Decoupled Potential Integral Equation for Electromagnetic Scattering From Arbitrarily Shaped Dielectric Objects

Recently, integral equation formulations that use potentials as opposed to fields as unknown quantities have been developed for scattering from dielectric objects. It has been shown that these formulations can be construed so that they are well-conditioned across a broad frequency spectrum, a result that has been theoretically proven for spherical systems. Unfortunately, to date, this formulation has not been implemented on practical discretizations of objects. This is the goal of this article. Specifically, we present a well-conditioned and well-tested decoupled potential integral equation (DPIE) formulation and all the necessary implementation details for electromagnetic scattering from homogeneous, dielectric, arbitrarily shaped objects. The resulting decoupled systems do not suffer from low-frequency breakdown. Results that demonstrate these properties are presented for a number of different dielectric targets. Furthermore, in order to fully validate each of the two integral equations for the potentials, we develop analytical solutions for spherical systems.