To model a magnet, the surface charge model can be used. This results in fast and accurate analytical solutions when the relative permeability is equal to one. If this is not the case, the model has to be calculated numerically and the computational time increases significantly. In this paper, a polynomial approximation of the surface charge is therefore proposed to obtain a semianalytical model. The results are less accurate than the numerical model. It is, however, about 300 times faster. This 3-D model is used to model, a magnet, a soft-magnetic block in an external field, and a gravity compensator, which is a combination of magnets and a soft-magnetic plate.
Casteren, van, D. T. E. H., Paulides, J. J. H., & Lomonova, E. A. (2014). 3-D semianalytical surface charge model including relative permeability using polynomial approximation. IEEE Transactions on Magnetics, 50(11), . https://doi.org/10.1109/TMAG.2014.2331984