Implicit Gauging of Electromagneto-Quasistatic Field Formulations

Electromagneto-quasistatic (EMQS) field models exhibit capacitive, resistive, and inductive effects, in the absence of wave propagation, while the associated initial boundary value problems are ill-posed. A framework that is based on penalizing a Coulomb-type differential constraint that recovers well-posedness is proposed here. The advocated strategy yields two classes of EMQS formulations that implicitly gauge the magnetic vector potential. Comparative numerical tests demonstrate the performance of the resulting formulations relative to the recently introduced two-step Maxwell scheme.