Direct Solution of the Acoustic Wave Equation using the Wavelet-Galerkin Method
Rodrigo Burgos, Marco Antônio Cetale Santos, Raul Rosas e Silva · 2013
The use of compactly supported wavelet functions has become increasingly popular in the development of numerical solutions for differential equations. The present work discusses an alternative to the usual finite difference (FDM) 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. Examples in 1-D were formulated using a central difference (second order) scheme for time differentiation. Encouraging results were obtained when compared with the FDM using the same time steps.