WAVELETS IN ELECTROMAGNETICS - THE IMPEDANCE MATRIX COMPRESSION (IMC)METHOD

The use of wavelet expansions in numerical solutions of electromagneti c frequency-domain integral equation formulations is steadily growing. In this paper we review the recently suggested impedance matrix compr ession (IMC) method for a more effective integration of wavelet-based transforms into existing numerical solvers. The difference between the LMC method and the previous approaches to applying wavelets in comput ational electromagnetics is twofold. Firstly, the transformation is ef fected 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. Secondly, the conventional thresholding procedure applied to the impedance matrix is substituted for by a compression process in which only the significant terms in t he expansion of the (yet unknown) current are retained and hence a sub stantially smaller number of coefficients has to be determined. A few numerical results are included to demonstrate the advantages of the pr esented method over the currently used ones. The feasibility of ensuri ng a slow growth in the number of unknowns even when there is a rapid increase in the problem complexity is shown by an illustrative example . (C) 1998 John Wiley & Sons, Ltd.