| Issue |
ESAIM: M2AN
Volume 60, Number 4, July-August 2026
|
|
|---|---|---|
| Page(s) | 1715 - 1739 | |
| DOI | https://doi.org/10.1051/m2an/2026047 | |
| Published online | 03 August 2026 | |
A separable and asymptotic-preserving dynamical low-rank method for the Vlasov–Poisson–Fokker–Planck system
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
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Received:
16
January
2026
Revised:
2
May
2026
Accepted:
13
May
2026
Abstract
We present a dynamical low-rank (DLR) method for the Vlasov–Poisson–Fokker–Planck (VPFP) system. Our main contributions are twofold: (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.
Mathematics Subject Classification: 35Q83 / 35Q84 / 65F30 / 65M06 / 65M12
Key words: Vlasov–Poisson–Fokker–Planck (VPFP) / dynamical low-rank (DLR) / projector-splitting / asymptotic-preserving (AP) / IMEX time integration
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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