A multiresolution theory of scattering and diffraction

Using the recently developed theory of multiresolution decomposition and wavelets, a formulation that governs the response of a scatter with arbitrary geometry is reduced to two coupled formulations, one governing the response smoothed on an arbitrary chosen reference scale and one governing the response fine details. By substituting the formal solution of the former in the latter, a new framework, specifically tuned to describe the microscale components of the body response is obtained. Localization of across-scale couplings, as well as the dependence of the microscale response on the microscale and macroscale geometries and the illuminating wave are investigated via general asymptotic considerations and specific numerical examples. Simple approximate relations describing the dependence of the microscale response on the incident wave are developed and tested.