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Bisection-Based Triangulations of Nested Hypercubic Meshes

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Proceedings of the 19th International Meshing Roundtable

Abstract

Hierarchical spatial decompositions play a fundamental role in many disparate areas of scientific and mathematical computing since they enable adaptive sampling of large problem domains. Although the use of quadtrees, octrees, and their higher dimensional analogues is ubiquitous, these structures generate meshes with cracks, which can lead to discontinuities in functions defined on their domain. In this paper, we propose a dimension-independent triangulation algorithm based on regular simplex bisection to locally decompose adaptive hypercubic meshes into high quality simplicial complexes with guaranteed geometric and adaptivity constraints.

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Author information

Authors and Affiliations

  1. University of Maryland, College Park, USA

    Kenneth Weiss

  2. University of Genova, Genova, Italy

    Leila De Floriani

Authors
  1. Kenneth Weiss
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  2. Leila De Floriani
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Editor information

Editors and Affiliations

  1. Pennsylvania State University, 343J IST Building, 16802, University Park, PA, USA

    Suzanne Shontz

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Weiss, K., De Floriani, L. (2010). Bisection-Based Triangulations of Nested Hypercubic Meshes. In: Shontz, S. (eds) Proceedings of the 19th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15414-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-15414-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15413-3

  • Online ISBN: 978-3-642-15414-0

  • eBook Packages: EngineeringEngineering (R0)

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