Resolution enhancement and small perturbation analysis using wavelet transforms in scattering problems

Summary form only. We suggest a novel method which combines the use of models of fictitious sources and wavelet transforms. The idea is to integrate wavelet transforms into the simple and efficient source-model technique and thereby obtain accurate numerical results while using a highly sparse approximation to the typically full impedance matrix. The wavelet transform is applied to both the unknown current vector and the excitation vector. It can be effected either by matrix multiplication or by a hierarchical structure of digital filters. The use of digital filtering is preferable because it makes the computation more efficient and allows one to adapt the transform to the problem at hand. The proposed method facilitates a convenient way to go into higher resolution levels only where necessary. Moreover, if the original scatterer is slightly deformed, there will be no need to recompute the whole matrix; minor add-ons to the matrix will suffice. The idea presented in this paper is illustrated by a study of the problem of TM plane-wave scattering by an infinite cylinder of elliptic cross section. This cylinder is analyzed at a certain level of resolution. Then, the cylinder surface is assumed to have a small protruding part and the analysis is repeated for a higher resolution level using additional sources, transformed to generate wavelet basis functions of finer scale, but only in the vicinity of the protrusion.