论文标题
使用多级方差降低蒙特卡洛方法的Boltzmann方程BGK模型的不确定性定量
Uncertainty quantification for the BGK model of the Boltzmann equation using multilevel variance reduced Monte Carlo methods
论文作者
论文摘要
我们为玻尔兹曼方程的动力学BGK模型提出了一种控制变量多级蒙特卡洛法，但受随机输入的约束。该方法将多级蒙特卡洛技术与最佳控制变量乘数的计算结合在一起，该乘数从局部或全球方差最小化问题得出。还进行了配备有二阶阳性阳性和渐近保护方案的方法的一致性和收敛分析。各种数值示例证实，优化的多级蒙特卡洛方法的表现优于经典的多级蒙特卡洛法，尤其是对于不连续性问题而言。
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.
