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This paper describes a three-dimensional integral method that models electromagnetic phenomena taking place during inductive melting. The method is well suited to inductive systems undergoing sinusoidal excitation at midrange or high frequencies. Under these conditions, only the surfaces of the conductors need to be meshed. The unknowns of the model are current density and scalar electrical potential. Power density, electromagnetic forces, and electrical impedance can easily be derived. Comparisons between numerical results and measurements confirm the accuracy of the model.