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. Convergence and stability theorems are proven. Finally, convergence results in actual computations are compared with results for the usual volume integral method used in GFUN3D.
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Joseph E. Pasciak (1984) studied this question.