New electric-magnetic field integral equation for the scattering analysis of perfectly conducting sharp-edged objects at very low or extremely low frequencies

The MoM-EFIE implementation is normally preferred in front of the MoM-MFIE discretization because of its better accuracy and because it can also be applied to the scattering analysis of open surfaces. The great advantage of the MoM-MFIE lies in producing very well-conditioned matrices all over the frequency range. In this paper, we present a new scheme to compute the electric current over the conductor. We apply two field boundary conditions on the surface: (i) [Magnetic] the cross-product of the unitary normal vector with tangential component of the magnetic field equals the electric current and (ii) [Electric] the normal component of the electric flux density equals the charge density. In order to capture unambiguously the charge density, we decompose through the Loop-Star decomposition the current space into solenoidal and nonsolenoidal contributions. The condition number of the resulting matrix becomes stable all over the frequency range. There exist other Integral Equation implementations that consider the surface-normal electric-field boundary condition but they assign different unknowns to the current and to the charge density and do not provide for the solenoidal-nonsolenoidal decomposition of the current.