多级混合蒙特卡洛/确定性方法用于粒子输运问题
Multi-Level Hybrid Monte Carlo / Deterministic Methods for Particle Transport Problems
AI总结：
本文提出多级混合输运方法解决中性粒子Boltzmann输运方程，结合多级蒙特卡洛方法和准扩散法，通过空间网格序列递归估计解功能值，实现高效计算。
摘要：
本文提出了多级混合输运（MLHT）方法，用于求解中性粒子Boltzmann输运方程。所提出的MLHT方法基于多级蒙特卡洛（MLMC）方法，在一系列空间网格上进行建模。一般MLMC算法通过递归估计相邻网格解功能值的期望值来定义。MLMC理论优化了在目标精度下估计功能值的总计算成本。所提出的MLHT算法基于准扩散（变量Eddington因子）和二阶矩方法。对于这些方法，低阶方程的角动量角通量被空间离散化。蒙特卡洛技术计算低阶方程的闭合条件；然后求解方程，得到全局通量解的单次实现。实现在所有实现的集合平均值给出该级的解。1-D slab输运问题的结果显示功能的弱收敛性。我们观察到修正因子的方差比生成MLMC样本的计算成本的增长更快。在所考虑的问题中，MLMC解的方差和成本由粗网格计算驱动。
英文摘要：
This paper presents multilevel hybrid transport (MLHT) methods for solving the neutral-particle Boltzmann transport equation. The proposed MLHT methods are formulated on a sequence of spatial grids using a multilevel Monte Carlo (MLMC) approach. The general MLMC algorithm is defined by recursively estimating the expected value of the correction to a solution functional on a neighboring grid. MLMC theory optimizes the total computational cost for estimating a functional to within a target accuracy. The proposed MLHT algorithms are based on the quasidiffusion (variable Eddington factor) and second-moment methods. For these methods, the low-order equations for the angular moments of the angular flux are discretized in space. Monte Carlo techniques compute the closures for the low-order equations; then the equations are solved, yielding a single realization of the global flux solution. The ensemble average of the realizations yields the level solution. The results for 1-D slab transport problems demonstrate weak convergence of the functionals. We observe that the variance of the correction factors decreases faster than the computational cost of generating an MLMC sample increases. In the problems considered, the variance and cost of the MLMC solution are driven by the coarse-grid calculations.
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