DESCRIPTION OF RANDOM LEVEL SETS BY POLYNOMIAL CHAOS EXPANSIONS

被引：0
|
作者：
Bambach, Markus [1 ]
Gerster, Stephan [2 ]
Herty, Michael [3 ]
Sikstel, Aleksey [4 ]
机构：
[1] Swiss Fed Inst Technol, Adv Mfg Lab, CH-8005 Zurich, Switzerland
[2] Johannes Gutenberg Univ Mainz, Inst Math, D-55122 Mainz, Germany
[3] RWTH Aachen Univ Technol, Inst Geometrie & Prakt Math, D-52056 Aachen, Germany
[4] Tech Univ Darmstadt, Dept Math, D-64289 Darmstadt, Germany
来源：
COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2024年 / 22卷 / 01期
关键词：
Level sets; uncertainty quantification; Hamilton-Jacobi equations; hyperbolic conser-vation laws; stochastic Galerkin; finite-volume method; HAMILTON-JACOBI EQUATIONS; STOCHASTIC GALERKIN METHOD; CONSERVATION-LAWS; VISCOSITY SOLUTIONS; SYSTEMS; PROPAGATION; IMAGES;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a novel approach to determine the evolution of level sets under uncertainties in their velocity fields. This leads to a stochastic description of level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the equations for the propagation of level sets. A novel intrusive Galerkin formulation is presented and proven to be hyperbolic. It induces a corresponding finite-volume scheme that is specifically tailored to uncertain velocities.
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页码：95 / 112
页数：18
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