Treatment of Multiply Connected Domains in Time-Domain Discontinuous Galerkin $H$ – $\Phi$ Eddy Current Analysis

This paper presents a method for the treatment of multiply connected regions within the semi-explicit time-domain discontinuous Galerkin (DG) eddy current solver based on the H-Φ field formulation. The suggested method utilizes a multivalued magnetic scalar potential over a cutting surface that divides a multiply connected domain into two simply connected regions. The multivalued magnetic scalar potential in the nonconductive domain (Φ-domain) is regularly updated after a sequence of time steps of the explicit vector DG-finite element method solver in the electrically conductive domain (H-domain) yielding an accurate time-domain solution of the magnetic field in the multiply connected space surrounding the eddy current region. The efficiency and accuracy of the method are demonstrated by a 3-D example and the obtained results are verified by comparison against the corresponding frequency-domain solution.