Reduced representation of matrices generated by the method of moments

In this paper, an algorithm is presented that accelerates the iterative solution of boundary integral equations. The matrices generated in the MoM discretization of boundary integral equations exhibit special properties, which are exploited in the proposed algorithm. In fact, the algorithm does not require the computation of the entire MoM matrix, but, rather, only calls for the computation of a judiciously selected, small set of elements of the original matrix. As a consequence, the algorithm can easily be incorporated into existing MoM codes. We show that knowledge of the set of elements suffices to compute the product of the dense MoM matrix and a trial solution vector. A single-stage version of the algorithm reduces the computational cost of a matrix-vector multiplication from O(N/sup 2/) to at least O(N/sup 1.5/), and a multi-stage version further reduces the cost, in principle, to O(NlogN). The proposed algorithm is motivated by the fact that the fields in an observation domain due to sources in a ´well separated´ source domain can be represented in terms of the fields radiated by a reduced set of equivalent sources. The number of sources in the reduced set is directly related to the number of degrees of freedom (DOF) of the field radiated by the original set in the direction of the observation domain. The algorithm exhibits similarities with the multilevel algorithm proposed by Brandt (1991).<>