Random batch particle methods for the homogeneous Landau equation

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 $O(N)$ 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.

References in corpus (10)

• On the Random Batch Method for second order interacting particle systems
• Entropy dissipation estimates for the Landau equation in the Coulomb case and applications
• A stochastic version of Stein Variational Gradient Descent for efficient sampling
• A Conservative Scheme for Vlasov Poisson Landau modeling collisional plasmas
• The Landau equation as a Gradient Flow
• Hermite spectral method for Fokker-Planck-Landau equation modeling collisional plasma
• A gradient flow approach to the Boltzmann equation
• Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations
• Boltzmann to Landau from the Gradient Flow Perspective
• Random Batch Methods for classical and quantum interacting particle systems and statistical samplings

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• Mean field error estimate of the random batch method for large interacting particle system
• Some remarks on the effect of the Random Batch Method on phase transition
• Intrinsic statistical regularity of topological charges revealed in dynamical disk model