Cancellation errors in an integral for calculating magnetic field from reduced scalar potential

IEEE Transactions on Magnetics, 39(4):1997-2002 (2003).

Stéphane Balac
Laboratoire de Mathématiques Appliquées (MAPLY)
INSA de Lyon
20 Av. Albert Einstein
69621 Villeurbanne, France

Gabriel Caloz
IRMAR, Université de Rennes 1
Campus de Beaulieu
35042 Rennes Cedex, France

Abstract

In magnetostatic field computation with regions containing current sources, it is classical to write the corresponding magnetostatic problem in terms of the reduced scalar magnetic potential $\phi$. Usually numerical differentiation is used to get the magnetic field H from the potential values, which implies loss in accuracy. An alternative is to compute H from $\phi$ from an integral formula. In fact the formula does not give, as its current form, a straightforward method due to a cancellation in the integral. In this paper we investigate the reason why the formula is not suited for numerical purposes and propose a way to circumvent this difficulty based on sort of decomposition method.