A Discontinuous Galerkin Time-Domain Method With Dynamically Adaptive Cartesian Mesh for Computational Electromagnetics

A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian mesh (ACM) is developed for a full-wave analysis of electromagnetic (EM) fields. The benefits of hierarchical Cartesian grids and adaptive mesh refinement are demonstrated for linear EM propagation problems. The developed DGTD-ACM achieves a desired accuracy by refining nonconformal meshes near material interfaces to reduce stair-casing errors without sacrificing the high efficiency afforded with uniform Cartesian meshes. More importantly, DGTD-ACM can dynamically refine the mesh to resolve the local variation of the fields during propagation of EM pulses. A local time-stepping scheme is adopted to alleviate the constraint on the time-step size due to the stability condition of the explicit time integration. It is shown by numerical examples that the proposed method can achieve a good numerical accuracy and reduce the computational time effectively for linear problems of EM propagation in dispersive media. With further development, the method is expected to provide a powerful tool for solving nonlinear EM problems in plasma physics and electronics.