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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.