A multiresolution study of two-dimensional scattering by metallic cylinders

The application of wavelet transforms in method of moments (MoM) solutions for scattering problems is extended to cases involving metallic cylinders whose periphery contains a variety of length-scale features ranging from smoothly varying large-scale features (characterized by a radius of curvature of several wavelengths) to rapidly varying small scale ones (characterized by a radius of curvature that is small compared with the wavelength). The basic idea is to first consider a periodic extension of the equivalent current in the arc-length variable with a period identical to the scatterer circumference, and then to expand this representation using a set of periodic wavelets derived from a conventional basis of wavelets by a periodic extension. Using a Galerkin method and subsequently applying a threshold operation, a substantial reduction in the number of elements of the moment-method matrix is attained without virtually affecting the solution accuracy. The proposed extension is illustrated by a numerical analysis of TM (transverse magnetic) and TE (transverse electric) scattering from a cylinder of elliptic cross section. A thorough study is carried out showing how the solution accuracy improves with increasing resolution level, and how this accuracy is affected by a thresholding process which renders the moment matrix sparsely populated.