Time parallelism and Newton-adaptivity of the two-derivative deferred correction discontinuous Galerkin method

Abstract

In this work, we consider a high-order discretization of compressible viscous flows allow- ing parallelization both in space and time. The discontinuous Galerkin spectral element method, which is well-suited for massively parallel simulations, is used for spatial discretization. The main novelty in this work is the additional demonstration of time-parallel capabilities within an implicit two-derivative timestepping procedure to further increase the parallel speedup. Temporal parallelism is made possible by a predictor-corrector-type time discretization that allows to split the as- sociated workload onto multiple processors. We identify a homogeneous load balance with respect to the linear (GMRES) iterations on each processor as a key for parallel efficiency. To homogenize the load and to enable practical simulations, an adaptive strategy for Newton’s method is introduced. It is shown that the time-parallel method provides a parallel efficiency of approx. 60 −70% on 4 −7 computational partitions. Moreover, the capabilities of the novel method for the simulation of large-scale problems are illustrated with a mixed temporal and spatial parallelization on more than 10 0 0 processors.