[2405.10392] Transport based particle methods for the Fokker-Planck-Landau equation
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Mathematics > Numerical Analysis

arXiv:2405.10392 (math)
[Submitted on 16 May 2024]

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

Authors:Vasily Ilin, Jingwei Hu, Zhenfu Wang
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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.
Comments: 26 pages, 6 figures, code this https URL
Subjects: Numerical Analysis (math.NA); Machine Learning (cs.LG); Analysis of PDEs (math.AP)
MSC classes: 35Q84, 65M75, 49Q22, 68T07
Cite as: arXiv:2405.10392 [math.NA]
  (or arXiv:2405.10392v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2405.10392

Submission history

From: Vasily Ilin [view email]
[v1] Thu, 16 May 2024 18:37:35 UTC (1,213 KB)
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