Title: Decoupled Potential Integral Equations for Electromagnetic Scattering from Dielectric Objects,
Abstract: Recent work on developing novel integral equation formulations has involved
using potentials as opposed to fields. This is a consequence of the additional
flexibility offered by using potentials to develop well conditioned systems.
Most of the work in this arena has wrestled with developing this formulation
for perfectly conducting objects (Vico et al., 2014 and Liu et al., 2015), with
recent effort made to addressing similar problems for dielectrics (Li et al.,
2017). In this paper, we present well-conditioned decoupled potential integral
equation (DPIE) formulated for electromagnetic scattering from homogeneous
dielectric objects, a fully developed version of that presented in the
conference communication (Li et al., 2017). The formulation is based on
boundary conditions derived for decoupled boundary conditions on the scalar and
vector potentials. The resulting DPIE is the second kind integral equation, and
does not suffer from either low frequency or dense mesh breakdown. Analytical
properties of the DPIE are studied. Results on the sphere analysis are provided
to demonstrate the conditioning and spectrum of the resulting linear system.