  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.
