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1
Floyd, Stewart Allen. "A qualitative analysis of finite difference equations in R[superscript n]." Thesis, Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/29441.
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Ampadu, Ebenezer. "Implementation of some finite difference methods for the pricing of derivatives using C++ programming." Link to electronic thesis, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/.
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Kama, Phumezile. "Non-standard finite difference methods in dynamical systems." Thesis, Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-07132009-163422.
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Chirvasa, Mihaela. "Finite difference methods for 1st Order in time, 2nd order in space, hyperbolic systems used in numerical relativity." Phd thesis, Universität Potsdam, 2010. http://opus.kobv.de/ubp/volltexte/2010/4213/.
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This thesis is concerned with the development of numerical methods using finite difference techniques for the discretization of initial value problems (IVPs) and initial boundary value problems (IBVPs) of certain hyperbolic systems which are first order in time and second order in space. This type of system appears in some formulations of Einstein equations, such as ADM, BSSN, NOR, and the generalized harmonic formulation.
For IVP, the stability method proposed in [14] is extended from second and fourth order centered schemes, to 2n-order accuracy, including also the case when some first order derivatives are approximated with off-centered finite difference operators (FDO) and dissipation is added to the right-hand sides of the equations.
For the model problem of the wave equation, special attention is paid to the analysis of Courant limits and numerical speeds. Although off-centered FDOs have larger truncation errors than centered FDOs, it is shown that in certain situations, off-centering by just one point can be beneficial for the overall accuracy of the numerical scheme.
The wave equation is also analyzed in respect to its initial boundary value problem. All three types of boundaries - outflow, inflow and completely inflow that can appear in this case, are investigated. Using the ghost-point method, 2n-accurate (n = 1, 4) numerical prescriptions are prescribed for each type of boundary. The inflow boundary is also approached using the SAT-SBP method.
In the end of the thesis, a 1-D variant of BSSN formulation is derived and some of its IBVPs are considered. The boundary procedures, based on the ghost-point method, are intended to preserve the interior 2n-accuracy.
Numerical tests show that this is the case if sufficient dissipation is added to the rhs of the equations.Diese Doktorarbeit beschäftigt sich mit der Entwicklung numerischer Verfahren für die Diskretisierung des Anfangswertproblems und des Anfangs-Randwertproblems unter Einsatz von finite-Differenzen-Techniken für bestimmte hyperbolischer Systeme erster Ordnung in der Zeit und zweiter Ordnung im Raum. Diese Art von Systemen erscheinen in einigen Formulierungen der Einstein'schen-Feldgleichungen, wie zB. den ADM, BSSN oder NOR Formulierungen, oder der sogenanten verallgemeinerten harmonischen Darstellung. Im Hinblick auf das Anfangswertproblem untersuche ich zunächst tiefgehend die mathematischen Eigenschaften von finite-Differenzen-Operatoren (FDO) erster und zweiter Ordnung mit 2n-facher Genaugigkeit. Anschließend erweitere ich eine in der Literatur beschriebene Methode zur Stabilitätsanalyse für Systeme mit zentrierten FDOs in zweiter und vierter Genauigkeitsordung auf Systeme mit gemischten zentrierten und nicht zentrierten Ableitungsoperatoren 2n-facher Genauigkeit, eingeschlossen zusätzlicher Dämpfungsterme, wie sie bei numerischen Simulationen der allgemeinen Relativitätstheorie üblich sind. Bei der Untersuchung der einfachen Wellengleichung als Fallbeispiel wird besonderes Augenmerk auf die Analyse der Courant-Grenzen und numerischen Geschwindigkeiten gelegt. Obwohl unzentrierte, diskrete Ableitungsoperatoren größere Diskretisierungs-Fehler besitzen als zentrierte Ableitungsoperatoren, wird gezeigt, daß man in bestimmten Situationen eine Dezentrierung des numerischen Moleküls von nur einem Punkt bezüglich des zentrierten FDO eine höhere Genauigkeit des numerischen Systems erzielen kann. Die Wellen-Gleichung in einer Dimension wurde ebenfalls im Hinblick auf das Anfangswertproblem untersucht. In Abhängigkeit des Wertes des sogenannten Shift-Vektors, müssen entweder zwei (vollständig eingehende Welle), eine (eingehende Welle) oder keine Randbedingung (ausgehende Welle) definiert werden. In dieser Arbeit wurden alle drei Fälle mit Hilfe der 'Ghost-point-methode' numerisch simuliert und untersucht, und zwar auf eine Weise, daß alle diese Algorithmen stabil sind und eine 2n-Genauigkeit besitzen. In der 'ghost-point-methode' werden die Evolutionsgleichungen bis zum letzen Punkt im Gitter diskretisiert unter Verwendung von zentrierten FDOs und die zusätzlichen Punkte die am Rand benötigt werden ('Ghost-points') werden unter Benutzung von Randwertbedingungen und Extrapolationen abgeschätzt. Für den Zufluß-Randwert wurde zusätzlich noch eine andere Implementierung entwickelt, welche auf der sogenannten SBP-SAT (Summation by parts-simulatanous approximation term) basiert. In dieser Methode werden die diskreten Ableitungen durch Operatoren angenähert, welche die 'Summation-by-parts' Regeln erfüllen. Die Randwertbedingungen selber werden in zusätzlichen Termen integriert, welche zu den Evolutionsgleichnungen der Punkte nahe des Randes hinzuaddiert werden und zwar auf eine Weise, daß die 'summation-by-parts' Eigenschaften erhalten bleiben. Am Ende dieser Arbeit wurde noch eine eindimensionale (kugelsymmetrische) Version der BSSN Formulierung abgeleitet und einige physikalisch relevanten Anfangs-Randwertprobleme werden diskutiert. Die Randwert-Algorithmen, welche für diesen Fall ausgearbeitet wurden, basieren auf der 'Ghost-point-Methode' and erfüllen die innere 2n-Genauigkeit solange genügend Reibung in den Gleichungen zugefügt wird.
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FANTI, ALESSANDRO. "A generalized finite difference approach to the computation of modes." Doctoral thesis, Università degli Studi di Cagliari, 2012. http://hdl.handle.net/11584/266145.
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This thesis deals with numerical techniques for the computation of modes in electromagnetic structures with arbitrary geometry. The approach proposed in
this work is based on the Finite Difference (FD) and Vector Finite Difference (VFD), which are applied to rectangular, circular, elliptical geometries, and to combination of them. The FD is applied using a 2D cartesian, polar and elliptical grid in the waveguide section. A suitable Taylor expansion of the mode function allows, either for scalar and for vector FD, to take exactly into account the
boundary condition. To prevent the raising of spurious modes, the VFD approximation results in a constrained eigenvalue problem, that has been solved using a decomposition method. All approaches presented have been validated comparing the results to the analytical modes of rectangular and circular waveguide, and to known data for
the elliptic case. The standard calculation of the waveguide modes using FD requires the use of two different grids, namely one for TE modes and the other for TM modes, due to the different boundary condition. It has been shown that a single grid can be used for all modes, thus allowing an effective mode-matching solution. The FD approach has been extended to waveguides (and apertures) with irregular boundaries, and therefore non-regular discretization grids. It has been shown that a suitable FD approximation of the Laplace operator is still possible. A ridged-waveguide, with trapezoidal ridges, and a rounded-ended waveguide
have been considered in detail.
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Munerato, Fernando Perin. "Remigração na profundidade mediante a equação da onda imagem." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307301.
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Orientadores: Joerg Schleicher, Amelia NovaisDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho aborda a questão de como resolver a equação da onda imagem para o problema de remigração na profundidade através de métodos numéricos. O objetivo deste problema é a reconstrução de uma imagem das camadas geológicas do subsolo a partir de uma imagem previamente migrada com um modelo de velocidade, geralmente, incorreto. Nosso principal objetivo neste trabalho é a investigação de possíveis métodos que possam resolver os problemas que surgiram ao usarmos esquemas explícitos do método de diferenças _nitas na solução da equação da onda imagem em trabalhos anteriores, como, por exemplo, a dispersão numérica. Para isso, estudamos aqui o método de volumes _nitos, assim como esquemas implícitos do método de diferenças _nitas. O método de volumes _nitos possui como característica principal propagar as médias das células da malha ao invés de simplesmente os dados pontuais como é feito no método de diferenças _nitas. As outras tentativas para solucionar o problema da dispersão foram dois tipos de implementação de esquemas implícitos do método de diferenças _nitas, isto é, implementações implícitas de esquemas convencionais avaliados em pontos da malha e um esquema avaliado nos centros das células. A qualidade dos algoritmos estudados foi testada numericamente. Estes testes numéricos mostram que o método de volumes _nitos não é adequado para resolver o problema da dispersão, uma vez que a média calculada a cada passo aumenta o estiramento do pulso. Além disso, as implementações implícitas dos esquemas convencionais mostram o mesmo comportamento de dispersão que as implementações explícitas. Unicamente o esquema centrado foi capaz de melhorar a dispersão numérica em comparação com as implementações anteriores,porém somente para dados contendo exclusivamente baixas freqüências
Abstract: This work approaches the question of how to solve the image-wave equation for depth remigration by numerical methods. The objective is the reconstruction of an image of the geologic layers of the subsoil from a previously migrated image with a different velocity model. Our main objective in this work is the investigation of possible methods that can solve the problems that appeared when using explicit _nite-difference schemes for the solution of the image-wave equation in previous works, particularly numerical dispersion. For this purpose, we study the method of _nite volumes, as well as implicit _nite-difference schemes. The main characteristic of the _nite-volume method is to simply propagate the averages in the cells of the mesh instead of the discretized data themselves as it is done in the _nitedifference method. As another attempt to solve the problem of the dispersion, we study two types of implementation of implicit _nite-difference schemes, that is, implicit implementations of conventional schemes evaluated out the edge of the cell and a scheme evaluated in the center of the cell. The quality of the studied algoritms has been tested numerically. These numerical tests show that the method of _nite volumes is not adequate to solve the problem of dispersion, for the average calculated in each step additionally increases the pulse stretch. Moreover, the implicit implementations of the conventional schemes show the same dispersion behavior as the explicit implementations. Solely the centered scheme was capable to improve the numerical dispersion in comparison with the previous implementations, however only for data containing
Mestrado
Geofisica Computacional
Mestre em Matemática Aplicada
7
Teramoto, Elias Hideo [UNESP]. "Caracterização hidrogeológica e simulação numérica de fluxo em uma região situada no distrito industrial de Paulínia (SP)." Universidade Estadual Paulista (UNESP), 2007. http://hdl.handle.net/11449/92749.
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Em área contaminada por hidrocarbonetos, situada no município de Paulínia, a migração dos contaminantes e a eficiência do sistema de bombeamento são governadas pela heterogeneidade litológica do aqüífero local, constituído por rochas do Subgrupo Itararé, rochas intrusivas básicas da Formação Serra Geral e por sedimentos cenozóicos correlatos à Formação Rio Claro. Desta forma, o entendimento da heterogeneidade que caracteriza este aqüífero e suas propriedades hidráulicas é essencial para a otimização e o aprimoramento do processo de remediação. Visando delinear o entendimento e a caracterização hidrogeológica local, foi elaborado modelo hidrogeológico conceitual, por meio da integração de dados provenientes de técnicas tradicionais de investigação, tais como métodos geofísicos, monitoramento dos níveis piezométricos de poços de monitoramento, descrições geológicas e análises granulométricas, para entendimento da dinâmica de fluxo local, distribuição litológica do substrato aqüífero e seus valores de condutividade hidráulica. Foram ainda realizadas simulações numéricas de fluxo em regime permanente, utilizando o software Visual Modflow, que emprega o método de diferenças finitas para testar o modelo conceitual concebido. A simulação numérica apresentou excelentes correlações entre os valores de cargas hidráulicas medidas e simuladas e os resultados obtidos permitiram verificar a consistência do modelo conceitual.
In an hydrocarbon contaminated area locate in Paulínia city, lithological heterogeneity of local aquifer controls the migration of contaminant and the efficiency of pump system. The aquifer is composed by sedimentary rocks of Itararé Sub-group, basic intrusive of Serra Geral Formation and cenozoic sediments correlated to Rio Claro Formation. Therefore, understanding heterogeinity that characterize the aquifer and its hydraulic properties is vital to optimization and improvement of remediation process. For hydrogeological characterization of the local aquifer, a conceptual hydrogeological model was elaborated by integrating traditional investigations tools, such as geophysical methods, piezometric level monitoring, and geological descriptions in drillings and granulometric analysis to understanding of local dynamic flow, lithological distributions and hydraulic conductivity. Numerical simulation under steady-state condition using Visual Modflow, which utilizes the finite differences method were performed to test the conceived conceptual model. The measured and calculated hydraulic heads are in excellent agreement, showing the consistency of the conceptual model.
8
Sousa, Nadson de. "Metodos de diferenças finitas : conceitos e interpretações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306426.
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Orientador: Ricardo Caetano Azevedo BilotiDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: O presente trabalho aborda os métodos de diferenças finitas com suas propriedades e aplicações. Iniciamos com uma revisão histórica, destacando alguns matemáticos que participaram do desenvolvimento da teoria de métodos de diferenças. Em seguida, apresentamos alguns modelos matemáticos compostos por equações diferenciais. Através da equação de advecção, estudamos métodos de diferenças explícitos, com especial enfoque para as propriedades de erro de truncamento, consistência, estabilidade e convergência dando ênfase ao Teorema de Lax. Estudamos a análise de Fourier e a condição de von Neumann para interpretar a amplitude, a dissipação e a dispersão das soluções numéricas. Abordamos os métodos Upwind, de Lax-Friedrichs e de Lax-Wendroff. Por fim, exemplificamos numericamente os conceitos e propriedades estudados com comparações entre os métodos, aplicados em um problema teste.
Abstract: The present work approaches finite-difference methods, their properties, and their applications. We present a historical review, including some mathematieians who participated in the development of the theory of differences. Furthermore, we present some mathematical models consisting of differential equatiolls. Through the advection equationl, we study explicit finite-difference methods, detailing their truncation error, consistency, stability and conlvergence properties. We employ Fourier analysis and the von Neumann condition to study the amplitude, dissipation and dispersion of numerical solutions. We compare three methods: Upwind, Lax-Friedrichs and Lax-Wendroff. Finally, we perform numerical tests to illustrate the concepts and properties studied in this work.
Mestrado
Analise Numerica
Mestre em Matemática
9
Alves, Diogo Stuani. "Investigação do efeito térmico no comportamento dinâmico de mancais hidrodinâmicos." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/264183.
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Orientador: Kátia Lucchesi Cavalca DediniDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: Os mancais lubrificados hidrodinamicamente estão presentes em muitas aplicações modernas, especialmente em maquinas rotativas que necessitam de operações mais precisas. Nestes casos, a lubrificação é essencial para a máquina, pois, diminui o atrito entre as peças internas e previne o contato metal-metal, além de agir como elemento de vinculo dinâmico para as pistas do mancal. Devido ao cisalhamento do lubrificante durante a operação, tem-se o aquecimento do fluido e com isso uma modificação nas condições de lubrificação, já que a viscosidade, parâmetro que caracteriza as particularidades do escoamento, diminui com o aumento da temperatura. A diminuição da viscosidade causa diminuição do atrito viscoso, o que acarreta em diminuição da capacidade de carga, gerando efeitos negativos nos coeficientes equivalentes e sendo possível, em alguns casos, a observação de contato direto entre as partes metálicas. Sendo assim, o estudo do atrito e das condições de lubrificação durante a operação de máquinas é de extrema importância em problemas como manutenção, durabilidade e confiabilidade de máquinas. Utilizando o método das diferenças finitas, é possível resolver simultaneamente as equações de Reynolds e da energia, que são responsáveis pelas distribuições de pressão e temperatura, respectivamente. Com isso, é possível analisar as diferenças de pressão, disposição do eixo no interior do mancal e coeficientes equivalentes de rigidez e amortecimento, de um modelo em que se usa viscosidade variante com a temperatura (termohidrodinâmico) e de um modelo que não apresenta esse fenômeno (isotérmico). Finalmente, utilizando um software de dinâmica de rotores, foi obtida a resposta dinâmica de um sistema mancal-rotor para turbocompressores
Abstract: The hydrodynamic lubricated bearings are present in modern applications, especially in rotational machines that need precisely operations. In those cases, the lubrication is essential for the machine, because it reduces the wear between the internal parts and prevents the metallic contact, and also, acts like an element of dynamic link for the bearing. Due to the lubricant shear, the fluid heats up and modifications on the lubrication conditions occurs, since the viscosity, parameter that characterize the flow, decreases with the increase of the temperature. The decrease of visco ity causes a decrease in the viscous friction, which entails in a decrease of the load sustaining capacity, negative effects in the equivalent coefficients and possible observation of metallic contact. So, the study of friction and lubrication conditions during the machine operation is extremely important on maintenance, durability and reliability of machines. Using the finite difference method it is possible to solve, simultaneously, the Reynolds and the energy equations that are responsible for the pressure and temperature distribution, respectively. Therewith, it is possible to analyze the differences in pressure, shaft position in the bearing and equivalent stiffness and damping coefficients, for a model that uses changes in viscosity with the temperature (thermohydrodynamic) and for a model that does not take it in account (isothermal). Finally, using a rotordynamic software (ROTORTEST), the dynamic response of a turbocharger bearing-rotor system was obtained and analyzed
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica
10
Campos, Marco Donisete de 1976. "Aplicações do método das diferenças finitas de alta ordem na solução de problemas de convecção-difusão : Applications of high-order finite difference method in the solution of the convection-diffusion equation." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/265963.
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Orientador: Luiz Felipe Mendes de MouraTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica
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Resumo: O presente trabalho tem como objetivo aplicar o método de diferenças finitas de alta ordem na solução de problemas bi e tridimensionais convectivo-difusivos transientes. As simulações numéricas foram realizadas para investigar, nos problemas lineares, o termo de dissipação viscosa na equação de transferência de calor bidimensional com ênfase, no caso tridimensional, na aplicação envolvendo troca de calor num canal retangular. Para problemas não lineares, o método de Newton para a linearização do termo convectivo foi usado para resolver a equação de Burgers bi e tridimensionais. O esquema desenvolvido mostrou-se simples, computacionalmente rápido, podendo ser aplicado para problemas bi e tridimensionais. Nas aplicações propostas, quando possível, as soluções analíticas disponíveis na revisão da literatura foram utilizadas para comparações com as soluções numéricas e validação do código, sendo a análise dos resultados feita a partir das normas L2 e L?
Abstract: The present study aims to apply the high-order Finite Difference Method to transient diffusive-convective problems in two and three dimensions. Numerical simulations have been undertaken to investigate, in the linear problems, the viscous dissipation term in the two-dimensional heat transfer equation with emphasis, in the three-dimensional case, on the application involving heat exchange in a rectangular channel. For nonlinear problems, the Newton's method for the linearization of the convective term was used for solving the two and three dimensional Burgers equation. This scheme is simple, computationally fast and can be applied for two or three-dimensional problems. For the proposed applications, whenever possible, the analytical solutions found in the literature review were used to compare with the numerical solutions. The analysis of results was done from the L2 and L? norms
Doutorado
Termica e Fluidos
Doutor em Engenharia Mecânica
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Teramoto, Elias Hideo. "Caracterização hidrogeológica e simulação numérica de fluxo em uma região situada no distrito industrial de Paulínia (SP) /." Rio Claro : [s.n.], 2007. http://hdl.handle.net/11449/92749.
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Resumo: Em área contaminada por hidrocarbonetos, situada no município de Paulínia, a migração dos contaminantes e a eficiência do sistema de bombeamento são governadas pela heterogeneidade litológica do aqüífero local, constituído por rochas do Subgrupo Itararé, rochas intrusivas básicas da Formação Serra Geral e por sedimentos cenozóicos correlatos à Formação Rio Claro. Desta forma, o entendimento da heterogeneidade que caracteriza este aqüífero e suas propriedades hidráulicas é essencial para a otimização e o aprimoramento do processo de remediação. Visando delinear o entendimento e a caracterização hidrogeológica local, foi elaborado modelo hidrogeológico conceitual, por meio da integração de dados provenientes de técnicas tradicionais de investigação, tais como métodos geofísicos, monitoramento dos níveis piezométricos de poços de monitoramento, descrições geológicas e análises granulométricas, para entendimento da dinâmica de fluxo local, distribuição litológica do substrato aqüífero e seus valores de condutividade hidráulica. Foram ainda realizadas simulações numéricas de fluxo em regime permanente, utilizando o software Visual Modflow, que emprega o método de diferenças finitas para testar o modelo conceitual concebido. A simulação numérica apresentou excelentes correlações entre os valores de cargas hidráulicas medidas e simuladas e os resultados obtidos permitiram verificar a consistência do modelo conceitual.Abstract: In an hydrocarbon contaminated area locate in Paulínia city, lithological heterogeneity of local aquifer controls the migration of contaminant and the efficiency of pump system. The aquifer is composed by sedimentary rocks of Itararé Sub-group, basic intrusive of Serra Geral Formation and cenozoic sediments correlated to Rio Claro Formation. Therefore, understanding heterogeinity that characterize the aquifer and its hydraulic properties is vital to optimization and improvement of remediation process. For hydrogeological characterization of the local aquifer, a conceptual hydrogeological model was elaborated by integrating traditional investigations tools, such as geophysical methods, piezometric level monitoring, and geological descriptions in drillings and granulometric analysis to understanding of local dynamic flow, lithological distributions and hydraulic conductivity. Numerical simulation under steady-state condition using Visual Modflow, which utilizes the finite differences method were performed to test the conceived conceptual model. The measured and calculated hydraulic heads are in excellent agreement, showing the consistency of the conceptual model.
Orientador: Chang Hung Kiang
Banca: Edson Cézar Wedland
Banca: Ewerton de Oliveira
Mestre
12
Postell, Floyd Vince. "High order finite difference methods." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/28876.
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Lame, John. "p-adic finite difference equations /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487936356158483.
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Rodriguez, Miranda Juan Carlos 1984. "Estudio y análisis de sistemas lineales generados en problemas de contorno con frontera discontínua a partir de métodos espectrales/hp = Estudo e análise de sistemas lineares gerados nos problemas de contorno com fronteira descontinua a partir de métodos espectrais/hp." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306347.
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Orientador: Petronio PulinoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: O Método dos Elementos Finitos representou nos últimos anos uma ferramenta fundamental no estudo de problemas de contorno. A evolução desde sua formulação fundamental a partir do Método de Galerkin clássico até sua versão com refinamento hp, se tornou na base dos métodos numéricos mais avançados como é o Método de Galerkin Descontinuo. O Método dos Elementos Finitos de Alta Ordem juntamente com os Métodos Espectrais usados na obtenção de soluções numéricas para problemas de contorno com fronteira descontinua, serão nosso objeto de estudo nesta Dissertação. Desde sua formulação matemática fundamental, por intermédio da escolha apropriada das funções hierárquicas que compõem os espaços de aproximação, assim como a montagem dos sistemas lineares locais e sua respectiva utilização no sistema linear global esparso, cuja solução é obtida pelo método iterativo de Gradiente Conjugado usando diversos Precondicionadores, será o caminho a seguir
Abstract: The Finite Element Method developed in the last decades has been the most important tool in the study of Boundary Value Problems. Your evolution from its fundamental formulation using the Galerkin Method to the hp-adaptive finite element methods (hp-FEM), provided the necessary foundation for more advanced Numerical Methods like the Galerkin Discontinuous Method. The Finite Element Method of Higher Order, together with the Spectral formulation as a numerical method to solve Boundary Problems with Discontinuous Boundary, is the objective of study to this dissertation. The fundamental mathematical formulation of the finite element methods, passing through of to choose of hierarchical basis functions, also the assembly of local linear systems and it posteriorly use to construct a Sparse Linear System, whose solution is obtained for an iterative Preconditioner Gradient Method
Mestrado
Matematica Aplicada
Mestre em Matemática Aplicada
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Ağıroğlu, İzzet Onur Tanoğlu Gamze. "An application of the finite differences method to a dynamical interface problem/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000445.pdf.
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Demirayak, Murat Neslitürk Ali İhsan. "Analysis Of Finite Difference Methods For Convection-Diffusion Problem/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000481.pdf.
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Fernandes, Daniel Thomas. "Métodos de Elementos Finitos e Diferenças Finitas para o Problema de Helmholtz." Laboratório Nacional de Computação Científica, 2009. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=167.
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É bem sabido que métodos clássicos de elementos finitos e diferenças finitas para o problema de Helmholtz apresentam efeito de poluição, que pode deteriorar seriamente a qualidade da solução aproximada. Controlar o efeito de poluição é especialmente difícil quando são utilizadas malhas não uniformes. Para malhas uniformes com elementos quadrados são conhecidos métodos (p. e. o QSFEM, proposto por Babuska et al) que minimizam a poluição. Neste trabalho apresentamos inicialmente dois métodos de elementos finitos de Petrov-Galerkin com formulação relativamente simples, o RPPG e o QSPG, ambos com razoável robustez para certos tipos de distorções dos elementos. O QSPG apresenta ainda poluição mínima para elementos quadrados. Em seguida é formulado o QOFD, um método de diferenças finitas aplicável a malhas não estruturadas. O QOFD apresenta grande robustez em relação a distorções, mas requer trabalho extra para tratar problemas não homogêneos ou condições de contorno não essenciais. Finalmente é apresentado um novo método de elementos finitos de Petrov-Galerkin, o QOPG, que é formulado aplicando a mesma técnica usada para obter a estabilização do QOFD, obtendo assim a mesma robustez em relação a distorções da malha, com a vantagem de ser um método variacionalmente consistente. Resultados numéricos são apresentados ilustrando o comportamento de todos os métodos desenvolvidos em comparação com os métodos de Galerkin, GLS e QSFEM.It is well known that classical finite elements or finite difference methods for Helmholtz problem present pollution effects that can severely deteriorate the quality of the approximate solution. To control pollution effects is especially difficult on non uniform meshes. For uniform meshes of square elements pollution effects can be minimized with the Quasi Stabilized Finite Element Method (QSFEM) proposed by Babusv ska el al, for example. In the present work we initially present two relatively simple Petrov-Galerkin finite element methods, referred here as RPPG (Reduced Pollution Petrov-Galerkin) and QSPG (Quasi Stabilized Petrov-Galerkin), with reasonable robustness to some type of mesh distortion. The QSPG also shows minimal pollution, identical to QSFEM, for uniform meshes with square elements. Next we formulate the QOFD (Quasi Stabilized Finite Difference) method, a finite difference method for unstructured meshes. The QOFD shows great robustness relative to element distortion, but requires extra work to consider non-essential boundary conditions and source terms. Finally we present a Quasi Optimal Petrov-Galerkin (QOPG) finite element method. To formulate the QOPG we use the same approach introduced for the QOFD, leading to the same accuracy and robustness on distorted meshes, but constructed based on consistent variational formulation. Numerical results are presented illustrating the behavior of all methods developed compared to Galerkin, GLS and QSFEM.
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Hayman, Kenneth John. "Finite-difference methods for the diffusion equation." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phh422.pdf.
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蔡景華 and King-wah Choi. "Finite difference modelling of estuarine hydrodynamics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1985. http://hub.hku.hk/bib/B30425153.
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Benhamouche, Mehdi. "Retournement temporel électromagnétique : cartographies d'énergie et localisation, du modèle numérique à l'expérimentation contrôlée." Thesis, Paris 11, 2012. http://www.theses.fr/2012PA112405.
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Le retournement temporel exploite la réversibilité temporelle de l’équation d’onde dans les milieux sans perte. Cela implique qu’une onde émise par une source peut rebrousser chemin et se focaliser sur sa source originale par le biais d’un miroir à retournement temporel. Cette focalisation permet de situer l’emplacement de cette source. Le but de cette thèse est d’exploiter le phénomène de retournement temporel d’ondes électromagnétiques en vue de la localisation et la caractérisation partielle d’objets diffractants enfouis dans un milieu sans perte. Notre étude est menée dans le domaine temporel large bande en se basant sur une modélisation numérique par la technique d’intégration finie.Le domaine temporel est un domaine assez peu exploré dans la littérature contrairement au domaine fréquentiel. La principale problématique est la détermination de l’instant de focalisation qui nous permet de choisir la distribution des champs à partir de laquelle les objets diffractants seront localisés. Nous introduisons dans ce manuscrit un critère de choix d’instant de focalisation qui est comparé tout au long des études entreprises au critère du minimum d’entropie.La démarche empruntée exploite l’analyse de cartographies d’énergie électromagnétique en deux et trois dimensions. Elle est validée dans un premier temps par l’analyse de configurations canoniques exploitant des données synthétiques obtenues par simulation. L’influence de divers paramètres relatifs aux objets diffractants est étudiée de même que l’impact du nombre d’émetteurs récepteurs du miroir à retournement temporel. Dans une seconde étape une expérimentation contrôlée en chambre anéchoïque à SUPELEC est réalisée en utilisant des antennes en régime harmonique et en régime impulsionnelTime reversal is, as is now well-known, exploiting the temporal reversibility of the wave equation in assumed lossless media. To summarize, it implies that a wave emitted by a given source may turn back and thereupon focus onto its original source by means of a so-called Time Reversal Mirror (TRM), which operation, properly simulated from field data acquired in a given measurement domain, could enable us to locate the source indeed. The aim of this thesis is to exploit the phenomenon of time reversal for the localization and the partial characterization, whenever possible, of diffracting objects (dielectric and conducting scatterers, in which sources are induced by given antennas, usually dipole-like) that are buried in a lossless medium (it can be a free space or a half-space) within a fully 3-D transient electromagnetic context. Time-domain certainly is a less explored area in the literature than frequency-domain, and this 3-D context (even if some 2-D validation studies are led also in the present work) is particularly demanding, computatinally speaking as well as at the level of real laboratory experiments. In addition, it requires that we be able to accurately compute the vector electromagnetic field in this time domain in an appropriate wideband situation, as well as whatever field is time reversed during the experiments, which are tasks performed via a full-wave Finite Integration Technique (FIT) developed at LGEP as is validated and discussed in some length in the manuscript. The main problem however is the determination of the moment of focus which would enable us determine the location of the scatterers at least to some extent. Here, to that effect, we introduce and discuss in depth a new criterion of choice of the instant of focus, which is in particular compared throughout the studies undertaken to the usually employed minimum entropy criterion. Influences of the various parameters of the scatterers themselves and of the measurement set-ups are thoroughly discussed on the way. Let us emphasize that what matters to us is the behavior of the (time-reversed) electromagnetic energy and not only of the electric field as standard, that is, the approach taken builds and uses the analysis of energy maps obtained by the aforementioned 3-D numerical modeling. Beyond the modeling of pure synthetic field data and discussions thereof, much attention is also given to leading controlled experiments on canonical targets using both transient and frequency-diverse time-harmonic sources within an anechoic chamber which was made available to us in SUPELEC
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Milagre, Alexandre Magno. "Condições de fronteiras de absorção no método FDTD." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-07012008-164204/.
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Em muitas simulações eletromagnéticas utilizando o método FDTD, é desejado que os campos radiados pelas estruturas em análise sejam transmitidos para fora do domínio computacional. Infelizmente isto não é possível de ser realizado através do método FDTD em sua forma original. Para resolver este problema, deve-se implementar, nas superfícies limítrofes dos domínios computacionais, condições especiais denominadas na literatura técnica de Condições de Fronteiras de Absorção, ou, em inglês, \"Absorbing Boundary Conditions\" (ABC´s). Essas Condições de Fronteiras de Absorção impedem que os campos radiados sejam refletidos nas superfícies limítrofes dos domínios computacionais, retornando para o interior do domínio e interferindo no resultado final das simulações. Não existe uma técnica de absorção ideal, ou seja, que elimine totalmente a reflexão. As técnicas atualmente existentes possuem vantagens e desvantagens, podendo ser mais ou menos eficientes, o que faz com que esse tema ainda seja motivo de extensivos estudos. O objetivo deste trabalho consiste no estudo, implementação e comparação de Condições de Fronteiras de Absorção e na indicação de uma possível melhoria nessa área. São realizadas simulações em domínios bidimensionais e tridimensionais para se determinar vantagens e desvantagens de cada técnica de absorção. A análise dos resultados das simulações está focalizada no grau de atenuação que as ABCs possuem e na carga computacional despendidas por elas. Este trabalho é concluído com simulações empregando as condições de fronteiras analisadas para três estruturas clássicas. As vantagens e desvantagens de cada ABC são apresentadas e uma melhoria proposta na técnica de Auto Teleportação de Campos, ou, em inglês, \"Self Teleportation of Fields\" é validada. As estruturas analisadas são uma microlinha de transmissão, um filtro planar e um cilindro metálico iluminado por uma onda plana uniforme.In many electromagnetic computational simulations using the FDTD method, it is desired that the electromagnetic fields radiated by the structures under analysis can be transmitted outwards the computational domain. Unfortunately, this is impossible to be done by the FDTD method in its original form. To mitigate this problem, one must apply special conditions to the computational domain boundaries, known in the technical literature as Absorbing Boundary Conditions (ABCs) These Absorbing Boundaries Conditions prevent the radiated fields to be reflected by boundaries back into the computational domain. Without them, these fields would interfere with the final simulation results. However, there is no ideal technique that completely eliminates the reflections. The existing techniques have advantages and disadvantages, which make them more or less efficient, still making this subject a theme of extensive studies. This work is aimed at studying, implementing and comparing these Absorbing Boundary Conditions and at indicating a possible improvement in this field. Simulations in bi-dimensional and three-dimensional domains were made to evaluate advantages and disadvantages of each absorption technique. The analysis of the simulation results was focused in the attenuation degree of the ABCs and their computational burden. The work is concluded with simulations using the analyzed ABCs for three classic structures. The advantages and disadvantages of each ABC are presented and a proposed improvement on the \"Self Teleportation of Fields\" technique is validated. The analyzed structures are a microstrip line, a planar filter and a metallic cylinder illuminated by a uniform plane wave.
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Chavannes, Nicolas Pierre. "Local mesh refinement algorithms for enhanced modeling capabilities in the FDTD method /." Konstanz : Hartung-Gorre, 2002. http://www.loc.gov/catdir/toc/fy0801/2006483066.html.
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Trojan, Alice von. "Finite difference methods for advection and diffusion." Title page, abstract and contents only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phv948.pdf.
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Includes bibliographical references (leaves 158-163). Concerns the development of high-order finite-difference methods on a uniform rectangular grid for advection and diffuse problems with smooth variable coefficients. This technique has been successfully applied to variable-coefficient advection and diffusion problems. Demonstrates that the new schemes may readily be incorporated into multi-dimensional problems by using locally one-dimensional techniques, or that they may be used in process splitting algorithms to solve complicatef time-dependent partial differential equations.
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Siam, Mohamed. "The finite difference method in photonics." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=32263.
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This thesis explains and implements the Finite Difference Method to simulate for the propagating modes in integrated waveguides. The equidistant and non-equidsitant methods are explained and implemented. A shape recognition engine is implemented to recognize rectangular waveguide structures provided by the user in the form of images. A geometric meshing algorithm is developed to improve accuracy.Cette thèse explique et met en oeuvre la méthode des diffrences finis pour simuler la propagation de modes de guides d'ondes intgré. La méthode équidistante et non-équidistante est expliquée et mise en oeuvre. Un moteur de reconnaissance de formes est mise en oeuvre pour reconnaître la structure des guides d'ondes rectangulaire prévues par l'utilisateur sous forme d'images. Un algorithme géomtrique de maillage est développé pour améliorer l'exactitude.
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Hartenstein, Margaret. "Finite groups of chain difference one /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487953204281192.
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Choi, King-wah. "Finite difference modelling of estuarine hydrodynamics /." [Hong Kong] : University of Hong Kong, 1985. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1232503X.
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Pezant, Joannes Charles. "High temperature thickness monitoring using ultrasonic waves." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26577.
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Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009.Committee Chair: Michaels, Jennifer; Committee Member: Jacobs, Laurence; Committee Member: Michaels, Thomas. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Abenius, Erik. "Direct and Inverse Methods for Waveguides and Scattering Problems in the Time Domain." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-6013.
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Kung, Christopher W. "Development of a time domain hybrid finite difference/finite element method for solutions to Maxwell's equations in anisotropic media." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1238024768.
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Kress, Wendy. "High Order Finite Difference Methods in Space and Time." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3559.
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Reimers, Mark Allan. "Hyper-finite methods for multi-dimensional stochastic processes." Thesis, University of British Columbia, 1986. http://hdl.handle.net/2429/27515.
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In this thesis we introduce Non-Standard Methods, in particular the use of hyperfinite difference equations, to the study of space-time random processes. We obtain a new existence theorem in the spirit of Keisler (1984) for the one dimensional heat equation forced non-linearly by white noise. We obtain several new results on the sample path properties of the Critical Branching Measure Diffusion, and show that in one dimension it has a density which satisfies a non-linearly forced heat equation. We also obtain results on the dimension of the support of the Fleming-Viot Process.Science, Faculty of
Mathematics, Department of
Graduate
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Grinchpoun, Vadim. "Spectre ponctuel d'operateurs aux differences finies aleatoires multidimensionnels." Paris 7, 1994. http://www.theses.fr/1994PA077144.
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Dans cette these nous considerons un operateur aux differences finies d'ordre infini multidimensionnel qui soit la somme d'un operateur de toeplitz dont les coefficients non diagonaux decroissent exponentiellement, et d'un operateur de multiplication aleatoire (champ aleatoire engendre par des variables i. I. D. ). Nous prouvons que le spectre d'un tel operateur possede une localisation exponentielle dans chacun des deux cas suivants: a basse energie, a grand desordre. La demonstration que nous donnons ici fournit une description explicite de la fonction de green et du spectre d'un operateur agissant sur tout l'espace, a partir des memes notions pour les operateurs agissant sur des sous-espaces de dimension finie. Ceci nous donne beaucoup d'informations sur la structure des fonctions propres et ne requiert que des hypotheses assez faibles sur la distribution de potentiel. A titre d'applications, les resultats ci-dessus nous permettent de prouver la presence de spectre ponctuel dans chacun des cas suivants: pour un operateur de schrodinger discret a potentiel aleatoire porte par un hyperplan, pour un operateur defini sur un demi-espace avec conditions aux limites aleatoires
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LAFORTUNE, STEPHANE. "Symetries et integrabilite des equations aux differences finies." Paris 7, 2000. http://www.theses.fr/2000PA077122.
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La theorie des groupes de lie joue un role tres important dans l'etude des equations differentielles. De plus, l'analyse de painleve est une technique mathematique nous permettant d'etudier l'integrabilite des equations differentielles. Tout comme les equations differentielles, les equations aux differences finies (edf) sont souvent utilisees en physique. Il est donc necessaire de developper un formalisme nous permettant d'etudier les symetries et l'integrabilite des equations aux differences finies tout comme on le fait presentement pour le cas continu. Dans ma these, les symetries sont utilisees dans un premier temps pour la classification d'un systeme d'equations differentielles aux differences finies. Un des resultats les plus interessants obtenus dans cette these concerne l'existence de certains systemes possedant un groupe de symetrie de dimension infinie. Nous etudions aussi des systemes de toda generalises du point de vue de ses symetries. Un des resultats interessants que nous avons obtenu est l'identification de cas n'etant pas completement integrables mais possedant un groupe de symetrie conforme. Pour ce qui est de l'integrabilite, la presente these porte principalement sur des equations dites linearisables, i. E. Des equations qui sont equivalentes a un systeme lineaire. Ce travail s'insere dans le vaste projet de recherche dont le but est de classifier toutes les equations discretes integrables a une variable. Nous classifions de grandes familles de systemes linearisables. Finalement, nous utilisons l'equation de riccati afin d'obtenir des equations du troisieme ordre integrables.
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Dea, John R. "High-order non-reflecting boundary conditions for the linearized Euler equations." Monterey, Calif. : Naval Postgraduate School, 2008. http://edocs.nps.edu/npspubs/scholarly/theses/2008/Sept/08Sep%5FDea%5FPhD.pdf.
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Dissertation (Ph.D. in Applied Mathematics)--Naval Postgraduate School, September 2008.Dissertation Advisor(s): Neta, Beny. "September 2008." Description based on title screen as viewed on November 6, 2008. Includes bibliographical references (p. 161-170). Also available in print.
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Eng, Ju-Ling. "Higher order finite-difference time-domain method." Connect to resource, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1165607826.
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Persson, Jonas. "Accurate Finite Difference Methods for Option Pricing." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-7097.
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Filipovic, Zlatko. "Finite difference methods for pricing financial derivatives." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.420931.
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Kenny, Ciaran. "TLM and finite-difference : an algebraic comparison." Thesis, University of East Anglia, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338403.
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Demir, Ismail. "Seismic wave modelling using finite difference methods." Thesis, University of South Wales, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284896.
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Lee, Check Fu. "Finite difference method for electromagnetic scattering problems." Thesis, Massachusetts Institute of Technology, 1990. http://hdl.handle.net/1721.1/14041.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1990.Includes bibliographical references (leaves 184-192).
by Check F. Lee.
Ph.D.
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Steinle, Peter John. "Finite difference methods for the advection equation /." Title page, table of contents and abstract only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phs8224.pdf.
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Johnson, Fen Rui. "A study of finite and linear elasticity." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1096.
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Wang, Huan. "Modeling of the plasmon resonance of metallic nanopaticles embedded in liquid crystal." Thesis, Troyes, 2014. http://www.theses.fr/2014TROY0004/document.
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Les nanoparticules métalliques ont des propriétés optiques uniques, dont le contrôle et l'optimisation ont un intérêt grandissant tant pour la recherche fondamentale qu'appliquée. Une propriété spectaculaire de ces nanoparticules est la résonance plasmon de surface localisé, qui est une conséquence des oscillations des électrons libres à l'interface métal/diélectrique.La position spectrale de la résonance plasmon est largement dépendante de la géométrie des nanoparticules, mais aussi de la constante diélectrique du milieu environnant. Un moyen pour contrôler cette résonance consiste donc à faire varier l'indice du milieu qui entoure les nanostructures. Les cristaux liquides nématiques sont un excellent moyen pour modifier et contrôler la résonance plasmon. En effet, par rotation des molécules du cristal liquide on peut induire un changement d'indice qui se traduit par un changement de la réponse optique des nanostructures. L'objectif de la thèse est de simuler des réseaux de nanoparticules d'or, dans un cristal liquide nématique afin de prédire l'influence de l'orientation du CL sur les propriétés optiques de ces nanostructures. Le formalisme numérique utilisé est basé sur la méthode des différences finies dans le domaine temporel (FDTD). Nous avons pris en compte les phénomènes d'ancrage des molécules aux interfaces avec la cellule contenant les cristaux liquides et les structures métalliques, et comparé les résultats avec le cas d'une orientation uniforme des molécules dans la cellule. La possibilité d'avoir une double résonance a été étudiée, ainsi que les gain SERS associés à ces structures spécifiquesMetal nanoparticles have unique optical properties, the control and optimization have a growing interest in fundamental research as same as applied research. A spectacular property of these nanoparticles is the localized surface plasmon resonance ( LSPR ), which is a consequence of the oscillations of free electrons at the interface between metal and dielectric.The spectral position of the plasmon resonance is largely dependent on the geometry of the nanoparticles, but also on the dielectric properties of the surrounding medium. It implies that the variation of the index of the medium surrounding the metallic nanostructures can control the LSPR resonance. Nematic liquid crystals are a great way to modify and control the plasmon resonance. Indeed, rotation of the liquid crystal molecules can induce a change in refractive index which results in a change in the optical response of the nanostructures. The aim of the thesis is to simulate arrays of gold nanoparticles in a nematic liquid crystal in order to predict the influence of the orientation of the LC molcules on the optical properties of these nanostructures. Numerical method we used is based on the finite difference time domain ( FDTD ) method. We have considered anchoring effects of molecules at the interfaces between the cell containing the liquid crystal and the substrates. And the results are compared with the case of uniform orientation of the LC molecules in the cell. The possibility of having double resonances was studied as well as the Surface Enhanced Raman Scattering (SERS ) gain associated with these specific structures
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Pham, Du. "Comparison of finite volume and finite difference methods and convergence results for finite volume schemes." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3277975.
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Thesis (Ph. D.)--Indiana University, Dept. of Mathematics, 2007.Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6004. Adviser: Roger Temam. Title from dissertation home page (viewed May 8, 2008).
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Pila, Matheus Fabiano 1979. "Modelamento sismico assintotico utilizando diferenças finitas." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307616.
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Orientadores: Lucio Tunes dos Santos, Maria Amélia Novais SchleicherDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Mestrado
Geofisica Computacional
Mestre em Matemática Aplicada
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Carvalho, Rafael Aleixo de. "As equações da onda imagem para remigração em meios elipticamente anisotropicos." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307299.
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Orientador: Joerg SchleicherDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: As equações da onda imagem para os problemas de remigração na profundidade eno tempo em meios elipticamente anisotrópicos são equações diferenciais parciais de segunda ordem similares a equação da onda acústica. A variável de propagação é a velocidade vertical ou a elipticidade do meio. Essas equações são deduzidas a partir das propriedades cinemáticas da remigração em meios anisotrópicos. O objetivo é propiciar a construção de imagens do subsolo que correspondam a diferentes velocidades verticais e/ou diferentes graus de anisotropia do meio diretamente de uma imagem migrada. ?Painéis de anisotropia? podem ser obtidos de maneira completamente análoga aos painéis de velocidade para a análise de velocidade de migração. Um exemplo numérico mostra a validade desta teoria
Abstract: The image-wave equations for the problems of depth and time remigration in elliptically anisotropic media are second-order partial differential equations similar to the acoustic wave equation. The propagation variable is the vertical velocity or the medium ellipticity. These differential equations are derived from the kinematic properties of anisotropic remigration. The objective is to enable the construction of subsurface images that correspond to different vertical velocity and/or different degrees of medium anisotropy directly from a single migrated image. In this way, ?anisotropy panels? can be obtained in a completely analogous way to velocity panels for a migration velocity analysis. A simple numerical example demonstrates the validity of the theory
Mestrado
Mestre em Matemática Aplicada
47
Sano, Dayene Miralha de Carvalho. "Simulação numérica da fase líquida na deposição de filmes finos via sol-gel: aplicações para dióxido de estanho /." Bauru : [s.n.], 2010. http://hdl.handle.net/11449/100923.
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Orientador: Luis Vicente de Andrade ScalviBanca: Valdemir Garcia Ferreira
Banca: Julio Ricardo Sambrano
Banca: Carlos José Leopoldo Constantino
Banca: Carlos Antonio Ruggiero
O Programa de Pós-Graduação em Ciência e Tecnologia de Materiais, PosMat, tem caráter institucional e integra as atividades de pesquisa em materiais de diversos campi da Unesp
Resumo: Neste trabalho foi realizada a simulação numérica da fase líquida no processo de deposição de filmes finos pela técnica de molhamento (dip-coating), via sol-gel, utilizando como aplicação soluções precursoras de dióxido de estanho (Sn'IND. 2'). Dióxido de estanho é um semicondutor transparente de gap largo, amplamente utilizado em muitos tipos de dispositivos. Além da técnica convencional, o trabalho analisa uma nova proposta da técnica de deposição dip-coating onde a solução se encontra em uma temperatura diferente da ambiente. Para ambas as técnicas foram realizadas a modelagem matemática dos problemas e desenvolveu-se um método numérico apropriado baseado no método MAC (Marker and Cell). O problema foi resolvido em coordenadas cartesianas bidimensionais e as equações foram discretizadas pela técnica de diferenças finitas. Os resultados numéricos são visualizados por meio da distribuição de temperatura e vetores velocidade da solução precursora, que fornecem subsídios para investigação da influência dos vetores velocidade na obtenção de filmes com boas propriedades, em relação à uniformidade e homogeneidade. Verifica-se que estas características refletem diretamente na qualidade óptica dos filmes investigados, tornando-se parâmetros importantes para aplicações em dispositivos opto-eletrônicos. Através dos resultados numéricos verificou-se que nas regiões do fluido próximas ao substrato, os módulos dos vetores velocidade são maiores, há uma maior quantidade de material sendo depositado. Notou-se também, através da distribuição de velocidades em direção ao substrato que o filme tem uma melhor uniformidade na sua espessura quando os vetores velocidade possuem os valores de seus módulos mais próximos uns dos outros. Portanto, mudando os parâmetros iniciais de viscosidade, densidade, velocidade de imersão/emersão do substrato ou temperatura no fluido pode-se estudar o comportamento.
Abstract: In this work, the numerical simulation of liquid phase in the thin film deposition, by the sol-gel-dip-coating technique, was carried out. The method was applied to tin dioxide (Sn'IND. 2') solutions. Tin dioxide is a transparent semiconductor of wide bandgap, extensively used in many types of devices. Besides the conventional procedure, this work analyses a new proposal for the deposition technique, where the solution is heated above room temperature. In both cases, the mathematical modeling was done and the appropriated numerical method was developed, based on MAC (Marker and Cell) approach. The problem was solved in two-dimensional Cartesian coordinates and the equations were discretized by the finite difference technique. The numerical results are visualized through temperature and vector velocity distributions in the precursos solution, yielding subsides to the investigation of the influence of vectors velocity in the deposition of good property films, concerning uniformity and homogeneity. It was verified that these characteristics point directly toward the optical quality of investigated films, becoming important parameters for application in optoelectronic devices. The numerical results allow verifying that in the fluid regions close to the substrate, where the velocity modulus is highter, there is a larger amount of material being deposited. It was also noticed, through the velocity distribution towards the substrate, that the film has a better thickness uniformity when the vectors velocity have modulus values closer to each other. Therefore, changing initial parameters such as viscosity, density, substrate dipping rate or fluid temperature, it is possible to evaluate the fluid behavior during the thin film deposition.
Doutor
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Miyaoka, Tiago Yuzo 1990. "Impacto ambiental e populações que interagem : uma modelagem inovadora, aproximação e simulações computacionais." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307267.
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Orientador: João Frederico da Costa Azevedo MeyerDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Este trabalho trata da modelagem matemática e da simulação computacional de um problema de dinâmica populacional, mais precisamente a interação de um poluente tóxico a duas espécies que competem entre si por espaço e alimento. A modelagem é feita a partir de dispersão e advecção populacional juntamente com o modelo clássico de Lotka-Volterra e reprodução do tipo de Verhulst, mas com um termo inovador para a interação entre poluente e população. Este termo inovador visa a melhoria do modelo a médio e longo prazos, pois tem comportamento assintótico em relação ao tempo. Temos assim um sistema de equações diferenciais parciais não-linear, cuja solução analítica é impossível de ser obtida. Recorremos então a métodos numéricos e simulações computacionais para obter soluções aproximadas. Para isso, utilizamos os métodos de Elementos Finitos (com elementos triangulares de primeira ordem) nas variáveis espaciais e de Diferenças Finitas (mais especificamente, o método de Crank-Nicolson) na temporal, além do método preditor-corretor de Douglas e Dupont para tratar não linearidades, detalhando o procedimento de se obter um software capaz de gerar cenários qualitativamente realistas (os parâmetros utilizados foram estimados). Com o software obtido apresentamos gráficos das soluções aproximadas em cenários hipotéticos distintos, de forma a poder analisar possíveis impactos ambientais causados pela poluição despejada no meio ambiente
Abstract: This work treats the mathematical modeling and computational simulation of a populational dynamics problem, more precisely the interaction of a toxic pollutant in two species which compete with each other for space and food. The modeling is done from populational dispersion and advection together with the classical model of Lotka-Volterra and Verhulst type reproduction, but with a innovative term for the interaction of pollutant and population. This innovative term aims the improvement of the model in the medium and long time, because it has asymptotic behaviour in relation to time. Therefore we have a system of non linear partial differential equations, whose analytical solution is impossible to be obtained. We then appeal to numerical methods and computational simulations to obtain approximated solutions. For this, we use the Finite Elements method (with first order triangular elements) in spatial variables and Finite Differences method (more specifically the Crank-Nicolson method), in addition to the Douglas and Dupont predictor-corrector method to treat non linearities, detailing the process of obtaining a software capable of generating qualitatively realistic scenarios (the parameters used were estimated). With the obtained software we present plots of approximate solutions in different hypothetical scenarios, in order to analyze possible enviromental impacts caused by pollution released into the environment
Mestrado
Matematica Aplicada
Mestre em Matemática Aplicada
49
Tesser, Federico. "Solveur parallèle pour l’équation de Poisson sur mailles superposées et hiérarchiques, dans le cadre du langage Python." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0129/document.
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Les discrétisations adaptatives sont importantes dans les problèmes de fluxcompressible/incompressible puisqu'il est souvent nécessaire de résoudre desdétails sur plusieurs niveaux, en permettant de modéliser de grandes régionsd'espace en utilisant un nombre réduit de degrés de liberté (et en réduisant letemps de calcul).Il existe une grande variété de méthodes de discrétisation adaptative, maisles grilles cartésiennes sont les plus efficaces, grâce à leurs stencilsnumériques simples et précis et à leurs performances parallèles supérieures.Et telles performance et simplicité sont généralement obtenues en appliquant unschéma de différences finies pour la résolution des problèmes, mais cetteapproche de discrétisation ne présente pas, au contraire, un chemin faciled'adaptation.Dans un schéma de volumes finis, en revanche, nous pouvons incorporer différentstypes de maillages, plus appropriées aux raffinements adaptatifs, en augmentantla complexité sur les stencils et en obtenant une plus grande flexibilité.L'opérateur de Laplace est un élément essentiel des équations de Navier-Stokes,un modèle qui gouverne les écoulements de fluides, mais il se produit égalementdans des équations différentielles qui décrivent de nombreux autres phénomènesphysiques, tels que les potentiels électriques et gravitationnels. Il s'agitdonc d'un opérateur différentiel très important, et toutes les études qui ontété effectuées sur celui-ci, prouvent sa pertinence.Dans ce travail seront présentés des approches de différences finies et devolumes finis 2D pour résoudre l'opérateur laplacien, en appliquant des patchsde grilles superposées où un niveau plus fin est nécessaire, en laissant desmaillages plus grossiers dans le reste du domaine de calcul.Ces grilles superposées auront des formes quadrilatérales génériques.Plus précisément, les sujets abordés seront les suivants:1) introduction à la méthode des différences finies, méthode des volumes finis,partitionnement des domaines, approximation de la solution;2) récapitulatif des différents types de maillages pour représenter de façondiscrète la géométrie impliquée dans un problème, avec un focussur la structure de données octree, présentant PABLO et PABLitO. Le premier estune bibliothèque externe utilisée pour gérer la création de chaque grille,l'équilibrage de charge et les communications internes, tandis que la secondeest l'API Python de cette bibliothèque, écrite ad hoc pour le projet en cours;3) la présentation de l'algorithme utilisé pour communiquer les données entreles maillages (en ignorant chacune l'existence de l'autre) en utilisant lesintercommunicateurs MPI et la clarification de l'approche monolithique appliquéeà la construction finale de la matrice pour résoudre le système, en tenantcompte des blocs diagonaux, de restriction et de prolongement;4) la présentation de certains résultats; conclusions, références.Il est important de souligner que tout est fait sous Python comme framework deprogrammation, en utilisant Cython pour l'écriture de PABLitO, MPI4Py pour lescommunications entre grilles, PETSc4py pour les parties assemblage et résolutiondu système d'inconnues, NumPy pour les objets à mémoire continue.Le choix de ce langage de programmation a été fait car Python, facile àapprendre et à comprendre, est aujourd'hui un concurrent significatif pourl'informatique numérique et l'écosystème HPC, grâce à son style épuré, sespackages, ses compilateurs et pourquoi pas ses versions optimisées pour desarchitectures spécifiquesAdaptive discretizations are important in compressible/incompressible flow problems since it is often necessary to resolve details on multiple levels,allowing large regions of space to be modeled using a reduced number of degrees of freedom (reducing the computational time).There are a wide variety of methods for adaptively discretizing space, but Cartesian grids have often outperformed them even at high resolutions due totheir simple and accurate numerical stencils and their superior parallel performances.Such performance and simplicity are in general obtained applying afinite-difference scheme for the resolution of the problems involved, but this discretization approach does not present, by contrast, an easy adapting path.In a finite-volume scheme, instead, we can incorporate different types of grids,more suitable for adaptive refinements, increasing the complexity on thestencils and getting a greater flexibility.The Laplace operator is an essential building block of the Navier-Stokes equations, a model that governs fluid flows, but it occurs also in differential equations that describe many other physical phenomena, such as electric and gravitational potentials, and quantum mechanics. So, it is a very importantdifferential operator, and all the studies carried out on it, prove itsrelevance.In this work will be presented 2D finite-difference and finite-volume approaches to solve the Laplacian operator, applying patches of overlapping grids where amore fined level is needed, leaving coarser meshes in the rest of the computational domain.These overlapping grids will have generic quadrilateral shapes.Specifically, the topics covered will be:1) introduction to the finite difference method, finite volume method, domainpartitioning, solution approximation;2) overview of different types of meshes to represent in a discrete way thegeometry involved in a problem, with a focuson the octree data structure, presenting PABLO and PABLitO. The first one is anexternal library used to manage each single grid’s creation, load balancing and internal communications, while the second one is the Python API ofthat library written ad hoc for the current project;3) presentation of the algorithm used to communicate data between meshes (beingall of them unaware of each other’s existence) using MPI inter-communicators and clarification of the monolithic approach applied building the finalmatrix for the system to solve, taking into account diagonal, restriction and prolongation blocks;4) presentation of some results; conclusions, references.It is important to underline that everything is done under Python as programmingframework, using Cython for the writing of PABLitO, MPI4Py for the communications between grids, PETSc4py for the assembling and resolution partsof the system of unknowns, NumPy for contiguous memory buffer objects.The choice of this programming language has been made because Python, easy to learn and understand, is today a significant contender for the numerical computing and HPC ecosystem, thanks to its clean style, its packages, its compilers and, why not, its specific architecture optimized versions
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Carnevale, Kevin A. "Finite-Difference Model of Cell Dehydration During Cryopreservation." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/7258.
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A numerical model for describing the kinetics of intracellular water transport during cryopreservation was developed. As ice is formed outside the cell, depleting the extracellular liquid of water, the cell will experience an osmotic pressure difference across its membrane, which causes cell dehydration and concomitant shrinkage. Although Mazur (1963) has previously modeled this phenomenon as a two-compartment system with membrane limited transport, the assumption of well-mixed compartments breaks down at large Biot numbers. Therefore, we have developed a numerical solution to this moving-boundary problem, including diffusive transport in the intracellular liquid, in addition to the osmotically driven membrane flux. Our model uses a modified Crank-Nicolson scheme with a non-uniform Eulerian-Lagrangian grid, and is able to reproduce predictions from Mazurs model at low Biot numbers, while generating novel predictions at high Biot numbers. Given that cell damage may result from excessive water loss, our model can be used to predict freezing methods that minimize the probability of cell injury during the cryopreservation process.