A Novel h-φ approach for solving eddy-current problems in multiply connected regions

A novel h-φ approach for solving 3-D time-harmonic eddy current problems is presented. It makes it possible to limit the number of degrees of freedom required for the discretization such as the T-Ω method, while overcoming topological issues related to it when multiply connected domains are considered. Global basis functions, needed for representing magnetic field in the insulating region, are obtained by a fast iterative solver. The computation of thick cuts by high-complexity computational topology tools, typically required by the T-Ω method, is thus avoided. The final matrix system turns out to be symmetric and full-rank unlike the more classical A-A method, which requires gauging of magnetic vector potential to ensure uniqueness. Numerical tests show that the proposed method is accurate and the field problem solution is obtained in a reasonable computational time even for 3-D models with millions of mesh elements.