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

共 50 条

[1] POLYNOMIAL CHAOS EXPANSIONS FOR STIFF RANDOM ODEs
Shi, Wenjie
Tartakovsky, Daniel M.
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2022, 44 (03): : A1021 - A1046
[2] Polynomial chaos expansions for dependent random variables
Jakeman, John D.
Franzelin, Fabian
Narayan, Akil
Eldred, Michael
Plfueger, Dirk
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2019, 351 : 643 - 666
[3] Generalized polynomial chaos expansions for the random fractional Bateman equations
Jornet, Marc
APPLIED MATHEMATICS AND COMPUTATION, 2024, 479
[4] Polynomial chaos expansions for optimal control of nonlinear random oscillators
Peng, Yong-Bo
Ghanem, Roger
Li, Jie
JOURNAL OF SOUND AND VIBRATION, 2010, 329 (18) : 3660 - 3678
[5] PARAMETRIZATION OF RANDOM VECTORS IN POLYNOMIAL CHAOS EXPANSIONS VIA OPTIMAL TRANSPORTATION
Stavropoulou, Faidra
Mueller, Johannes
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2015, 37 (06): : A2535 - A2557
[6] Application of Conditional Random Fields and Sparse Polynomial Chaos Expansions to Geotechnical Problems
Schobi, Roland
Sudret, Bruno
GEOTECHNICAL SAFETY AND RISK V, 2015, : 445 - 450
[7] Adaptive polynomial chaos expansions applied to statistics of extremes in nonlinear random vibration
Li, R
Ghanem, R
PROBABILISTIC ENGINEERING MECHANICS, 1998, 13 (02) : 125 - 136
[8] GENERALIZED POLYNOMIAL CHAOS EXPANSIONS WITH WEIGHTS
Obermaier, Josef
Stavropoulou, Faidra
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2015, 18 (01) : 30 - 45
[9] Computing Invariant Sets of Random Differential Equations Using Polynomial Chaos
Breden, Maxime
Kuehn, Christian
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2020, 19 (01): : 577 - 618
[10] ON THE CONVERGENCE OF GENERALIZED POLYNOMIAL CHAOS EXPANSIONS
Ernst, Oliver G.
Mugler, Antje
Starkloff, Hans-Joerg
Ullmann, Elisabeth
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2012, 46 (02) : 317 - 339

← 1 2 3 4 5 →