MNM: a technique for the iterative solution of matrix equations arising in the method of moments formulation

The advent of the fast multipole method (FMM) and other techniques for carrying out the matrix vector product in an efficient manner, in the context of the method of moments (MoM) formulation, has made it possible for us to take a quantum leap forward towards solving a class of large problems involving perfectly conducting scatterers. Among a plethora of different iterative algorithms available in the literature, the conjugate gradient (CG) and its variants are among the most widely used. The speed with which convergence to the correct solution is achieved in employing this iteration algorithm, is dependent upon the choice of the preconditioner, as well as the initial guess. The authors focus on introducing a technique the (Maxwell and Markov technique, referred to herein as MNM) for choosing the initial guess. This can help reduce the number of iterations and, consequently the solution time, over the typical choice of a zero initial guess in the context of CG. The application of the method is illustrated via a number of numerical examples that combine the FMM with MNM, to derive the solution of representative electromagnetic scattering problems.