Parallel Time Integration with Multigrid Reduction for a Compressible Fluid Dynamics Application

We describe our eorts to speed up the computational uid dynamics (CFD) application code Strand2D via the parallel multigrid reduction in time (MGRIT) software library XBraid. The need for parallel-in-time approaches, such as MGRIT, is being driven by current trends in computer architectures where performance improvements are coming from greater parallelism, not faster clock speeds. This leads to a bottleneck for sequential time integration methods, such as those used in Strand2D, because they lack parallelism in the time dimension. Thus, the ability to apply parallelin-time approaches to CFD codes is of interest, and MGRIT is particularly well suited given its non-intrusiveness, which only requires users to wrap existing time stepping codes in the XBraid framework. The contributions of this paper are the description of the nonlinear version of MGRIT and the corresponding software implementation XBraid. We also discuss the steps needed to use XBraid with Strand2D and present the corresponding results for unsteady laminar ow over a cylinder. These results demonstrate a signicant speedup when sucient

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