Fast multipole representation of Green´s function for an impedance half-space

In this paper, exact and approximate multipole representations for fields of a horizontal or a vertical infinitesimal dipole above impedance surfaces are derived from the exact image formulation. These multipole expansions are appropriate for applications in the method of moments through a formulation known as the fast multipole method. Unlike the existing approximate formulations, these new multipole representations of the Green´s function for the half-space impedance surface problem do not impose any restrictions on the location of source or observation points and are computationally very efficient.