An integral equation method for the electromagnetic scattering from a scatterer on an absorbing plane

Consider a time-harmonic electromagnetic plane wave incident on a scatterer on a grounded absorbing plane modelized as an infinite impedance plane. In this paper, a new integral representation formula is rigorously derived. Existence and uniqueness of weak solutions for the model problem are also established. The proof of existence is based on an extension of the Hodge decomposition technique to open boundaries. The results reported in this paper form a basis for numerical solutions of the electromagnetic scattering problem from a scatterer on an absorbing plane.