Parallel in Time for a Fully Space-Time Adaptive Mesh Refinement Algorithm

摘要

In order to solve time-periodic problems in computation fluid dynamics, typically the characteristic time is iterated over multiple times to drive out transients. This can lead to a large number of steps to achieve a well-converged solution. Parallel-in-time methods excel in cases like these problems characterized by time periodicity and provide a speedup over time-sequential codes. In particular, time-parallel methods using multigrid only need to solve a single characteristic time due to the iterative nature of the method. In this study, we apply space-time multigrid with adaptivity to solve time-periodic problems. To verify and validate the implementation, Stokes second problem is solved in time-parallel and compared to the time-sequential solutions. A strong scaling test demonstrates that this time-parallel method is able to achieve speedups of 13× over the time-sequential algorithm without loss of accuracy.