An analytic model for the convergence of turbulent simulations time-parallelized via the parareal algorithm Articles uri icon

publication date

  • December 2013

start page

  • 293

end page

  • 315


  • 15 Diciembre


  • 255

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716


  • Parareal is a recent time parallelization algorithm based on a predictor-corrector mechanism. Recently, it has been applied for the first time to a fully-developed plasma turbulent simulation, and a qualitative understanding of how parareal converges exists for this case. In this paper, we construct an analytical framework of the process of convergence that should be applicable to parareal simulations of general turbulent systems. This framework allows one to gain a quantitative understanding of the dependence of the convergence on the physics of the problem and the choices that must be made to implement parareal. The analytical knowledge provided by this new framework can be used to optimize the implementation of parareal. We illustrate the inner workings of the framework and demonstrate its predictive capabilities by applying it to the modeling of the parareal convergence of drift-wave plasma turbulent simulations.


  • time parallelization; parareal algorithm; turbulent transport; plasma turbulence; magnetically confined plasmas