3.1 Introduction

In this chapter the problems of magnetodynamics in low frequency will be covered. This study concerns the problems of induced eddy currents in the conductors. Thus, the volume electric charges ? and the displacement currents ? _t are omitted. Figure 3.1 shows a typical problem of eddy currents. It deals with the calculation, under the excitation of a time-varying current , of the distribution of the magnetic field ( or ) in every point of the study domain ? and of the density of current in the study domain ? _c for any time higher than zero. Maxwell's equations relating to this problem are:

with the constitutive relations of materials:

Figure 3.1: Eddy current problem

Equations [3.1] and [3.2] involve in particular the conservation laws of the magnetic flux and the conduction current . They are to be solved with the boundary conditions such that the fields and are imposed respectively on ? _e and ? _h.

^[1]

In a conducting region, it is possible to directly consider the field (electric or magnetic) as a working variable. In the finite element approximation, these fields can be approximated by nodal elements or edge elements. The edge elements have the characteristic of imposing between elements only the continuity of the tangential component of the field, whereas the nodal elements impose at the same time the tangential and normal continuity of the field. In a magnetic formulation, the discretization of...