Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 186-201).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Chandrajit L. Bajaj. Vita. Includes bibliographical references.

Thesis (Ph.D.)--Montana State University--Bozeman, 2006. / Typescript. Chairperson, Graduate Committee: Durward K. Sobek II. Includes bibliographical references.

Electrostatics interaction plays a very important role in almost all biomolecular systems. The Poisson-Boltzmann equation is widely used to treat this electrostatic effect in an ionic solution. In this work, a simple mixed discrete-continuum model is considered and boundary element method is used to solve for the solution. / Singapore-MIT Alliance (SMA)

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Neste trabalho utiliza-se a formulação direta do Método dos Elementos de Contorno aplicada ao problema de flexão de placas com vinculação interna. Através da utilização da teoria baseada nas hipóteses de Reissner é possível atender em cada ponto, a três condições físicas de contorno. Admite-se a aplicação de cargas transversais distribuídas e concentradas, além de momentos distribuídos em linha. Os elementos de contorno apresentam geometria linear com aproximação quadrática para as variáveis de contorno. As equações integrais dos deslocamentos são escritas para pontos de colocação dispostos fora do domínio, evitando-se assim problemas de singularidades. O sistema de equações algébricas originado da análise de placas via MEC é modificado para incorporar o enrijecimento produzido pela vinculação interna. Primeiramente é analisado o enrijecimento produzido por apoios internos pontuais ou distribuídos em áreas pequenas e, em seguida, é estudada a associação da placa com uma estrutura qualquer, formada por barras. O enrijecimento produzido por esta estrutura é obtido utilizando-se o Método dos Elementos Finitos. Finalmente, são apresentados alguns exemplos simples que mostram a boa precisão da técnica utilizada. / The direct formulation of the Boundary Element Method is applied to the analysis of internally restrained plates in bending. By employing Reissner\'s theory, the three boundary conditions are satisfied at each point. Loading conditions include concentrated or uniformly distributed loads as well as linearly distributed moments. The boundary elements are geometrically linear with quadratic approximation for the boundary variables. The displacement integral equations are written for collocation points outside the domain thus avoiding any singularity problem. The resulting system of algebraic equations is modified to include the stiffening effects. Plates with internal point restraints and restrained over small areas are analyzed as well as plates connected to others structures made up of bars. In this last case, the stiffening effect is calculated through the Finite Element Method. The results obtained in simple problems indicate the accuracy of the procedure.

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Orientador: Carlos Henrique Daros / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-23T13:53:37Z (GMT). No. of bitstreams: 1 Borges_RicardoVendrame_M.pdf: 7836020 bytes, checksum: 6416c1d8724fe2108b090c71bec11800 (MD5) Previous issue date: 2013 / Resumo: A presente dissertação concentra-se no estudo da elasticidade não-linear através do Método dos Elementos de Contorno. A elasticidade não-linear possui um importante campo de aplicações, da simulação de materiais que se comportam como a borracha a novas aplicações como a simulação de tecidos biológicos. A dissertação apresenta como resultado principal a elaboração de um código computacional em Matlab ®, o qual é capaz de modelar materiais elásticos, não-lineares, sujeitos à deformações não-lineares, incrementais. O programa de elementos de contorno foi utilizado na simulação da resposta quasi-estática em materiais incompressíveis como a borracha, aproximados através do modelo constitutivo de Mooney-Rivlin / Abstract: The present work focuses on the modelling of non-linear elastic problems via the Boundary Element Method. Non-linear elasticity has several important applications, from the modelling of rubber-like materials to new areas of research such as the study of biological tissues. The work's main result is the construction of a computer code (in Matlab ®) which can model non-linear elastic materials subjected to incremental non-linear deformations. The code was used within the realm of quasi-static simulations of incompressible rubber-like materials, approximated via the Mooney-Rivlin constitutive model / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestra em Engenharia Mecânica

Orientador: Leandro Palermo Junior / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-24T13:49:30Z (GMT). No. of bitstreams: 1 Millan_LeandroPrearo_D.pdf: 4533018 bytes, checksum: e773a91ae0a43139a214d9f81b444917 (MD5) Previous issue date: 2014 / Resumo: O problema de transferência de calor com controle de temperatura incluindo um algoritmo genético para otimização do processo é estudado neste trabalho. O problema ocorre na terapia de tratamento de câncer denominada hipertermia em que tecidos ao redor do tumor são aquecidos a cerca de 40 ºC por um conjunto de antenas que envolvem o paciente, com orientação em fase e direcionadas a um ponto que recebe calor devido à incidência das ondas eletromagnéticas. O problema de transferência de calor em biosistemas emprega a equação de Pennes e as equações de Maxwell para determinação do campo elétrico e magnético. Um modelo bidimensional é estudado com o Método dos Elementos de Contorno incluindo o Método da Reciprocidade Dual (MECRD). A heterogeneidade do meio pode ser tratada com a associação de vários meios homogêneos pela inclusão de sub-regiões no tratamento pelo MECRD. É proposta uma nova função aproximadora no MECRD para tratar os efeitos de domínio das equações integrais relacionadas às equações de Maxwell e Pennes no regime estacionário, reduzidas a equações não homogêneas do tipo de Helmholtz. A convergência da função é avaliada em exemplos com geometria simples. O modelo foi testado para um caso com tumores em diferentes profundidades sendo os resultados comparados aos disponíveis na literatura / Abstract: The problem of heat transfer with temperature control including a genetic algorithm for optimization of the process is studied in this work. The problem occurs in the cancer therapy called hyperthermia in which tissue around the tumor is heated to about 40 ºC by a set o antennas that involve the patient, with phase orientation and directed to a spot that receives heat due the incidence of electromagnetic waves. The problem o heat transfer in biosystems employs the Pennes¿ equation and Maxwell¿s equations for determining the electric and magnetic field. A two-dimensional model is studied with the Boundary Element Method including the Dual Reciprocity Method (DRBEM). The heterogeneity of the medium can be treated with the combination of various homogeneous media by the inclusion of sub-regions in the DRBEM. It is proposed a new approximating function for DRBEM to treat the domain effects of the integral equations related to Maxwell¿s and Pennes¿ equations in steady state, reduced to non-homogeneous Helmholtz equations. The convergence of the function is evaluated in examples with simple geometry. The model was tested for a case with tumors in different depths been the results compared with the available literature / Doutorado / Estruturas / Doutor em Engenharia Civil

Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers. Compared with other methods exploiting the low rank character of off-diagonal blocks of the dense resolvent operator, FMM-preconditioned Krylov iteration may reduce the amount of communication because it is matrix-free and exploits the tree structure of FMM. Fast multipole-based solvers and preconditioners are demonstrably poised to play a leading role in exascale computing.