Uncertainty Quantification for the BGK Model of the Boltzmann Equation Using Multilevel Variance Reduced Monte Carlo Methods

被引：7
|
作者：
Hu, Jingwei [1 ]
Pareschi, Lorenzo [2 ]
Wang, Yubo [1 ]
机构：
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[2] Univ Ferrara, Dept Math & Comp Sci, Via Machiavelli 30, I-44121 Ferrara, Italy
来源：
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION | 2021年 / 9卷 / 02期
关键词：
kinetic equation; BGK model; multilevel Monte Carlo method; control variate method; uncertainty quantification; random inputs; IMPLICIT-EXPLICIT SCHEMES; CONSERVATION-LAWS; PROPAGATION; SYSTEMS;
D O I：
10.1137/20M1331846
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We propose a control variate multilevel Monte Carlo method for the kinetic Bhatnagar-Gross-Krook model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carlo technique with the computation of the optimal control variate multipliers derived from local or global variance minimization problems. Consistency and convergence analysis for the method equipped with a second-order positivity-preserving and asymptotic-preserving scheme in space and time is also performed. Various numerical examples confirm that the optimized multilevel Monte Carlo method outperforms the classical multilevel Monte Carlo method especially for problems with discontinuities.
引用
收藏
页码：650 / 680
页数：31
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