Stability Analysis of Time Domain Discontinuous Galerkin H– $\Phi$ Method for Eddy Current Simulations

A rigorous stability analysis of the previously published semi-explicit time domain discontinuous Galerkin (DG) H-Φ approach for eddy current simulations is presented. The considered DG finite-element method (FEM) enables explicit time stepping in electrically conducting regions and eliminates the need for solving large sparse ill-conditioned equation systems. The considered method utilizes the magnetic scalar potential in electrically non-conducting regions computed by using the nodal finite elements. The theoretical stability limit of the considered semi-explicit time domain approach is obtained by applying the z-transform on the discrete time domain DG-FEM equations and by performing an eigenvalue analysis of the underlying elemental DG-FEM matrices. The obtained results are tested on simple 3-D examples, and an excellent agreement between the theoretical stability limit and the empirically obtained values was found.