reluctivity

The differential reluctivity tensor can be obtained by

the relative reluctivity of the material [[upsilon].sub.r] = 1/[[mu].sub.r] is a function of the magnetic flux density, which is a function of the unknown vector [{a}.sup.n+1], the residual {r} in Eq.

(13), the relative reluctivity is a function of B = [parallel]B[parallel]

The reluctivity v = v(x) is supposed to be uniformly positive and independent of |curl u|, i.e., we assume the eddy current problem (3.2) to be linear.

In order to obtain this simpler norm [parallel]*[[parallel].sub.[??]], we have to pay the price that the norm equivalence depends on the minimal value of the reluctivity v, i.e.,

where [[upsilon].sub.0] = 1/[[micro].sub.0] is the reluctivity in free-space, [[bar.[xi]].sup.d.sub.r] is the relative differential magnetizability tensor, and [[bar.[upsilon]].sup.d.sub.r] is the relative differential reluctivity tensor.

the differential reluctivity and magnetizability tensors can be related as