Direct Solution of Wave Propagation in Rods using the Wavelet-Galerkin Method
Rodrigo Bird Burgos1; Marco Antonio Cetale Santos2; Raul Rosas e Silva3
1 UERJ; 2 UFF; 3 PUC-Rio
doi:10.20906/CPS/COB-2015-2132
Resumo
The use of wavelet-based numerical methods has become popular since the construction of compactly supported continuous functions by Ingrid Daubechies. Wavelet scaling functions have several properties that are quite useful for representing solutions of partial differential equations (PDEs), such as orthogonality, compact support and exact representation of polynomials of a certain degree. The present work discusses an alternative to the usual finite difference (FDM) or finite element (FEM) approach to the acoustic wave equation modeling by using a space discretization scheme based on the Galerkin Method. The combination of this method with wavelet analysis results in the Wavelet Galerkin Method (WGM) which has been adapted for the direct solution of the wave differential equation in a meshless formulation. This work also introduces Deslauriers-Dubuc wavelets (Interpolets) as interpolating functions. For a given order, Interpolets present the highest number of vanishing moments among all wavelet families. Some examples were formulated using a central difference (second order) scheme for time differentiation. Results using the WGM were compared with the ones obtained by the FDM using the same time steps in terms of numerical dispersion.
Palavras-chave: Wavelets; Wave propagation; Wavelet-Galerkin Method