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arXiv · 2606.20496

Coarse Solvers for Exascale Solution of Poisson Problems

Thilina Ratnayaka·Paul Fischer·Luke Olson
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Abstract

We present a two-level Schwarz method as an alternative to Algebraic Multigrid method(AMG) used as the last level (coarse) solver of the p-multigrid pMG preconditioner for pressure Poisson equation resulting from Spectral/Finite element descretization of incompressible Navier-Stokes equation. Proposed Schwarz method consits of a local problem in the original pMG coarse space and a global coarse problem. Main contribution of the paper is a novel, structured and a non-nested coarse space for the global coarse problem. Structured nature of the proposed global coarse space enable communication-free interpolation between the original p-multgrid coarse space and the global coarse problem. We demonstrate the effectiveness of the proposed method compared to the state of the art AMG solver BoomerAMG by a series of experiments performed using Nek5000/RS, a suite of highly scalable incompressible Navier-Stokes solvers, on Summit/Frontier supercomputers at Oak Ridge Leadership Computing Facility.

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Thilina Ratnayaka, Paul Fischer, Luke Olson. 2026-06-18. Coarse Solvers for Exascale Solution of Poisson Problems. https://arxiv.org/abs/2606.20496

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