Development of Stable A-$\Phi$ Time-Domain Integral Equations for Multiscale Electromagnetics

Applications involving quantum physics are becoming an increasingly important area for electromagnetic engineering. To address practical problems in these emerging areas, appropriate numerical techniques must be utilized. However, the unique needs of many of these applications require new computational electromagnetic solvers to be developed. The A-Φ formulation is a novel approach that can address many of these needs. This formulation utilizes equations developed in terms of the magnetic vector potential (A) and electric scalar potential (Φ). The resulting equations overcome many of the limitations of traditional solvers and are ideal for coupling to quantum mechanical calculations. In this paper, the A-Φ formulation is extended by developing time-domain integral equations suitable for multiscale perfect electric conducting objects. These integral equations can be stably discretized and constitute a robust numerical technique that is a vital step in addressing the needs of many emerging applications. To validate the proposed formulation, numerical results are presented, which demonstrate the stability and accuracy of the method.