Métodos híbridos adaptativos para o problema de Helmholtz

• Autor(a) principal: Mello, Leonardo Fagundes de
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/358
• topic: Método dos elementos finitos; Equação de Helmholtz; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In the last decades the development about finite element methods to solve wave propagation on the frequence domain modeled with Helmholtz equation, has been broadly explored. Although apparently simple, from the numerical methods point of view, this problem has been shown a challenging to solve the Helmholtz problem efficiently with high wave number k and to minimize the "numerical-pollution". Classical Galerkin methods or second order finite difference schemes produces unstable approximations, at least with the use of extremely refined mesh. Other promissing alternative presented in this work is the hybrid finite element characterized for introducing a lagrangean multiplier to guarantee the continuity between elements. This kind of methodology promoves the global system which envolves only the degrees of freedom over the multiplier. This technique has easy implementation, including h and p adaptiveness, furthermore it has a flexible choice to the approximation spaces. In this context, we introduced a hybrid formulation to solve the wave problem, where the multiplier is the trace of the pressure on the element edges and adding least squares residuals from Helmholtz equation and mass balance. To ilustrate the flexibilities and robustness, numerical estudies were realized comparing continuous and discontinuous methods in the homogeneous and heterogeneous media, adopting micro-wave frequency schemes and, if necessary, the p-adaptive technique to get a more accurate approach.