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Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method

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Abstract

The adaptive variable p- and hp-version finite element method can achieve exponential convergence rate when a near optimal finite element mesh is provided. For general 3D domains, near optimal p-version meshes require large curved elements over the smooth portions of the domain, geometrically graded curved elements to the singular edges and vertices, and a controlled layer of curved prismatic elements in the thin sections. This paper presents a procedure that accepts a CAD solid model as input and creates a curved mesh with the desired characteristics. One key component of the procedure is the automatic identification of thin sections of the model through a set of discrete medial surface points computed from an Octree-based tracing algorithm and the generation of prismatic elements in the thin directions in those sections. The second key component is the identification of geometric singular edges and the generation of geometrically graded meshes in the appropriate directions from the edges. Curved local mesh modification operations are applied to ensure the mesh can be curved to the geometry to the required level of geometric approximation.

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Acknowledgments

This work was supported by the National Science Foundation through SBIR grant number DMI-0132742.

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Authors and Affiliations

  1. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Xiao-Juan Luo, Mark S. Shephard & Lu-Zhong Yin

  2. Kitware Inc., Clifton Park, NY, 12065, USA

    Robert M. O’Bara

  3. Simmetrix Inc., Clifton Park, NY, 12065, USA

    Rocco Nastasi & Mark W. Beall

Authors
  1. Xiao-Juan Luo
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  2. Mark S. Shephard
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  3. Lu-Zhong Yin
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  4. Robert M. O’Bara
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  5. Rocco Nastasi
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  6. Mark W. Beall
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Corresponding author

Correspondence to Mark S. Shephard.

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Luo, XJ., Shephard, M.S., Yin, LZ. et al. Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method. Engineering with Computers 26, 215–229 (2010). https://doi.org/10.1007/s00366-009-0163-0

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  • DOI: https://doi.org/10.1007/s00366-009-0163-0

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