Multilevel Monte Carlo simulation of Coulomb collisions
| Autor: | Rosin, M. S., Ricketson, L. F., Dimits, A. M., Caflisch, R. E., Cohen, B. I. |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jcp.2014.05.030 |
| Popis: | 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 epsilon, the computational cost of the method is order(epsilon^{-2}) or order(epsilon^{-2} (\ln epsilon)^2), depending on the underlying discretization, Milstein or Euler-Maruyama respectively. This is to be contrasted with a cost of order(epsilon^{-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 Levy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for epsilon = 10^{-5}. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations. Comment: 32 pages |
| Databáze: | arXiv |
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