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

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 pseudotime 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.

A sweep-based low-rank method for the discrete ordinate transport equation

“…This would give another dimension to potentially compress and potentially give even greater memory savings. Recent work on diffusion-based particle transport problems with multigroup indicates that this could be a fruitful investigation [25].…”