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

Abstract

We study the stability properties of, and the phase error present in, a nite element scheme for Maxwell's equations coupled with Debye or Lorentz polarization. In one dimension we consider a second order formulation for the electric eld with an ordinary di erential equation for the polarization added as an auxiliary constraint. The nite element method uses linear nite elements in space for the electric eld as well as the 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 nite di erence methods that have been analyzed in the literature. We also conduct numerical simulations that verify the stability and dispersion properties of the scheme.

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Document Details

Document Type
Technical Report
Publication Date
Aug 22, 2006
Accession Number
ADA455630

Entities

People

  • H. Thomas Banks
  • N. L. Gibson
  • V. A. Bokil

Organizations

  • North Carolina State University

Tags

Communities of Interest

  • Advanced Electronics
  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Composite Materials
  • Detection
  • Dielectric Permittivity
  • Dielectric Properties
  • Dielectrics
  • Differential Equations
  • Dispersion Relations
  • Dispersions
  • Electric Fields
  • Electrical Properties
  • Electromagnetic Fields
  • Equations
  • Finite Element Analysis
  • Frequency
  • Magnetic Fields
  • Materials
  • Relaxation Time

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Distributed Systems and Data Platform Development
  • Plasma Physics / Magnetohydrodynamics

Technology Areas

  • Space