A fast algorithm for particle simulations
Journal of Computational Physics
Astrophysical N-body simulations using hierarchical tree data structures
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
A parallel hashed Oct-Tree N-body algorithm
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
A parallel algorithm for multilevel graph partitioning and sparse matrix ordering
Journal of Parallel and Distributed Computing
A New Fast-Multipole Accelerated Poisson Solver in Two Dimensions
SIAM Journal on Scientific Computing
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
An adaptive fast solver for the modified Helmholtz equation in two dimensions
Journal of Computational Physics
A massively parallel adaptive fast-multipole method on heterogeneous architectures
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
Architectural Constraints to Attain 1 Exaflop/s for Three Scientific Application Classes
IPDPS '11 Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium
Adaptive fast multipole methods on the GPU
The Journal of Supercomputing
A CPU: GPU Hybrid Implementation and Model-Driven Scheduling of the Fast Multipole Method
Proceedings of Workshop on General Purpose Processing Using GPUs
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Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (fmm) appears as a rising star. Our previous recent work showed scaling of an fmm on gpu clusters, with problem sizes of the order of billions of unknowns. That work led to an extremely parallel fmm, scaling to thousands of gpus or tens of thousands of cpus. This paper reports on a campaign of performance tuning and scalability studies using multi-core cpus, on the Kraken supercomputer. All kernels in the fmm were parallelized using OpenMP, and a test using 107 particles randomly distributed in a cube showed 78% efficiency on 8 threads. Tuning of the particle-to-particle kernel using single instruction multiple data (SIMD) instructions resulted in 4 脙聴 speed-up of the overall algorithm on single-core tests with 103-107 particles. Parallel scalability was studied in both strong and weak scaling. The strong scaling test used 108 particles and resulted in 93% parallel efficiency on 2048 processes for the non-SIMD code and 54% for the SIMD-optimized code (which was still 2 脙聴 faster). The weak scaling test used 106 particles per process, and resulted in 72% efficiency on 32,768 processes, with the largest calculation taking about 40 seconds to evaluate more than 32 billion unknowns. This work builds up evidence for our view that fmm is poised to play a leading role in exascale computing, and we end the paper with a discussion of the features that make it a particularly favorable algorithm for the emerging heterogeneous and massively parallel architectural landscape. The code is open for unrestricted use under the MIT license.