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A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0002-6321-8619
2016 (English)In: SIAM/ASA Journal on Uncertainty Quantification, ISSN 1560-7526, E-ISSN 2166-2525, Vol. 4, no 1, p. 1084-1110Article in journal (Refereed) Published
Abstract [en]

We 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, u(epsilon), 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 |u(epsilon)|(2) are smooth, with derivatives in the stochastic space uniformly bounded in epsilon, where epsilon 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.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2016. Vol. 4, no 1, p. 1084-1110
National Category
Mathematics
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URN: urn:nbn:se:kth:diva-214529DOI: 10.1137/15M1029230ISI: 000407996700042Scopus ID: 2-s2.0-85033578756OAI: oai:DiVA.org:kth-214529DiVA, id: diva2:1145663
Note

QC 20170929

Available from: 2017-09-29 Created: 2017-09-29 Last updated: 2017-11-24Bibliographically approved

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Malenova, GabrielaRunborg, Olof

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