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.