A Dependency-Driven Formulation of Parareal: Parallel-in-Time Solution of PDEs as a Many-Task Application

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 proces-sor 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 introduc-ing a moving window for time slices, which avoids the ex-ecution 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 utiliza-tion efficiency as a function of the compute resources applied to the problem