Abstract:
Particle-based simulation methods are prevalent in the study of both plasma and rarefied gas dynamics. They are usually called particle-in-cell (PIC) schemes in the former context, and direct-simulation Monte Carlo (DSMC) in the latter. Despite the naming discrepancies, the mathematical structure of the underlying equations and the numerical methods have much in common. In particular, many instances of each may be viewed as a system of particles undergoing stochastic motion through interaction with some mean-field determined by the particles themselves. Mathematically, this takes the form of a McKean-Vlasov equation. We present a generalization of the multilevel Monte Carlo (MLMC) method - popular in financial applications - to McKean-Vlasov equations. The resulting efficiency improvements are demonstrated on problems from plasma physics. |