Generalized equivalence integral equations

A generalized equivalence integral equation (GEIE) approach to formulating surface scattering problems is proposed. GEIE invokes the generalized surface field equivalence to partially fill the volume originally occupied by the scatterer with judiciously selected materials, as opposed to the conventional replacement of the scatterer by the free-space. A specific type and shape of the material inclusions is selected to allow for a numerically efficient construction of the modified Green´s function. Introduction of impenetrable and lossy materials is advocated to confine the field interactions along the scatterer surface and reduce the coupling between the distant parts of the scatterer, thus facilitating development of fast solvers. GEIE also resolves the non-uniqueness problem of the electric and magnetic field integral equations by eliminating the internal resonances.