Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

Abstract : In this paper, we are concerned with the numerical modelling of the propagation of electromagnetic waves in dispersive materials for nanophotonics applications. We focus on a generalized model that allows for the description of a wide range of dispersive media. The underlying differential equations are recast into a generic form, and we establish an existence and uniqueness result. We then turn to the numerical treatment and propose an appropriate discontinuous Galerkin time domain framework. We obtain the semidiscrete convergence and prove the stability (and to a larger extent, convergence) of a Runge--Kutta 4 fully discrete scheme via a technique relying on energy principles. Finally, we validate our approach through two significant nanophotonics test cases.
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Stephane Lanteri, Claire Scheid, Jonathan Viquerat. Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2017, 39 (3), pp.A831 - A859. ⟨10.1137/15M105207X⟩. ⟨hal-01674031⟩

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