A Shape calculus approach for time harmonic solid-fluid interaction problem in stochastic domains

TL;DR

This paper develops a shape calculus framework to analyze time harmonic solid-fluid interactions in domains with stochastic boundary perturbations, providing high-accuracy approximations of solution moments.

Contribution

It introduces a shape derivative and Hessian approach for stochastic solid-fluid problems, offering third-order accurate moment approximations.

Findings

Shape derivative and Hessian are derived for stochastic domains.

Moment approximations achieve third-order accuracy.

Analytical example validates theoretical results.

Abstract

The present paper deals with the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. Analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions is provided. Moments of the random solutions are approximated by those of the shape derivative and shape Hessian, and the approximations are of third order accuracy in terms of the size of the boundary perturbation. Our theoretical results are supported by an analytical example on a square domain.