Uncertainty quantification for the BGK model of the Boltzmann equation using multilevel variance reduced Monte Carlo methods

We propose a control variate multilevel Monte Carlo method for the kinetic BGK 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 minimi...

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Bibliographic Details
Published inarXiv.org
Main Authors Hu, Jingwei, Pareschi, Lorenzo, Wang, Yubo
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.04.2020
Subjects
Asymptotic methods
BGK model
Boltzmann transport equation
Computer simulation
Control methods
Mathematical analysis
Monte Carlo simulation
Multilevel
Optimal control
Optimization
Variance
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ISSN2331-8422

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Summary:We propose a control variate multilevel Monte Carlo method for the kinetic BGK 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.
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ISSN:2331-8422