Journal of Scientific Computing

, Volume 17, Issue 1–4, pp 405–422 | Cite as

Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics

  • S. Abarbanel
  • D. Gottlieb
  • J. S. Hesthaven


We investigate the long time behavior of two unsplit PML methods for the absorption of electromagnetic waves. Computations indicate that both methods suffer from a temporal instability after the fields reach a quiescent state. The analysis reveals that the source of the instability is the undifferentiated terms of the PML equations and that it is associated with a degeneracy of the quiescent systems of equations. This highlights why the instability occurs in special cases only and suggests a remedy to stabilize the PML by removing the degeneracy. Computational results confirm the stability of the modified equations and is used to address the efficacy of the modified schemes for absorbing waves.

computational electromagnetics PML stability 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • S. Abarbanel
    • 1
  • D. Gottlieb
    • 2
  • J. S. Hesthaven
    • 2
  1. 1.Department of Applied MathematicsTel Aviv UniversityTel AvivIsrael
  2. 2.Division of Applied MathematicsBrown UniversityProvidence

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