Computational Aspects for Interface Identification Problems with Stochastic Modelling
Optimization and Control
2020-02-04 v2
Abstract
In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume coefficients and inputs are subject to uncertainty. The problem is posed as a minimization of the expectation of a random objective functional depending on the uncertain parameters. A numerical method for iteratively solving the problem is presented, which is a generalization of the classical stochastic gradient method in shape spaces. Moreover, we perform numerical experiments, which demonstrate the effectiveness of the algorithm.
Cite
@article{arxiv.1902.01160,
title = {Computational Aspects for Interface Identification Problems with Stochastic Modelling},
author = {Caroline Geiersbach and Estefania Loayza and Kathrin Welker},
journal= {arXiv preprint arXiv:1902.01160},
year = {2020}
}