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dc.contributor.authorMalenova, G.
dc.contributor.authorMotamed, M.
dc.contributor.authorRunborg, O.
dc.contributor.authorTempone, Raul
dc.date.accessioned2017-11-23T11:51:28Z
dc.date.available2017-11-23T11:51:28Z
dc.date.issued2016-09-08
dc.identifier.citationMalenova G, Motamed M, Runborg O, Tempone R (2016) A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty. SIAM/ASA Journal on Uncertainty Quantification 4: 1084–1110. Available: http://dx.doi.org/10.1137/15M1029230.
dc.identifier.issn2166-2525
dc.identifier.doi10.1137/15M1029230
dc.identifier.urihttp://hdl.handle.net/10754/626193
dc.description.abstractWe consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase, and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we combine a high-frequency method based on Gaussian beams with sparse stochastic collocation. Although the wave solution, uϵ, is highly oscillatory in both physical and stochastic spaces, we provide theoretical arguments for simplified problems and numerical evidence that quantities of interest based on local averages of |uϵ|2 are smooth, with derivatives in the stochastic space uniformly bounded in ϵ, where ϵ denotes the short wavelength. This observable related regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We present numerical tests that demonstrate this advantage.
dc.description.sponsorshipThe work of the first author was partially supported by the Swedish Research Council under grant 2012-3808. The work of the fourth author was supported by the King Abdullah University of Science and Technology (KAUST) SRI Center for Uncertainty Quantification in Computational Science and Engineering.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/15M1029230
dc.rightsArchived with thanks to SIAM/ASA Journal on Uncertainty Quantification
dc.subjectAsymptotic approximation
dc.subjectGaussian beam summation
dc.subjectHigh frequency
dc.subjectSparse grids
dc.subjectStochastic collocation
dc.subjectStochastic regularity
dc.subjectUncertainty quantification
dc.subjectWave propagation
dc.titleA Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalSIAM/ASA Journal on Uncertainty Quantification
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionDepartment of Mathematics and Swedish E-Science Research Center (SeRC), KTH, Stockholm, 100 44, , Sweden
dc.contributor.institutionDepartment of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, 87131, , United States
dc.identifier.arxividarXiv:1507.05508
kaust.personTempone, Raul
refterms.dateFOA2018-06-13T14:19:57Z
dc.date.published-online2016-09-08
dc.date.published-print2016-01


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