Multilevel Monte Carlo simulation of Coulomb collisions
- 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)
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.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1297655
- Report Number(s):
- LLNL-JRNL-644834
- Journal Information:
- Journal of Computational Physics, Vol. 274, Issue C; ISSN 0021-9991
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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