Spectral element poisson preconditioners for heterogeneous architectures

Phillips, Malachi

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https://hdl.handle.net/2142/121461 Copy

Description

Title

Spectral element poisson preconditioners for heterogeneous architectures

Author(s)

Phillips, Malachi

Issue Date

2023-07-06

Director of Research (if dissertation) or Advisor (if thesis)

Fischer, Paul

Doctoral Committee Chair(s)

Fischer, Paul

Committee Member(s)

• Olson, Luke
• Kloeckner, Andreas
• Kolev, Tzanio
• Lottes, James

Department of Study

Computer Science

Discipline

Computer Science

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Preconditioning
• Multigrid
• Poisson equation
• Navier-Stokes equations
• Spectral element method
• Heterogeneous computing
• High-performance computing

Abstract

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.

Graduation Semester

2023-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2023 Malachi Phillips

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