A dependency-driven formulation of parareal: parallel-in-time solution of PDEs as a many-task application

  • Authors:

  • Wael R. Elwasif;Samantha S. Foley;David E. Bernholdt;Lee A. Berry;Debasmita Samaddar;David E. Newman;Raul Sanchez

  • Affiliations:

  • Oak Ridge National Laboratory, OaK rIDGE, TN, USA;Oak Ridge National Laboratory, Oak Ridge, TN, USA;Oak Ridge National Laboratory, Oak Ridge, TN, USA;Oak Ridge National Laboratory, Oak Ridge, TN, USA;ITER Organization, St. Paul-lez-Durance, France;University of Alaska, Fairbanks, AK, USA;Universidad Carlos III de Madrid, Madrid, Spain

  • Venue:
  • Proceedings of the 2011 ACM international workshop on Many task computing on grids and supercomputers
  • Year:
  • 2011

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Abstract

Parareal is a novel algorithm that allows the solution of time-dependent systems of differential or partial differential equations (PDE) to be parallelized in the temporal domain. Parareal-based implementations of PDE problems can take advantage of this parallelism to significantly reduce the time to solution for a simulation (though at an increased total cost) while making effective use of the much larger processor counts available on current high-end systems. In this paper, we present a dynamic, dependency-driven version of the parareal algorithm which breaks the final sequential bottleneck remaining in the original formulation, making it amenable to a "many-task" treatment. We further improve the cost and execution time of the algorithm by introducing a moving window for time slices, which avoids the execution of tasks which contribute little to the final global solution. We describe how this approach has been realized in the Integrated Plasma Simulator (IPS), a framework for coupled multiphysics simulations, and examine the trade-offs among time-to-solution, total cost, and resource utilization efficiency as a function of the compute resources applied to the problem.