An integral equation method for the electromagnetic scattering from cavities

Consider a time-harmonic electromagnetic plane wave incident on a cavity in a ground plane. The physical process is modelled by Maxwell's equations. In this paper, integral representations of the solutions to the model problem in both fundamental polarizations are derived and studied. Existence and uniqueness of the solutions for the integral equations are established. The integral equations approach forms a basis for numerical solution of the model problem. In particular, for each fundamental polarization, an integral formulation with Gårding-type estimates is derived. These formulations provide a basis for variational boundary element methods for solving the cavity problem. The Gårding-type estimates imply convergence results for conforming boundary element methods.