Numerical Analysis of the Potential Formulation of the Volume Integral Equation for Electromagnetic Scattering

We present a discretization of the potential volume integral equation for electromagnetic scattering by dielectric objects. The equations are written for the vector and scalar potentials combined with the Lorenz gauge condition. The advantage of the potential formulation over the more conventional formulations, that is, the field, flux, or current formulations, is that the potentials are continuous across material interfaces enabling the use of fully continuous basis functions. The discretization with the fully continuous basis functions leads to a better conditioned system matrix compared to those of the other formulations discretized with the fully or partially discontinuous functions. Thus, it speeds up the iterative solution. The method is accelerated with the precorrected fast Fourier transform algorithm.