Computing Quantities of Interest for Random Domains with Second Order Shape Sensitivity Analysis

We consider random perturbations of a given domain. The characteristic amplitude of these perturbations is assumed small. We are interested in quantities of interest depending on the random domain through a boundary value problem. We provide asymptotic expansions of the first moments of the distribution of this output function. When the random perturbation has a small rank spectral representation, we give an simple and efficient method to compute the coefficients of these expansions and provide numerical illustrations in order to compare our expansions with Monte Carlo simulations.