Discontinuous Galerkin Time-Domain solution of Maxwell's equations on locally-refined grids with fictitious domains

The use of the prominent FDTD method for the time-domain scattering of electromagnetic waves by devices with small geometrical details can require very fine grids and lead to unmanageable computational time and storage. We propose an extension of a Discontinuous Galerkin Time-Domain (DGTD) method to locally-refined, possibly non-conforming meshes, coupled to a fictitious domain approach. The DGTD method we use is set on block-structured grids of orthogonal elements and is based on centered flux approximations for surface integrals and a second-order leap-frog scheme for advancing in time. The stability of the method has been analyzed previously, it is proved that a discrete electromagnetic energy is exactly preserved. The dispersion analysis is completed in this paper. Also, new features of the method are introduced herein: the use of PML regions in a DG context has been detailed, and a first step towards the coupling with a fictitious domain approach has been done, leading to very promising preliminary numerical results