Energy Decay and Stability of a Perfectly Matched Layer For the Wave Equation

  • Daniel H. BaffetEmail author
  • Marcus J. Grote
  • Sébastien Imperiale
  • Maryna Kachanovska


In Grote and Sim (Efficient PML for the wave equation. Preprint, arXiv:1001.0319 [math:NA], 2010; in: Proceedings of the ninth international conference on numerical aspects of wave propagation (WAVES 2009, held in Pau, France, 2009), pp 370–371), a PML formulation was proposed for the wave equation in its standard second-order form. Here, energy decay and \(L^2\) stability bounds in two and three space dimensions are rigorously proved both for continuous and discrete formulations with constant damping coefficients. Numerical results validate the theory.


Perfectly matched layers Stability Numerical stability 



The fourth author acknowledges the partial support of a public Grant as part of the Investissement d’avenir Project, Reference ANR-11-LABX-0056-LMH, LabEx LMH.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Daniel H. Baffet
    • 1
    Email author
  • Marcus J. Grote
    • 1
  • Sébastien Imperiale
    • 2
  • Maryna Kachanovska
    • 3
  1. 1.Department of Mathematics and Computer ScienceUniversity of BaselBaselSwitzerland
  2. 2.Inria — LMS, Ecole Polytechnique, CNRS — Institut Polytechnique de ParisPalaiseauFrance
  3. 3.POEMS (UMR 7231 CNRS, ENSTA, INRIA), INRIA, Institut Polytechnique de ParisPalaiseauFrance

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