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

Abstract

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.2000MSC: 60G35, 65N75, 65N99.

A rapid and efficient isogeometric design space exploration framework with application to structural mechanics

“…This lends to the notion of a stochastic geometric family which can be used to quantify the impact of tolerances on engineering designs, namely how geometric uncertainties in design propagate through the solution manifold. Similar ideas have been considered in the field of shape uncertainty quantification, on the analysis of random domains, such as those presented in [29,15,22]. Additionally, tools such as compressed sensing shows promise in obtaining coefficients to high-order modes, and consequently an increase in surrogate model fidelity, without incurring additional sampling expense in solution fields which are inherently sparse [20,28].…”

The second order perturbation approach for elliptic partial differential equations on random domains

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