The convergence of iterative solutions to the Electric Field Integral Equation

The Jacobi iterative method is applied to the system of linear equations arising from the discretization of the Electric Field Integral Equation (EFIE). It is shown that the resulting matrix equation is a contraction mapping, guaranteeing monotonic mean square convergence, for any initial guess, and for a preferred choice of a relaxation parameter (). Both the criterion for convergence and for the generation of the initial guess are discussed in detail. Results are shown for the 2-dimensional TM scattering by a perfectly conducting strip which illustrates the major points of this paper. The mathematical criterion herein may be applied to any electromagnetic problem employing the EFIE for perfectly conducting surfaces.