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Uncertainty quantification for high frequency waves
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

We consider high frequency waves satisfying the scalar wave equationwith highly oscillatory initial data. The speed of propagation of the mediumas well as the phase and amplitude of the initial data is assumed to beuncertain, described by a finite number of independent random variables withknown probability distributions. We introduce quantities of interest (QoIs)aslocal averages of the squared modulus of the wave solution, or itsderivatives.The regularity of these QoIs in terms of the input random parameters and thewavelength is important for uncertainty quantification methods based oninterpolation in the stochastic space. In particular, the size of thederivativesshould be bounded and independent of the wavelength. In the contributedpapers, we show that the QoIs indeed have this property, despite the highlyoscillatory character of the waves.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. , vii, 25 p.
Series
TRITA-MAT-A, 2016-06
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-186287OAI: oai:DiVA.org:kth-186287DiVA: diva2:926761
Presentation
2016-06-03, L21, Drottning Kristinas väg 30, KTH Campus, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20160510

Available from: 2016-05-11 Created: 2016-05-09 Last updated: 2016-05-20Bibliographically approved
List of papers
1. A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
Open this publication in new window or tab >>A Sparse Stochastic Collocation Technique for High-Frequency Wave Propagation with Uncertainty
(English)In: SIAM/ASA Journal on Uncertainty Quantification, ISSN 1560-7526, E-ISSN 2166-2525Article in journal (Refereed) Submitted
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-186285 (URN)
Note

QC 20160511

Available from: 2016-05-09 Created: 2016-05-09 Last updated: 2017-11-30Bibliographically approved
2. Regularity of Stochastic Observables in Gaussian Beam Superposition of High-Frequency Waves
Open this publication in new window or tab >>Regularity of Stochastic Observables in Gaussian Beam Superposition of High-Frequency Waves
(English)Manuscript (preprint) (Other academic)
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-186286 (URN)
Note

QS 20160509

Available from: 2016-05-09 Created: 2016-05-09 Last updated: 2016-05-11Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • Other locale
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Output format
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