  The finite-element analysis of three-dimensional magnetostatic problems in
terms of magnetic vector potential has proven to be one of the most efficient
tools capable of providing the excellent quality results but becoming
computationally expensive when employed to modeling of large-scale
magnetization problems in the presence of applied currents and nonlinear
materials due to subnational number of the model degrees of freedom. In order
to achieve a similar quality of calculation at lower computational cost, we
propose to use for modeling such problems the combination of magnetic vector
and total scalar potentials as an alternative to magnetic vector potential
formulation. The potentials are applied to conducting and nonconducting parts
of the problem domain, respectively and coupled together across their common
interfacing boundary. For nonconducting regions, the thin cuts are constructed
to ensure their simply connectedness and therefore the consistency of the mixed
formulation. The implementation in the finite-element method of both
formulations is discussed in detail with difference between the two emphasized.
The numerical performance of finite-element modeling in terms of combined
potentials is assessed against the magnetic vector potential formulation for
two magnetization models, the Helmholtz coil, and the dipole magnet. We show
that mixed formulation can provide a substantial reduction in the computational
cost as compared to its vector counterpart for a similar accuracy of both
methods.
