## 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) |
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Pages (from-to) | 140-157 |

Number of pages | 18 |

Journal | Journal of Computational Physics |

Volume | 274 |

DOIs | |

State | Published - Oct 1 2014 |

## Keywords

- Coulomb collisions
- Monte Carlo
- Multilevel Monte Carlo
- Particle in cell
- Plasma

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics