Description of random level sets by polynomial chaos expansions
Probability
2023-05-10 v3 Numerical Analysis
Numerical Analysis
Abstract
We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the level-set equations. A novel intrusive Galerkin formulation is presented and proven hyperbolic. It induces a corresponding finite-volume scheme that is specifically taylored for uncertain velocities.
Keywords
Cite
@article{arxiv.2110.08065,
title = {Description of random level sets by polynomial chaos expansions},
author = {Markus Bambach and Stephan Gerster and Michael Herty and Aleksey Sikstel},
journal= {arXiv preprint arXiv:2110.08065},
year = {2023}
}