, including a 1D mesh generator by global grade-adaptive method, a 2D initial triangulation algorithm by improved sweep line technique and an automatic 2D shape-quality unstructured mesh generator by modified incremental Delaunay refinement technique. Secondly, a Finite Element Navier-Stokes solver based on unstructured meshes was developed and validated. Enhanced turbulence models based on the classical mixing-length or k-l model, together with a generic transformation method to avoid negative k when solving the turbulent kinetic energy equation by the Newton-Raphson iterative method were introduced and implemented. Moreover, laminar and turbulent mathematical models governing the gas convection, thermal distribution and oxygen concentration were developed, and Finite Element numerical methods to solve these governing equations on unstructured meshes were implemented, while appropriate numerical approaches to capture the wall shear stress exerted by the gas flow and experienced by the silicon melt were investigated. Finally, a series of numerical experiments devoted to investigate the industrial Czochralski crystal growth process under various growth conditions are presented based on all the developments implemented. Comparisons of the simulation results with literature and available experimental observations are also presented, and conclusions are drawn based on these simulation results and observations.

This thesis focuses on special arterial fluid mechanics techniques developed for patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. These techniques are used in conjunction with the core computational technique, which is the space–time version of the variational multiscale (VMS) method and is called “DST/SST-VMST.” The special techniques include using NURBS for the spatial representation of the surface over which the stent mesh is built, mesh generation techniques for both the finite- and zero-thickness representations of the stent, techniques for generating refined layers of mesh near the arterial and stent surfaces, and models for representing double stent. We compute the unsteady flow patterns in the aneurysm and investigate how those patterns are influenced by the presence of single and double stents. We also compare the flow patterns obtained with the finite- and zero-thickness representations of the stent.