A fast algorithm for particle simulations
Journal of Computational Physics
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Journal of Parallel and Distributed Computing
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Polygon-assisted JPEG and MPEG compression of synthetic images
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multipole algorithms for molecular dynamics simulation on high performance computers
Multipole algorithms for molecular dynamics simulation on high performance computers
Greengard's N-Body Algorithm is Not Order N
SIAM Journal on Scientific Computing
Error Analysis of Symplectic Multiple Time Stepping
SIAM Journal on Numerical Analysis
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ACM Transactions on Graphics (TOG)
Improving Error Bounds for Multipole-Based Treecodes
SIAM Journal on Scientific Computing
Parallel hierarchical solvers and preconditioners for boundary element methods
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
Single Resolution Compression of Arbitrary Triangular Meshes with Properties
DCC '99 Proceedings of the Conference on Data Compression
Parallel multigrid summation for the N-body problem
Journal of Parallel and Distributed Computing
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This article presents an analytical and computational framework for the compression of particle data resulting from hierarchical approximate treecodes such as the Barnes--Hut and Fast Multipole Methods. Due to approximations introduced by hierarchical methods, various parameters (such as position, velocity, acceleration, potential) associated with a particle can be bounded by distortion radii. Using this distortion radii, we develop storage schemes that guarantee error bounds while maximizing compression. Our schemes make extensive use of spatial and temporal coherence of particle behavior and yield compression ratios higher than 12:1 over raw data, and 6:1 over gzipped (LZ) raw data for selected simulation instances. We demonstrate that for uniform distributions with 2M particles, storage requirements can be reduced from 24 MB to about 1.8 MB (about 7 bits per particle per timestep) for storing particle positions. This is significant because it enables faster storage/retrieval, better temporal resolution, and improved analysis. Our results are shown to scale from small systems (2K particles) to much larger systems (over 2M particles). The associated algorithm is asymptotically optimal in computation time (O(n)) with a small constant. Our implementations are demonstrated to run extremely fast---much faster than the time it takes to compute a single time-step advance. In addition, our compression framework relies on a natural hierarchical representation upon which other analysis tasks such as segmented and window retrieval can be built.