A Unifying Data Structure for Hierarchical Methods

We present a data structure for supporting the access patterns required by most scientific applications that employ hierarchical methods. The data structure, termed the Distribution Independent Adaptive Tree, efficiently supports both grid-based and particle-based methods. We present efficient algorithms for most access patterns encountered in such applications: particle insertion/deletion/splitting, grid cell insertion/deletion, nearest neighbor queries, spherical region queries and computing long-range interactions. Apart from being an efficient data structure for an individual hierarchical method, the data structure is useful in applications that involve simultaneous application of multiple methods.

[1]  S. Rao Kosaraju,et al.  A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields , 1995, JACM.

[2]  Valerie E. Taylor,et al.  Parallel Molecular Dynamics: Implications for Massively Parallel Machines , 1997, J. Parallel Distributed Comput..

[3]  M. S. Warren,et al.  A parallel hashed Oct-Tree N-body algorithm , 1993, Supercomputing '93.

[4]  J.C. Browne,et al.  A Common Data Management Infrastructure for Adaptive Algorithms for PDE Solutions , 1997, ACM/IEEE SC 1997 Conference (SC'97).

[5]  Hanan Samet,et al.  Applications of spatial data structures , 1989 .

[6]  Pravin M. Vaidya,et al.  AnO(n logn) algorithm for the all-nearest-neighbors Problem , 1989, Discret. Comput. Geom..

[7]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[8]  Marios D. Dikaiakos,et al.  A performance study of cosmological simulations on message-passing and shared-memory multiprocessors , 1996, ICS '96.

[9]  Michael Norman,et al.  Autonomous hierarchical adaptive mesh refinement for multiscale simulations , 1996 .

[10]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

[11]  L. Greengard.  The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[12]  Karsten Schwan,et al.  Design and Analysis of a Parallel Molecular Dynamics Application , 1996, J. Parallel Distributed Comput..

[13]  James C. Browne,et al.  Distributed Dynamic Data-Structures for Parallel Adaptive Mesh-Refinement , 1995 .

[14]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[15]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[16]  Kenneth L. Clarkson,et al.  Fast algorithms for the all nearest neighbors problem , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[17]  L. Hernquist,et al.  TREESPH: A Unification of SPH with the Hierarchical Tree Method , 1989 .

[18]  Courtenay T. Vaughan,et al.  Parallel Transient Dynamics Simulations: Algorithms for Contact Detection and Smoothed Particle Hydrodynamics , 1998, J. Parallel Distributed Comput..

[19]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .