New technique for solving three-dimensional multiply connected eddy-current problems

In three-dimensional eddy-current computation, when the conductors are multiply connected, the use of a scalar potential in exterior regions leads to a multivalued problem. To avoid this difficulty, in a hybrid finite-element/boundary-integral model, We propose to use the electric field as the state variable in both conducting and non-conducting regions. A vectorial boundary-integral method, based on the use of a current sheet on the boundary, is applied in exterior regions. A spanning tree technique is introduced to ensure the null divergence of the boundary current sheet. This technique permits also a reduction in the number of boundary unknowns.