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A new method for approximating magnetostatic field problems is given in this paper. The new method approximates the scalar potential for the magnetic intensity and is based on a volume integral formulation. The derivation of the new computational method uses the spectral properties of the relevant integral operator. The corresponding algorithm is similar to that obtained from coupled differential and boundary integral approaches. Conver- gence and stability theorems are proven. Finally, convergence results in actual computations are compared with results for the usual volume integral method used in GFUN3D. 1. Introduction. In this paper we define a new numerical method for magnetostatic field computation. We specifically consider the problem of calculating the nonlinear static field effects produced by the presence of iron-type materials. Applications for these problems occur in, for example, the design of accelerator and beam control magnets, fusion devices, electric motor design, and magnetic tape head design. A variety of numerical methods for the solution of magnetostatics problems have been proposed and some general purpose codes have been produced (1), (2), (4), (5), (8), (12), (13). For examples of magnetic field calculations, see (4), and the references therein. The magnetostatic field problem can be stated as an elliptic interface problem and the analysis presented in (3), (8) is applicable. Integral formulations of this problem have also been considered (6), (11). In this paper, a new scalar potential integral formulation of the nonlinear magnetostatic field problem is defined and analyzed. To motivate the new method, we give an analysis for constant permeability problems which shows that the large errors in the iron domain observed with the usual volume integral method lie in subspaces perpendicular to gradient functions. The new method is designed to eliminate errors of this type while generalizing to a method for nonlinear problems which exhibits uniform convergence in the iron domain even as the permeability becomes uniformly large. The new method is derived as a volume integral formulation which approximates the magnetic intensity H in terms of the gradient of a scalar potential. It is then

A new scalar potential formulation of the magnetostatic field problem