Article ID Journal Published Year Pages File Type
519900 Journal of Computational Physics 2014 18 Pages PDF
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)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)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=10−5ε=10−5. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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