A Novel Coulomb-Gauged Magnetic Vector Potential Formulation for 3-D Eddy-Current Field Analysis Using Edge Elements

Magnetic vector potential (MVP) formulation combined with finite edge elements has gained substantial application in 3-D eddy-current field computation. Compared with its magnetic scalar potential counterpart, the MVP formulation is much easier to treat multiply-connected conductors. With the availability of advanced direct linear solvers with high performance on parallel or multi-core platforms, it becomes more and more important to develop gauged MVP formulations. To this end, the gauging technique is essential to ensure that the MVP formulation is uniquely solvable by direct solvers. In this paper, a novel method for imposing Coulomb gauge to transient eddy-current problems using edge elements for approximating the MVP is proposed. The resultant linear matrix equation is symmetric and uniquely solvable. Current excitations and voltage excitations for stranded conductors and solid conductors are formulated, respectively. Field-circuit coupled scheme for solid conductors is also presented. Extensive numerical examples are computed using the proposed formulation, which has proved to be promising in further engineering applications.