Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping

Handle URI:
http://hdl.handle.net/10754/599712
Title:
Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping
Authors:
De Basabe, Jonás D.; Sen, Mrinal K.
Abstract:
We investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively. © 2010 The Authors Journal compilation © 2010 RAS.
Citation:
De Basabe JD, Sen MK (2010) Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping. Geophysical Journal International 181: 577–590. Available: http://dx.doi.org/10.1111/j.1365-246X.2010.04536.x.
Publisher:
Oxford University Press (OUP)
Journal:
Geophysical Journal International
Issue Date:
Apr-2010
DOI:
10.1111/j.1365-246X.2010.04536.x
Type:
Article
ISSN:
0956-540X; 1365-246X
Sponsors:
for their valuable feedback, and to Jean Virieux for his careful review. This work was partially supported by an AEA grant from the King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDe Basabe, Jonás D.en
dc.contributor.authorSen, Mrinal K.en
dc.date.accessioned2016-02-28T06:08:06Zen
dc.date.available2016-02-28T06:08:06Zen
dc.date.issued2010-04en
dc.identifier.citationDe Basabe JD, Sen MK (2010) Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping. Geophysical Journal International 181: 577–590. Available: http://dx.doi.org/10.1111/j.1365-246X.2010.04536.x.en
dc.identifier.issn0956-540Xen
dc.identifier.issn1365-246Xen
dc.identifier.doi10.1111/j.1365-246X.2010.04536.xen
dc.identifier.urihttp://hdl.handle.net/10754/599712en
dc.description.abstractWe investigate the stability of some high-order finite element methods, namely the spectral element method and the interior-penalty discontinuous Galerkin method (IP-DGM), for acoustic or elastic wave propagation that have become increasingly popular in the recent past. We consider the Lax-Wendroff method (LWM) for time stepping and show that it allows for a larger time step than the classical leap-frog finite difference method, with higher-order accuracy. In particular the fourth-order LWM allows for a time step 73 per cent larger than that of the leap-frog method; the computational cost is approximately double per time step, but the larger time step partially compensates for this additional cost. Necessary, but not sufficient, stability conditions are given for the mentioned methods for orders up to 10 in space and time. The stability conditions for IP-DGM are approximately 20 and 60 per cent more restrictive than those for SEM in the acoustic and elastic cases, respectively. © 2010 The Authors Journal compilation © 2010 RAS.en
dc.description.sponsorshipfor their valuable feedback, and to Jean Virieux for his careful review. This work was partially supported by an AEA grant from the King Abdullah University of Science and Technology (KAUST).en
dc.publisherOxford University Press (OUP)en
dc.subjectComputational seismologyen
dc.subjectNumerical approximations and analysisen
dc.subjectNumerical solutionsen
dc.subjectWave propagationen
dc.titleStability of the high-order finite elements for acoustic or elastic wave propagation with high-order time steppingen
dc.typeArticleen
dc.identifier.journalGeophysical Journal Internationalen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
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