A hybrid explicit-implicit discontinuous Galerkin spectral-element time-domain algorithm for multi-scale computation

摘要

In this paper, we propose a hybrid explicit-implicit discontinuous Galerkin spectral-element time-domain (DG-SETD) algorithm for the analysis of multi-scale electromagnetic problems. Usually very small cells and extremely small time step size is needed in multi-scale simulation. However, when using this method, the time step size is no longer constrained by the Courant-Friedrichs-Levy (CFL) condition and the number of unknowns will also be greatly reduced by nonconformal mesh, which can greatly shorten the computation time. The Crank-Nicholson (CN) difference scheme is employed for the small cells with UMFPACK solver and leapfrog difference is for the large cells with direct solution procedure. Consequently, a relatively large time step size can be adopted. Finally, numerical results demonstrate the accuracy and effectiveness of the proposed method.