Power decomposition method for compression of the electric-field integral equation

Abstract

We focus on the problem of compression of farfield interactions in the matrices of the method of moments. We present a new point of view with respect to other alternatives: instead of compressing each block of the impedance matrix (corresponding to the mutual coupling between a pair of geometry groups), our hypothesis here is that this compression can be separately obtained inside of each group. In this manner each group is compressed only once, which allows us to obtain larger compression rates than the usual mutual-coupling based schemes. With this idea, we propose a recursive mechanism similar to that used in the multilevel fast multipole method, leading to a hi erarchical multilevel building of macro basis functions that finally provides a O(N logN) algorithm for computational electromagnetics. Moreover, the proposed calculation of compressed basis functions is completely independent on the excitation.