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 φ
ⁱⁿ
, and the scattered vector potential A
^scat
is computed from the incoming vector potential A
ⁱⁿ
. 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
.