A wavelet-packet transformation for the fast solution of oscillatory integral equations
Daan Huybrechs, Stefan Vandewalle · 2005
Wavelets can be used as basis functions in a Galerkin method for numerically solving integral or partial differ-ential equations. It is well known that the resulting dis-crete representation of the problem can be highly com-pressed by discarding small elements. The resulting spar-sity decreases however as the frequency of the problem increases. In this paper, we consider the use of wavelet packets as basis functions for integral equations with an oscillatory kernel. We show that the use of wavelet packets leads to a much improved compression compared to the classical wavelet case. The method is applied to the scattering of an incoming wave by a wire grid.