Mechanisms for the convergence of time-parallelized, parareal turbulent plasma simulations

Parareal is a recent algorithm able to parallelize the time dimension in spite of its sequential nature. It has been applied to several linear and nonlinear problems and, very recently, to a simulation of fully-developed, two-dimensional drift wave turbulence. The mere fact that parareal works in su...

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Bibliographic Details
Published in:Journal of computational physics 2012-10, Vol.231 (23), p.7851-7867
Main Authors: Reynolds-Barredo, J.M., Newman, D.E., Sanchez, R., Samaddar, D., Berry, L.A., Elwasif, W.R.
Format: Article
Language:English
Subjects:
ALGORITHMS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computational techniques
CONVERGENCE
DIMENSIONS
Exact sciences and technology
IMPLEMENTATION
Magnetically confined plasmas
Mathematical methods in physics
NONLINEAR PROBLEMS
Parareal algorithm
Physics
PLASMA
PLASMA SIMULATION
Plasma turbulence
SENSITIVITY
SIMULATION
Time parallelization
TURBULENCE
Turbulent transport
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Summary:Parareal is a recent algorithm able to parallelize the time dimension in spite of its sequential nature. It has been applied to several linear and nonlinear problems and, very recently, to a simulation of fully-developed, two-dimensional drift wave turbulence. The mere fact that parareal works in such a turbulent regime is in itself somewhat unexpected, due to the characteristic sensitivity of turbulence to any change in initial conditions. This fundamental property of any turbulent system should render the iterative correction procedure characteristic of the parareal method inoperative, but this seems not to be the case. In addition, the choices that must be made to implement parareal (division of the temporal domain, election of the coarse solver and so on) are currently made using trial-and-error approaches. Here, we identify the mechanisms responsible for the convergence of parareal of these simulations of drift wave turbulence. We also investigate which conditions these mechanisms impose on any successful parareal implementation. The results reported here should be useful to guide future implementations of parareal within the much wider context of fully-developed fluid and plasma turbulent simulations.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2012.07.028