A MULTIRESOLUTION STUDY OF EFFECTIVE PROPERTIES OF COMPLEX ELECTROMAGNETIC SYSTEMS

A systematic study of the across scale coupling phenomenology in elect romagnetic (EM) scattering problems is addressed using the theory of m ultiresolution decomposition and orthogonal wavelets. By projecting an integral equation formulation of the scattering problem onto a set of subspaces that constitutes a multiresolution decomposition of L-2(R), one can derive two coupled formulations, The first governs the macros cale response, and the second governs the microscale response.:By subs tituting the formal solution of the latter in the former, a new self-c onsistent formulation that governs the macroscale response component i s obtained. This formulation is written on a macroscale grid, where th e effects of the microscale heterogeneity are expressed via an across scale coupling operator. This operator can also be interpreted as repr esenting the effective properties of the microstructure. We study the properties of this operator versus the characteristics of the Green fu nction and the microstructure for various electromagnetic problems, us ing general asymptotic considerations. A specific numerical example of TM scattering from a laminated complex structure is provided.