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

Kühn, Martin Joachim and Holke, Johannes and Lutz, Annette and Thies, Jonas and Röhrig-Zöllner, Melven and Bleh, Alexander and Backhaus, Jan and Basermann, Achim (2023) SIMD vectorization for simultaneous solution of locally varying linear systems with multiple right hand sides. Journal of Supercomputing. Springer Nature. doi: 10.1007/s11227-023-05220-4. ISSN 0920-8542.

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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.

Item URL in elib:https://elib.dlr.de/195599/
Document Type:Article
Title:SIMD vectorization for simultaneous solution of locally varying linear systems with multiple right hand sides
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Kühn, Martin JoachimUNSPECIFIEDhttps://orcid.org/0000-0002-0906-6984UNSPECIFIED
Lutz, AnnetteDepartment of Mathematics, Technische Universität Darmstadt, Darmstadt, GermanyUNSPECIFIEDUNSPECIFIED
Thies, JonasInstitute of Applied Mathematics, Delft University of Technology, Delft, the NetherlandsUNSPECIFIEDUNSPECIFIED
Röhrig-Zöllner, MelvenUNSPECIFIEDhttps://orcid.org/0000-0001-9851-5886UNSPECIFIED
Basermann, AchimUNSPECIFIEDhttps://orcid.org/0000-0003-3637-3231137544728
Date:April 2023
Journal or Publication Title:Journal of Supercomputing
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Publisher:Springer Nature
Keywords:sparse iterative solvers, high performance computing, performance engineering, SIMD optimization, computational fluid dynamics, frequency domain methods
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Tasks SISTEC
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology > High-Performance Computing
Institute for Software Technology
Institute of Propulsion Technology
Institute of Propulsion Technology > Numerical Methodes
Deposited By: Kühn, Dr. Martin Joachim
Deposited On:26 Jun 2023 13:05
Last Modified:21 Nov 2023 13:06

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