Integral equation formulation for iterative calculation of scattering from lossy rough surfaces

Abstract

The dependence of the convergence properties of iterative solution algorithms on the specific integral equation formulation that is discretized to describe the electromagnetic scattering from one-dimensional (1-D) rough, high loss surfaces is examined. A magnetic field integral equation (MFIE) formulated using impedance boundary conditions typically used to describe vertically polarized (VV) scattering from large-conductivity, single-valued open surfaces yields well-conditioned interaction matrices that lead to quick convergence. The corresponding electric field integral equation (EFIE) typically used for horizontal polarization (HH) (found from duality) results in much poorer conditioning, with correspondingly slower convergence. An impedance-boundary condition magnetic field integral equation (MFIE) valid at horizontal polarization is formulated that leads to convergence nearly as rapid that observed with the vertical polarization MFIE. Numerical integration of some off-diagonal terms is required to prevent a strong singularity in the HH MFIE from introducing errors in the calculated far-field scattering. A simple example also shows that the EFIE and MFIE for the same polarization can be linearly combined to improve the convergence characteristics with lossy closed-body problems, analogous to the combined field integral equation (CFIE) perfectly conducting case.