Optimized Cascadic Multigrid Parareal Method for Explicit Time-Marching Schemes

High-performance computing research is entering the exascale computing era. Large-scale simulations have more than enough parallel resources but reach a saturation point in spatial parallelization due to the communication cost and synchronization overhead. Parallel-in-time (PinT) methods are a solution to the saturation problem. To date, many efficient PinT methods have been proposed, but most experiments focus on small problems with a large number of time steps. Applications that are solved by explicit time-marching schemes, especially, are highly scalable in the spatial domain. Therefore very few researchers use PinT methods on explicit time-marching schemes. Furthermore, PinT methods often require many processors to achieve faster computation than sequential code. This work proposes a PinT method for explicit schemes that provide efficient parallelization with few working processes. The numerical experiment of advection equation and compressible viscous flow simulation shows that the proposed method could achieve better parallel efficiency than spatial parallelization.