The reduced scalar potential representation of magnetic fields is widely believed to be numerically unstable where large permeability contrasts (e.g., 1000:1) prevail. This belief is theoretically unfounded. Computational errors reported in the literature are shown to arise mainly in the process of finite element discretization, where extraneous source densities are introduced when applied magnetic fields are approximated by fields not wholly solenoidal. Simple experiments show local energy density errors of several per cent even in regions of uniform permeability, independently of element order.
Silvester, P.P. and Dufresne, M. (1992), "COMPUTATIONAL ERROR IN REDUCED SCALAR MAGNETIC POTENTIAL PROBLEMS", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 11 No. 1, pp. 65-68. https://doi.org/10.1108/eb051753
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