Task graph-based performance analysis of parallel-in-time methods

In this paper, we present a performance model based on task graphs for various iterative parallel-in-time (PinT) methods. PinT methods have been developed to speed up the simulation time of time-dependent problems using modern parallel supercomputers. The performance model is based on a data-driven notation of the methods, from which a task graph is generated. Based on this task graph and a distribution of time points across processes typical for PinT methods, a theoretical lower runtime bound for the method can be obtained, as well as a prediction of the runtime for a given number of processes. In particular, the model is able to cover the large parameter space of PinT methods and make predictions for arbitrary parameter settings. Here, we describe a general procedure for generating task graphs based on three iterative PinT methods, namely, Parareal, multigrid-reduction-in-time (MGRIT), and the parallel full approximation scheme in space and time (PFASST). Furthermore, we discuss how these task graphs can be used to analyze the performance of the methods. In addition, we compare the predictions of the model with parallel simulation times using five different PinT libraries.