Young Researchers Workshop:
Multiscale phenomena: modeling, analysis and computation

Multilevel methods for the kinetic equations of plasma dynamics

Lee Ricketson

New York University

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. An adaptation of this method for the Monte Carlo simulation of Coulomb collisions in a plasma will be presented; more specifically, its use in accelerating the solution of the spatially homogeneous Landau-Fokker-Planck equation will be discussed. 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.