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

Autor:	Ilin, Vasily, Hu, Jingwei, Wang, Zhenfu
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Computer Science - Machine Learning Mathematics - Analysis of PDEs 35Q84 65M75 49Q22 68T07
Druh dokumentu:	Working Paper
Popis:	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. Comment: 26 pages, 6 figures, code https://github.com/Vilin97/GradientFlows.jl
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.10392 Zobrazit plný text záznamu View this record from Arxiv