DocumentCode :
3236878
Title :
Parallel Fast Gauss Transform
Author :
Sampath, Rahul S. ; Sundar, Hari ; Veerapaneni, Shravan K.
Author_Institution :
Oak Ridge Nat. Lab., Oak Ridge, TN, USA
fYear :
2010
fDate :
13-19 Nov. 2010
Firstpage :
1
Lastpage :
10
Abstract :
We present fast adaptive parallel algorithms to compute the sum of N Gaussians at N points. Direct sequential computation of this sum would take O(N2) time. The parallel time complexity estimates for our algorithms are O (N/np) for uniform point distributions and O (N/np log N/+ np log np ) for nonuniform distributions using np CPUs. We incorporate a planewave representation of the Gaussian kernel which permits "diagonal translation". We use parallel octrees and a new scheme for translating the plane-waves to efficiently handle nonuniform distributions. Computing the transform to six-digit accuracy at 120 billion points took approximately 140 seconds using 4096 cores on the Jaguar supercomputer at the Oak Ridge National Laboratory. Our implementation is kernel-independent and can handle other "Gaussian-type" kernels even when an explicit analytic expression for the kernel is not known. These algorithms form a new class of core computational machinery for solving parabolic PDEs on massively parallel architectures.
Keywords :
Gaussian processes; computational complexity; octrees; parallel algorithms; parallel architectures; parallel machines; partial differential equations; Gaussian-type kernels; Jaguar supercomputer; adaptive parallel algorithms; oak ridge national laboratory; parabolic PDE; parallel architectures; parallel fast Gauss transform; parallel octrees; parallel time complexity; uniform point distributions; Complexity theory; Heuristic algorithms; Kernel; Octrees; Partitioning algorithms; Program processors; Transforms;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
High Performance Computing, Networking, Storage and Analysis (SC), 2010 International Conference for
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-7557-5
Electronic_ISBN :
978-1-4244-7558-2
Type :
conf
DOI :
10.1109/SC.2010.39
Filename :
5645554
Link To Document :
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