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Master's Dissertation
DOI
10.11606/D.45.2018.tde-07052018-124115
Document
Author
Full name
Ellen Thais Alves Cerciliar
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Roma, Alexandre Megiorin (President)
Peixoto, Pedro da Silva
Silveira Neto, Aristeu da
Title in Portuguese
Esquema compacto de diferenças finitas de alta ordem em malhas hierárquicas
Keywords in Portuguese
Equações elípticas
Malhas hierárquicas
Método das diferenças finitas compactas
Abstract in Portuguese
Este trabalho propõe um esquema de diferenças finitas compacta de alta ordem para resolver problemas elípticos com coeficientes variáveis em malhas composta. São apresentados a formulação matemática e a dedução do método compacto de quarta ordem aplicado à problemas elípticos bidimensionais, em malha regular e composta. Foi adotado o uso da biblioteca PETSc com os seus pré-condicionadores e métodos numéricos para resolver os sistemas lineares resultantes da discretização do problema. Por fim, testes visando verificar o código foram feitos, utilizando o método de soluções manufaturadas, para mostrar alta eficiência e acurácia do método desenvolvido.
Title in English
Higher-order finite-difference schemes for hierarchical meshes
Keywords in English
Compact finite difference methods
Elliptic equations
Hierarchical meshes
Abstract in English
This paper proposes a scheme of compact finite difference higher order for solve elliptic problems with variable coeficients in composite meshes. we present the mathematical formulation and the deduction of the compact method of fourth order applied to two-dimensional elliptic problems in regular and composite mesh . It was adopted using the PETSc library with its pre- conditioners and numerical methods for solving linear systems resulting from discretization of the problem. Finally , tests to verify the code were made using the method of manufactured solutions to show high eficiency and accuracy of the method developed .
 
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Publishing Date
2018-05-09
 
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