A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions
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We 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
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Xin, Zixing, Xia, Jianlin, de Hoop, Maarten V., et al.. "A Distributed-Memory Randomized Structured Multifrontal Method for Sparse Direct Solutions." SIAM Journal on Scientific Computing, 39, no. 4 (2017) Society for Industrial and Applied Mathematics: C292-C318. https://doi.org/10.1137/16M1079221.