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Doctoral Thesis
DOI
https://doi.org/10.11606/T.3.2007.tde-08082007-174735
Document
Author
Full name
Mauro Massayoshi Sakamoto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Cardoso, José Roberto (President)
Lebensztajn, Luiz
Luz, Mauricio Valencia Ferreira da
Machado, José Márcio
Silva, Viviane Cristine
Title in Portuguese
Algoritmo de refinamento de Delaunay a malhas seqüenciais, adaptativas e com processamento paralelo.
Keywords in Portuguese
Algoritmo de Delaunay
Malha adaptativa
Método dos elementos finitos
Programação paralela
Abstract in Portuguese
Este trabalho apresenta o desenvolvimento de um gerador de malha de elementos finitos baseado no Algoritmo de Refinamento de Delaunay. O pacote é versátil e pode ser aplicado às malhas seriais e adaptativas ou à decomposição de uma malha inicial grossa ou pré-refinada usando processamento paralelo. O algoritmo desenvolvido trabalha com uma entrada de dados na forma de um gráfico de linhas retas planas. A construção do algoritmo de Delaunay foi baseada na técnica de Watson para a triangulação fronteiriça e nos métodos seqüenciais de Ruppert e Shewchuk para o refinamento com paralelismo. A técnica elaborada produz malhas que mantêm as propriedades de uma triangulação de Delaunay. A metodologia apresentada foi implementada utilizando os conceitos de Programação Orientada a Objetos com o auxílio de bibliotecas de código livre. Aproveitando a flexibilidade de algumas dessas bibliotecas acopladas foi possível parametrizar a dimensão do problema, permitindo gerar malhas seqüenciais bidimensionais e tridimensionais. Os resultados das aplicações em malhas seriais, adaptativas e com programação paralela mostram a eficácia desta ferramenta. Uma versão acadêmica do algoritmo de refinamento de Delaunay bidimensional para o Ambiente Mathematica também foi desenvolvido.
Title in English
Delaunay refinement algorithm to sequential, adaptable meshes and with parallel computing.
Keywords in English
Adaptive mesh
Delaunay algorithm
Finite element methods
Parallel programming
Abstract in English
This work presents the development of a finite elements mesh generation based on Delaunay Triangulation Algorithm. The package is versatile and applicable to the serial and adaptable meshes or to either the coarse or pre-refined initial mesh decomposition using parallel computing. The developed algorithm works with data input in the form of Planar Straight Line Graphics. The building of the Delaunay Algorithm was based on the Watson's technique for the boundary triangulation and in both Ruppert and Shewchuk sequential methods for the parallel refinement. The proposed technique produces meshes maintaining the properties of the Delaunay triangulation. The presented methodology was implemented using the Programming Object-Oriented concepts, which is supported by open source libraries. Taking advantage of the flexibility of some of those coupled libraries the parametrization of the problem dimension was possible, allowing to generate both two and three-dimensional sequential meshes. The results obtained with the applications in serial, adaptive and in parallel meshes have shown the effectiveness of this tool. An academic version of the twodimensional Delaunay refinement algorithm for the Mathematica Environment was also developed.
 
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DPEAMauroSakamoto.doc (74.50 Kbytes)
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TeseMauroSakamoto.pdf (2.94 Mbytes)
Publishing Date
2007-08-29
 
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