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

Abstract

The traditional surface integral formulations for the scattering analysis of perfectly conducting objects are the Electric Field Integral Equation (EFIE) and the Magnetic Field Integral Equation (MFIE). Both Integral Equations are based on enforcing the boundary conditions of the tangential components of the electric or the magnetic fields, respectively, over the conductor surface. The discretization in Method of Moments (MoM) of the EFIE with the RWG basis functions [1] leads to the accurate computation of the electric currents and the Radar Cross Section (RCS) for arbitrary surfaces. However, the resulting impedance matrices become very ill-conditioned at very low frequencies. The Loop-Star basis functions [2] stand for a rearrangement of the RWG basis functions so that the condition number of the resulting matrix at very low frequencies is improved. The RWG MoM-discretization of the MFIE leads to some inaccuracy in the current and RCS solutions when compared with the EFIE. This misbehavior is especially evident in the scattering analysis of electrically moderately small sharp-edged objects. Some basis functions sets have been proposed instead to mitigate it [3][4]. Another problem arising from the MFIE discretizations is the incapacity of providing accurate RCS results at very low or extremely low frequencies [5][6]. This error is barely noticeable in the electric current because it lies in the real part of the nonsolenoidal part of the current [5], which, at very low frequencies, provides a minor contribution compared to the solenoidal terms. However, it appears clearly in the RCS computation because the static solenoidal part of the current does not radiate. Although this error has been identified also in the scattering analysis of smooth objects like a sphere [5], it is in the analysis of sharp-edged objects that it is most evident [6].