Suppressing the numerical dispersion at high frequencies in 2D

I will present my last results on wavelet compression of the stiffness matrix of a linear vibratory problem at high frequencies.
This vibratory problem is the Dirichlet problem of Helmholtz in the complement of a 2D non-convex domain S. This wave equation problem corresponds to a radar scattering diffraction problem by a metallic object of shape S. The object S may have corners. We use the integral formulation Combined Field Integral Equation (CFIE) by a Fredholm operator of second type to compute, as an intermediary result, the surface current on the object S.
With a careful stationary phase application and a special derivation fitted to Hankel's functions, I show that it suffices to take the discretization stepwidth small enough relatively to the condition number. Hence, the wavelet discretization does not cause numerical dispersion. This is not the case with finite element methods. To compress our stiffness matrix, we rely on Malvar and Packet Wavelets.
A second part of my talk will describe some of my current projects : wavelet multifractal decomposition to analyse a material, and the translation of this data to compute the homogenized equivalent of an heterogeneous environment