A Finite-Element Analysis of Nonlinear Magnetization Problems in Terms of Total Scalar Potential

A novel approach to the finite-element modeling of 3D magnetostatic fields based solely on the use of the total scalar potential is proposed for solving the large-scale magnetization problems involving prescribed currents and nonlinear magnetic materials. The use of the potential is first adopted for multiply connected, current-free regions by creating the imaginary cut surfaces, and is then extended to the whole problem domain via replicating the inductive effect of conductor currents by other equivalent means. The two different techniques are described to substitute this effect exactly; the first deploys the scalar potential discontinuities across thin cuts, whereas the second uses the remanent magnetizations of linear and nonlinear permanent magnets. Exploiting the magnetic scalar potential under such circumstances is assessed and validated by comparing it with a reference model of magnetostatic fields produced by a coil current in the dipole magnet and calculated in terms of magnetic vector potential formulation. For this modeling example, the proposed approach is shown to produce the expected results with a similar accuracy but at a much lower computational cost.