Optimized Schwarz methods are iterative domain decomposition procedures with greatly improved convergence properties, for solving second order elliptic boundary value problems. The enhanced convergence is obtained by replacing the Dirichlet transmission conditions in the classical Schwarz iteration with more general conditions that are optimized for performance. The convergence is optimized through the solution of a min-max problem. The theoretical study of the min-max problems gives explicit formulas or characterizations for the optimized transmission conditions for practical use, and it permits the analysis of the asymptotic behavior of the convergence. / In the first part of this work, we continue the study of optimized transmission conditions for advection-diffusion problems with smooth coefficients. We derive asymptotic formulas for the optimized parameters for small mesh sizes, in the overlapping and non-overlapping cases, and show that these formulas are accurate when the component of the advection tangential to the interface is not too large. / In a second part, we consider a diffusion problem with a discontinuous coefficient and non-overlapping domain decompositions. We derive several choices of optimized transmission conditions by thoroughly solving the associated min-max problems. We show in particular that the convergence of optimized Schwarz methods improves as the jump in the coefficient increases, if an appropriate scaling of the transmission conditions is used. Moreover, we prove that optimized two-sided Robin conditions lead to mesh-independent convergence. Numerical experiments with two subdomains are presented to verify the analysis. We also report the results of experiments using the decomposition of a rectangle into many vertical strips; some additional analysis is carried out to improve the optimized transmission conditions in that case. / On a third topic, we experiment with different coarse space corrections for the Schwarz method in a simple one-dimensional setting, for both overlapping and non-overlapping subdomains. The goal is to obtain a convergence that does not deteriorate as we increase the number of subdomains. We design a coarse space correction for the Schwarz method with Robin transmission conditions by considering an augmented linear system, which avoids merging the local approximations in overlapping regions. With numerical experiments, we demonstrate that the best Robin conditions are very different for the Schwarz iteration with, and without coarse correction.

A new parallel implicit adaptive mesh refinement (AMR) algorithm is developed for the prediction of unsteady behaviour of laminar flames. The scheme is applied to the solution of the system of partial-differential equations governing time-dependent, two- and three-dimensional, compressible laminar flows for reactive thermally perfect gaseous mixtures. A high-resolution finite-volume spatial discretization procedure is used to solve the conservation form of these equations on body-fitted multi-block hexahedral meshes. A local preconditioning technique is used to remove numerical stiffness and maintain solution accuracy for low-Mach-number, nearly incompressible flows. A flexible block-based octree data structure has been developed and is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. The data structure also enables an efficient and scalable parallel implementation via domain decomposition. The parallel implicit formulation makes use of a dual-time-stepping like approach with an implicit second-order backward discretization of the physical time, in which a Jacobian-free inexact Newton method with a preconditioned generalized minimal residual (GMRES) algorithm is used to solve the system of nonlinear algebraic equations arising from the temporal and spatial discretization procedures. An additive Schwarz global preconditioner is used in conjunction with block incomplete LU type local preconditioners for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. The scheme was applied to solutions of steady and unsteady laminar diffusion and premixed methane-air combustion and was found to accurately predict key flame characteristics. For a premixed flame under terrestrial gravity, the scheme accurately predicted the frequency of the natural buoyancy induced oscillations. The performance of the proposed parallel implicit algorithm was assessed by comparisons to more conventional solution procedures and was found to significantly reduce the computational time required to achieve a solution in all cases investigated.

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Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Tableau d'honneur de la Faculté des études supérieures et postdoctorales, 2015-2016 / La formule de Schwarz–Christoffel permet de trouver une transformation conforme entre un domaine polygonal et un disque. Par contre, cette formule ne s’applique qu’aux domaines simplement connexes. Récemment, Darren Crowdy a obtenu une généralisation de cette formule pour les domaines multiplement connexes. Celle-ci envoie des domaines circulaires sur des domaines polygonaux. Ce mémoire vise à faire la démonstration de la formule développée par Crowdy. Pour ce faire, il faudra définir la fonction de Schottky–Klein ainsi que la fonction de Green modifiée. Il faudra aussi introduire les domaines canoniques.

In this thesis, we set out to provide an enhanced set of techniques for determining the eigenvalues of the Laplacian in polygonal domains. Currently, finite-element methods provide a numerical means by which we can approximate these eigenvalues with ease. However, we would like a more analytic method which may allow us to avoid a basic parameter sweep in finite-element software such as COMSOL to determine what could possibly be an "optimal" distribution of eigenvalues. The hope is that this would allow us to draw conclusions about the acoustic quality of a pentagonally-shaped room. First, we find the eigenvalues using a common finite-element method through COMSOL Multiphysics. We then examine another method which makes use of conformal maps and Schwarz-Christoffel transformations with the prospect that it might provide a more analytic understanding of the calculation of these eigenvalues and possibly allow for variation of certain parameters. This method, as far as we could find, had not yet been developed on the pentagon. We end up carrying this method through nearly all of the steps necessary in finding these eigenvalues. We find that the finite-element method is not only easier to use, but is also more efficient in terms of computing power. / Master of Science

Partindo de uma sensação de desconforto em relação a certo modo de encaminhamento da reflexão crítica contemporânea no Brasil, este trabalho propõe uma análise comparativa de alguns ensaios de dois autores de notória importância para a teoria literária brasileira, a saber, Roberto Schwarz e Silviano Santiago. Por meio de um recorte que privilegia as proposições e avaliações sobre os aspectos socioculturais do país realizadas por eles, pretende-se explicitar como a perspectiva contrastiva que leva em consideração as oposições, mas também as semelhanças entre tais obras pode configurar uma possibilidade de formulações outras para questões que há muito são fundamentais no pensamento nacional. Desse modo, sem nos isentarmos de uma posição na disputa do campo, almejamos flagrar as tensões que os textos críticos estabelecem entre si e vislumbrar nesse procedimento uma potência particular. Deteremo-nos, sobretudo, nos modos como o tópico da subordinação econômica versus (in)dependência cultural (e sua relação com o nacionalismo) são desenvolvidos e envolvem estratégias de autolegitimação, bem como o embate entre pressupostos teóricos de escasso diálogo: a desconstrução e o materialismo dialético. / Motivated by a certain discomfort related to a specific direction Brazils contemporary critical thought has taken, this paper proposes a comparative analysis between a few essays from two highly regarded authors in Brazilian literary criticism: Roberto Schwarz and Silviano Santiago. Through a point of view that privileges the proposals and assessments concerning the countrys socio cultural aspects carried out by them, it is intended to highlight how the contrastive perspective which takes into consideration the oppositions, but also the similarities between the aforementioned works can configure a possibility of formulating other questions that for long have been quintessential in the national thought. Thus, without excusing ourselves from taking a stand in the dispute, we aspire to point out the tensions set between the critical texts and conjecture a common faculty in this procedure. We shall focus, mostly, on the manners the topic economic subordination versus cultural (in)dependence (and its relation to nationalism) are developed and regard self-legitimization strategies, as well as the confrontation between theoretical moulds of rare dialogue: deconstruction and dialectic materialism.

Para o estudo de relações entre as literaturas brasileira e portuguesa durante o século XIX esta dissertação de mestrado buscará identificar e compreender o favor, como definido por Roberto Schwarz em Ao Vencedor as Batatas, no contexto luso-brasileiro e em algumas obras nas quais o favor ainda não foi objeto de análise. Para discutirmos as prefigurações do favor, escolhemos obras do Brasil, Portugal e França nas quais algo muito semelhante ao favor descrito por Schwarz na obra machadiana já pode ser observado. São elas: O Filho do Pescador, de Teixeira e Sousa; A Mão do Finado, de Alfredo Hogan e Eugènie Grandet, de Balzac. Já, para tentarmos entender um pouco mais do favor brasileiro e fazer relações com Portugal oitocentista, escolhemos uma obra de Machado de Assis e outra de Camilo Castelo Branco que foram publicadas em períodos muito próximos aos grandes sucessos dos autores. São elas Iaiá Garcia de Machado de Assis, publicada três anos antes de Memórias Póstumas de Brás Cubas e As Três Irmãs de Camilo Castelo Branco, publicada no mesmo ano que Amor de Perdição. Esperamos que as semelhanças e diferenças encontradas nas descrições literárias das sociedades brasileira e portuguesa feita pelos autores nos possibilite evidenciar o favor como uma ponte que colaborou para o entendimento do romance nos países em questão. / In order to study the relations between Brazilian and Portuguese literatures of the 19th century, this Master\'s thesis intends to identify and understand the favor, as defined by Roberto Schwarz in Ao Vencedor as Batatas, in Portuguese-Brazilian context and in some literary works in which the favor has not yet been object of analysis. To discuss the prefiguration of favor, we chose works from Brazil, Portugal and France in which something very similar to the favor described by Schwarz in Machado\'s work can already be observed. They are: O Filho do Pescador, by Teixeira e Sousa; A Mão do Finado, by Alfredo Hogan e Eugènie Grandet, by Balzac. To try to understand a little more of Brazilian favor and make relations with Portugal, we chose a work by Machado de Assis and another by Camilo Castelo Branco, which were published in periods very close to the great successes of the authors. They are Iaiá Garcia by Machado de Assis, published three years before Memórias Póstumas de Brás Cubas and As Três Irmãs by Camilo Castelo Branco, published in the same year as Amor de Perdição. We hope that the similarities and differences found in the literary descriptions of Brazilian and Portuguese societies made by the authors allow us to highlight the favor as a bridge that contributed to the understanding of the novel in the discussed countries.

Não fornecido pelo autor. / Não fornecido pelo autor.

Diss. Universiẗat Köln, 2003. / Bibliogr.: p. 273-297.