A decentralized parallelization-in-time approach with parareal

Abstract

With steadily increasing parallelism for high-performance architectures, simulations requiring a good strong scalability are prone to be limited in scalability with standard spatial-decomposition strategies at a certain amount of parallel processors. This can be a show-stopper if the simulation results have to be computed with wallclock time restrictions or as fast as possible. Here, the time-dimension is the only one left for parallelisation and we focus on Parareal as one particular parallelisationin-time method. We present a software approach for making Parareal parallelisation transparent for application developers, hence allowing fast prototyping for Parareal. Further, we introduce a decentralized Parareal which results in autonomous simulation instances which only require communicating with the previous and next simulation instances. This concept is evaluated by solving the rotational shallow water equations parallel-in-time: We provide speedup benchmarks and an in-depth analysis of our results based on state-plots and a performance model. This allows us to show the applicability of the Parareal approach with the rotational shallow water equations and also to evaluate the limitations of Parareal.