Toward an algorithm to make cuts for magnetic scalar potentials in finite element meshes

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Abstract
Kotiuga [J. Appl. Phys. 6 1, 3916 (1987)] showed that the integral (co)homology groups of a region Ω in R3 are torsion free and that cuts for magnetic scalar potentials can be realized by embedded orientable submanifolds which represent generators of the homology group H2(Ω,∂Ω;Z). The present paper makes these formal results intuitive by appealing to concepts familiar from electromagnetics and clarifies several issues relating to an algorithm for finite element meshes. Sufficiency conditions for the intersection of different cuts show that when several cuts are required it may not be possible to avoid intersections. This in turn clarifies the question of what data must necessarily be given in order for an algorithm to work.

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