Publications Details

Low frequency stable and accurate potential-based time domain integral equations for dielectric regions

Roth, Thomas E.; Chew, W.C.

Potential-based formulations are new approaches gaining interest for deriving computational electromagnetics methods that perform markedly better for low frequencies and complicated structures (e.g., subwavelength and multiscale geometries) compared to traditional field-based formulations. Further, these methods are also more directly applicable to coupling into quantum physics problems that are becoming more prevalent in engineering applications. These methods derive their improved performance by developing systems to be discretized directly in terms of the magnetic vector potential and electric scalar potential, which are deemed more fundamental quantities for quantum applications than the electric and magnetic fields. Performing derivations in this way has resulted in equations that can accurately capture both wave physics (where the electric and magnetic fields are tightly coupled) and quasistatic phenomena (where the electric and magnetic fields become increasingly uncoupled) at the same time. This work focuses on continuing the development of time domain integral equations (TDIEs) based on the potential-based formulation to meet the demanding bandwidth requirements needed to efficiently analyze a wide range of quantum electromagnetic physics. Past work on potential-based TDIEs were applicable to perfect electrically conducting objects, and were shown to be stable and accurate over broad frequency ranges. More recently, initial efforts at developing potential-based TDIEs for dielectric regions were introduced. However, these initial equations did not exhibit the low frequency accuracy and stability properties desired from this formulation. This work demonstrates a new set of TDIEs that overcome the limitations of the original formulation, achieving high accuracy and good stability at analyzing dielectric objects at very low frequencies. These properties of the improved formulation are demonstrated through numerical results.