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Formulations of three-dimensional magnetostatic fields are reviewed for their finite-element analysis. Partial differential equations and boundary conditions are set up for various kinds of potentials. Besides the method using two scalar potentials, several vector potential formulations are also discussed. Galerkin techniques combined with the finite element method are applied for the numerical solution of the boundary value problems. The effect of gauging the vector potential upon the numerical performance is investigated. Solutions by different formulations to a simple test problem and a benchmark problem involving relatively thin saturated iron plates are presented. The latter is compared to measured results.>
Preis et al. (Sun,) studied this question.