An all-frequency weakly-singular surface integral equation for electromagnetism in dielectric media: Reformulation and well-posedness analysis

We develop and analyze a surface integral equation (SIE) whose solution pertains to numerical simulations of propagating time-harmonic electromagnetic waves in three-dimensional dielectric media. The formulae to evaluate the far-field pattern and propagation of the electric and magnetic fields in the interior and exterior of a dielectric body, through surface integrals, require the solution of a 2×2$2\times 2$ system of weakly-singular SIEs for the two unknown electric and magnetic fields at the interface surface of the dielectric body. The SIE is governed by an operator that is of the classical identity plus compact form. The tangential surface currents and normal surface charges of the dielectric model can be easily computed from the surface electric and magnetic fields.