Low frequency scaling of the mixed MFIE for scatterers with a non-simply connected surface

The Magnetic Field Integral Equation (MFIE) is a widely used integral equation for the solution of electromagnetic scattering problems involving perfectly conducting objects. It is usually discretized by means of RWG functions as both basis and test functions. This discretization of the MFIE is well-known for its good condition number. However, it is equally well-known for the inferior accuracy of its solution when compared to the Electric Field Integral Equation (EFIE). What is less-known is that this accuracy problem becomes even more serious when the frequency is lowered. Recently it has been proved that the so-called mixed discretization of the MFIE, also called ´mixed MFIE´, eliminates this low-frequency accuracy problem on simply connected scatterers. The mixed MFIE utilizes the so-called Buffa-Christiansen or Chen-Wilton functions for testing. In this contribution, the low frequency behavior of the mixed MFIE is investigated for scatterers with a non-simply connected surface. An analysis shows the presence of an approximate nullspace in the mixed MFIE at low frequencies. This nullspace becomes exact when the frequency is zero. This behavior matches known results for the continuous MFIE. Numerical results are presented that confirm this analysis. Despite the approximate nullspace at low frequencies, numerical results indicate that the mixed MFIE still delivers accurate results for toroidal scatterers.