Spectra of integral operators and convergence of iterative solutions to electromagnetic scattering problems

The convergence of iterative solutions to electromagnetic scattering equations of investigated from the viewpoint of special properties of the pertinent integral operators. A detailed analysis is reported for an infinite perfectly conducting strip illuminated with TM- and TE-polarized plane waves. These two cases are characterized by very different expansions of the currents induced on the strip in terms of the eigenfunctions of the integral operators involved. The authors´ analysis explains the origin of the poor convergence of the iterative methods for the TE-polarized wave. The spectral distribution of the current in the TE case is particularly unfavorable for iterative schemes: for a fixed number of iterations, the accuracy of the solution deteriorates with an increasing number of discretization points. Preconditions are found which modify the spectra of the operators and accelerate dramatically the convergence of iterative solutions for both the TM-polarized and the TE-polarized waves.<>