A geometric integral formulation for eddy-currents

In the computational electromagnetism community it is known how the differential formulation of an eddy-current problem, can be translated into a finite dimensional system of equations involving circulations and fluxes, by means of the so-called Discrete Geometric Approach. This is done by exploiting the geometric structure behind Maxwell's equations. In this paper, we will show how the same Discrete Geometric Approach can be profitably used also to discretize an eddy-current problem formulated in an integral way. We rely on a purely geometric definition of a novel set of face vector basis functions that we use to construct the discrete counterparts-matrices-of both the Ohm's constitutive relation and of the integral relation between the magnetic vector potential and the eddy-current density vector. The symmetry and positive-definiteness of such matrices will be demonstrated and their geometric structure will be apparent.