Impedance matrix compression using adaptively constructed basis functions

Wavelet expansions have been employed recently in numerical solutions of commonly used frequency-domain integral equations. In this paper, we propose a novel method for integrating wavelet-based transforms into existing numerical solvers. The newly proposed method differs from the presently used ones in two ways. First, the transformation is affected by means of a digital filtering approach. This approach renders the transform algorithm adaptive and facilitates the derivation of a basis which best suits the problem at hand. Second, the conventional thresholding procedure applied to the impedance matrix is substituted for by a compression process in which only the significant terms in the expansion of the (yet unknown) current are retained and subsequently derived. Numerical results for a few TM scattering problems are included to demonstrate the advantages of the proposed method over the presently used ones.