Técnicas de otimização evolutiva aplicadas à solução de grandes sistemas lineares

Detalhes bibliográficos
Ano de defesa: 2010
Autor(a) principal: Purcina, Lúcio Aurélio
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Uberlândia
BR
Programa de Pós-graduação em Engenharia Mecânica
Engenharias
UFU
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: https://repositorio.ufu.br/handle/123456789/14850
Resumo: Many fields of engineering and other applied sciences demand the use of the solution of algebraic linear systems. Depending on the mathematical model used to represent the phenomenon, the linear systems will have high dimensions. Traditionally, large linear systems are resolved by using iterative methods. The convergence of these methods depends on the eigenvalues of the coefficients matrix. Thus, when the coefficients matrix loses one of the following characteristics as being symmetric or positive definite, the iterative methods (stationary and nonstationary) lose efficiency. Many methods exist for solving the linear systems. The aim is to find the most effective method for a particular problem. However, a method that works well for one type of problem might not work so well for others. Indeed, it may not even work. Thus, several researches are still being developed and improved in this area of knowledge. The aim of this works is to propose the application of some techniques in solving large linear systems. On this purpose, classic no stationary iterative methods are tested (Conjugate Gradients, Minimal Residual, Bi-Conjugate Gradients, Generalized Minimal Residual) and compared with two evolutionary optimization methods, Differential Evolution and Genetic Algorithms. In this research, problems like bi-dimensional Laplace equation and identification indirect of dynamical forces are solved. The analytical solution is compared with the numerical solutions calculated by using the mentioned methods. Results are presented, analyzing the most important parameters and their influence on the convergence and efficiency of the tested methods.