A Two-Step Formulation of Maxwell’s Equations Using Generalized Tree–Cotree Gauges for Low-Frequency Stability

This article presents a new low-frequency stabilization for a two-step formulation solving the full set of Maxwell’s equations. The formulation is based on an electric scalar and magnetic vector potential equation using the electroquasistatic problem as gauge condition. The proposed stabilization technique consists of an adequate frequency scaling for the electroquasistatic problem and a tree-cotree decomposition of the magnetic vector potential such that its divergence remains consistent with the partial decoupling of the magnetic and electric potentials. This article discusses two variants and demonstrates the effectiveness by a few computational examples.