A new scalar potential formulation for 3-D magnetostatics necessitating no source field calculation

The authors present a new scalar potential formulation for 3-D magnetostatic field analysis. The method is based on a convenient partition of the magnetic field that permits representation of multiply connected multifilamentary conductors by means of a fictitious field with known distribution. This technique permits the efficient modeling of laminated iron cores with or without air gaps and needs no prior source field calculation. It is implemented in a finite element scheme using first-order tetrahedral elements. The method is validated by comparing the results to an almost-closed-form solution in the case of an iron-free 3-D problem. A transformer example has also been treated