Low-frequency excitation in unbounded 3D dielectric media: Formulation, analysis and applications

Abstract: 

We consider electromagnetic wave propagation in three dimensional (3D) unbounded dielectric media governed by the Maxwell partial differential equations (PDE), radiation and interface conditions. The piecewise constant PDE coefficients are such that the continuous PDE model is well-posed for all frequencies, and as the frequency tends to zero, the electric and magnetic fields uncouple gracefully. It was an open problem to develop an equivalent bounded surface integral equation (SIE) model (based only on integral operators) and prove that the SIE does not from spurious resonances and low-frequency breakdown. In this talk, we discuss our (surface currents and charges based) solution to this challenging reformulation and analysis problem, and briefly explore its applications using associated forward and inverse uncertain quantification models.