Multilevel Monte Carlo simulation of Coulomb collisions

Journal Article · Wed Oct 01 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.05.030· OSTI ID:22382115

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

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1. Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90036 (United States)
2. Lawrence Livermore National Laboratory, L-637, P.O. Box 808, Livermore, CA 94511-0808 (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{sup −2}) or O(ε{sup −2}(lnε){sup 2}), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε{sup −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{sup −5}. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.

• OSTI ID: 22382115
• Journal Information: Journal of Computational Physics, Vol. 274; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ACCURACY
APPROXIMATIONS
COLLISIONS
COMPUTERIZED SIMULATION
DIFFUSION
FOKKER-PLANCK EQUATION
MATHEMATICAL SOLUTIONS
MONTE CARLO METHOD
PLASMA