Iterative solution of the normal-equations form of the electric-field integral equation

Abstract

In this paper, we show that transforming the original equations into normal equations improves the convergence of EFIE significantly. We present the solutions of EFIE by employing the least-squares QR (LSQR) algorithm, which corresponds to a stable application of the conjugate gradient (CG) algorithm on the normal equations. Despite the squaring of the condition number due to such a transformation into the normal equations, LSQR improves the convergence rate of the iterative solutions of EFIE and performs better than many other iterative algorithms that are commonly used in the literature. In addition to LSQR, we present the accelerated convergence of the normal equations in the context of the generalized minimal residual (GMRES) algorithm, where the memory requirement is reduced significantly due to the improved convergence characteristics.