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Automatic p-version mesh generation for curved domains

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Abstract

To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.

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Notes

  1. A mesh face or edge that lies on a model face is “classified on that model face” and a mesh edge that lies on a model classified on a model edge is “classified on that model edge.”

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Acknowledgements

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

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

    Robert M. O’Bara, Rocco Nastasia & Mark W. Beall

Authors
  1. Xiao-Juan Luo
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  2. Mark S. Shephard
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  3. Robert M. O’Bara
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  4. Rocco Nastasia
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  5. Mark W. Beall
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Correspondence to Xiao-Juan Luo.

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Luo, XJ., Shephard, M.S., O’Bara, R.M. et al. Automatic p-version mesh generation for curved domains. Engineering with Computers 20, 273–285 (2004). https://doi.org/10.1007/s00366-004-0295-1

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  • DOI: https://doi.org/10.1007/s00366-004-0295-1

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