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Author: Lee F Ricketson
Requested Type: Pre-Selected Invited
Submitted: 2016-02-15 18:28:33

Co-authors: A.J. Cerfon

Contact Info:
Courant Institute / NYU
251 Mercer St
New York, NY   10034

Abstract Text:
The particle-in-cell method has remained a standard simulation tool for fusion plasmas for 50 years, yet a quantitatively accurate simulation in complex, three-dimensional geometry still typically requires many hours on a massively parallel machine. Two prominent reasons for this are the statistical noise introduced by the particle representation, and the fact that multiple disparate time-scales necessitate taking enormous numbers of time-steps. We present approaches to circumventing each of these difficulties. First, we propose the use of 'sparse grids' (see e.g. Griebel et al, 1990) to estimate grid-based quantities from particle information. In doing so, we can dramatically increase the effective number of particles per cell for a given grid resolution while only increasing grid-based error by a logarithmic factor. Second, we present a multilevel - in time - technique in the spirit of the multilevel Monte Carlo (MLMC) method (see e.g. Giles, 2008). The idea is to combine information from simulations using many particles and a large time step on the one hand with simulations using few particles and a small time step on the other. This is done in such a way as to generate a new solution that mimics one with many particles and a small time-step, but at dramatically reduced cost. Scalings of the computational complexity of PIC codes using each of these approaches will be discussed, and proof-of-principle results will be presented from 2-D electrostatic simulations with fixed background magnetic field. Finally, we will discuss the prospects for fusion-relevant simulations, combining the two approaches, and parallel issues.