Analysis and computation of the elastic wave equation with random coefficients

Handle URI:
http://hdl.handle.net/10754/622172
Title:
Analysis and computation of the elastic wave equation with random coefficients
Authors:
Motamed, Mohammad; Nobile, Fabio; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
We consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest. We study the convergence rate of the error in the stochastic collocation method. In particular, we show that, the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space, which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest. We demonstrate that a fast rate of convergence is possible in two cases: for the elastic wave solutions with high regular data; and for some high regular quantities of interest even in the presence of low regular data. We perform numerical examples, including a simplified earthquake, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo sampling method for approximating quantities with high stochastic regularity.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program
Citation:
Motamed M, Nobile F, Tempone R (2015) Analysis and computation of the elastic wave equation with random coefficients. Computers & Mathematics with Applications 70: 2454–2473. Available: http://dx.doi.org/10.1016/j.camwa.2015.09.013.
Publisher:
Elsevier BV
Journal:
Computers & Mathematics with Applications
Issue Date:
21-Oct-2015
DOI:
10.1016/j.camwa.2015.09.013
Type:
Article
ISSN:
0898-1221
Sponsors:
The authors would like to recognize the support of the PECOS center at ICES, University of Texas at Austin (Project Number 024550, Center for Predictive Computational Science). Support from the VR project "Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar" and King Abdullah University of Science and Technology (KAUST) AEA project "Bayesian earthquake source validation for ground motion simulation" is also acknowledged. The third author is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. The second author has been supported by the Italian grant FIRB-IDEAS (Project n. RBID08223Z) "Advanced numerical techniques for uncertainty quantification in engineering and life science problems".
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorMotamed, Mohammaden
dc.contributor.authorNobile, Fabioen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2017-01-02T08:42:35Z-
dc.date.available2017-01-02T08:42:35Z-
dc.date.issued2015-10-21en
dc.identifier.citationMotamed M, Nobile F, Tempone R (2015) Analysis and computation of the elastic wave equation with random coefficients. Computers & Mathematics with Applications 70: 2454–2473. Available: http://dx.doi.org/10.1016/j.camwa.2015.09.013.en
dc.identifier.issn0898-1221en
dc.identifier.doi10.1016/j.camwa.2015.09.013en
dc.identifier.urihttp://hdl.handle.net/10754/622172-
dc.description.abstractWe consider the stochastic initial-boundary value problem for the elastic wave equation with random coefficients and deterministic data. We propose a stochastic collocation method for computing statistical moments of the solution or statistics of some given quantities of interest. We study the convergence rate of the error in the stochastic collocation method. In particular, we show that, the rate of convergence depends on the regularity of the solution or the quantity of interest in the stochastic space, which is in turn related to the regularity of the deterministic data in the physical space and the type of the quantity of interest. We demonstrate that a fast rate of convergence is possible in two cases: for the elastic wave solutions with high regular data; and for some high regular quantities of interest even in the presence of low regular data. We perform numerical examples, including a simplified earthquake, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo sampling method for approximating quantities with high stochastic regularity.en
dc.description.sponsorshipThe authors would like to recognize the support of the PECOS center at ICES, University of Texas at Austin (Project Number 024550, Center for Predictive Computational Science). Support from the VR project "Effektiva numeriska metoder for stokastiska differentialekvationer med tillampningar" and King Abdullah University of Science and Technology (KAUST) AEA project "Bayesian earthquake source validation for ground motion simulation" is also acknowledged. The third author is a member of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering. The second author has been supported by the Italian grant FIRB-IDEAS (Project n. RBID08223Z) "Advanced numerical techniques for uncertainty quantification in engineering and life science problems".en
dc.publisherElsevier BVen
dc.subjectCollocation methoden
dc.subjectElastic wave equationen
dc.subjectError analysisen
dc.subjectStochastic partial differential equationsen
dc.subjectUncertainty quantificationen
dc.titleAnalysis and computation of the elastic wave equation with random coefficientsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalComputers & Mathematics with Applicationsen
dc.contributor.institutionDepartment of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM 87131, USAen
dc.contributor.institutionMATHICSE-CSQI, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerlanden
kaust.authorTempone, Raulen
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