Um refinamento h-adaptativo de malhas para o método dos elementos finitos utilizando uma estrutura de grafo

• Ano de defesa: 2008
• Autor(a) principal: Brandão, Diego Nunes
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• dARK ID: ark:/87559/0013000008kmd
• Idioma: por
• Instituição de defesa: Programa de Pós-Graduação em Computação; Computação
• Palavras-chave em Português: Refinamento-h; ALG; Método dos elementos finitos; Malhas não-conformes; Equações diferenciais parciais; Computer science; Refinement; Method of the finite elements; Not-in agreement meshes; Partial distinguishing equations; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO
• Link de acesso: https://app.uff.br/riuff/handle/1/18261

In several areas of natural sciences and engineering phenomena are studied with the aid di_erential equations. Adaptive strategies can improve the e-cency of computational processes, since they provide means of increasing the level of detail of the discretized problem only in regions where and when this is needed. This work presents an h-adaptive refinement for use with Finite Element Methods (FEM) which is based on a graph data structure to connect the existing elements of domain discretizations. This structure, named Autonomous Leaves Graph (ALG), was initially proposed for use with Finite Volume discretizations of boundary value problems (BVPs). In this representation, a Modified Hilbert Curve is employed in order to define the total ordering of the mesh. In the case of FEM, for each element swept, the mesh nodes generate a contribution which is stored in a chained list. In order to solve the linear systems arising from the FEM discretization of BVPs, an iterative method based on minimization of functionals is utilized. Numerical results show e_ectiveness and e_ciency of integrating ALG concepts to the FEM framework.