A sparse stochastic collocation technique for high-frequency wave propagation with uncertainty

G. Malenova, M. Motamed, O. Runborg, R. Tempone

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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, 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.

Original languageEnglish (US)
Pages (from-to)1084-1110
Number of pages27
JournalSIAM-ASA Journal on Uncertainty Quantification
Issue number1
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016 Sharif Rahman.


  • Asymptotic approximation
  • Gaussian beam summation
  • High frequency
  • Sparse grids
  • Stochastic collocation
  • Stochastic regularity
  • Uncertainty quantification
  • Wave propagation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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