SIMD vectorization for simultaneous solution of locally varying linear systems with multiple right-hand sides

Martin J. Kühn*, Johannes Holke, Annette Lutz, Jonas Thies, Melven Röhrig-Zöllner, Alexander Bleh, Jan Backhaus, Achim Basermann

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

Developments in numerical simulation of flows and high-performance computing influence one another. More detailed simulation methods create a permanent need for more computational power, while new hardware developments often require changes to the software to exploit new hardware features. This dependency is very pronounced in the case of vector-units which are featured by all modern processors to increase their numerical throughput but require vectorization of the software to be used efficiently. We study the vectorization of a simulation method that exhibits an inherent level of vector-parallelism. This is of particular interest as SIMD operations will hopefully be available with std::simd in a future C++ standard. The simulation method considered here results in the simultaneous solution of multiple sparse linear systems of equations which only differ by their main diagonal and right-hand sides. Such structure arises in the simulation of unsteady flow in turbomachinery by means of a frequency domain approach called harmonic balance.

Original languageEnglish
Pages (from-to)14684-14706
Number of pages23
JournalJournal of Supercomputing
Volume79
Issue number13
DOIs
Publication statusPublished - 2023

Keywords

  • Computational fluid dynamics
  • Frequency domain methods
  • High-performance computing
  • Performance engineering
  • SIMD optimization
  • Sparse iterative solvers

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