A low-rank power iteration scheme for neutron transport criticality problems

TL;DR

This paper introduces a low-rank power iteration method using dynamical low-rank approximation to efficiently compute eigenvalues in neutron transport problems, reducing memory usage while maintaining convergence speed.

Contribution

The paper develops a novel low-rank power iteration scheme based on DLRA for neutron transport eigenvalue problems, improving efficiency and memory requirements.

Findings

Significant reduction in memory usage demonstrated in numerical experiments.

Method retains convergence speed of classical inverse power iteration.

Applicable to neutron transport problems with low-rank solution structures.

Abstract

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.