Lightweight AMG preconditioners for CFD simulations on symmetric domains
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Divergence constraints appear in the governing equations of many physical phenomena, often leading to a Poisson equation whose solution is one of the most challenging parts of incompressible CFD codes. Algebraic Multigrid (AMG) is likely the most effective preconditioner for Poisson's equation. Its effectiveness stems from the combined roles of the smoother, which dampens high-frequency error components, and the coarse-grid correction, which reduces low-frequency modes. This work presents an AMG reduction framework to leverage spatial symmetries, often present in academic and industrial configurations, for making AMG more compute-intensive. In particular, we introduce an aggressive coarsening to the top level of the multigrid hierarchy, reducing the setup, memory footprint and application costs of the top-level smoother. Numerical experiments on a model problem confirm the advantages of the resulting preconditioner.
