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A Sparse Stochastic Collocation Technique for High Frequency Wave Propagation with Uncertainty

Bibliography:

Gabriela Malenova, Mohammad Motamed, Olof Runborg, Raul Tempone, A Sparse Stochastic Collocation Technique for High Frequency Wave Propagation with Uncertaintyaccepted for publication in Journal on Uncertainty Quantification, May 2016

Authors:

Gabriela Malenova, Mohammad Motamed, Olof Runborg, Raul Tempone

Keywords:

A Sparse Stochastic Collocation Technique for High Frequency Wave Propagation with Uncertainty

Year:

2016

Abstract:

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 space, we show theoretical arguments and numerical evidence that quantities of interest based on local averages of |uε|2 are smooth, with derivatives in stochastic space uniformly bounded in frequency. The stochastic regularity makes the sparse stochastic collocation approach more efficient than Monte Carlo methods. We show numerical tests that demonstrate this advantage.

ISSN:

2016