TITLE:
An Approximate Time-Parallel Method for the Fast and Accurate Computation of Particle Trajectories in a Magnetic Field*
AUTHORS:
Carl Lederman, David Bilyeu
KEYWORDS:
Hybridization, Time-Parallel, Numerical Methods, Differential Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.3,
March
19,
2018
ABSTRACT: A temporal multiscale hybridization method is
presented that carefully couples coarse scale gyrokinetic models with exact
charged particle solution trajectories (that is, with full phase information) in
a magnetic field. The approach is based on the careful approximation of a sum,
generally employed for time-parallel (TP) computing applications. While the
hybridization method presented is highly parallelizable, a computational
efficiency gain is seen from considering serial computations only. A complete
numerical method is only presented for the aforementioned charged particle
application, however, the general approach depicted likely has relevance to a
wide swath of challenging multiscale/multiphysics problems. Additionally, the
approach has obvious relevance to TP computing applications (such as variable
selection on which to perform TP calculations and fine scale sampling
strategies).