Integral equation formulation for iterative calculation of scattering fromlossy rough surfaces

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