A well-conditioned combined field integral equation for electromagnetic scattering

This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: resonant instability and dense discretization breakdown. The remedy to resonant instability is a combined field integral equation, and dense discretization breakdown is eliminated by means of operator preconditioning. The exterior traces of single and double layer potentials are complemented by their interior counterparts of a pure imaginary wave number. We derive the corresponding variational formulation in the natural trace space for electromagnetic fields and establish its well-posedness for all wave numbers. A Galerkin discretization scheme is employed using conforming edge boundary elements on dual meshes, which produces well-conditioned discrete linear systems of the variational formulation. Some numerical results are also provided to support the numerical analysis.