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Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Dispersive Media

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  • We study the stability properties of, and the phase error present in, a finite element scheme for Maxwell’s equations coupled with a Debye or Lorentz polarization model. In one dimension we consider a second order formulation for the electric field with an ordinary differential equation for the electric polarization added as an auxiliary constraint. The finite element method uses linear finite elements in space for the electric field as well as the electric polarization, and a theta scheme for the time discretization. Numerical experiments suggest the method is unconditionally stable for both Debye and Lorentz models. We compare the stability and phase error properties of the method presented here with those of finite difference methods that have been analyzed in the literature.We also conduct numerical simulations that verify the stability and dispersion properties of the scheme.
  • This is the pre-peer reviewed version of the following article: H. T. Banks, V. A. Bokil and N. L. Gibson, Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Media, Numerical Methods for Partial Differential Equations, 25(4), pp 885-917, July 2009, which has been published in final form at http://www3.interscience.wiley.com/journal/122341241/issue.
  • Keywords: Debye, dissipation, Lorentz, dispersion, finite elements, FDTD, Maxwell's equations
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  • H. T. Banks, V. A. Bokil and N. L. Gibson, Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Media, Numerical Methods for Partial Differential Equations, 25(4), pp 885-917, July 2009
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  • 25
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  • Contract grant sponsor: U.S. Air Force Office of Scientific Research; contract grant number: AFOSR FA9550-04-1-0220 Contract grant sponsor: National Institute of Aerospace (NIA) Contract grant sponsor: NASA; contract grant number: NIA/NCSU-03-01-2536-NC
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