Multilevel fast-multipole algorithm for scattering from conducting targetsabove or embedded in a lossy half space

An extension of the multilevel fast multipole algorithm (MLFMA), originally developed for targets in free space, is presented for the electromagnetic scattering from arbitrarily shaped three-dimensional (3-D), electrically la rge, perfectly conducting targets above or embedded within a lossy half spa ce. We have developed and implemented electric-field, magnetic-field, and c ombined-field integral equations for this purpose. The nearby terms in the MLFMA framework are evaluated by using the rigorous half-space dyadic Green 's function, computed via the method of complex images, Non-nearby (far) ML FMA interactions, handled efficiently within the multilevel clustering cons truct, employ an approximate dyadic Green's function. This is expressed in terms of a direct radiation term plus a single real image (representing the asymptotic far-field Green's function), with the image amplitude character ized by the polarization-dependent Fresnel reflection coefficient. Examples are presented to validate the code through comparison with a rigorous meth od of-moments (MoM) solution. Finally, results are presented for scattering from a model unexploded ordnance (UXO) embedded in soil and for a realisti c 3-D vehicle over soil.