For some specific cases, the vector field formulation can be useful. One example is the modeling of superconducting materials that have highly nonlinear electric conductivity. In this case, it is convenient to use the magnetic field formulation since the nonlinear constitutive relation between the electric field E and the current density J can be included naturally. This formulation, referred to as the H formulation, is used by The Magnetic Field Formulation Interface. Different from The A Formulation which solves Ampère’s law, The H Formulation solves Faraday’s law. For more details, see the Theory for the Magnetic Field Formulation Interface.