IMPEDANCE MATRIX COMPRESSION WITH THE USE OF WAVELET EXPANSIONS

Wavelet expansions have been used recently in numerical solutions of i ntegral equations encountered in various electromagnetic scattering pr oblems. In these solutions one utilizes the power of the wavelet basis functions to localize the problem impedance matrix. Thus, after the i mpedance matrix has been computed it can be rendered sparse via a thre sholding procedure, and the resultant matrix equation can be solved in more quickly without any significant loss in accuracy In this article we propose a novel approach, where instead of thresholding the impeda nce matrix in a conventional manner, it is compressed to a reduced-siz e form. This is effected by first singling out a small number of basis functions, which are expected to accurately represent the unknown, an d keeping only the matrix elements needed for finding the coefficients of these basis functions. A method to carry out this matrix compressi on automatically is described Numerical examples are given for the cas e of TM scattering by perfectly conducting cylinders of triangular and square cross sections. The advantages of the proposed approach are sh own. (C) 1996 John Wiley & Sons, Inc.