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Distributed Octree Data Structures and Local Refinement Method for the Parallel Solution of Three-Dimensional Conservation Laws

  • J. E. Flaherty
  • R. M. Loy
  • M. S. Shephard
  • M. L. Simone
  • B. K. Szymanski
  • J. D. Teresco
  • L. H. Ziantz
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 113)

Abstract

Conservation laws are solved by a local Galerkin finite element procedure with adaptive space-time mesh refinement and explicit time integration. A distributed octree structure representing a spatial decomposition of the domain is used for mesh generation, and later may be used to correct for processor load imbalances introduced at adaptive enrichment steps. A Courant stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size. Computational results are presented for the three-dimensional Euler equations of compressible flow solved on an IBM SP2 computer. The problem examined is the flow inside a perforated shock tube.

Keywords

Mesh Generation Error Indicator Adaptive Finite Element Size Weighting Rejection Threshold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • J. E. Flaherty
    • 1
  • R. M. Loy
    • 1
  • M. S. Shephard
    • 1
  • M. L. Simone
    • 1
  • B. K. Szymanski
    • 1
  • J. D. Teresco
    • 1
  • L. H. Ziantz
    • 1
  1. 1.Scientific Computation Research CenterRensselaer Polytechnic InstituteTroyUSA

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