Thesis (MSc)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisors: Mary F. Wheeler and Clint N. Dawson. Vita. Includes bibliographical references.

Zugl.: Heidelberg, Univ., Habil.-Schr., 2004. / Also available in print.

Heidelberg, University, Diss., 2002.

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em Matemática e Computação Científica. / Made available in DSpace on 2012-10-23T05:38:14Z (GMT). No. of bitstreams: 1 235620.pdf: 1113903 bytes, checksum: 9d8a15fc0ffd9b004d1de68372276b2d (MD5) / Os métodos de Galerkin descontínuo desenvolvidos recentemente para equações elípticas de segunda ordem envolvem a idéia de penalizar o salto da solução nas interfaces dos elementos. Esta idéia permite impor a suavidade da solução numérica do problema de maneira fraca e ao mesmo tempo estabilizar a forma bilinear garantindo sua coercividade e consequentemente, a estabilidade da solução numérica. Entretanto, a introdução do termo de penalização que envolve o salto da solução torna o método não conservativo, o que prejudica possíveis aplicações do método, na dinâmica de fluídos computacional, por exemplo. Este trabalho estuda inovadoras técnicas de estabilização de fluxos da solução numérica que foram introduzidas, com o objetivo de resolver o problema acima exposto, por A. Romkes, J. Oden e S. Prudhomme (2003) para problemas elípticos e por E. Burman e A. Ern (2005) para problemas com advecção predominante. Com base em recentes resultados de aproximação polinomial para funções em espaços de Sobolev particionado e usando a estabilização de fluxos, são apresentadas estimativas a priori do erro para os métodos, que são ótimas em h (parâmetro de discretização da malha) e subótimas em p (ordem de aproximação polinomial). Uma série de experiências numéricas são realizadas para comprovar as taxas de convergência teóricas e para demonstrar possíveis aplicações à problemas práticos.

Orientador : Maria Cristina Cunha Bezerra / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-14T07:30:16Z (GMT). No. of bitstreams: 1 Fernandes_JoseAugustoNunes_M.pdf: 2150258 bytes, checksum: 56ea11c01ee943c40f869660f63d923e (MD5) Previous issue date: 1988 / Resumo: Não informado / Abstract: Not informed / Mestrado / Mestre em Matemática Aplicada

The potential flow initial-boundary value problem describing fluid-structure interaction with fully nonlinear free surface boundary conditions has been studied using a mixed Lagrangian-Eulerian formulation. The boundary-value problem has been solved in the physical domain by means of a Bubnov-Galerkin formulation of the Laplace equation. The initialvalue problem related to the behavior of some of the moving boundaries has been discretized using various numerical techniques. Among these is a series of predictor-corrector methods. These methodologies proved to require considerable numerical smoothing to maintain stability of the numerical scheme. In turn, dissipation led to inaccuracies in the solution of the problem. In order to avoid this negative effect, a semi-implicit semi-Lagrangian two-time level iterative scheme that is almost free from smoothing has been developed. A Bubnov-Galerkin formulation of an elliptic system for the generation of boundary fitted curvilinear coordinates has been used. When solved iteratively, this method provides orthogonal meshes of very good characteristics for both symmetric and non-symmetric domains. Previous publications concluded that the present system was inadequate for non-symmetric regions leading to lack of convergence in the iterative process. Solutions described in this work show that this limitation has been overcome. Fluid responses to periodic excitation of surface-piercing and submerged bodies have been calculated. Both linear and nonlinear cases show agreement with published results. Very low total energy/work error has been obtained which demonstrates accuracy, good stability and convergence characteristics of the numerical scheme. The impulsive response of tanks of various shapes has also been simulated. Resulting natural frequencies show good agreement with available data. A slender body representation of the flow around a hull advancing with forward speed in otherwise calm water has also been simulated. Numerical calculations of a number of quantities of engineering interest are presented for different length Froude numbers. Results compare favorably with experimental data. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods. / Master of Science

No description available.

A simple Richardson iteration procedure converges slowly when applied to thick, diffusive problems with scattering ratios near unity. The current state of the art for overcoming this is to use a Krylov method with a diffusion preconditioner. However, the diffusion preconditioner must be tailored to the discretization of the transport operator to ensure effectiveness. We expand work from the bilinear discontinuous (BLD) finite element method (FEM) in two dimensions into a preconditioner applicable to all Discontinuous Galerkin FEMs in two and three dimensions. We demonstrate the effectiveness of our approach by applying it to the piecewise linear discontinuous (PWLD) FEM, which is notable for its flexibility with unstructured meshes. We employ a vertex-centered continuous FEM diffusion solution followed by local one-cell calculations to generate discontinuous solution corrections. Our goal is to achieve the same level of performance for PWLD and other methods, in two and three dimensions, as was previously achieved for BLD in two dimensions. We perform a Fourier analysis of this preconditioner applied to the PWLD FEM and we test the preconditioner on a variety of test problems. The preconditioned Richardson method is found to perform well in both ne and coarse mesh limits; however, it degrades for high-aspect ratio cells. These properties are typical for partially consistent diffusion synthetic acceleration (DSA) schemes, and in particular they are exactly the properties of the method that was previously developed for BLD in two dimensions. Thus, we have succeeded in our goal of generalizing the previous method to other Discontinuous Galerkin schemes. We also explore the effectiveness of our preconditioner when used within the GMRES iteration scheme. We find that with GMRES there is very little degradation for cells with high aspect ratios or for problems with strong heterogeneities. Thus we find that our preconditioned GMRES method is efficient and effective for all problems that we have tested. We have cast our diffusion operator entirely in terms of the single-cell matrices that are used by the discontinuous FEM transport method. This allows us to write our diffusion preconditioner without prior knowledge of the underlying FEM basis functions or cell shapes. As a result, a single software implementation of our preconditioner applies to a wide variety of transport options and there is no need to re-derive or re-implement a diffusion preconditioner when a new transport FEM is introduced.