# First order second moment analysis for stochastic interface problems based on low-rank approximation

- Volume: 47, Issue: 5, page 1533-1552
- ISSN: 0764-583X

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topHarbrecht, Helmut, and Li, Jingzhi. "First order second moment analysis for stochastic interface problems based on low-rank approximation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.5 (2013): 1533-1552. <http://eudml.org/doc/273178>.

@article{Harbrecht2013,

abstract = {In this paper, 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.},

author = {Harbrecht, Helmut, Li, Jingzhi},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {elliptic interface problem; stochastic interface; low-rank approximation; pivoted Cholesky decomposition; perturbation approach; stochastic elliptic interface problem; error estimates; Monte Carlo method},

language = {eng},

number = {5},

pages = {1533-1552},

publisher = {EDP-Sciences},

title = {First order second moment analysis for stochastic interface problems based on low-rank approximation},

url = {http://eudml.org/doc/273178},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Harbrecht, Helmut

AU - Li, Jingzhi

TI - First order second moment analysis for stochastic interface problems based on low-rank approximation

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 5

SP - 1533

EP - 1552

AB - In this paper, 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.

LA - eng

KW - elliptic interface problem; stochastic interface; low-rank approximation; pivoted Cholesky decomposition; perturbation approach; stochastic elliptic interface problem; error estimates; Monte Carlo method

UR - http://eudml.org/doc/273178

ER -

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