Numerical solution of magnetostatic boundary-value problems by iterative integration using the Green’s function

Abstract

The integral equation associated with magnetostatic problems is expressed by two different representations in which the unknown variable in one case is the charge density, while in the other it is the current density at the surfaces of magnetizable and superconducting bodies. Both representations are mathematically equivalent and complement each other in spatial field calculations which involve integrals of different numerical convergence. An iterative numerical integration method is proposed for solving the integral equations, whose kernel contains a Green’s function. The method is demonstrated for a superconducting cylindrical shield in an outer longitudinal field and for magnetic pole shoes of given permeability. The results of the first four iterative steps are seen to exhibit rapid convergence.