An Efficient Local-Time-Stepping Scheme for Discontinuous Galerkin Time Domain for Solving Multiscale Electromagnetic Problems

Abstract

A novel local-time-stepping (LTS) scheme is introduced into the discontinuous Galerkin time domain (DGTD) method to enhance the efficiency of solving multiscale electromagnetic (EM) problems. The proposed LTS scheme partitions mesh elements into a number of classes based on the minimum time step multiplied by the powers of two, whose total time nodes (TTNs) are fewer than the widely used LTS scheme. Moreover, instead of a backward/forward approximation, an inter/extrapolation approach is exploited for achieving accurate exchange of the electric and magnetic field information at the interfaces between coarse and fine mesh elements at asynchronous time nodes. A series of numerical examples is presented for verification, demonstrating that the proposed LTS scheme outperforms the conventional LTS schemes in addressing multiscale EM challenges.