A Sweep-Based Low-Rank Method for the Discrete Ordinate Transport Equation

@article{Peng2022ASL,
  title={A Sweep-Based Low-Rank Method for the Discrete Ordinate Transport Equation},
  author={Zhuogang Peng and Ryan G. McClarren},
  journal={SSRN Electronic Journal},
  year={2022}
}
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold… 

A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations

TLDR
A predictor-corrector strategy for constructing rank-adaptive, dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems is presented and applied to several versions of DLRA methods found in the literature, as well as a new variant.

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