Author(s)

Carl Lederman¹, David Bilyeu²

¹ERC Inc., Edwards, CA, USA.
²Air Force Research Laboratory, Edwards, CA, USA.

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).

Hybridization, Time-Parallel, Numerical Methods, Differential Equations

Lederman, C. and Bilyeu, D. (2018) An Approximate Time-Parallel Method for the Fast and Accurate Computation of Particle Trajectories in a Magnetic Field*. Journal of Applied Mathematics and Physics, 6, 498-519. doi: 10.4236/jamp.2018.63046.