Estudo de cavidades acusticas usando o metodo de elementos finitos via Galerkin/minimos quadrados

AUTOR(ES)

Khaled Mohamed Ahmida

DATA DE PUBLICAÇÃO

1996

RESUMO

The numerical solution of the Helrnholtz equation, as finite element or finite difference solution, does not preserve the nondispersive character of the exact solution. I?iscrete solutions of this type are functions of a discrete wave number that depends on the frequency. The Galerkin finite element method is capable of modeling increasingly higher wave numbers by refining the mesh. However, this may become prohibitively expensive, as long as, an acceptable resolution of ten elements per wave, according to mIe of thumb, is to be considered. This would result in a large number of equations to be solved. The method of Galerkin Least Square (GLS), here utilized, for the numerical solution of the Helrnholtz equation can possibly eliminate the dispersive numerical effects by modification of the variational model in one-dimensional problems. However, in twodimensional problems, it is not possible to eliminate the pollution in the finite element error but can still be reduced. A resolution of four elements per wave is required for good results. In this work, the GLS method is applied to two-dimensional problems described by Helrnholtz equation, using results obtained in one-dimensional problems. Exponential decay problems and wave propagation problems with Dirichlet boundary conditions are considered. Numerical results are obtained using linear triangular and quadrilateral finite elements

ASSUNTO(S)

galerkin metodo dos elementos finitos metodos de acustica

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