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Title: 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 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.
Authors:
 [1] ;  [2] ;  [1] ;  [3] ;  [1] ;  [2] ;  [3]
  1. Mathematics Department, University of California at Los Angeles, Los Angeles, CA 90036 (United States)
  2. (United States)
  3. Lawrence Livermore National Laboratory, L-637, P.O. Box 808, Livermore, CA 94511-0808 (United States)
Publication Date:
OSTI Identifier:
22382115
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 274; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
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