A multilevel Monte Carlo method for asymptotic-preserving particle schemes in the diffusive limit

摘要: Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested studying the long-time behavior high-collisional regimes which an approximate (advection)-diffusion holds. In this paper we consider diffusive scaling. Classical particle-based techniques suffer from a strict time-step restriction limit, to maintain stability. Asymptotic-preserving schemes avoid problem, but introduce additional time discretization error, possibly resulting unacceptably large bias for larger steps. Here, present and analyze multilevel Monte Carlo scheme that reduces by combining estimates using hierarchy different step sizes. We demonstrate how correlate trajectories scheme, also strategy selecting levels scheme. Our approach significantly computation required perform accurate simulations considered kinetic equations, compared classical approaches.