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dc.contributor.authorPoulson, Jack
dc.contributor.authorDemanet, Laurent
dc.contributor.authorMaxwell, Nicholas
dc.contributor.authorYing, Lexing
dc.date.accessioned2016-02-25T12:31:48Z
dc.date.available2016-02-25T12:31:48Z
dc.date.issued2014-02-04
dc.identifier.citationPoulson J, Demanet L, Maxwell N, Ying L (2014) A Parallel Butterfly Algorithm. SIAM Journal on Scientific Computing 36: C49–C65. Available: http://dx.doi.org/10.1137/130921544.
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.doi10.1137/130921544
dc.identifier.urihttp://hdl.handle.net/10754/597370
dc.description.abstractThe butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform (Equation Presented.) at large numbers of target points when the kernel, K(x, y), is approximately low-rank when restricted to subdomains satisfying a certain simple geometric condition. In d dimensions with O(Nd) quasi-uniformly distributed source and target points, when each appropriate submatrix of K is approximately rank-r, the running time of the algorithm is at most O(r2Nd logN). A parallelization of the butterfly algorithm is introduced which, assuming a message latency of α and per-process inverse bandwidth of β, executes in at most (Equation Presented.) time using p processes. This parallel algorithm was then instantiated in the form of the open-source DistButterfly library for the special case where K(x, y) = exp(iΦ(x, y)), where Φ(x, y) is a black-box, sufficiently smooth, real-valued phase function. Experiments on Blue Gene/Q demonstrate impressive strong-scaling results for important classes of phase functions. Using quasi-uniform sources, hyperbolic Radon transforms, and an analogue of a three-dimensional generalized Radon transform were, respectively, observed to strong-scale from 1-node/16-cores up to 1024-nodes/16,384-cores with greater than 90% and 82% efficiency, respectively. © 2014 Society for Industrial and Applied Mathematics.
dc.description.sponsorshipThis work was partially supported by NSF CAREER grant 0846501 (L.Y.), DOE grant DE-SC0009409 (L.Y.), and KAUST. Furthermore, this research used resources of the Argonne Leadership Computing Facility at Argonne National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-06CH11357.
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectBlue Gene/Q
dc.subjectButterfly algorithm
dc.subjectEgorov operator
dc.subjectParallel
dc.subjectRadon transform
dc.titleA Parallel Butterfly Algorithm
dc.typeArticle
dc.identifier.journalSIAM Journal on Scientific Computing
dc.contributor.institutionStanford University, Palo Alto, United States
dc.contributor.institutionMassachusetts Institute of Technology, Cambridge, United States
dc.contributor.institutionUniversity of Houston, Houston, United States
dc.date.published-online2014-02-04
dc.date.published-print2014-01


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