论文标题
带有Krylov线性求解器的准蒙特卡洛法，用于多群中子传输模拟
A Quasi-Monte Carlo Method with Krylov Linear Solvers for Multigroup Neutron Transport Simulations
论文作者
论文摘要
在这项工作中，我们研究了用固定播种的准蒙特卡罗计算代替确定性线性求解器中使用的标准正交技术，以获取对中子传输方程（NTE）的更准确，有效的溶液。准蒙特卡罗（QMC）是使用低静止序列来对传统蒙特卡洛（MC）使用的伪随机数发电机进行采样。 QMC技术降低了随机运输扫描的方差，因此提高了迭代方法的准确性。从历史上看，QMC在很大程度上被粒子运输群落忽略了，因为它打破了模拟模拟MC粒子模拟中散射所需的马尔可夫假设。但是，通过使用迭代方法，可以将NTE建模为纯吸收问题。这消除了明确模型粒子散射的需求，并提供了适合QMC的应用程序。为了获得解决方案，我们对三个独立的迭代求解器进行了实验：标准源迭代（SI）和两个线性Krylov求解器，GMRES和BICGSTAB。评估了所得的混合迭代QMC（IQMC）求解器，以三个一维板几何问题进行评估。在每个样本问题中，Krylov求解器以比源迭代更少的迭代（最高8倍）获得收敛。无论使用哪种线性求解器，与预期的$ O（N^{ - 1}）$的近似收敛速率相比，与所有测试问题相比，传统MC模拟的预期$ O（N^{ - 1/2}）$相比。
In this work we investigate replacing standard quadrature techniques used in deterministic linear solvers with a fixed-seed Quasi-Monte Carlo calculation to obtain more accurate and efficient solutions to the neutron transport equation (NTE). Quasi-Monte Carlo (QMC) is the use of low-discrepancy sequences to sample the phase space in place of pseudo-random number generators used by traditional Monte Carlo (MC). QMC techniques decrease the variance in the stochastic transport sweep and therefore increase the accuracy of the iterative method. Historically, QMC has largely been ignored by the particle transport community because it breaks the Markovian assumption needed to model scattering in analog MC particle simulations. However, by using iterative methods the NTE can be modeled as a pure-absorption problem. This removes the need to explicitly model particle scattering and provides an application well-suited for QMC. To obtain solutions we experimented with three separate iterative solvers: the standard Source Iteration (SI) and two linear Krylov Solvers, GMRES and BiCGSTAB. The resulting hybrid iterative-QMC (iQMC) solver was assessed on three one-dimensional slab geometry problems. In each sample problem the Krylov Solvers achieve convergence with far fewer iterations (up to 8x) than the Source Iteration. Regardless of the linear solver used, the hybrid method achieved an approximate convergence rate of $O(N^{-1})$, as compared to the expected $O(N^{-1/2})$ of traditional MC simulation, across all test problems.
