A fast algorithm for particle simulations
Journal of Computational Physics
Numerical study of a three-dimensional vortex method
Journal of Computational Physics
A modified tree code: don't laugh; it runs
Journal of Computational Physics
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
An implementation of the fast multipole method without multipoles
SIAM Journal on Scientific and Statistical Computing
Hairpin removal in vortex interactions II
Journal of Computational Physics
Journal of Computational Physics
Skeletons from the treecode closet
Journal of Computational Physics
Journal of Parallel and Distributed Computing
A new diffusion procedure for vortex methods
Journal of Computational Physics
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Accelerating exact k-means algorithms with geometric reasoning
KDD '99 Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining
A fast adaptive multipole algorithm for calculating screened Coulomb (Yukawa) interactions
Journal of Computational Physics - Special issue on computational molecular biophysics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Improving Error Bounds for Multipole-Based Treecodes
SIAM Journal on Scientific Computing
Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry
Journal of Computational Physics
A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow
Journal of Computational Physics
A vortex particle method for two-dimensional compressible flow
Journal of Computational Physics
A Data-Clustering Algorithm on Distributed Memory Multiprocessors
Revised Papers from Large-Scale Parallel Data Mining, Workshop on Large-Scale Parallel KDD Systems, SIGKDD
Axisymmetric vortex method for low-mach number, diffusion-controlled combustion
Journal of Computational Physics
On Partitioning Dynamic Adaptive Grid Hierarchies
HICSS '96 Proceedings of the 29th Hawaii International Conference on System Sciences Volume 1: Software Technology and Architecture
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Fast, adaptive summation of point forces in the two-dimensional Poisson equation
Journal of Computational Physics
Modified interpolation kernels for treating diffusion and remeshing in vortex methods
Journal of Computational Physics
The N-body problem throughout the computer science curriculum
Journal of Computing Sciences in Colleges - Papers of the twelfth annual CCSC Northeastern Conference
A fast 3D particle method for the simulation of buoyant flow
Journal of Computational Physics
Cluster based partitioning for agent-based crowd simulations
Winter Simulation Conference
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode
SIAM Journal on Scientific Computing
Grid-based partitioning for large-scale distributed agent-based crowd simulation
Proceedings of the Winter Simulation Conference
Hi-index | 31.47 |
A number of complex physical problems can be approached through N-body simulation, from fluid flow at high Reynolds number to gravitational astrophysics and molecular dynamics. In all these applications, direct summation is prohibitively expensive for large N and thus hierarchical methods are employed for fast summation. This work introduces new algorithms, based on k-means clustering, for partitioning parallel hierarchical N-body interactions. We demonstrate that the number of particle-cluster interactions and the order at which they are performed are directly affected by partition geometry. Weighted k-means partitions minimize the sum of clusters' second moments and create well-localized domains, and thus reduce the computational cost of N-body approximations by enabling the use of lower-order approximations and fewer cells. We also introduce compatible techniques for dynamic load balancing, including adaptive scaling of cluster volumes and adaptive redistribution of cluster centroids. We demonstrate the performance of these algorithms by constructing a parallel treecode for vortex particle simulations, based on the serial variable-order Cartesian code developed by Lindsay and Krasny [Journal of Computational Physics 172 (2) (2001) 879-907]. The method is applied to vortex simulations of a transverse jet. Results show outstanding parallel efficiencies even at high concurrencies, with velocity evaluation errors maintained at or below their serial values; on a realistic distribution of 1.2 million vortex particles, we observe a parallel efficiency of 98% on 1024 processors. Excellent load balance is achieved even in the face of several obstacles, such as an irregular, time-evolving particle distribution containing a range of length scales and the continual introduction of new vortex particles throughout the domain. Moreover, results suggest that k-means yields a more efficient partition of the domain than a global oct-tree.