A high order locally corrected Nyström implementation of the Decoupled Potential Integral Equation

In this paper we present a numerical implementation of the Decoupled Potential Integral Equation (DPIE) based on a high order locally corrected Nyström method. The DPIE formulation allows to describing the scattering electromagnetic field by a perfect electric conductor in a decoupled way. The scattered scalar potential φ^scat is obtained entirely from the incoming scalar potential φⁱⁿ, and the scattered vector potential A^scat is computed from the incoming vector potential Aⁱⁿ. This formulation is exact for any frequency ω ≥ 0. The time harmonic scattered potentials are obtained in the Lorenz gauge, this allows us to compute the scattered electric and magnetic fields E^scat, H^scat.