Computing quantities of interest for random domains with second order shape sensitivity analysis

Dambrine, Marc; Harbrecht, Helmut; Puig, Bénédicte

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1285-1302.

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.

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