A fast Newton-Raphson technique (FNR) for the computation of nonlinear three-dimensional finite-element magnetic fields in electrical devices is presented. The technique reduces by more than 50% the CPU time required for converged nonlinear three-dimensional magnetic field solutions. This is in comparison with the standard Newton-Raphson (NR) technique. The reduction in CPU time was achieved without any sacrifice in the accuracy of the converged solutions in the values of the device terminal parameters. To illustrate the advantages of the method, a single-phase transformer was implemented with widely varying degrees of magnetic saturation. Values of magnetic vector potential, as well as flux density components obtained using the FNR technique were compared with the values obtained using standard NR method. The saturated values of magnetizing inductances were compared using the fast and standard NR methods. No numerical errors were introduced as a result of using the new technique. The numerical values matched not only in the whole part of the value, but also in the fraction part to the third and fourth digit. It was observed that the higher the degree of magnetic saturation in the example considered the faster the new technique converged to accurate values.
