Nyström discretization of an augmented electric field integral equation with magnetic field constraint

Abstract

The locally corrected Nystrom (LCN) discretization of an augmented electric field integral equation (AEFIE) can partially overcome the low frequency breakdown problem inherent in the conventional electric field integral equation (EFIE). The LCN AEFIE is frequency stable and provides accurate and high-order solutions for the electric field. However, the magnetic field computed using the AEFIE at low frequencies is incorrect. A similar situation was recently encountered in developing a new EFIE-based formulation that relies on a globally constrained Helmholtz decomposition (HD) (EFIE-hd) of the current. In the latter case, it was found that introducing an additional constraint on the normal component of the magnetic field was sufficient to obtain accurate H-fields at all frequencies. This presentation will demonstrate that a similar strategy can be used with an AEFIE-type formulation to obtain accurate solutions for the electric current and the magnetic field while also improving the conditioning of the formulation.