We consider random perturbations of a given domain. The characteristic amplitude of these perturbations is assumed to be small. We are interested in quantities of interest which depend on the random domain through a boundary value problem. We derive asymptotic expansions of the first moments of the distribution of this output function. A simple and efficient method is proposed to compute the coefficients of these expansions provided that the random perturbation admits a low-rank spectral representation. By numerical experiments, we compare our expansions with Monte–Carlo simulations.
DOI : 10.1051/m2an/2015012
Mots-clés : Random domain, second order shape sensitivity, low-rank approximation
@article{M2AN_2015__49_5_1285_0, author = {Dambrine, Marc and Harbrecht, Helmut and Puig, B\'en\'edicte}, title = {Computing quantities of interest for random domains with second order shape sensitivity analysis}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1285--1302}, publisher = {EDP-Sciences}, volume = {49}, number = {5}, year = {2015}, doi = {10.1051/m2an/2015012}, zbl = {1351.60062}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2015012/} }
TY - JOUR AU - Dambrine, Marc AU - Harbrecht, Helmut AU - Puig, Bénédicte TI - Computing quantities of interest for random domains with second order shape sensitivity analysis JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1285 EP - 1302 VL - 49 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2015012/ DO - 10.1051/m2an/2015012 LA - en ID - M2AN_2015__49_5_1285_0 ER -
%0 Journal Article %A Dambrine, Marc %A Harbrecht, Helmut %A Puig, Bénédicte %T Computing quantities of interest for random domains with second order shape sensitivity analysis %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1285-1302 %V 49 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2015012/ %R 10.1051/m2an/2015012 %G en %F M2AN_2015__49_5_1285_0
Dambrine, Marc; Harbrecht, Helmut; Puig, Bénédicte. Computing quantities of interest for random domains with second order shape sensitivity analysis. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1285-1302. doi : 10.1051/m2an/2015012. http://archive.numdam.org/articles/10.1051/m2an/2015012/
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