Augmented Müller Equations for Low-frequency Modeling of Penetrable Objects

The Müller equations (MEs) are the surface integral equations (SIEs) of describing electromagnetic (EM) problems with homogeneous penetrable objects, but they are less addressed compared with the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equations which are more widely-used. Similar to the PMCHWT equations, the MEs are formed by summating the individual electric field integral equations (EFIEs) and magnetic field integral equations (MFIEs), but with different weighting coefficients, and they have shown different merits. The MEs also include the $\mathcal{L}$ operator which has a well-known low-frequency-breakdown (LFB) problem. The LFB problem with homogeneous dielectric objects has been overcome by using the augmented EFIEs (AEFIEs), but requiring the use of dual basis function (DBF) which is complicated. This paper aims to the MEs to propose the augmented MEs (AMEs) for low-frequency modeling of homogeneous penetrable objects so that the merits of MEs can be fully used. In the augmentation, the magnetic charge density is selected as a new unknown function and the continuity equation of magnetic current density is used as a new constraint equation, thus the $\mathcal{L}$ operator of exerting on the magnetic current density can also be augmented. Numerical results show that the proposed method is effective and robust for the EM modeling of penetrable objects at very low frequencies.