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.

Im Rahmen der Arbeit in der damaligen DFG-Forschungsgruppe ¨Scientific Parallel Computing¨ wurde ein hierarchischer paralleler Netzgenerator fuer das Finite-Elemente- Programmpaket SPC-PM CFD unter dem Namen NETGEN69 entwickelt. Als Programmiersprache wurde seinerzeit - wie auch in den FEM-Programmen selbst - FORTRAN benutzt. Im Rahmen des Teilprojektes B2 im Sonderforschungsbereich 393 bestand nunmehr die Aufgabe, den Netzgenerator in ein objektorientiertes Layout zu fassen und in C++zu implementieren. Die Beschreibung von Ein- und Ausgabedaten kann in [3] nachgelesen werden. Die Form der Eingabedaten hat sich aus Kompatibilitaetsgruenden nicht geaendert und wird auch in Zukunft so beibehalten werden. Auch das der Assemblierung und FEM-Rechnung zuge- wandte Interface wurde vorerst nicht geaendert. Ein Wrapper, der fuer die Generierung der erwarteten Ausgabedaten aus den netzgeneratoreigenen Datenbestaenden sorgt, ist derzeit in Planung. Diese Lösung ist freilich nur voruebergehender Natur; sie ermoeglicht es uns, den Netzgenerator innerhalb der FEM-Bibliotheken zu testen.

We present an $hp$-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in $L^2$-orthogonal polynomails on a triangle or a tetrahedron. This method is justified by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other $hp$-adaptive strategies.

Data-dependent triangulation (DDT) based mesh-generation schemes for image representation are studied. A flexible mesh-generation framework and a highly effective mesh-generation method that employs this framework are proposed. The proposed framework is derived from frameworks proposed by Rippa and Garland and Heckbert by making a number of key modifications to facilitate the development of much more effective mesh-generation methods. As the proposed framework has several free parameters, the effects of different choices of these parameters on mesh quality (both in terms of squared error and subjectively) are studied, leading to the recommendation of a particular set of choices for these parameters. A new mesh-generation method is then introduced that employs the proposed framework with these best parameter choices. Experimental results show our proposed mesh-generation method outperforms several competing approaches, namely, the DDT-based incremental scheme proposed by Garland and Heckbert, the COMPRESS scheme proposed by Rippa, and the adaptive thinning scheme proposed by Demaret and Iske. More specifically, in terms of PSNR, our proposed method was found to outperform these three schemes by median margins of 4.1 dB, 10.76 dB, and 0.83 dB, respectively. The subjective qualities of reconstructed images were also found to be correspondingly better. In terms of computational cost, our proposed method was found to be comparable to the schemes proposed by Garland and Heckbert and Rippa. Moreover, our proposed method requires only about 5 to 10% of the time of the scheme proposed by Demaret and Iske. In terms of memory cost, our proposed method was shown to require essentially same amount of memory as the schemes proposed by Garland and Heckbert and Rippa, and orders of magnitude (33 to 800 times) less memory than the scheme proposed by Demaret and Iske. / Graduate

In this thesis, three mesh generation software packages have been developed and implemented. The first two were based on structured mesh generation algorithms and used to solve structured surface and volume mesh generation problems of three-dimensional domains. Structured mesh generation algorithms were based on the concept of isoparametric coordinates. In structured surface mesh generation software, quadrilateral mesh elements were generated for complex three-dimensional surfaces and these elements were then triangulated in order to obtain high-quality triangular mesh elements. Structured volume mesh generation software was used to generate hexahedral mesh elements for volumes. Tetrahedral mesh elements were constructed from hexahedral elements using hexahedral node insertion method. The results, which were produced by the mesh generation algorithms, were converted to a required format in order to be saved in output files. The third software package is an unstructured quality tetrahedral mesh generator and was used to generate exact Delaunay tetrahedralizations, constrained (conforming) Delaunay tetrahedralizations and quality conforming Delaunay tetrahedralizations. Apart from the mesh generation algorithms used and implemented in this thesis, unstructured mesh generation techniques that can be used to generate quadrilateral, triangular, hexahedral and tetrahedral mesh elements were also discussed.

VIEIRA, Rafael Siqueira Telles. Técnicas para geração de malhas de quadriláteros convexos e sua aplicação em reservatórios naturais. 2011. 169 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2011. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-12T15:46:11Z No. of bitstreams: 1 2011_dis_rstvieira.pdf: 3132905 bytes, checksum: e4b5cfff20b3d685dc1674c91df9babc (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-21T15:26:34Z (GMT) No. of bitstreams: 1 2011_dis_rstvieira.pdf: 3132905 bytes, checksum: e4b5cfff20b3d685dc1674c91df9babc (MD5) / Made available in DSpace on 2016-07-21T15:26:34Z (GMT). No. of bitstreams: 1 2011_dis_rstvieira.pdf: 3132905 bytes, checksum: e4b5cfff20b3d685dc1674c91df9babc (MD5) Previous issue date: 2011 / This work describes four methods implemented to achieve a convex quadrilaterization of the two- -dimensional space that may have polygonal lines or holes. Two of these methods, midpoint and ortoquad make use of guide elements, the centroid of a region or the locus of maximum tangent circles inside a geometry, to produce a mesh for the domain. The other two methods, triquad and incremental quadrilatezation use a implicit and explicit triangulation while combining elements in pairs to generate a mesh. All these methods are made through domain decomposition which assure quadrilaterization at the end, since the domain is always partitioned at each iteration. These techniques are compared by a criterion of geometry and topology in order to make clear its advantages and disadvantages and as means of promoting future improvements. The techniques are applied to some samples, including a natural reservoir, in order to view its operation in a real environment or near reality according to the sample used. Also it intends to present throughout this work the requirements, according to the experience with the theme of this author, to develop a technique for quadrilateral mesh generation. / Esta dissertação descreve quatro métodos implementados para realizar uma quadrilaterização convexa do espaço bidimensional que pode conter linhas poligonais ou buracos. Dois destes métodos, ponto médio e ortoquad, utilizam de elementos guia, o baricentro de uma região ou o locus de círculos máximos tangentes e internos a geometria, para produzir uma malha conforme o domínio. Os outros dois, triquad e quadrilaterização incremental, utilizam de uma triangulação explícita e implícita combinando elementos aos pares para realizar a geração da malha. Todas as técnicas são feitas por decomposição de regiões o que garante uma quadrilaterização final, já que o domínio é sempre segmentado a cada iteração. Estas técnicas são comparadas por um critério de geometria e topologia de forma a tornar evidentes suas vantagens e desvantagens assim como promover melhorias futuras. As técnicas são aplicadas a alguns exemplos, incluindo-se um reservatório natural, a fim de exibir seu funcionamento em um ambiente real ou próximo do mesmo, conforme as amostras utilizadas. Também se pretende apresentar ao longo deste trabalho os requisitos necessários, segundo a experiência deste autor com o tema, para o desenvolvimento de uma técnica de geração de malha quadrilateral.

FREITAS, Markos Oliveira. Geração em Paralelo de Malhas Tetraédricas com Fraturas por Decomposição Espacial Binária. 2015. 129 f. Tese (Doutorado em Ciência da Computação)-Universidade Federal do Ceará, Fortaleza, 2015. / Submitted by Vitor Campos (vitband@gmail.com) on 2016-09-27T23:47:57Z No. of bitstreams: 1 2015_tese_mofreitas.pdf: 15114037 bytes, checksum: 7028f6c9f4d930ab2cc67a73f135ff47 (MD5) / Approved for entry into archive by Jairo Viana (jairo@ufc.br) on 2016-09-27T23:51:14Z (GMT) No. of bitstreams: 1 2015_tese_mofreitas.pdf: 15114037 bytes, checksum: 7028f6c9f4d930ab2cc67a73f135ff47 (MD5) / Made available in DSpace on 2016-09-27T23:51:14Z (GMT). No. of bitstreams: 1 2015_tese_mofreitas.pdf: 15114037 bytes, checksum: 7028f6c9f4d930ab2cc67a73f135ff47 (MD5) Previous issue date: 2015 / This work describes a technique for generating three-dimensional tetrahedral meshes using parallel computing, with shared, distributed, or hybrid memory processors. The input for the algorithm is a triangular mesh that models the surface of one of several objects, that might have holes in its interior or internal or boundary cracks. A binary tree structure for spatial partitioning is proposed in this work to recursively decompose the domain in as many subdomains as processes or threads in the parallel system, in which every subdomain has the geometry of a rectangular parallelepiped. This decomposition attempts to balance the amount of work in all the subdomains. The amount of work, known as load, of any mesh generator is usually given as a function of its output size, i.e., the size of the generated mesh. Therefore, a technique to estimate the size of this mesh, the total load of the domain, is needed beforehand. This work uses a refined octree, generated from the surface mesh, to estimate this load, and the decomposition is performed on top of this octree. Once the domain is decomposed, each process/thread generates the mesh in its subdomain by means of an advancing front technique, in such a way that it does not overpass the limits defined by its subdomain, and applies an improvement on it. Some of the processes/threads are responsible for generating the meshes connecting the subdomains, i.e., the interface meshes, in order to generate the whole mesh. This technique presented good speed-up results, keeping the quality of the mesh comparable to the quality of the serially generated mesh. / Este trabalho descreve uma técnica para gerar malhas tridimensionais tetraédricas utilizando computação paralela, com processadores de memória compartilhada, memória distribuída ou memória híbrida. A entrada para o algoritmo é uma malha triangular que modela a superfície de um ou vários objetos, que podem conter buracos no interior ou fraturas internas ou na borda. Uma estrutura em forma de árvore binária de partição espacial é proposta neste trabalho para, recursivamente, decompor o domínio em tantos subdomínios quantos forem os processos ou threads no sistema paralelo, em que cada subdomínio tem a geometria de um paralelepípedo retangular. Esta decomposição tenta equilibrar a quantidade de trabalho em todos os subdomínios. A quantidade de trabalho, conhecida como carga, de qualquer gerador de malha é geralmente dada em função do tamanho da saída do algoritmo, ou seja, do tamanho da malha gerada. Assim, faz-se necessária uma técnica para estimar previamente o tamanho dessa malha, que é carga total do domínio. Este trabalho faz uso de uma octree refinada, gerada a partir da malha de superfície dada como entrada, para estimar esta carga, e a decomposição é feita a partir dessa octree. Uma vez decomposto o domínio, cada processo/thread gera a malha em seu subdomínio por uma técnica de avanço de fronteira, de forma que ela não ultrapasse os limites definidos pelo seu subdomínio, e aplica um melhoramento nela. Alguns dos processos/threads ficam responsáveis por gerar as malhas conectando os subdomínios, ou seja, as malhas de interface, até que toda a malha tenha sido gerada. Esta técnica apresentou bons resultados de speed-up, mantendo a qualidade da malha comparável à qualidade da malha gerada sequencialmente.

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.

In this thesis, we propose a general computational framework for generating mesh models of single-component (e.g., grayscale) and multi-component (e.g., RGB color) images. This framework builds on ideas from the previously-proposed GPRFSED method for single-component images to produce a framework that can handle images with any arbitrary number of components. The key ideas embodied in our framework are Floyd-Steinberg error diffusion and greedy-point removal. Our framework has several free parameters and the effect of the choices of these parameters is studied. Based on experimentation, we recommend two specific sets of parameter choices, yielding two highly effective single/multi-component mesh-generation methods, known as MED and MGPRFS. These two methods make different trade offs between mesh quality and computational cost. The MGPRFS method is able to produce high quality meshes at a reasonable computational cost, while the MED method trades off some mesh quality for a reduction in computational cost relative to the MGPRFS method. To evaluate the performance of our proposed methods, we compared them to three highly-effective previously-proposed single-component mesh generators for both grayscale and color images. In particular, our evaluation considered the following previously-proposed methods: the error diffusion (ED) method of Yang et al., the greedy-point-removal from-subset (GPRFSED) method of Adams, and the greedy-point removal (GPR) method of Demaret and Iske. Since these methods cannot directly handle color images, color images were handled through conversion to grayscale as a preprocessing step, and then as a postprocessing step after mesh generation, the grayscale sample values in the generated mesh were replaced by their corresponding color values. These color-capable versions of ED, GPRFSED, and GPR are henceforth referred to as CED, CGPRFSED, and CGPR, respectively. Experimental results show that our MGPRFS method yields meshes of higher quality than the CGPRFSED and GPRFSED methods by up to 7.05 dB and 2.88 dB respectively, with nearly the same computational cost. Moreover, the MGPRFS method outperforms the CGPR and GPR methods in mesh quality by up to 7.08 dB and 0.42 dB respectively, with about 5 to 40 times less computational cost. Lastly, our MED method yields meshes of higher quality than the CED and ED methods by up to 7.08 and 4.72 dB respectively, where all three of these methods have a similar computational cost. / Graduate