Augmented Hybrid Integral Equations for Low-Frequency Analysis of Lossy Conducting Objects

Electromagnetic (EM) integral equations include either $\mathcal{L}$ operator or $\mathcal{K}$ operator or both. The $\mathcal{L}$ operator has a low-frequency-breakdown (LFB) problem at low frequencies, and as a remedy, the augmented electric field integral equation (AEFIE) for conducting objects was proposed. Later on, the AEFIE was extended to AEFIEs for dielectric objects which include both $\mathcal{L}$ operator and $\mathcal{K}$ operator and the dual basis function (DBF) is used to represent the magnetic current density. In this work, the hybrid field integral equations (HFIEs) are employed for lossy conducting objects, and the HFIEs consist of the EFIE in the exterior and magnetic field integral equation (MFIE) in the interior of the lossy conducting object, respectively. Both electric and magnetic current densities can be expanded by the Rao-Wilton-Glisson (RWG) basis function which is also a testing function and the resultant impedance matrix is well-conditioned due to the feature of HFIEs. At low frequencies, the HFIEs are extended to the augmented HFIEs (AHFIEs) by introducing the continuity equation of magnetic current and magnetic charge density as an extra unknown function. A numerical example is shown to demonstrate the approach and good performance has been verified.