Multi-scale control variate methods for uncertainty quantification in kinetic equations

被引：23

作者：

Dimarco, Giacomo ^{[1
]}

Pareschi, Lorenzo ^{[1
]}

机构：

[1] Univ Ferrara, Dept Math & Comp Sci, Via Machiavelli 30, I-44121 Ferrara, Italy

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2019年 / 388卷

关键词：

Uncertainty quantification; Kinetic equations; Monte Carlo methods; Control variate; Multi-scale methods; Multi-fidelity methods; Fluid-dynamic limit; STOCHASTIC COLLOCATION METHOD; BOLTZMANN-EQUATION; GALERKIN METHOD; CONVERGENCE; SCHEMES; EQUILIBRIUM; DIFFUSION; BOUNDS;

D O I：

10.1016/j.jcp.2019.03.002

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries. These uncertainties, however, contribute to the curse of dimensionality and the development of efficient numerical methods is a challenge. In this paper we consider the construction of novel multi-scale methods for such problems which, thanks to a control variate approach, are capable to reduce the variance of standard Monte Carlo techniques. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：63 / 89

页数：27

共 46 条

[1] Uncertainty Quantification in Control Problems for Flocking Models [J].