A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

Handle URI:
http://hdl.handle.net/10754/597373
Title:
A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media
Authors:
Duru, Kenneth ( 0000-0002-5260-7942 )
Abstract:
A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.
Citation:
Duru K (2014) A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media. Journal of Computational Physics 257: 757–781. Available: http://dx.doi.org/10.1016/j.jcp.2013.10.022.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Jan-2014
DOI:
10.1016/j.jcp.2013.10.022
Type:
Article
ISSN:
0021-9991
Sponsors:
This project was completed during the author's postdoctoral program at the Geophysics Department, Stanford University, California. The author acknowledges the support from Eric M. Dunham. This work was supported by King Abdullah University of Science and Technology (KAUST) through a joint KAUST Academic Excellence Alliance (AEA) grant with Stanford.
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Full metadata record

DC FieldValue Language
dc.contributor.authorDuru, Kennethen
dc.date.accessioned2016-02-25T12:31:52Zen
dc.date.available2016-02-25T12:31:52Zen
dc.date.issued2014-01en
dc.identifier.citationDuru K (2014) A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media. Journal of Computational Physics 257: 757–781. Available: http://dx.doi.org/10.1016/j.jcp.2013.10.022.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2013.10.022en
dc.identifier.urihttp://hdl.handle.net/10754/597373en
dc.description.abstractA mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.en
dc.description.sponsorshipThis project was completed during the author's postdoctoral program at the Geophysics Department, Stanford University, California. The author acknowledges the support from Eric M. Dunham. This work was supported by King Abdullah University of Science and Technology (KAUST) through a joint KAUST Academic Excellence Alliance (AEA) grant with Stanford.en
dc.publisherElsevier BVen
dc.subjectGuided wavesen
dc.subjectHigh order accuracyen
dc.subjectInterface wavesen
dc.subjectPerfectly matched layeren
dc.subjectReflected wavesen
dc.subjectRefracted wavesen
dc.subjectSBP-SATen
dc.subjectStabilityen
dc.subjectSurface wavesen
dc.titleA perfectly matched layer for the time-dependent wave equation in heterogeneous and layered mediaen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
kaust.grant.programAcademic Excellence Alliance (AEA)en
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