## On Partitioning Dynamic Adaptive Grid Hierarchies (1996)

Venue: | Proceedings of the 29th Annual Hawaii International Conference on System Sciences |

Citations: | 74 - 22 self |

### BibTeX

@INPROCEEDINGS{Parashar96onpartitioning,

author = {Manish Parashar and James C. Browne},

title = {On Partitioning Dynamic Adaptive Grid Hierarchies},

booktitle = {Proceedings of the 29th Annual Hawaii International Conference on System Sciences},

year = {1996},

pages = {604--613}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents a computationally efficient runtime partitioning and load-balancing scheme for the Distributed Adaptive Grid Hierarchies that underlie adaptive mesh-refinement methods. The partitioning scheme yields an efficient parallel computational structure that maintains locality to reduce communications. Further, it enables dynamic re-partitioning and loadbalancing of the adaptive grid hierarchy to be performed cost-effectively. The run-time partitioning support presented has been implemented within the framework of a data-management infrastructure supporting dynamic distributed data-structures for parallel adaptive numerical techniques. This infrastructure is the foundational layer of a computational toolkit for the Binary Black-Hole NSF Grand Challenge project. 1 Introduction Dynamically adaptive methods for the solution of partial differential equations that employ locally optimal approximations can yield highly advantageous ratios for cost/accuracy when compared to metho...

### Citations

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Design and Analysis of Spatial Data Structures
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Citation Context ...to appropriately decomposing its one-dimensional representation. The partitioning scheme first defines an extendable, ordered index space using extendible hashing techniques [1]. Space-filling curves =-=[2, 3]-=- are then used to define a mapping from the multi-dimensional grid hierarchy to the linear index-space. The self-similar nature of these mappings is exploited to maintain locality across levels of the... |

416 |
Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations
- Berger, Oliger
- 1984
(Show Context)
Citation Context ...even finer grids are overlayed on these regions. The resulting grid structure is a dynamic adaptive grid hierarchy. The adaptive grid hierarchy corresponding to the AMR formulation by Berger & Oliger =-=[4]-=- is shown in Figure 1. Operation on the hierarchy defined by this algorithm are outlined below: Time Integration: Time integration is the update operation performed on each grid at each level of the a... |

299 |
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- Sagan
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Citation Context ...etailed discussion of the design of these data-structures is presented in [5]. 4.1 Space-Filling Curves Peano-Hilbert Order Morton Order Figure 3: Space-Filling Curves - Examples Space-filling curves =-=[2, 3, 6]-=- are a class of locality preserving mappings from d-dimensional space to 1dimensional space, i.e. N d ! N 1 , such that each point in N d is mapped to a unique point or index in N 1 . Two such mapping... |

96 |
Sur une courbe, qui remplit toute une aire plane
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Citation Context ...to appropriately decomposing its one-dimensional representation. The partitioning scheme first defines an extendable, ordered index space using extendible hashing techniques [1]. Space-filling curves =-=[2, 3]-=- are then used to define a mapping from the multi-dimensional grid hierarchy to the linear index-space. The self-similar nature of these mappings is exploited to maintain locality across levels of the... |

37 | Distributed Dynamic Data-Structures for Parallel Adaptive Mesh Refinement
- Parashar, Browne
- 1995
(Show Context)
Citation Context ...ire adaptive grid hierarchy. The SDDG/DAGH linear representation is generated using space-filling curves introduced below. A detailed discussion of the design of these data-structures is presented in =-=[5]-=-. 4.1 Space-Filling Curves Peano-Hilbert Order Morton Order Figure 3: Space-Filling Curves - Examples Space-filling curves [2, 3, 6] are a class of locality preserving mappings from d-dimensional spac... |

12 | An infrastructure for parallel adaptive mesh-refinement techniques
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Citation Context ... a set of SDDG lists. 5 Experimental Evaluations The run-time partitioning support described in this paper has been incorporated into a data-management infrastructure for distributed hierarchical AMR =-=[7]-=-. The infrastructure is implemented as a C++ class library on top of the MPI [8] communication system, P2 P3 P0 P1 P2 P3 P0 P1 1 2 3 7 11 15 14 13 12 0 4 8 1 2 3 7 5 6 9 10 11 15 14 13 12 {0 1-0 1 5 4... |

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Extendible Hashing - A Fast Access Mechanism for Dynamic Files
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Citation Context ...hierarchy is thus reduced to appropriately decomposing its one-dimensional representation. The partitioning scheme first defines an extendable, ordered index space using extendible hashing techniques =-=[1]-=-. Space-filling curves [2, 3] are then used to define a mapping from the multi-dimensional grid hierarchy to the linear index-space. The self-similar nature of these mappings is exploited to maintain ... |

4 |
Hyperbolic System for Numerical Relativity
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Citation Context ... the datamanagement infrastructure. H3expresso is a "concentrated " version of the full H version 3.3 code that solves the general relativistic Einstein's Equations in a variety of physical =-=scenarios [9]-=-. The original H3expresso code is non-adaptive and is implemented in Fortran 90. A distributed and adaptive version of H3expresso has been implemented on top of the data-management infrastructure by s... |