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Second moment analysis for stochastic interface problems based on low-rank
【2014.7.7 9:30am, N602】

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 2014-6-27 

  Colloquia & Seminars 

  Speaker

李景治 副教授,南方科技大学 理学院

  Title

Second moment analysis for stochastic interface problems based on low-rank

  Time

2014.7.7 9:30am                                          

  Venue

N602

  Abstract

In this talk, we propose a numerical method to solve stochastic elliptic interface problems with random interfaces. Shape calculus is first employed to derive the shape-Taylor expansion in the framework of the asymptotic perturbation approach. Given the mean field and the two-point correlation function of the random interface, we can thus quantify the mean field and the variance of the random solution in terms of certain orders of the perturbation amplitude by solving a deterministic elliptic interface problem and its tensorized counterpart with respect to the reference interface. Error estimates are derived for the interface-resolved finite element approximation in both, the physical and the stochastic dimension. In particular, a fast finite difference scheme is proposed to compute the variance of random solutions by using a low-rank approximation based on the pivoted Cholesky decomposition. Numerical experiments are presented to validate and quantify the method.

  Affiliation

 

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