Computing quantities of interest for random domains with second order shape sensitivity analysis
Revised: 9 February 2015
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.
Mathematics Subject Classification: 60G35 / 65N75 / 65N99
Key words: Random domain / second order shape sensitivity / low-rank approximation
© EDP Sciences, SMAI 2015