Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-02-11T16:36:52.266Z Has data issue: false hasContentIssue false
  • English
  • Français

Perfectly Matched Layer with Mixed Spectral Elements for the Propagation of Linearized Water Waves

Published online by Cambridge University Press:  20 August 2015

Gary Cohen  and
Sébastien Imperiale
Gary Cohen*
Affiliation:
INRIA, Domaine de Voluceau, Rocquencourt-BP 105, 78153 Le Chesnay Cedex, France
Sébastien Imperiale*
Affiliation:
INRIA, Domaine de Voluceau, Rocquencourt-BP 105, 78153 Le Chesnay Cedex, France
*
Email address:[email protected]
Corresponding author.Email:[email protected]
Get access

Abstract

After setting a mixed formulation for the propagation of linearized water waves problem, we define its spectral element approximation. Then, in order to take into account unbounded domains, we construct absorbing perfectly matched layer for the problem. We approximate these perfectly matched layer by mixed spectral elements and show their stability using the “frozen coefficient” technique. Finally, numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions.

Keywords

35J0541.20.cv43.20.HqLinearized water wavesperfectly matched layermixed finite elements
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 285 - 302
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Hammack, J. L., A note on tsunamis: their generation and propagation in an ocean of uniform depth, J. Fluid Mech., 60 (1973), 769–799.Google Scholar
[2]Bérenger, J.-P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114(2) (1994), 185–200.Google Scholar
[3]Cohen, G., Higher Order Numerical Methods for Transient Wave Equations, Springer, 2001.Google Scholar
[4]Cohen, G. and Fauqueux, S., Mixed spectral finite elements for the linear elasticity system in unbounded domains, SIAM J. Sci. Comput., 26(3) (2005), 864–884.Google Scholar
[5]Chew, W. C. and Weedon, W. H., A 3D perfectly matched medium from modified Maxwell equations with stretched coordinates, IEEE Microw. Optic. Tech. Lett., 7(13) (1999), 599–604.Google Scholar
[6]Duruflé, M., Intégration Numérique et Éléments Finis D’ordre Élevé Appliqués auxÉquations de Maxwell en Régime Harmonique, PhD Thesis, Université de Paris IX Dauphine, 2006.Google Scholar
[7]Dgaygui, K. and Joly, P., Absorbing boundary conditions for linear gravity waves, SIAM J. Appl. Math., 54(1) (1994), 93–131.Google Scholar
[8]Becache, E., Fauqueux, S. and Joly, P., Stability of perfeclt matched layers, group velocities and anistropic waves, J. Comput. Phys., 188(2) (2003), 399–433.Google Scholar
[9]Kreiss, H-O. and Lorenz, J., Initial-boundary value problems and the Navier-Stokes equations, Pure Appl. Math., 136 (1989), 403–407.Google Scholar