ON THE USE OF WAVELET EXPANSIONS IN THE METHOD OF MOMENTS

A new approach which brings into use the recently developed theory of wavelet transforms in method of moments solutions for electromagnetic wave interaction problems is presented. In this approach, the unknown field or response is expressed as a twofold summation of shifted and dilated forms of a properly chosen basis function, which is often referred to as the mother wavelet. The wavelet expansion can adaptively fit itself to the various length scales associated with the scatterer by distributing the localized functions near the discontinuities and the more spatially diffused ones over the smooth expanses of the scatterer. The approach is thus best suited for the analysis of scatterers which contain a broad spectrum of length scales ranging from a subwavelength to several wavelengths. Using a Galerkin method and subsequently applying a threshold procedure, the moment-method matrix is rendered sparsely populated. The structure of the matrix also reveals the localized scale-fitting distribution long before the matrix equation is solved. The performance of the proposed discretization scheme is illustrated by a numerical study of electromagnetic coupling through a double-slot aperture in a planar conducting screen separating two identical half-space regions.