Computation of the current density in nonlinear materials subjected to large current pulses

The finite element method and the finite difference method are used to calculate the current distribution in two nonlinear conductors. The first conductor is a small ferromagnetic wire subjected to a current pulse that rises to 10000 A in 10 mu s. Results from the transient thermal and transient magnetic solvers of the finite element code FLUX2D are used to compute the current density in the wire. The second conductor is a metal oxide varistor. Maxwell´s equations, Ohm´s law, and the varistor relation for the resistivity and the current density of rho = alpha j^{- beta} are used to derive a nonlinear differential equation. The solutions of the differential equation are obtained by a finite difference approximation and a shooting method. The behavior predicted by these calculations is in agreement with experiments.