We present a new systematic methodology to efficiently solve coupled electromagnetic problems with nonlinear hysteresis at low frequency (10 kHz), called static hysteresis, by the finite-element method. The methodology integrates a new domain-wall-motion hysteresis model for power magnetic components (POMACs) into a finite-element potential formulation via an implicit-inverse model calculation. It uses a novel two-level iterative algorithm incorporating the efficient implicit-inverse model calculation to solve the complete Maxwell equations after the finite-element discretization. Our formulation does not require an explicit inversion of the hysteresis model as usually done in previous work. The efficient and accurate full-order model simulations applied to POMAC examples show that the proposed procedure can be applied to other electromagnetic problems with nonlinear static hysteresis. Index Terms—Converters, finite element, hysteresis, power electronics, power magnetic component. I.