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Alya towards Exascale: Algorithmic Scalability using PSCToolkit

Herbert Owen, Oriol Lehmkuhl, Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone

TL;DR

An upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for solving a Large Eddy Simulation formulation of the incompressible Navier–Stokes equations is described.

Abstract

In this paper, we describe an upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for solving a Large Eddy Simulation formulation of the incompressible Navier-Stokes equations. We developed a software module in Alya's kernel to interface the libraries included in the current version of PSCToolkit, a framework for the iterative solution of sparse linear systems on parallel distributed-memory computers by Krylov methods coupled to Algebraic MultiGrid preconditioners. The Toolkit has undergone various extensions within the EoCoE-II project with the primary goal of facing the exascale challenge. Results on a realistic benchmark for airflow simulations in wind farm applications show that the PSCToolkit solvers significantly outperform the original versions of the Conjugate Gradient method available in the Alya's kernel in terms of scalability and parallel efficiency and represent a very promising software layer to move the Alya code towards exascale.

Alya towards Exascale: Algorithmic Scalability using PSCToolkit

TL;DR

An upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for solving a Large Eddy Simulation formulation of the incompressible Navier–Stokes equations is described.

Abstract

In this paper, we describe an upgrade of the Alya code with up-to-date parallel linear solvers capable of achieving reliability, efficiency and scalability in the computation of the pressure field at each time step of the numerical procedure for solving a Large Eddy Simulation formulation of the incompressible Navier-Stokes equations. We developed a software module in Alya's kernel to interface the libraries included in the current version of PSCToolkit, a framework for the iterative solution of sparse linear systems on parallel distributed-memory computers by Krylov methods coupled to Algebraic MultiGrid preconditioners. The Toolkit has undergone various extensions within the EoCoE-II project with the primary goal of facing the exascale challenge. Results on a realistic benchmark for airflow simulations in wind farm applications show that the PSCToolkit solvers significantly outperform the original versions of the Conjugate Gradient method available in the Alya's kernel in terms of scalability and parallel efficiency and represent a very promising software layer to move the Alya code towards exascale.
Paper Structure (13 sections, 11 equations, 14 figures, 1 table)

This paper contains 13 sections, 11 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Alya Description
  3. PSCToolkit: PSBLAS and AMG4PSBLAS
  4. AMG preconditioners
  5. Interfacing Alya to PSCToolkit
  6. The Bolund test case
  7. Parallel Performance Results
  8. Comparison of AMG Preconditioners
  9. Strong scalability
  10. Weak scalability
  11. Results at extreme scales
  12. Conclusions
  13. Declarations

Figures (14)

  • Figure 1: Depiction of the structure of the hybrid forward/backward Gauss-Seidel method on a general row-block parallel distribution of symmetric positive definite matrix $A$.
  • Figure 2: Matching of the graph bcspwr01 from the Harwell-Boeing collection. The matched nodes in the graph are highlighted by a bold red edge.
  • Figure 3: Mesh partitioning into (\ref{['fig:meshleft']}) disjoint sets of nodes, and (\ref{['fig:meshright']}) disjoint sets of elements.
  • Figure 4: Photograph of the Bolund hill BolundWP.
  • Figure 5: Volume rendering of the velocity over Bolund obtained with Alya.
  • ...and 9 more figures

Theorems & Definitions (1)

  • Remark 1