A separable and asymptotic-preserving dynamical low-rank method for the Vlasov-Poisson-Fokker-Planck system
Numerical Analysis
2026-05-28 v2 Numerical Analysis
Abstract
We present a dynamical low-rank (DLR) method for the Vlasov-Poisson-Fokker-Planck (VPFP) system. Our main contributions are two-fold: (i) a conservative spatial discretization of the Fokker-Planck operator that factors into velocity-only and space-only components, enabling efficient low-rank projection, and (ii) a time discretization within the DLR framework that properly handles stiff collisions. We propose both first-order and second-order low-rank IMEX schemes. For the first-order scheme, we prove an asymptotic-preserving (AP) property when the field fluctuation is small. Numerical experiments demonstrate accuracy, robustness, and AP property at modest ranks.
Cite
@article{arxiv.2601.11900,
title = {A separable and asymptotic-preserving dynamical low-rank method for the Vlasov-Poisson-Fokker-Planck system},
author = {Shiheng Zhang and Jingwei Hu},
journal= {arXiv preprint arXiv:2601.11900},
year = {2026}
}