Multilevel Monte Carlo simulation of Coulomb collisions
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 (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:
-
- 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:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1297655
- Report Number(s):
- LLNL-JRNL-644834
Journal ID: ISSN 0021-9991
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 274; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- 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
Citation Formats
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., 2014.
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. https://doi.org/10.1016/j.jcp.2014.05.030
Rosin, M. S., Ricketson, L. F., Dimits, A. M., Caflisch, R. E., and Cohen, B. I. Thu .
"Multilevel Monte Carlo simulation of Coulomb collisions". United States. https://doi.org/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 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.},
doi = {10.1016/j.jcp.2014.05.030},
journal = {Journal of Computational Physics},
number = C,
volume = 274,
place = {United States},
year = {Thu May 29 00:00:00 EDT 2014},
month = {Thu May 29 00:00:00 EDT 2014}
}
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