Engquist, B., Li, X., Ren, W. and Vanden-Eijnden, E. (2007) Heterogeneous Multiscale Methods: A Review. Communications in Computational Physics, 2, 367-450.

has been cited by the following article:

• 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).