Multilevel Monte Carlo simulation of Coulomb collisions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:274

Article

Rosin, M. S.^1,2  Ricketson, L. F.¹  Dimits, A. M.³  Caflisch, R. E.^1,4  Cohen, B. I.³ 

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90036 USA

[2] Pratt Inst, Dept Math & Sci, Brooklyn, NY 11205 USA

[3] Lawrence Livermore Natl Lab, Livermore, CA 94511 USA

[4] Univ Calif Los Angeles, Inst Pure & Appl Math, Los Angeles, CA 90095 USA

关键词: Coulomb collisions;    Plasma;    Monte Carlo;    Multilevel Monte Carlo;    Particle in cell;   

DOI  :  10.1016/j.jcp.2014.05.030

来源: Elsevier

【 摘 要 】

We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau-Fokker-Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy epsilon, the computational cost of the method is O(epsilon(-2)) or O(epsilon(-2)(ln epsilon)(2)), depending on the underlying discretization, Milstein or Euler-Maruyama respectively. This is to be contrasted with a cost of O(epsilon(-3)) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Levy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for epsilon = 10(-5). We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free