Description of random level sets by polynomial chaos expansions

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED
Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel
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引用次数: 1

Abstract

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.
用多项式混沌展开描述随机水平集
我们提出了一种新方法来确定水平集在其速度场不确定的情况下的演变。这导致了对水平集的随机描述。为了计算随机水平集的量值,我们使用随机伽勒金方法对水平集传播方程进行双曲重述。我们提出了一种新颖的侵入式 Galerkin 公式,并证明它是双曲的。该方法可产生专门针对不确定速度的相应有限体积方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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