A T formulation for 3D finite element Eddy current computation

The calculation of three-dimensional eddy currents is of primary interest for many applications. Several formulations of the electromagnetic problem have been proposed. In this paper the Galerkin method is applied to the integral formulation in terms of current density so as to consider only two scalar functions as unknowns instead of four (the current density vector
\underline{J}
and the electrical scalar potentials φ). These simplifications can be achieved by exploiting the definition of an auxiliary vector potential
\underline{T}
so that the shape functions for the current density intrinsically verify both solenoidality and boundary conditions.