no / In this paper, we extend the use of the partial differential equation (PDE) method to head visualization with computed tomography (CT) data and show how the two primary medical visualization means, surface reconstruction, and volume rendering can be integrated into one single framework through PDEs. Our scheme first performs head segmentation from CT slices using a variational approach, the output of which can be readily used for extraction of a small set of PDE boundary conditions. With the extracted boundary conditions, head surface reconstruction is then executed. Because only a few slices are used, our method can perform head surface reconstruction more efficiently in both computational time and storage cost than the widely used marching cubes algorithm. By elaborately introducing a third parameter w to the PDE method, a solid head can be created, based on which the head volume is subsequently rendered with 3D texture mapping. Instead of designing a transfer function, we associate the alpha value of texels of the 3D texture with the PDE parameter w through a linear transform. This association enables the production of a visually translucent head volume. The experimental results demonstrate the feasibility of the developed head visualization method.

Yes / Polygon, subdivision, and NURBS are three mainstream modeling techniques widely applied in commercial software packages. They require heavy manual operations, and involve a lot of design variables leading to big data, high storage costs and slow network transmissions. In this paper, we integrate the strengths of boundary-based surface creation and partial differential equation (PDE)-based geometric modeling to obtain the first analytical C continuous 4-sided PDE patches involving sculpting force-based shape creation and manipulation and use them to develop an interactive modeling technique for easy and quick creation of 3D models with small data from vertex-frames. With this modeling technique, a vertex frame is defined by eight vertices, and a C continuous 4-sided PDE patch is created from the vertex-frame through an analytical solution to a vector-valued second-order PDE subjected to the boundary conditions determined by the eight vertices of a vertex-frame. A user-friendly interface is developed from the obtained analytical solution, which enables users to interactively input and modify vertex-frame models easily and create 3D models in real time. Different surface modeling tasks are carried out to test the developed interactive tool and compare our proposed method with polygon and NURBS modeling and Coons surfaces. The results demonstrate the effectiveness of our proposed method and its advantages in reducing design variables, saving storage costs, and effective shape creation and manipulation. / European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 778035; MCIN/ AEI /10.13039/501100011033/ FEDER “Una manera de hacer Europa”

Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency. Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numerical accuracy of the solution is typically just one of the challenges. Measurements can be included in the simulation to constrain the numerical solution through a process called data assimilation in order to anchor the simulation in reality. In this thesis we investigate adaptive discretization methods and data assimilation approaches for large-scale numerical simulations. We develop and investigate novel multirate and implicit-explicit methods that are appropriate for multiscale and multiphysics numerical discretizations. We construct and explore data assimilation approaches for, but not restricted to, atmospheric chemistry applications. A generic approach for describing the structure of the uncertainty in initial conditions that can be applied to the most popular data assimilation approaches is also presented. We show that adaptive numerical methods can effectively address the discretization of large-scale problems. Data assimilation complements the adaptive numerical methods by correcting the numerical solution with real measurements. Test problems and large-scale numerical experiments validate the theoretical findings. Synergistic approaches that use adaptive numerical methods within a data assimilation framework need to be investigated in the future. / Ph. D.

The methods for solving domain optimization problems depends on the case of study. There are methods that have been developed for the discretized problem, but not much is done in the infinite dimensional case. We analyze the theoretical aspects of the infinite dimensional case for a particular domain optimization problem where a portion of the boundary is parametrized, these results involve the existence of the solution to our problem and the calculation of the derivative of the shape functional. Shape optimization problems have a long history of mathematical study and a wide range of applications. In recent decades there has been an interest in solving these problems with partial differential equation (PDE) constraints. We consider a special class of PDE-constrained shape optimization problems where different boundary condition types (Dirichlet and Neumann) are imposed on the same boundary segment. We also consider the case where the interface between these different boundary condition types may also be parameter dependent. This study also includes special cases where the shape of the region where the PDE is imposed does not change, but the domain of the partial differential operator is parameter dependent, due to the change in boundary condition type. Our treatment centers on the infinite dimensional formulation of the optimization problem. We consider existence of solutions as well as the calculation of derivatives of the associated shape functionals via adjoint solutions. These derivative formulations serve as a starting point for practical numerical approximations. / Ph. D.

No / Parameterisation of facial expressions on PDE surface representations of human faces are presented in this work. Taking advantage of the boundary-value approach inherent to Bloor-Wilson PDE method, facial expressions are achieved by manipulating the original boundary curves. Such curves are responsible for generating a surface representation of a human face in its neutral configuration, so that regions on these curves represent a given facial expression in a fast and realistic manner. Additionally, the parameterisation proposed here is carried out by applying different mathematical transformations to the affected curves according to the corresponding facial expression. Full analytic expressions parameterising some of the most common facial expressions such as smiling and eyebrow raising are in this work. Some graphical examples of these facial expressions are used to illustrate the results obtained using Bloor-Wilson PDE method as the foundations of the parameterisation scheme proposed here. Thus, it is shown that an efficient, intuitive and realistic parameterisation of facial expressions is attainable using Bloor-Wilson PDE method in along with a suitable mathematical expression.

The primary motivation of this research is to develop and investigate parallel preconditioners for linear elliptic partial differential equations. Three preconditioners are studied: block-Jacobi preconditioner (BJ), a two-level tangential preconditioner (D0), and a three-level preconditioner (D1). Performance and scalability on a distributed memory parallel computer are considered. Communication cost and redundancy are explored as well. After experiments and analysis, we find that the three-level preconditioner D1 is the most efficient and scalable parallel preconditioner, compared to BJ and D0. The D1 preconditioner reduces both the number of iterations and computational time substantially. A new hybrid preconditioner is suggested which may combine the best features of D0 and D1. / Master of Science

Este trabalho avalia a implantação do PDE-Escola em duas instituições escolares no estado de Minas Gerais. O Programa, concebido de forma pouco representativa em sua elaboração macro, sugere uma maior representatividade em sua elaboração micro, mesmo com o MEC impondo um manual de implementação da política às escolas. É essa ambiguidade que motivou a presente pesquisa. Esse contexto cria um hiato de objetivos a serem investigados, tais como a incorporação por gestores e docentes das orientações de mais uma política verticalizada; a maneira em que esses grupos se relacionam na execução do Programa; e, por final, na constatação sobre como as demandas levantadas por diretores e professores na fase introdutória do Plano estão sendo materializadas nas escolas. As respostas a esses objetivos irão nos revelar o grau de incorporação das ideias do PDE-Escola, possibilitando a identificação dos ganhos e retrocessos da proposta governamental na ótica de seus protagonistas escolares. Para isso, duas escolas foram escolhidas, sendo que uma enfrentou a elaboração do PDE-Escola em sua forma clássica, com a metodologia que exigia da instituição um profundo levantamento de suas características, demandando a participação de todos os segmentos. Já a segunda, a partir de 2011, experimentou, e ainda experimenta, a elaboração em sua forma interativa, havendo, apenas, o gestor como interlocutor das informações levantadas, para muitos, descaracterizando o princípio participativo da política. Os resultados apontam para um acirramento nas relações entre gestores e docentes e uma transformação tímida no cotidiano pedagógico da escola, inclusive após a chegada dos equipamentos adquiridos com a verba do PDE-Escola, sendo que algumas das razões podem ser o caráter menos representativo da atual versão digital e a reedição de mais uma iniciativa governamental hierarquizada. / This work aims at evaluating the implementation of the PDE-School in two schools in Minas Gerais State. The program, conceived in a little representative way in its macro elaboration, suggests a greater representativity in its micro elaboration, even as MEC imposed an implementation guide of its politics to the schools. It is this ambiguity that motivated this present research. This context creates a number of objectives to be investigated, such as the incorporation of another verticalized politics by principals and teachers; the way these groups relate to one another in the execution of the Program; and finally, on how the demands raised by principals and teachers in the introductory phase of the Plan are being materialized in the schools. The answers to these objectives will reveal to our work the level of the incorporation of the PDE-Schools ideas making possible the identification of the gains as well as the setbacks of this governmental proposal from the view of its school protagonists. Thus, two schools were chosen, having in mind that one dealt with the PDE-School in its traditional format, using a methodology that demand from the institution a thorough survey of its features, requiring the participation of all its segments. The second school, since 2011, has experienced the PDE elaboration in its interactive format, being that only the Principal was the interlocutor of the gathered information, what may have, for some, mischaracterized the participative principle of its politics. The results lead to an intensification of the relations between school managers and teachers as well as to a minor transformation in the everyday pedagogics of the school, especially after the arrival of the equipment acquired with the PDE-School budget. Some of the reasons for these tensions and the few changes may be the least representative character of the present digital version and the re-edition of one more hierarchical government initiative.

Made available in DSpace on 2017-05-12T14:42:00Z (GMT). No. of bitstreams: 1 SERGIO ANDRE.pdf: 1311833 bytes, checksum: 6b752394956f266ebf4824a2b8b64959 (MD5) Previous issue date: 2013-09-10 / The study initiates with an analysis of the role of the State in the logic of Capitalism and its contributions to other educational policies of continued formation of teaching class. Regarding the State, one can understand that, even though it s an institution who serves the dominant class, it s an monolithic institution with sort of relative autonomy. Depending of the strength correlation between social classes, it is possible that educational policy can be established in the State by the working class. It is inside of this context that we sought to study the Educational Policy of PDE/PR. The research aimed to analyze the Educational Development Program PDE/PR as a Continued Formation of teachers in Geography discipline with a guidance of UNIOESTE Francisco Beltrão from 2007 to 2010. This Public Policy represents an important accomplishment to the teaching class of the state of Paraná, result of the struggle and participation, specifically the APP Syndicate along with the SEED, having as the result the regularization of the PDE/PR Program as public policy. Significant conquests can be noticed in teaching formation, specially in theory/practice articulation and material conditions for this study, however the fact that the State is the manager of the program presents certain contradictions. The PDE/PR Program is presented as an innovative Continued Formation, considering the approximation of teachers to the scientific theories of initial graduation, even though the emphasis in teaching methodology prevails. The analysis of Continued Formation of Geography Teachers mentored by UNIOESTE-FB, sought to evaluate both value and improvement of basic education PDE teachers, concerning the access to knowledge and its reflections through the IES; the thoughts about school practicing; the exchange of experiences; the sharing of knowledge; the professional development and the continuity in daily school. The qualitative interviews of the study proved that the Program has contributed to increase the intellectual level of Geography PDE s teachers, although, in a general context, some contradictions can be found in teachers formation policy. / O estudo inicia-se com uma análise do papel do Estado na lógica do capitalismo e suas contribuições para outras políticas educacionais de Formação Continuada da classe docente. Em relação ao Estado, entendemos que, embora seja uma instituição a serviço da classe dominante, o mesmo não é uma instituição monolítica e há certa autonomia relativa. Dependo da correlação de forças entre as classes sociais, há possibilidade da classe trabalhadora instituir no âmbito do Estado políticas educacionais que atendam seus interesses. É neste contexto que buscamos pesquisar a política educacional do PDE/PR. O trabalho de pesquisa se propôs analisar o Programa de Desenvolvimento Educacional - PDE/PR como Formação Continuada de Professores, na disciplina de Geografia com a orientação da UNIOESTE- Francisco Beltrão, do período de 2007 a 2010. Essa Política Pública representa uma conquista importante para a classe docente do Estado do Paraná, resultado da participação e luta dos trabalhadores, especificamente da APP Sindicato junto a SEED, em, tendo como resultado a regulamentação do Programa PDE/PR como política pública. Verificam-se conquistas importantes na formação docente, sobretudo da articulação teoria-prática e das condições materiais para o estudo, contudo, o fato do Estado estar como gerente do Programa traz certas contradições. O Programa PDE/PR apresenta-se como uma Formação Continuada inovadora considerando a aproximação dos professores a reflexão das teorias científicas da formação inicial, embora ainda prevaleça uma ênfase as metodologias de ensino. A análise da Formação Continuada de Professores de Geografia, orientada pela UNIOESTE-FB, buscou avaliar o aperfeiçoamento e a valorização dos professores PDE da Educação Básica, quando o acesso ao conhecimento e a reflexão desses e, por meio das IES; as reflexões sobre a prática; as trocas de experiências; o compartilhamento de saberes; o desenvolvimento profissional; e, a continuidade no cotidiano escolar. Constatou-se por meio de entrevistas qualitativas que o Programa contribui para a elevação do nível intelectual dos professores PDE/PR de Geografia, porém, a política de formação de professores no contexto geral apresenta contradições.

Made available in DSpace on 2017-07-10T17:30:24Z (GMT). No. of bitstreams: 1 SERGIO ANDRE.pdf: 1311833 bytes, checksum: 6b752394956f266ebf4824a2b8b64959 (MD5) Previous issue date: 2013-09-10 / The study initiates with an analysis of the role of the State in the logic of Capitalism and its contributions to other educational policies of continued formation of teaching class. Regarding the State, one can understand that, even though it s an institution who serves the dominant class, it s an monolithic institution with sort of relative autonomy. Depending of the strength correlation between social classes, it is possible that educational policy can be established in the State by the working class. It is inside of this context that we sought to study the Educational Policy of PDE/PR. The research aimed to analyze the Educational Development Program PDE/PR as a Continued Formation of teachers in Geography discipline with a guidance of UNIOESTE Francisco Beltrão from 2007 to 2010. This Public Policy represents an important accomplishment to the teaching class of the state of Paraná, result of the struggle and participation, specifically the APP Syndicate along with the SEED, having as the result the regularization of the PDE/PR Program as public policy. Significant conquests can be noticed in teaching formation, specially in theory/practice articulation and material conditions for this study, however the fact that the State is the manager of the program presents certain contradictions. The PDE/PR Program is presented as an innovative Continued Formation, considering the approximation of teachers to the scientific theories of initial graduation, even though the emphasis in teaching methodology prevails. The analysis of Continued Formation of Geography Teachers mentored by UNIOESTE-FB, sought to evaluate both value and improvement of basic education PDE teachers, concerning the access to knowledge and its reflections through the IES; the thoughts about school practicing; the exchange of experiences; the sharing of knowledge; the professional development and the continuity in daily school. The qualitative interviews of the study proved that the Program has contributed to increase the intellectual level of Geography PDE s teachers, although, in a general context, some contradictions can be found in teachers formation policy. / O estudo inicia-se com uma análise do papel do Estado na lógica do capitalismo e suas contribuições para outras políticas educacionais de Formação Continuada da classe docente. Em relação ao Estado, entendemos que, embora seja uma instituição a serviço da classe dominante, o mesmo não é uma instituição monolítica e há certa autonomia relativa. Dependo da correlação de forças entre as classes sociais, há possibilidade da classe trabalhadora instituir no âmbito do Estado políticas educacionais que atendam seus interesses. É neste contexto que buscamos pesquisar a política educacional do PDE/PR. O trabalho de pesquisa se propôs analisar o Programa de Desenvolvimento Educacional - PDE/PR como Formação Continuada de Professores, na disciplina de Geografia com a orientação da UNIOESTE- Francisco Beltrão, do período de 2007 a 2010. Essa Política Pública representa uma conquista importante para a classe docente do Estado do Paraná, resultado da participação e luta dos trabalhadores, especificamente da APP Sindicato junto a SEED, em, tendo como resultado a regulamentação do Programa PDE/PR como política pública. Verificam-se conquistas importantes na formação docente, sobretudo da articulação teoria-prática e das condições materiais para o estudo, contudo, o fato do Estado estar como gerente do Programa traz certas contradições. O Programa PDE/PR apresenta-se como uma Formação Continuada inovadora considerando a aproximação dos professores a reflexão das teorias científicas da formação inicial, embora ainda prevaleça uma ênfase as metodologias de ensino. A análise da Formação Continuada de Professores de Geografia, orientada pela UNIOESTE-FB, buscou avaliar o aperfeiçoamento e a valorização dos professores PDE da Educação Básica, quando o acesso ao conhecimento e a reflexão desses e, por meio das IES; as reflexões sobre a prática; as trocas de experiências; o compartilhamento de saberes; o desenvolvimento profissional; e, a continuidade no cotidiano escolar. Constatou-se por meio de entrevistas qualitativas que o Programa contribui para a elevação do nível intelectual dos professores PDE/PR de Geografia, porém, a política de formação de professores no contexto geral apresenta contradições.

The aim of the thesis is to find a method, in conjunction with the ordinary differential equation (ODE) based method of lines (MOL) solution of Richards’ equation, to model the steep wetting front infiltration in very dry soils, accurately and efficiently. Due to the steep pressure head or steep water volumetric content gradients, highly nonlinear soil hydraulic properties and the rapid movement of the wetting front, accurate solutions for infiltration into a dry soil are usually difficult to obtain. Additionally, such problems often require very small time steps and large computation times. As an enhancement to the used ODE/MOL approach, Higher Order Finite Differencing, Varying Order Finite Differencing, Vertical Scaling, Adaptive Schemes and Non-uniform Stretching Techniques have been implemented and tested in this thesis. Success has been found in the ability of Vertical Scaling to simulate very steep moving front solution for the Burgers’ equation. Unfortunately, the results also show that Vertical Scaling needs significant research and improvement before their full potential in routine applications for difficult nonlinear problems, such as Richard’s equation with very steep moving front solution, can be realized. However, we have also shown that the use of the composed form of RE and a 2nd order finite differencing for the first order derivative approximation is conducive for modelling steep moving front problem in a very dry soil. Additionally, with the combination of an optimal influx value at the edges of the inlet, the ODE/MOL approach is able to model a 2-D infiltration in very dry soils, effectively and accurately. Furthermore, one of the strengths of this thesis is the use of a MATLAB PDE template. Implementing the ODE/MOL approach via a MATLAB PDE template has shown to be most suitable for modelling of partial differential equations. The plug and play mode of modifying the PDE template for solving time-dependent partial differential equations is user-friendly and easy, as compared to more conventional approaches using Pascal, Fortran, C or C++. The template offers greater modularity, flexibility, versatility, and efficiency for solving PDE problems in both 1-D and 2-D spatial dimensions. Moreover, the 2-D PDE template has been extended for irregular shaped domains.