Exact weight cancellation in Monte Carlo eigenvalue transport problems,Physical Review E

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Exact weight cancellation in Monte Carlo eigenvalue transport problems
Physical Review E ( IF 2.2 ) Pub Date : 2021-07-16 , DOI: 10.1103/physreve.104.015306
Hunter Belanger ₁ , Davide Mancusi ₁ , Andrea Zoia ₁

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Random walks are frequently used as a model for very diverse physical phenomena. The Monte Carlo method is a versatile tool for the study of the properties of systems modeled as random walks. Often, each walker is associated with a statistical weight, used in the estimation of observable quantities. Weights are typically assumed to be positive; nonetheless, some applications require the use of positive and negative weights or complex weights and often pose particular challenges with convergence. In this paper we examine such a case from the field of nuclear reactor physics, where the negative particle weights prevent the power iteration algorithm from converging on the sought fundamental eigenstate of the Boltzmann transport equation. We demonstrate how the use of weight cancellation allows convergence on the physical eigenstate. To this end, we develop a method to perform weight cancellation in an exact manner, in three spatial dimensions. The viability of this algorithm is then demonstrated on a reactor physics problem.

中文翻译：

蒙特卡罗特征值传输问题中的精确重量抵消

随机游走经常被用作非常多样化的物理现象的模型。Monte Carlo 方法是一种通用工具，用于研究建模为随机游走的系统的特性。通常，每个步行者都与一个统计权重相关联，用于估计可观察量。权重通常被假定为正数；尽管如此，一些应用程序需要使用正负权重或复杂权重，并且经常对收敛提出特殊挑战。在本文中，我们研究了核反应堆物理学领域的这种情况，其中负粒子权重阻止幂迭代算法收敛于所寻求的玻尔兹曼传输方程的基本本征态。我们演示了如何使用权重抵消来实现物理本征态的收敛。为此，我们开发了一种方法，可以在三个空间维度上以精确的方式进行减重。然后在反应堆物理问题上证明了该算法的可行性。

更新日期：2021-07-16

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