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IMA Journal of Applied Mathematics 2001 66(3):293-318; doi:10.1093/imamat/66.3.293
© 2001 by Institute of Mathematics and its Applications
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Vector potential formulation for magnetostatics and modelling of permanent magnets

P. Fernandes1 and I. Perugia2

1 Istituto per la Matematica Applicata—CNR, Via De Marini 6, 16149 Genova, Italy. Email: fernandes@ima.ge.cnr.it 2 Dipartimento di Matematica—Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy. Email: perugia@dimat.unipv.it

A very general magnetostatic problem involving inhomogeneous anisotropic materials filling irregular regions and with mixed boundary conditions is formulated in terms of magnetic vector potential. Some restrictions inherent to the introduction of a vector potential become apparent and additional conditions for the uniqueness of the vector potential naturally arise. The modelling of permanent magnets is introduced in both the vector potential and the field formulations by weakening the regularity requirements on the source term. The vector potential formulation is also shown to be equivalent to a penalized formulation widely used in numerical applications.

Keywords: magnetostatic problems; permanent magnet modelling; vector potential formulations.


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