reluctivity

where [sigma], v and j denote the electrical conductivity, magnetic reluctivity, and the external current density, respectively, and where n is the outward normal vector to [partial derivative][OMEGA].

where [[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.

Here v is the reluctivity and o is the conductivity of the material.

where v is the magnetic reluctivity (reciprocal of magnetic permeability, [mu]) and is a constant for linear and isotopic magnetic material.

Indeed, in [31] a MinRes solver for the solution of multiharmonic eddy current optimal control problems is constructed that is robust with respect to the discretization parameter h and all involved parameters like frequency, conductivity, reluctivity, and the regularization parameter.

In order to solve the nonlinear PDE using the Newton-Raphson method, an estimated solution of the magnetic flux is provided and fed into the ODE, from which the differential reluctivity and the magnetic field are calculated and returned back to the PDE to generate the next estimated solution.

where [OMEGA] is the field solution region, A and [J.sub.z] the z-direction components of vector potential and current density, respectively, [J.sub.f] the equivalent current density of the excitation field, S the Dirichlet boundary, and V the reluctivity. Second, the armature circuit equation of the machine during motoring is given by: