O. Biro et al., ON THE USE OF THE MAGNETIC VECTOR POTENTIAL IN THE NODAL AND EDGE FINITE-ELEMENT ANALYSIS OF 3D MAGNETOSTATIC PROBLEMS, IEEE transactions on magnetics, 32(3), 1996, pp. 651-654
An overview of various finite element techniques based on the magnetic
vector potential for the solution of three-dimensional magnetostatic
problems is presented. If nodal finite elements are used for the appro
ximation of the vector potential, a lack of gauging results in an ill-
conditioned system. The implicit enforcement of the Coulomb gauge dram
atically improves the numerical stability, but the normal component of
the vector potential must be allowed to be discontinuous on iron/air
interfaces. If the vector potential is interpolated with the aid of ed
ge finite elements and no gauge is enforced, a singular system results
. It can be solved efficiently by conjugate gradient methods, provided
care is taken to ensure that the current density is divergence free.
Finally, if a tree-cotree gauging of the vector potential is introduce
d, the numerical stability depends on how the tree is selected with no
obvious optimal choice available.