A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions

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dc.citation.firstpageC292en_US
dc.citation.issueNumber4en_US
dc.citation.journalTitleSIAM Journal on Scientific Computingen_US
dc.citation.lastpageC318en_US
dc.citation.volumeNumber39en_US
dc.contributor.authorXin, Zixingen_US
dc.contributor.authorXia, Jianlinen_US
dc.contributor.authorde Hoop, Maarten V.en_US
dc.contributor.authorCauley, Stephenen_US
dc.contributor.authorBalakrishnan, Venkataramananen_US
dc.date.accessioned2017-11-17T14:39:05Zen_US
dc.date.available2017-11-17T14:39:05Zen_US
dc.date.issued2017en_US
dc.description.abstractWe design a distributed-memory randomized structured multifrontal solver for large sparse matrices. Two layers of hierarchical tree parallelism are used. A sequence of innovative parallel methods are developed for randomized structured frontal matrix operations, structured update matrix computation, skinny extend-add operation, selected entry extraction from structured matrices, etc. Several strategies are proposed to reuse computations and reduce communications. Unlike an earlier parallel structured multifrontal method that still involves large dense intermediate matrices, our parallel solver performs the major operations in terms of skinny matrices and fully structured forms. It thus significantly enhances the efficiency and scalability. Systematic communication cost analysis shows that the numbers of words are reduced by factors of about $O(\sqrt{n}/r)$ in two dimensions and about $O(n^{2/3}/r)$ in three dimensions, where $n$ is the matrix size and $r$ is an off-diagonal numerical rank bound of the intermediate frontal matrices. The efficiency and parallel performance are demonstrated with the solution of some large discretized PDEs in two and three dimensions. Nice scalability and significant savings in the cost and memory can be observed from the weak and strong scaling tests, especially for some 3D problems discretized on unstructured meshes.en_US
dc.identifier.citationXin, Zixing, Xia, Jianlin, de Hoop, Maarten V., et al.. "A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions." <i>SIAM Journal on Scientific Computing,</i> 39, no. 4 (2017) Society for Industrial and Applied Mathematics: C292-C318. https://doi.org/10.1137/16M1079221.en_US
dc.identifier.digital16m1079221en_US
dc.identifier.doihttps://doi.org/10.1137/16M1079221en_US
dc.identifier.urihttps://hdl.handle.net/1911/98834en_US
dc.language.isoengen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.titleA Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutionsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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