Theoretical and numerical analysis of local dispersion models coupled to a discontinuous Galerkin time-domain method for Maxwell's equations

摘要

This report focuses on a centered-fluxes discontinuous Galerkin method coupled to a second-order Leap-Frog time scheme for the propagation of electromagnetic waves in dispersive media. After a presentation of the physical phenomenon and the classical dispersion models (particularly the Drude one), a generalized dispersive model is introduced. An extit{a priori} stability and convergence study is lead for the Drude model, as well as in the generalized dispersive case. Eventually, numerical results are presented for various test-cases, highlighting the interest of a proper description of the dispersion phenomenon in metals at the nanoscale.