A Novel Formulation With Coulomb Gauge for 3-D Magnetostatic Problems Using Edge Elements

A novel magnetic vector potential (MVP) formulation with Coulomb gauge is proposed for solving 3-D magnetostatic problems. A dummy scalar variable is introduced in the whole computation domain to impose the Coulomb gauge. Unlike traditional Coulomb-gauged formulation using the penalty technique, which works only for nodal elements approximation of the MVP, the new formulation proposed in this paper allows the use of edge element approximation of the MVP. It can avoid possible large errors at material interfaces or re-entrant corners of the problem domain when using nodal discretizations for the MVP. This formulation is easy to implement, and the resultant matrix system is symmetric with a unique solution. Both linear and nonlinear numerical examples are presented to showcase the accuracy and usefulness of the proposed method for engineering computation.