Parallel fast gauss transform

Conference · Fri Jan 01 00:00:00 EST 2010

OSTI ID:1033540

Sampath, Rahul S ^[1]; Sundar, Hari ^[2]; Veerapaneni, Shravan ^[3]

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1. ORNL
2. Siemens Corporate Research
3. New York University

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(N{sup 2}) time. The parallel time complexity estimates for our algorithms are O(N/n{sub p}) for uniform point distributions and O( (N/n{sub p}) log (N/n{sub p}) + n{sub p}log n{sub p}) for non-uniform distributions using n{sub p} CPUs. We incorporate a plane-wave 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 non-uniform distributions. Computing the transform to six-digit accuracy at 120 billion points took approximately 140 seconds using 4096 cores on the Jaguar supercomputer. Our implementation is 'kernel-independent' and can handle other 'Gaussian-type' kernels even when 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.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)
• Sponsoring Organization: USDOE Office of Nuclear Energy (NE)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1033540
• Resource Relation: Conference: ACM/IEEE Supercomputing, New Orleans, LA, USA, 20101113, 20101113
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ACCURACY
ALGORITHMS
COMPUTER ARCHITECTURE
GAUSSIAN PROCESSES
KERNELS
MATHEMATICAL SOLUTIONS
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS