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

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dc.citation.firstpageC292
dc.citation.issueNumber4
dc.citation.journalTitleSIAM Journal on Scientific Computing
dc.citation.lastpageC318
dc.citation.volumeNumber39
dc.contributor.authorXin, Zixing
dc.contributor.authorXia, Jianlin
dc.contributor.authorde Hoop, Maarten V.
dc.contributor.authorCauley, Stephen
dc.contributor.authorBalakrishnan, Venkataramanan
dc.date.accessioned2017-11-17T14:39:05Z
dc.date.available2017-11-17T14:39:05Z
dc.date.issued2017
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.
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.
dc.identifier.digital16m1079221
dc.identifier.doihttps://doi.org/10.1137/16M1079221
dc.identifier.urihttps://hdl.handle.net/1911/98834
dc.language.isoeng
dc.publisherSociety for Industrial and Applied Mathematics
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.
dc.titleA Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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