Integral Equation Formulation for the Solution of Magnetic Field Problems Part I. Dipole and Current Models

Integral equations are shown to offer definite advantages over conventional finite difference techniques for solving magnetic field problems. In Part I of this paper two models are presented to account for the presence of a ferromagnetic medium. In the first model the magnetic material is replaced by an equivalent dipole distribution which gives rise to an integral equation for the scalar potential. The model is limited to problems involving nonmagnetic current carrying conductors. The second model uses a current distribution to represent the magnetic material. Therefore, it is not subject to the restrictions of the dipole model. Numerical solution of the resulting integral equation in both models is discussed. The technique offers considerable flexibility in the choice of the mesh size and shape. Also, geometries involving narrow air gaps and/or sharp corners are easily accommodated.