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

Daniel H. Baffet; Marcus J. Grote; Sébastien Imperiale; Maryna Kachanovska

doi:10.1007/s10915-019-01089-9

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

Daniel H. Baffet
, Marcus J. Grote
, Sébastien Imperiale
, Maryna Kachanovska

University of Basel
Department of Mechanics École Polytechnique

Research output: Contribution to journal › Article › peer-review

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 L² 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.

Original language	English
Pages (from-to)	2237-2270
Number of pages	34
Journal	Journal of Scientific Computing
Volume	81
Issue number	3
DOIs	https://doi.org/10.1007/s10915-019-01089-9
Publication status	Published - 1 Dec 2019

Keywords

Numerical stability
Perfectly matched layers
Stability

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title = "Energy Decay and Stability of a Perfectly Matched Layer For the Wave Equation",

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 L2 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.",

keywords = "Numerical stability, Perfectly matched layers, Stability",

author = "Baffet, \{Daniel H.\} and Grote, \{Marcus J.\} and S{\'e}bastien Imperiale and Maryna Kachanovska",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Baffet, Daniel H.

AU - Grote, Marcus J.

AU - Imperiale, Sébastien

AU - Kachanovska, Maryna

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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 L2 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.

AB - 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 L2 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.

KW - Numerical stability

KW - Perfectly matched layers

KW - Stability

U2 - 10.1007/s10915-019-01089-9

DO - 10.1007/s10915-019-01089-9

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JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -

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

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Keywords

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