Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems

Alexander Heinlein, Christian Hochmuth, Axel Klawonn

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared with preconditioners based on incomplete block factorizations. However, the computational costs for the setup and the application of monolithic preconditioners are typically higher. In this article, several techniques are applied to monolithic two-level generalized Dryja-Smith-Widlund (GDSW) preconditioners to further improve the convergence speed and the computing time. In particular, reduced dimension GDSW coarse spaces, restricted and scaled versions of the first level, hybrid, and parallel coupling of the levels, and recycling strategies are investigated. Using a combination of all these improvements, for a small time-dependent Navier-Stokes problem on 240 message passing interface (MPI) ranks, a reduction of 86% of the time-to-solution can be obtained. Even without applying recycling strategies, the time-to-solution can be reduced by more than 50% for a larger steady Stokes problem on 4608 MPI ranks. For the largest problems with 11 979 MPI ranks, the scalability deteriorates drastically for the monolithic GDSW coarse space. On the other hand, using the reduced dimension coarse spaces, good scalability up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, could be achieved.

Original languageEnglish
Pages (from-to)1101-1119
Number of pages19
JournalInternational Journal for Numerical Methods in Engineering
Volume121
Issue number6
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • algebraic preconditioner
  • GDSW
  • Navier-Stokes
  • overlapping domain decomposition
  • parallel computing
  • Stokes

Fingerprint Dive into the research topics of 'Reduced dimension GDSW coarse spaces for monolithic Schwarz domain decomposition methods for incompressible fluid flow problems'. Together they form a unique fingerprint.

Cite this