Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations

Brigitte Bidégaray-Fesquet (1)

1 EDP - Equations aux Dérivées Partielles

The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics", IEEE Transactions on Antennas and Propagation, vol. 42, no. 1, pp. 62--69, 1994), where numerical evidence for specific media have been used. We use von Neumann analysis to give necessary and sufficient stability conditions for these schemes for any medium, in accordance with the partial results of [1].

Mots clés: Stability analysis; Maxwell-Debye; Maxwell-Lorentz

Domaines: Analyse numérique [math.NA]

Brigitte Bidégaray-Fesquet. Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations. SIAM Journal on Numerical Analysis, 2008, 46 (5), pp.2551-2566. ⟨10.1137/060671255⟩. ⟨hal-00005368⟩