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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Basel, Spiegelgasse 1, 4051, Basel, Switzerland

    Daniel H. Baffet & Marcus J. Grote

  2. Inria — LMS, Ecole Polytechnique, CNRS — Institut Polytechnique de Paris, 1 rue Honoré d’Estienne d’Orves, 91120, Palaiseau, France

    Sébastien Imperiale

  3. POEMS (UMR 7231 CNRS, ENSTA, INRIA), INRIA, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, 91120, Palaiseau, France

    Maryna Kachanovska

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  1. Daniel H. Baffet
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  2. Marcus J. Grote
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  4. Maryna Kachanovska
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Correspondence to Daniel H. Baffet.

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Baffet, D.H., Grote, M.J., Imperiale, S. et al. Energy Decay and Stability of a Perfectly Matched Layer For the Wave Equation. J Sci Comput 81, 2237–2270 (2019). https://doi.org/10.1007/s10915-019-01089-9

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  • DOI: https://doi.org/10.1007/s10915-019-01089-9

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