Finite-Element A-V Formulation for EMQS Problems via Two-Domain Continuity Gauging

A finite-element (FE) A-V formulation is developed to solve electromagnetic quasistatic (EMQS), aka Darwin, problems in the time and frequency domains by making use of a two-domain continuity gauging strategy. The formulation utilizes the magnetic vector and the electric scalar potentials, and an additional scalar in the conducting regions to make the discretized Galerkin system symmetric. The resulting FE matrix is low-frequency (LF) stable in the frequency domain. As a result, the time-step size is not limited by the characteristics of the system matrix in the backward Euler time-stepping scheme. The system matrixes are also regular, which allows choosing a direct solver to speed up the temporal solution significantly. The formulation is verified in both the frequency and the time domains by solving benchmark problems, and the results are compared to full-wave and eddy-current solutions.