Finite element analysis of 3D multiply connected eddy current problems

Three-dimensional eddy-current problems with multiply connected conductors are formulated in terms of uniquely defined potentials. In the eddy-current-carrying regions, a magnetic vector potential and an electric scalar potential are used. These are coupled to a magnetic scalar potential in most parts of the nonconducting domain. However, in the nonconducting 'holes' in the conductors, a magnetic vector potential is used so that the region with the scalar description surrounds a simply connected domain. To ensure uniqueness of the vector potential, the Coulomb gauge is incorporated in the formulation and the normal component of the vector potential is set to zero on the interfaces between the vector-potential and scalar-potential regions. Solutions to two benchmark problems of the International TEAM Workshops involving multiply connected conductors are presented. The gain in computational time due to the use of unique potentials is pointed out.>