E-MFIE Formulation for Arbitrary PEC Sheets

The scattering of an electromagnetic wave by a perfectly conducting sheet of arbitrary shape can be solved with the Method of Moments (MoM), but the solution obtained with the electric field integral equation (EFIE) yields the sum of the electric current densities on every opposite faces of the sheet, while the magnetic field integral equation (MFIE) cannot be used. In this paper, we first explain in detail the singularities of the MoM impedance matrices formed with the EFIE and MFIE applied to any arbitrarily shaped perfectly conducting sheet. This study suggests a new formulation, the E-MFIE, which is developed first in the most general way, and then in a more efficient form, to obtain the complete solution for the electric current densities on each face individually as well as around all sheet borders.