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Doctoral Thesis
DOI
10.11606/T.18.2017.tde-13122017-152526
Document
Author
Full name
José Luiz de Souza
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1999
Supervisor
Committee
Venturini, Wilson Sergio (President)
Coda, Humberto Breves
Franco, Neide Maria Bertoldi
Laier, José Elias
Lindenberg Neto, Henrique
Title in Portuguese
A h-adaptabilidade no Método dos Elementos de Contorno (MEC): algumas considerações sobre singularidades, hipersingularidades e hierarquia
Keywords in Portuguese
h-adaptabilidade
Método dos elementos de contorno
Método numérico para a solução da equação de Laplace
Abstract in Portuguese
O principal objetivo deste trabalho é estudar as singularidades e hipersingularidades existentes nas formulações: singular - clássica - e hipersingular no Método dos Elementos de Contorno (MEC). Também é proposto um esquema residual h-adaptativo para a solução numérica do problema físico governado pela equação de Laplace. Usa-se malha poligonal, juntamente, com funções de interpolação - distribuição - de forma, dos tipos: constantes e lineares. Para controlar o erro a posteriori, é considerado o valor do resíduo, fora dos pontos de colocação. Também é testada uma técnica de quadratura numérica chamada adaptativa, específica para subelementos, no sentido de verificar se a precisão no cálculo das integrais com singularidades é melhorada. O uso de funções hierárquicas é discutido na forma de um algoritmo para atualização da matriz principal do sistema linear.
Title in English
The h-adaptability in the Boundary Element Method (BEM): some considerations about singularities, hypersingularities and hierarchy
Keywords in English
Boundary element method
h-adaptability
Numerical method for Laplace equation solution
Abstract in English
The main purpose of this work is to study the existing singularities and hypersingularities in the Boundary Element Method (BEM) with singular - classical - and hypersingular formulations. Also, an h-adaptive residual scheme for the numerical solution of the physical problem, driven by Laplace equation, is proposed. Boundary polygonal mesh, with constant and linear interpolation - distribution - shape functions together are used. To control the a posteriori error, is considered the residue value outside the collocation points. Also, a sub-element specific adaptive numerical quadrature technique, in an effort to verify if the precision when dealing with integrals possessing singularities is increased, is tested. The use of hierarchical functions is discussed, as an algorithm to update the linear system main matrix.
 
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Tese_Souza_JoseL.pdf (1.26 Mbytes)
Publishing Date
2017-12-13
 
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