Integral equations via saddle point problems for time-harmonic Maxwellʹs equations

We propose a new system of integral equations for the exterior time harmonic Maxwellʹs equation. This system is derived first from elementary manipulations of classical equations then by the minimization of a quadratic functional associated to incoming and outgoing electromagnetic waves. We analyze the inf–sup condition and various penalized problems related to this system. Then we prove that an iterative algorithm for the solution of the system of integral equations is convergent. Other numerical issues are also discussed.