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

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

We propose a particle method for numerically solving the Landau equation, a model widely used for describing Coulomb collisions in a plasma. Our method is inspired by the score-based transport modeling (SBTM) method for the Fokker-Planck equation (Boffi and Vanden-Eijnden, 2023) and can preserve some important physical properties of the Landau equation, such as the conservation of mass, momentum, and energy. 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 Maxwell 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. Based on the joint work with Vasily Ilin (University of Washington) and Zhenfu Wang (Peking University).

## Department of Mathematics and Statistics