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 language | English (US) |
|---|---|
| Pages (from-to) | 140-157 |
| Number of pages | 18 |
| Journal | Journal of Computational Physics |
| Volume | 274 |
| DOIs | |
| State | Published - Oct 1 2014 |
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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
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 journal › Article
}
TY - JOUR
T1 - Multilevel Monte Carlo simulation of Coulomb collisions
AU - Rosin, M. S.
AU - Ricketson, L. F.
AU - Dimits, A. M.
AU - Caflisch, Russel
AU - Cohen, B. I.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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.
AB - 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.
KW - Coulomb collisions
KW - Monte Carlo
KW - Multilevel Monte Carlo
KW - Particle in cell
KW - Plasma
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UR - http://www.scopus.com/inward/citedby.url?scp=84902603177&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2014.05.030
DO - 10.1016/j.jcp.2014.05.030
M3 - Article
VL - 274
SP - 140
EP - 157
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -