Open Access
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
  1. A. Arnold, J.A. Carrillo, I. Gamba and C.-W. Shu, Low and high field scaling limits for the Vlasov– and Wigner–Poisson–Fokker–Planck systems. Transp. Theory Stat. Phys. 30 (2001) 121–153. [Google Scholar]
  2. B. Carrel, D. Kressner, H.Y. Lam and B. Vandereycken, Interpolatory dynamical low-rank approximation: theoretical foundations and algorithms. Preprint arXiv:2510.19518 (2025). [Google Scholar]
  3. J.A. Carrillo, L. Wang, W. Xu and M. Yan, Variational asymptotic preserving scheme for the Vlasov–Poisson–Fokker–Planck system. Multiscale Model. Simul. 19 (2021) 478–505. [Google Scholar]
  4. C. Cercignani, I.M. Gamba, J.W. Jerome and C.-W. Shu, Device benchmark comparisons via kinetic, hydrodynamic, and high-field models. Comput. Methods Appl. Mech. Engrg. 181 (2000) 381–392. [Google Scholar]
  5. G. Ceruti, J. Kusch and C. Lubich, A rank-adaptive robust integrator for dynamical low-rank approximation. BIT Numer. Math. 62 (2022) 1149–1174. [CrossRef] [Google Scholar]
  6. G. Ceruti and C. Lubich, An unconventional robust integrator for dynamical low-rank approximation. BIT Numer. Math. 62 (2022) 23–44. [CrossRef] [Google Scholar]
  7. J. Coughlin and J. Hu, Efficient dynamical low-rank approximation for the Vlasov-Ampére-Fokker-Planck system. J. Comput. Phys. 470 (2022) 111590. [Google Scholar]
  8. A. Dektor and L. Einkemmer, Interpolatory dynamical low-rank approximation for the 3 + 3d Boltzmann–BGK equation. J. Comput. Phys. 547 (2026) 114515. [Google Scholar]
  9. Z. Ding, L. Einkemmer and Q. Li, Dynamical low-rank integrator for the linear Boltzmann equation: error analysis in the diffusion limit. SIAM J. Numer. Anal. 59 (2021) 2254–2285. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.P. Dougherty, Model Fokker-Planck equation for a plasma and its solution. Phys. Fluids 7 (1964) 1788–1799. [Google Scholar]
  11. L. Einkemmer, J. Hu and J. Kusch, Asymptotic-preserving and energy stable dynamical low-rank approximation. SIAM J. Numer. Anal. 62 (2024) 73–92. [Google Scholar]
  12. L. Einkemmer, J. Hu and Y. Wang, An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation. J. Comput. Phys. 439 (2021) 110353. [Google Scholar]
  13. L. Einkemmer, J. Hu and S. Zhang, Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation. J. Comput. Phys. 538 (2025) 114112. [Google Scholar]
  14. L. Einkemmer, K. Kormann, J. Kusch, R. McClarren and J.-M. Qiu, A review of low-rank methods for time-dependent kinetic simulations. J. Comput. Phys. 538 (2025) 114191. [Google Scholar]
  15. F. Filbet and S. Jin, A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources. J. Comput. Phys. 229 (2010) 7625–7648. [Google Scholar]
  16. M. Frank, J. Kusch and C. Patwardhan, Asymptotic-preserving and energy stable dynamical low-rank approximation for thermal radiative transfer equations. Multiscale Model Simul. 23 (2025) 278–312. [Google Scholar]
  17. S. Jin, Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21 (1999) 441–454. [Google Scholar]
  18. S. Jin, Asymptotic-preserving schemes for multiscale physical problems. Acta Numer. 31 (2022) 415–489. [Google Scholar]
  19. S. Jin and L. Wang, An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime. Acta Math. Sci. 31 (2011) 2219–2232. [Google Scholar]
  20. S. Jin and B. Yan, A class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation. J. Comput. Phys. 230 (2011) 6420–6437. [Google Scholar]
  21. O. Koch and C. Lubich, Dynamical low-rank approximation. SIAM J. Matrix Anal. Appl. 29 (2007) 434–454. [Google Scholar]
  22. J. Kusch, L. Einkemmer and G. Ceruti, On the stability of robust dynamical low-rank approximations for hyperbolic problems. SIAM J. Sci. Comput. 45 (2023) A1–A24. [Google Scholar]
  23. C. Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis. European Mathematical Society, Zürich (2008). [Google Scholar]
  24. C. Lubich and I.V. Oseledets, A projector-splitting integrator for dynamical low-rank approximation. BIT Numer. Math. 54 (2014) 171–188. [CrossRef] [Google Scholar]
  25. J. Nieto, F. Poupaud and J. Soler, High-field limit for the Vlasov-Poisson-Fokker-Planck system. Arch. Ration. Mech. Anal. 158 (2001) 29–59. [Google Scholar]
  26. F. Poupaud, Runaway phenomena and fluid approximation under high fields in semiconductor kinetic theory. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 72 (1992) 359–372. [Google Scholar]
  27. F. Poupaud and J. Soler, Parabolic limit and stability of the Vlasov–Fokker–Planck system. Math. Models Methods Appl. Sci. 10 (2000) 1027–1045. [Google Scholar]
  28. C. Villani, A review of mathematical topics in collisional kinetic theory. In Handbook of Mathematical Fluid Dynamics, Vol. I. North-Holland (2002) 71–305. [Google Scholar]
  29. S. Zhang and J. Hu, On the stability of the low-rank projector-splitting integrator for hyperbolic and parabolic equations. Preprint arXiv:2507.15192 (2025). [Google Scholar]
  30. S. Jin and Y. Zhu, Hypocoercivity and uniform regularity for the Vlasov–Poisson–Fokker–Planck system with uncertainty and multiple scales. SIAM J. Math. Anal. 50 (2018) 1790–1816. [CrossRef] [MathSciNet] [Google Scholar]

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