Multipole theory method of calculating 3D magnetostatic field problem

A new approach, the multipole theory (MT) method based on the magnetic scalar potential, is presented for calculating 3D magnetostatic field problem associated with piecewise homogeneous media. The essential concept is to represent the solution of the governing partial differential equation by the generalized MT formula of the 3D Laplace equation in each region. The MT matrix equation of 3D magnetostatic field problem associated with piecewise homogeneous media is derived. Three representative computational examples, ferromagnetic sphere and iron cube in uniform magnetic fields, and iron cylinder in the field of a cylindrical coil, are given to validate the accuracy and efficiency of the MT method. The results obtained by the MT method are in excellent agreement with the accurate data reported in the literatures.