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dc.contributor.authorMalenova, Gabriela
dc.contributor.authorMotamed, Mohammad
dc.contributor.authorRunborg, Olof
dc.contributor.authorTempone, Raul
dc.date.accessioned2017-06-08T06:32:29Z
dc.date.available2017-06-08T06:32:29Z
dc.date.issued2016-01-06
dc.identifier.urihttp://hdl.handle.net/10754/624837
dc.description.abstractWe consider the forward propagation of uncertainty in high-frequency waves, described by the second order wave equation with highly oscillatory initial data. The main sources of uncertainty are the wave speed and/or the initial phase and amplitude, described by a finite number of random variables with known joint probability distribution. We propose a stochastic spectral asymptotic method [1] for computing the statistics of uncertain output quantities of interest (QoIs), which are often linear or nonlinear functionals of the wave solution and its spatial/temporal derivatives. The numerical scheme combines two techniques: a high-frequency method based on Gaussian beams [2, 3], a sparse stochastic collocation method [4]. The fast spectral convergence of the proposed method depends crucially on the presence of high stochastic regularity of the QoI independent of the wave frequency. In general, the high-frequency wave solutions to parametric hyperbolic equations are highly oscillatory and non-smooth in both physical and stochastic spaces. Consequently, the stochastic regularity of the QoI, which is a functional of the wave solution, may in principle below and depend on frequency. In the present work, we provide theoretical arguments and numerical evidence that physically motivated QoIs based on local averages of |uE|2 are smooth, with derivatives in the stochastic space uniformly bounded in E, where uE and E denote the highly oscillatory wave solution and the short wavelength, respectively. This observable related regularity makes the proposed approach more efficient than current asymptotic approaches based on Monte Carlo sampling techniques.
dc.titleComputation of High-Frequency Waves with Random Uncertainty
dc.typePoster
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.conference.dateJanuary 5-10, 2016
dc.conference.nameAdvances in Uncertainty Quantification Methods, Algorithms and Applications (UQAW 2016)
dc.conference.locationKAUST
dc.contributor.institutionKTH Royal Institute of Technology
dc.contributor.institutionUniversity of New Mexico
kaust.personTempone, Raul
refterms.dateFOA2018-06-13T14:54:11Z


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