A Discontinuous Galerkin Time-Domain Method with Dynamically Adaptive Cartesian Meshes for Computational Electromagnetics

TL;DR

This paper introduces a discontinuous Galerkin time-domain method using adaptive Cartesian meshes for efficient and accurate electromagnetic simulations in complex dispersive media, with dynamic mesh refinement and local time-stepping.

Contribution

The novel DGTD-ACM method combines adaptive Cartesian meshes with dynamic refinement and local time-stepping for improved accuracy and efficiency in electromagnetic simulations.

Findings

Achieves high accuracy with reduced computational cost.

Effectively resolves material interfaces and local field variations.

Demonstrates good performance in diffraction and dispersive media simulations.

Abstract

A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close to that of structured grids and the flexibility of unstructured grids while being highly suited for adaptive mesh refinement (AMR). The developed DGTD-ACM achieves a desired accuracy by refining non-conformal meshes near material interfaces to reduce stair-casing errors without sacrificing the high efficiency afforded with uniform Cartesian meshes. Moreover, DGTD-ACM can dynamically refine the mesh to resolve the local variation of the fields during propagation of electromagnetic 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. Simulations of electromagnetic wave diffraction over conducting and dielectric cylinders and spheres demonstrate that the proposed method can achieve a good numerical accuracy at a reduced computational cost compared with uniform meshes. For simulations of dispersive media, the auxiliary differential equation (ADE) and recursive convolution (RC) methods are implemented for a local Drude model and tested for a cold plasma slab and a plasmonic rod. With further advances of the charge transport models, the DGTD-ACM method is expected to provide a powerful tool for computations of electromagnetic fields in complex geometries for applications to high-frequency electronic devices, plasmonic THz technologies, as well as laser-induced and microwave plasmas.