Partitioning and reordering for Spike-Based distributed-memory parallel Gauss--Seidel

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buir.contributor.authorTorun, Tuğba
buir.contributor.authorAykanat, Cevdet
buir.contributor.orcidTorun, Tuğba|0000-0001-6790-7094
buir.contributor.orcidAykanat, Cevdet|0000-0002-4559-1321
dc.citation.epageC123en_US
dc.citation.issueNumber2en_US
dc.citation.spageC99en_US
dc.citation.volumeNumber44en_US
dc.contributor.authorTorun, Tuğba
dc.contributor.authorTorun, F. Şükrü
dc.contributor.authorManguoğlu, Murat
dc.contributor.authorAykanat, Cevdet
dc.coverage.spatialUnited Statesen_US
dc.date.accessioned2023-02-21T05:44:21Z
dc.date.available2023-02-21T05:44:21Z
dc.date.issued2022
dc.departmentDepartment of Computer Engineeringen_US
dc.description.abstractGauss--Seidel (GS) is a widely used iterative method for solving sparse linear systems of equations and also known to be effective as a smoother in algebraic multigrid methods. Parallelization of GS is a challenging task since solving the sparse lower triangular system in GS constitutes a sequential bottleneck at each iteration. We propose a distributed-memory parallel GS (dmpGS) by implementing a parallel sparse triangular solver (stSpike) based on the Spike algorithm. stSpike decouples the global triangular system into smaller systems that can be solved concurrently and requires the solution of a much smaller reduced sparse lower triangular system which constitutes a sequential bottleneck. In order to alleviate this bottleneck and to reduce the communication overhead of dmpGS, we propose a partitioning and reordering model consisting of two phases. The first phase is a novel hypergraph partitioning model whose partitioning objective simultaneously encodes minimizing the reduced system size and the communication volume. The second phase is an in-block row reordering method for decreasing the nonzero count of the reduced system. Extensive experiments on a dataset consisting of 359 sparse linear systems verify the effectiveness of the proposed partitioning and reordering model in terms of reducing the communication and the sequential computational overheads. Parallel experiments on 12 large systems using up to 320 cores demonstrate that the proposed model significantly improves the scalability of dmpGS.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2023-02-21T05:44:21Z No. of bitstreams: 1 Partitioning_and_Reordering_for_Spike-Based_Distributed-Memory_Parallel_Gauss--Seidel.pdf: 10154189 bytes, checksum: 657827090b4066e99773e33418bc8a91 (MD5)en
dc.description.provenanceMade available in DSpace on 2023-02-21T05:44:21Z (GMT). No. of bitstreams: 1 Partitioning_and_Reordering_for_Spike-Based_Distributed-Memory_Parallel_Gauss--Seidel.pdf: 10154189 bytes, checksum: 657827090b4066e99773e33418bc8a91 (MD5) Previous issue date: 2022en
dc.identifier.doi10.1137/21M1411603en_US
dc.identifier.eissn1095-7197
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/11693/111554
dc.language.isoEnglishen_US
dc.publisherSIAMen_US
dc.relation.isversionofhttps://doi.org/10.1137/21M1411603en_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.subjectParallel Gauss--Seidelen_US
dc.subjectDistributed-memoryen_US
dc.subjectSpike algorithmen_US
dc.subjectParallel sparse triangular solveen_US
dc.subjectHypergraph partitioningen_US
dc.subjectSparse matrix reorderingen_US
dc.titlePartitioning and reordering for Spike-Based distributed-memory parallel Gauss--Seidelen_US
dc.typeArticleen_US

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