Stable and high order accurate difference methods for the elastic wave equation in discontinuous media

Handle URI:
http://hdl.handle.net/10754/599717
Title:
Stable and high order accurate difference methods for the elastic wave equation in discontinuous media
Authors:
Duru, Kenneth; Virta, Kristoffer
Abstract:
© 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.
Citation:
Duru K, Virta K (2014) Stable and high order accurate difference methods for the elastic wave equation in discontinuous media. Journal of Computational Physics 279: 37–62. Available: http://dx.doi.org/10.1016/j.jcp.2014.08.046.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Dec-2014
DOI:
10.1016/j.jcp.2014.08.046
Type:
Article
ISSN:
0021-9991
Sponsors:
The work of the first author was supported by King Abdullah University of Science and Technology (KAUST) through a joint KAUST Academic Excellence Alliance (AEA) grant with Stanford. The first author also acknowledges the support of Eric M. Dunham during this work.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDuru, Kennethen
dc.contributor.authorVirta, Kristofferen
dc.date.accessioned2016-02-28T06:08:12Zen
dc.date.available2016-02-28T06:08:12Zen
dc.date.issued2014-12en
dc.identifier.citationDuru K, Virta K (2014) Stable and high order accurate difference methods for the elastic wave equation in discontinuous media. Journal of Computational Physics 279: 37–62. Available: http://dx.doi.org/10.1016/j.jcp.2014.08.046.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2014.08.046en
dc.identifier.urihttp://hdl.handle.net/10754/599717en
dc.description.abstract© 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.en
dc.description.sponsorshipThe work of the first author was supported by King Abdullah University of Science and Technology (KAUST) through a joint KAUST Academic Excellence Alliance (AEA) grant with Stanford. The first author also acknowledges the support of Eric M. Dunham during this work.en
dc.publisherElsevier BVen
dc.subjectElastic wavesen
dc.subjectHigh order accuracyen
dc.subjectInterface wavesen
dc.subjectReflected wavesen
dc.subjectRefracted wavesen
dc.subjectSBP-SATen
dc.subjectTime-stabilityen
dc.subjectWellposednessen
dc.titleStable and high order accurate difference methods for the elastic wave equation in discontinuous mediaen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
dc.contributor.institutionUppsala Universitet, Uppsala, Swedenen
kaust.grant.programAcademic Excellence Alliance (AEA)en
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