An efficient parallel implementation of explicit multirate Runge–Kutta schemes for discontinuous Galerkin computations

Lambrechts, Jonathan [UCL] Seny, Bruno [UCL] Remacle, Jean-François [UCL]

Although explicit time integration schemes require small computational efforts per time step, their efficiency is severely restricted by stability limits. The multi-scale nature of some physical processes combined with highly unstructured meshes can lead to a very restrictive global stable time step. Multirate methods offer a way to increase the global efficiency by gathering grid cells in appropriate groups under local stability conditions, allowing to use a different time step for each group. The transition between groups has to be accommodated to preserve convergence and conservation properties. The extension of these strategies to the parallel framework is challenging since the computational load varies at each stage of the algorithm. We propose a strategy that shares the workload almost equitably between all processors at every multirate stage. Performance analyses are provided for ocean modeling applications. Performance analyses for two and three-dimensional practical applications confirm that multirate methods preserve important computational advantages of explicit methods up to a significant number of processors.