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oai:www.ideals.illinois.edu:2142/121461 2023-12-13 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Lottes, James 2023-08 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms The student, Malachi Phillips, accepted the attached license on 2023-07-06 at 11:28. The student, Malachi Phillips, submitted this Dissertation for approval on 2023-07-06 at 11:40. This Dissertation was approved for publication on 2023-07-06 at 15:03. DSpace SAF Submission Ingestion Package generated from Vireo submission #19530 on 2023-12-04 at 17:00:45 Fischer, Paul Fischer, Paul Olson, Luke Kloeckner, Andreas Kolev, Tzanio Spectral element poisson preconditioners for heterogeneous architectures Phillips, Malachi 2023-07-06 Preconditioning Multigrid Poisson Equation Navier-stokes Equations Spectral Element Method Heterogeneous Computing High-performance Computing The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. Two classes of preconditioners prove most effective: geometric p-multigrid and low-order refined methods. Low-order refined preconditioners, moreover, require the use of algebraic multigrid to approximate the inverse of the operator. The communication associated with the multigrid coarse-grid solve hinders the parallel scalability of both classes of preconditioners, especially on heterogeneous architectures. To mitigate the coarse-grid solve cost, novel smoothing strategies are considered. The fourth-kind Chebyshev polynomial smoothing proposed by James Lottes is utilized to accelerate additive Schwarz-based smoothers in a geometric p-multigrid preconditioner. Through these techniques, we develop geometric p-multigrid preconditioners capable of achieving up to an 81% speedup over the state-of-the-art p-multigrid preconditioners on the Summit supercomputer.A p-multigrid approach with an additive coarse-grid solve specifically designed for heterogeneous architectures is considered. We also propose a hybrid p-multigrid and low-order refined preconditioner that improve the time-to-solution by as much as 86% compared to the low-order preconditioner. We demonstrate the effectiveness of these novel approaches on a variety of problems arising from the spectral element discretization of the incompressible Navier-Stokes equations on GPU architectures spanning to P > 1024 NVIDIA V100 GPUs on Summit. Text eng https://hdl.handle.net/2142/121461 Copyright 2023 Malachi Phillips Ph.D. Dissertation Computer Science University of Illinois at Urbana-Champaign Computer Science