Multilevel Monte Carlo simulation of Coulomb collisions

Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; Caflisch, R. E.; Cohen, B. I.

doi:10.1016/j.jcp.2014.05.030

Title: Multilevel Monte Carlo simulation of Coulomb collisions

Journal Article · Thu May 29 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.05.030· OSTI ID:1297655

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

Univ. of California, Los Angeles, CA (United States); Pratt Institute, Brooklyn, NY (United States)
Univ. of California, Los Angeles, CA (United States)
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

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 ε , the computational cost of the method is O(ε^–2) or (ε^–2(lnε)²), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε^–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 Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10^–5. Lastly, we discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1297655

Report Number(s):: LLNL-JRNL-644834

Journal Information:: Journal of Computational Physics, Vol. 274, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 11 works

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97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
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