A multiresolution theory of scattering and diffraction

This paper addresses the problem of coupling across scales using the theory of multiresolution decomposition and wavelets. Based on a grid that possesses a hierarchy of lengthscales ("resolutions"), the multiresolution theory provides a natural framework for a rigorous resolution of the body response into macroscale and microscale components, and for a systematic investigation of the apparatus governing the coupling of the latter to the exciting field. Since the various building blocks associated with the multigrid construction are inherently local, the precise definition, representation and investigation of the coupling across scales phenomenon do not require high frequency asymptotic reduction of a global spectral integral, are not limited to a specific class of geometries, and the resulting theory can be naturally accommodated within a robust numerical scheme. Standard expressions describing the relation between the microscale response and the macroscale excitation, reminiscent of the GTD diffraction coefficients, can be derived.<>