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.

引用

页码：95 / 112

页数：18

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