Description of random level sets by polynomial chaos expansions

Markus Bambach; Stephan Gerster; Michael Herty; Aleksey Sikstel

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arXiv · 2110.08065

Description of random level sets by polynomial chaos expansions

Markus Bambach·Stephan Gerster·Michael Herty·Aleksey Sikstel

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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.

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Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel. 2021-10-15. Description of random level sets by polynomial chaos expansions. https://arxiv.org/abs/2110.08065

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