Tensorização de matrizes de rigidez para quadrados e hexaedros finitos de alta ordem / Tensorization of stiffness matrices for squares and hexaedral using high order FEM
AUTOR(ES)
Mariana Godoy Vazquez Miano
DATA DE PUBLICAÇÃO
2009
RESUMO
High-order Finite Element Methods have been applied with success to problems of Fluid Dynamics and Electromagnetism. The main feature of these methods is to present an exponential convergence rate for problems with polinomial solution. However, due to the use of high-order interpolation functions, the elemental matrices are denser. This work shows a mathematical formulation, with tensorization concepts applied to the base functions that make up the matricial system matrices which will enable to write uniformly the systems resulting from the application of mass, mix and stiffness matrices. This possibility arises from the proposed formulation, which makes the solution vector equal to the three systems. Consequently, the 1D array mass, usually dense, that makes up the formulation of the rigid 2D and 3D matrices, in squares and hexahedra, may be replaced by the stiffness matrix 1D, which shows itself very sparse related to the base functions used in this work. The formulation is validated to quadratic and hexahedral elements and it is extended to non-distorted meshes of the same elements in the Poisson problems resolution. Approximation errors in solution, sparsity of the global stiffness and run time are also observed
ASSUNTO(S)
metodo de elementos finitos finite element analysis
ACESSO AO ARTIGO
http://libdigi.unicamp.br/document/?code=000471631Documentos Relacionados
- Funções de interpolação e técnicas de solução para problemas de poisson usando método de elementos finitos de alta ordem
- h p POT.2 FEM : uma arquitetura de software p não-uniforme para o método de elementos finitos de alta ordem
- Implementation of high order finite element based on tensorial product
- Tensor-based interpolation functions and integration rules for the high order finite elements methods
- Latin squares and applications