Space-Time Parallelization Is Feasible For Highly Nonlinear Simulations

Realistic simulation of time-dependent processes requires long time evolution using very small time steps in order to resolve phenomena at different time scales. Traditional spatial parallelism offers some performance gain, which however may be insufficient. The parareal algorithm parallehzes partial differential equations by time decomposition, and has been employed for a range of physical problems. It faces particular challenges in the case of highly nonlinear dynamics, where the parareal corrections can cause significant instability. This talk describes strategies that have been used to deal with this instability, including grid coarsening techniques, filtering of grid-dependent features, and multistage convergence techniques, in the context of turbulent flow in computational fluid dynamics.