Multilevel methods for kinetic equations of plasma dynamics
Lee Ricketson, CIMS

Abstract: The multilevel Monte Carlo (MLMC) method, introduced in [M.B. Giles, Multilevel Monte Carlo path simulation, Operations Research, 56(3):607, 2008] for stochastic differential equations (SDEs) with financial applications, has proven to be a powerful and quite general computational tool for the rapid solution SDEs.  We will introduce this methods and present its adaptation to the Monte Carlo simulation of Coulomb collisions in a plasma.  We will then proceed to ongoing work toward expanding the role of MLMC in kinetic plasma simulations.  The primary stumbling block is that, unlike any present application of MLMC, the behavior of the system depends not only on local (path-wise), but on global (ensemble averaged), quantities - namely the electromagnetic fields.  Promising initial numerical results will be presented and directions for the future will be discussed.