On the Iteration of Surface Currents and the Magnetic Field Integral Equation

Abstract

In an effort to mathematically validate the convergence properties of various surface current-iterative methods, the magnetic field integral equation is analyzed for its contraction mapping properties. The analysis is performed first on the general integral operators and then on the matrices representing the discrete forms of the integral operators associated with the different iterative methods. The contraction mapping properties are determined by investigating the spectral radius of each linear operator. Conditions for the verification and validation of these iterative methods are provided, along with mathematical checks for the existence of spurious modes and the existence of internal resonance.