On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids

Handle URI:
http://hdl.handle.net/10754/626096
Title:
On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids
Authors:
Gao, Longfei; Ketcheson, David I. ( 0000-0002-1212-126X ) ; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
We consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Gao L, Ketcheson D, Keyes D (2017) On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids. Geophysical Journal International. Available: http://dx.doi.org/10.1093/gji/ggx470.
Publisher:
Oxford University Press (OUP)
Journal:
Geophysical Journal International
KAUST Grant Number:
CCF/CAF/URF/1/2596
Issue Date:
26-Oct-2017
DOI:
10.1093/gji/ggx470
Type:
Article
ISSN:
0956-540X; 1365-246X
Sponsors:
The authors acknowledge the support of the King Abdullah University of Science and Technology through the project CCF/CAF/URF/1/2596.
Additional Links:
https://academic.oup.com/gji/article/doi/10.1093/gji/ggx470/4569081
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGao, Longfeien
dc.contributor.authorKetcheson, David I.en
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2017-11-02T09:09:33Z-
dc.date.available2017-11-02T09:09:33Z-
dc.date.issued2017-10-26en
dc.identifier.citationGao L, Ketcheson D, Keyes D (2017) On Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Grids. Geophysical Journal International. Available: http://dx.doi.org/10.1093/gji/ggx470.en
dc.identifier.issn0956-540Xen
dc.identifier.issn1365-246Xen
dc.identifier.doi10.1093/gji/ggx470en
dc.identifier.urihttp://hdl.handle.net/10754/626096-
dc.description.abstractWe consider the long-time instability issue associated with finite difference simulation of seismic acoustic wave equations on discontinuous grids. This issue is exhibited by a prototype algebraic problem abstracted from practical application settings. Analysis of this algebraic problem leads to better understanding of the cause of the instability and provides guidance for its treatment. Specifically, we use the concept of discrete energy to derive the proper solution transfer operators and design an effective way to damp the unstable solution modes. Our investigation shows that the interpolation operators need to be matched with their companion restriction operators in order to properly couple the coarse and fine grids. Moreover, to provide effective damping, specially designed diffusive terms are introduced to the equations at designated locations and discretized with specially designed schemes. These techniques are applied to simulations in practical settings and are shown to lead to superior results in terms of both stability and accuracy.en
dc.description.sponsorshipThe authors acknowledge the support of the King Abdullah University of Science and Technology through the project CCF/CAF/URF/1/2596.en
dc.publisherOxford University Press (OUP)en
dc.relation.urlhttps://academic.oup.com/gji/article/doi/10.1093/gji/ggx470/4569081en
dc.rightsThis is a pre-copyedited, author-produced PDF of an article accepted for publication in Geophysical Journal International following peer review. The version of record is available online at: https://academic.oup.com/gji/article/doi/10.1093/gji/ggx470/4569081.en
dc.titleOn Long-Time Instabilities in Staggered Finite Difference Simulations of the Seismic Acoustic Wave Equations on Discontinuous Gridsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalGeophysical Journal Internationalen
dc.eprint.versionPost-printen
kaust.authorGao, Longfeien
kaust.authorKetcheson, David I.en
kaust.authorKeyes, David E.en
kaust.grant.numberCCF/CAF/URF/1/2596en
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