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Volume 31, Issue 4
Random Batch Particle Methods for the Homogeneous Landau Equation

José Antonio Carrillo, Shi Jin & Yijia Tang

Commun. Comput. Phys., 31 (2022), pp. 997-1019.

Published online: 2022-03

[An open-access article; the PDF is free to any online user.]

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  • Abstract

We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to $\mathcal{O}(N)$ per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

  • Keywords

Homogeneous Landau equation, random batch particle method, Coulomb collision.

  • AMS Subject Headings

65C35, 65Y20, 82C40, 82D10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-997, author = {Carrillo , José AntonioJin , Shi and Tang , Yijia}, title = {Random Batch Particle Methods for the Homogeneous Landau Equation}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {4}, pages = {997--1019}, abstract = {

We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to $\mathcal{O}(N)$ per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0200}, url = {http://global-sci.org/intro/article_detail/cicp/20374.html} }
TY - JOUR T1 - Random Batch Particle Methods for the Homogeneous Landau Equation AU - Carrillo , José Antonio AU - Jin , Shi AU - Tang , Yijia JO - Communications in Computational Physics VL - 4 SP - 997 EP - 1019 PY - 2022 DA - 2022/03 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0200 UR - https://global-sci.org/intro/article_detail/cicp/20374.html KW - Homogeneous Landau equation, random batch particle method, Coulomb collision. AB -

We consider in this paper random batch particle methods for efficiently solving the homogeneous Landau equation in plasma physics. The methods are stochastic variations of the particle methods proposed by Carrillo et al. [J. Comput. Phys.: X 7: 100066, 2020] using the random batch strategy. The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to $\mathcal{O}(N)$ per time step. Meanwhile, our methods can preserve the conservation of mass, momentum, energy and the decay of entropy. Several numerical examples are performed to validate our methods.

José Antonio Carrillo, Shi Jin & Yijia Tang. (2022). Random Batch Particle Methods for the Homogeneous Landau Equation. Communications in Computational Physics. 31 (4). 997-1019. doi:10.4208/cicp.OA-2021-0200
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