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

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

2005-06-15

arxiv.org/abs/math/0506289v1

SIAM Journal on Numerical Analysis 46, 5 (2008) 2551-2566

Mathematics

Numerical Analysis

Scientific paper

10.1137/060671255

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].

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