Transport based particle methods for the Fokker-Planck-Landau equation

Vasily Ilin, Jingwei Hu, Zhenfu Wang
5/16/2024
math.NAcs.LGmath.AP

No official code found. Best implementation: Vilin97/GradientFlows.jl (0 stars, MIT, last commit 2025-04-03).

Abstract

We propose a particle method for numerically solving the Landau equation, inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation. This method can preserve some important physical properties of the Landau equation, such as the conservation of mass, momentum, and energy, and decay of estimated entropy. We prove that matching the gradient of the logarithm of the approximate solution is enough to recover the true solution to the Landau equation with Maxwellian molecules. Several numerical experiments in low and moderately high dimensions are performed, with particular emphasis on comparing the proposed method with the traditional particle or blob method.

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Vilin97/GradientFlows.jlCommunity100%
MIT
00JuliaSep 25, 20231 years agoMIT

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Cite this paper

@article{ilin2024transport,
  title  = {Transport based particle methods for the Fokker-Planck-Landau equation},
  author = {Vasily Ilin and Jingwei Hu and Zhenfu Wang},
  year   = {2024},
  eprint = {2405.10392},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2405.10392v1}
}

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