Calculation of Eddy currents in terms of H on hexahedra

TLDR: In this article, the eddy current equations are formulated in terms of H, instead of the more usual vector potential A, where a combination with a scalar potential is necessary in the non conducting regions.

Abstract: The eddy current equations are formulated here in terms of H [1] instead of the more usual vector potential A [2,3]. In both cases a combination with a scalar potential is necessary in the non conducting regions. In the case of A this leads to either a non symmetric or not positive definite system of equations to be solved. This is avoided by the formulation in H, but special elements have to be chosen in order to satisfy the interface conditions between the two regions. The construction of such elements on tetrahedra or rectangular blocks can be found in [4]. The construction for hexahedra, or more specifically, isoparametric bricks, is shown here. Compared to filling a hexahedron with tetrahedra, this method reduces the number of unknowns by a half. The computed approximations for the eddy currents are exactly non divergent.