Diagonalization-Based Parallel-in-Time Preconditioners for Instationary Fluid Flow Control Problems
CoRR(2024)
摘要
We derive a new parallel-in-time approach for solving large-scale
optimization problems constrained by time-dependent partial differential
equations arising from fluid dynamics. The solver involves the use of a block
circulant approximation of the original matrices, enabling
parallelization-in-time via the use of fast Fourier transforms, and we devise
bespoke matrix approximations which may be applied within this framework. These
make use of permutations, saddle-point approximations, commutator arguments, as
well as inner solvers such as the Uzawa method, Chebyshev semi-iteration, and
multigrid. Theoretical results underpin our strategy of applying a block
circulant strategy, and numerical experiments demonstrate the effectiveness and
robustness of our approach on Stokes and Oseen problems. Noteably, satisfying
results for the strong and weak scaling of our methods are provided within a
fully parallel architecture.
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