Von-Neumann stability analysis of FD-TD methods in complex media

Brigitte Bidégaray-Fesquet (1, 2)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 EDP - Equations aux Dérivées Partielles

The stability analysis of Finite Difference-Time Difference (FD-TD) schemes can be reduced via the von Neumann approach to the study of a sequence of polynomials with coefficients depending on the physical parameters of the medium and the numerical parameters. Such computations are very tedious in 3D since the simplest medium involves 9th degree polynomials. A Computer Algebra environment has been designed to automize such calculations. This technique is demonstrated on schemes for Maxwell-Debye and Maxwell-Lorentz systems.

Domaines: Analyse numérique [math.NA]

Brigitte Bidégaray-Fesquet. Von-Neumann stability analysis of FD-TD methods in complex media. EMF 2006 - 7th International Symposium on Electric and Magnetic Fields -- From Numerical Models to Industrial Applications, Jun 2006, Aussois, France. pp.16: 1-4. ⟨hal-00171506⟩