A MULTIRESOLUTION THEORY OF SCATTERING AND DIFFRACTION

Using the recently developed theory of multiresolution decomposition a nd wavelets, a formulation that governs the response of a scatterer wi th arbitrary geometry is reduced to two coupled formulations, one gove rning the response smoothed on an arbitrary chosen reference scale and one governing the response fine details. By substituting the formal s olution of the former in the latter, a new framework, specifically tun ed to describe the microscale components of the body response is obtai ned. Localization of across-scale couplings, as well as the dependence of the microscale response on the microscale and macroscale geometrie s and the illuminating wave are investigated via general asymptotic co nsiderations and specific numerical examples. Simple approximate relat ions describing the dependence of the microscale response on the incid ent wave are developed and tested.