Handle URI:
http://hdl.handle.net/10754/597370
Title:
A Parallel Butterfly Algorithm
Authors:
Poulson, Jack; Demanet, Laurent; Maxwell, Nicholas; Ying, Lexing
Abstract:
The 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.
Citation:
Poulson 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.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
4-Feb-2014
DOI:
10.1137/130921544
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
This 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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPoulson, Jacken
dc.contributor.authorDemanet, Laurenten
dc.contributor.authorMaxwell, Nicholasen
dc.contributor.authorYing, Lexingen
dc.date.accessioned2016-02-25T12:31:48Zen
dc.date.available2016-02-25T12:31:48Zen
dc.date.issued2014-02-04en
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.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/130921544en
dc.identifier.urihttp://hdl.handle.net/10754/597370en
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.en
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.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBlue Gene/Qen
dc.subjectButterfly algorithmen
dc.subjectEgorov operatoren
dc.subjectParallelen
dc.subjectRadon transformen
dc.titleA Parallel Butterfly Algorithmen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
dc.contributor.institutionMassachusetts Institute of Technology, Cambridge, United Statesen
dc.contributor.institutionUniversity of Houston, Houston, United Statesen
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