In the context of time-accurate numerical simulation of incompressible flows, a Poisson equation needs to be solved at least once per time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is one of the most time consuming and difficult to parallelise parts of the code. In this paper, a parallel direct Poisson solver restricted to problems
with one uniform periodic direction is presented. It is a combination of a Direct
Schur-complement based Decomposition (DSD) and a Fourier diagonalisation. The latter decomposes the original system into a set of mutually independent 2D systems which are solved by means of the DSD algorithm. Since no restrictions are imposed in the non-periodic directions, the overall algorithm is well-suited for solving problems
discretised on extruded 2D unstructured meshes. A new overall parallelisation
strategy with respect to our earlier works is presented. This has allowed us to solve
discrete Poisson equations with up to 109 grid points in less than half a second, using
up to 8192 CPU cores of the MareNostrum Supercomputer.
CitationBorrell, R. [et al.]. FFT-based Poisson Solver for large scale numerical simulations of incompressible flows. A: International Conference on Parallel Computational Fluid Dynamics. "Parallel CFD 2011 : 23rd International Conference on Parallel Computational Fluid Dynamics". Barcelona: 2011, p. 1-5.
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