TY - JOUR

T1 - A Parallel Butterfly Algorithm

AU - Poulson, Jack

AU - Demanet, Laurent

AU - Maxwell, Nicholas

AU - Ying, Lexing

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2014/2/4

Y1 - 2014/2/4

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/597370

UR - http://epubs.siam.org/doi/10.1137/130921544

UR - http://www.scopus.com/inward/record.url?scp=84897016869&partnerID=8YFLogxK

U2 - 10.1137/130921544

DO - 10.1137/130921544

M3 - Article

VL - 36

SP - C49-C65

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 1

ER -