Multilevel Monte Carlo simulation of Coulomb collisions

M. S. Rosin, L. F. Ricketson, A. M. Dimits, Russel Caflisch, B. I. Cohen

Research output: Contribution to journalArticle

Abstract

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 O(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. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.

Original languageEnglish (US)
Pages (from-to)140-157
Number of pages18
JournalJournal of Computational Physics
Volume274
DOIs
StatePublished - Oct 1 2014

Fingerprint

Coulomb collisions
costs
Fokker Planck equation
collisions
plasma physics
Fokker-Planck equation
Costs
Numerical methods
Physics
simulation
sampling
Sampling
Plasmas
approximation
Monte Carlo simulation

Keywords

  • Coulomb collisions
  • Monte Carlo
  • Multilevel Monte Carlo
  • Particle in cell
  • Plasma

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

Cite this

Rosin, M. S., Ricketson, L. F., Dimits, A. M., Caflisch, R., & Cohen, B. I. (2014). Multilevel Monte Carlo simulation of Coulomb collisions. Journal of Computational Physics, 274, 140-157. https://doi.org/10.1016/j.jcp.2014.05.030

Multilevel Monte Carlo simulation of Coulomb collisions. / Rosin, M. S.; Ricketson, L. F.; Dimits, A. M.; Caflisch, Russel; Cohen, B. I.

In: Journal of Computational Physics, Vol. 274, 01.10.2014, p. 140-157.

Research output: Contribution to journalArticle

Rosin, MS, Ricketson, LF, Dimits, AM, Caflisch, R & Cohen, BI 2014, 'Multilevel Monte Carlo simulation of Coulomb collisions', Journal of Computational Physics, vol. 274, pp. 140-157. https://doi.org/10.1016/j.jcp.2014.05.030
Rosin, M. S. ; Ricketson, L. F. ; Dimits, A. M. ; Caflisch, Russel ; Cohen, B. I. / Multilevel Monte Carlo simulation of Coulomb collisions. In: Journal of Computational Physics. 2014 ; Vol. 274. pp. 140-157.
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