University of Illinois Urbana-Champaign

Spectral element poisson preconditioners for heterogeneous architectures

Phillips, Malachi

Content Files
PHILLIPS-DISSERTATION-2023.pdf

Permalink

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

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
Handle URL
https://hdl.handle.net/2142/121461
Copyright and License Information
Copyright 2023 Malachi Phillips

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois