论文标题
中子运输临界问题的低级功率迭代方案
A low-rank power iteration scheme for neutron transport criticality problems
论文作者
论文摘要
计算有效的中子运输特征值通常需要精细的数值分辨率。这种计算的主要挑战是经典求解器的高度记忆力，这限制了所选离散化的准确性。在这项工作中，我们得出了一种计算有效特征值的方法时，当基础解决方案具有低级结构时。这是通过利用动力学低级别近似（DLRA）来实现的，这是一种有效的策略，可以得出低级别溶液表示的时间演化方程。主要思想是将经典逆权迭代的迭代解释为伪时间步骤，并将DLRA概念应用于此框架。在我们的数值实验中，我们证明我们的方法在达到所需的准确性的同时大大降低了内存需求。分析研究表明，提出的迭代方案至少在简化的设置中继承了反功率迭代的收敛速度。
Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. The main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.
