Multilevel Monte Carlo simulation of Coulomb collisions
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 finitetimestep and finitesampling 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.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[2]};
^{[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)
 Publication Date:
 Report Number(s):
 LLNLJRNL644834
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 274; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 70 PLASMA PHYSICS AND FUSION; Coulomb collisions; plasma; Monte Carlo; multilevel Monte Carlo; particle in cell
 OSTI Identifier:
 1297655
Rosin, M. S., Ricketson, L. F., Dimits, A. M., Caflisch, R. E., and Cohen, B. I.. Multilevel Monte Carlo simulation of Coulomb collisions. United States: N. p.,
Web. doi:10.1016/j.jcp.2014.05.030.
Rosin, M. S., Ricketson, L. F., Dimits, A. M., Caflisch, R. E., & Cohen, B. I.. Multilevel Monte Carlo simulation of Coulomb collisions. United States. doi:10.1016/j.jcp.2014.05.030.
Rosin, M. S., Ricketson, L. F., Dimits, A. M., Caflisch, R. E., and Cohen, B. I.. 2014.
"Multilevel Monte Carlo simulation of Coulomb collisions". United States.
doi:10.1016/j.jcp.2014.05.030. https://www.osti.gov/servlets/purl/1297655.
@article{osti_1297655,
title = {Multilevel Monte Carlo simulation of Coulomb collisions},
author = {Rosin, M. S. and Ricketson, L. F. and Dimits, A. M. and Caflisch, R. E. and Cohen, B. I.},
abstractNote = {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 finitetimestep and finitesampling 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.},
doi = {10.1016/j.jcp.2014.05.030},
journal = {Journal of Computational Physics},
number = C,
volume = 274,
place = {United States},
year = {2014},
month = {5}
}