Abstract: I will discuss a numerical model based on an integral formulation for the efficient computation of 3-D magnetic fields in hysteretic media with (time) periodic sources. The hysteretic medium is described by an isotropic vector generalization of the classical scalar Jiles-Atherton model. The nonlinear algebraic system is solved using a Picard-Banach iterative procedure in the frequency domain. Its numerical convergence can be assured under reasonable assumptions. The full matrices arising after the discretization of the main (linear) operators are suitably compressed and distributed among the nodes of a parallel computer system. The numerical model will be described with reference to a device used for the the nondestructive micromagnetic characterization (of mechanical properties) of metallic materials. This example will give also the reference frame for discussing the steps done so far toward the experimental validation.