Geodesic
Computing quantities of interest for random domains with second order shape sensitivity analysis
Dambrine, Marc1  ; Harbrecht, Helmut2  ; Puig, Bénédicte1
1 Universitéde Pau et des Pays de l’Adour, 64000 Pau, France.
2 Universität Basel. 
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1285-1302

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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.

Reçu le :
DOI : 10.1051/m2an/2015012
Classification : 60G35, 65N75, 65N99
Keywords: Random domain, second order shape sensitivity, low-rank approximation

Dambrine, Marc 1 ; Harbrecht, Helmut 2 ; Puig, Bénédicte 1

1 Universitéde Pau et des Pays de l’Adour, 64000 Pau, France.
2 Universität Basel.  
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     title = {Computing quantities of interest for random domains with second order shape sensitivity analysis},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
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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

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