A decoupled charge-current formulation for the scattering of homogeneous lossless dielectrics

In this paper we present a new formulation for the scattering of lossless homogeneous dielectrics that is stable in low frequency and has no high density mesh breakdown. The formulation is based on the standard Müller surface integral equation where the unknowns are both electric and magnetic currents on the boundary of the dielectric. We introduce two additional decoupled scalar problems that correspond to the electric and magnetic charges. By doing that we find a second kind integral equation that has unique solution and is stable in low frequency and under mesh refinement. We implement the discretization using a high order locally corrected Nyström method.