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The finite-element analysis of three-dimensional magnetostatic problems interms of magnetic vector potential has proven to be one of the most efficienttools capable of providing the excellent quality results but becomingcomputationally expensive when employed to modeling of large-scalemagnetization problems in the presence of applied currents and nonlinearmaterials due to subnational number of the model degrees of freedom. In orderto achieve a similar quality of calculation at lower computational cost, wepropose to use for modeling such problems the combination of magnetic vectorand total scalar potentials as an alternative to magnetic vector potentialformulation. The potentials are applied to conducting and nonconducting partsof the problem domain, respectively and coupled together across their commoninterfacing boundary. For nonconducting regions, the thin cuts are constructedto ensure their simply connectedness and therefore the consistency of the mixedformulation. The implementation in the finite-element method of bothformulations is discussed in detail with difference between the two emphasized.The numerical performance of finite-element modeling in terms of combinedpotentials is assessed against the magnetic vector potential formulation fortwo magnetization models, the Helmholtz coil, and the dipole magnet. We showthat mixed formulation can provide a substantial reduction in the computationalcost as compared to its vector counterpart for a similar accuracy of bothmethods.

On the use of mixed potential formulation for finite-element analysis of large-scale magnetization problems with large memory demand