Interior Penalty Discontinuous Galerkin Time-Domain Method Based on Wave Equation for 3-D Electromagnetic Modeling

Abstract

Built on the vector wave equation, an interior penalty discontinuous Galerkin time domain (IPDG-WE) method is presented for 3-D real-life electromagnetic modeling in this paper. We develop the interior penalty fluxes corresponding to different types of boundary conditions which are commonly used in electromagnetic modeling to construct the IPDG-WE system in local elements. In addition, to model the incident wave excitation, the total-field/scattered-field approach is incorporated into the proposed method. The stability of the IPDG-WE method is studied analytically and demonstrated numerically. We also compare the performance between wave equation-based finite-element time-domain method, the Maxwell’s equation-based discontinuous Galerkin time-domain method, and the proposed method, both in CPU time and memory usage, which demonstrates that the IPDG-WE method is very competitive among time-domain solvers. Besides, the presented method shows good characteristics including the energy conservation and the optimal convergence rate of $O( {h^{p+1}})$ . Numerical examples are presented to illustrate the validity, versatility, and potential of the proposed method in 3-D electromagnetic problems modeling.