Impedance matrix compression (IMC) using iteratively selected wavelet basis for MFIE formulations

Wavelet expansions have been employed in method of moments (MoM) solutions of frequency-domain integral equations. In these solutions the unknown quantity of interest (usually the current on the scatterer) is first represented in terms of a set of wavelet basis functions, and then the difference between the two sides of the equation is forced to be orthogonal to a set of wavelet testing functions. While this approach generally yields satisfactory solutions, it has two disadvantages. We propose a new approach which overcomes these two drawbacks. The new approach concerns the incorporation of wavelets into MoM solutions to magnetic field integral equation (MFIE) formulations of scattering problems. In this approach, rather than merely resorting to the sparseness of the operator in the wavelet expansion, we also utilize the sparse representation of the (yet unknown) current in the wavelet expansion. It is well known that wavelets can represent non-stationary signals with just a few terms. This fact has also been used in the context of computational electromagnetics, where the idea of impedance matrix compression (IMC) has been introduced. The new approach, combined with an iterative procedure, yields a new algorithm, that has many advantages over the present methods for incorporating wavelets.