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Distortion and quality measures for validating and generating high-order tetrahedral meshes

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Abstract

A procedure to quantify the distortion (quality) of a high-order mesh composed of curved tetrahedral elements is presented. The proposed technique has two main applications. First, it can be used to check the validity and quality of a high-order tetrahedral mesh. Second, it allows the generation of curved meshes composed of valid and high-quality high-order tetrahedral elements. To this end, we describe a method to smooth and untangle high-order tetrahedral meshes simultaneously by minimizing the proposed mesh distortion. Moreover, we present a \(p\)-continuation procedure to improve the initial configuration of a high-order mesh for the optimization process. Finally, we present several results to illustrate the two main applications of the proposed technique.

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Acknowledgments

Work partially sponsored by the Spanish Ministerio de Ciencia e Innovación (Grant DPI2011-23058), by the Ferran Sunyer i Balaguer Foundation (Grant FSB 2013), and by CUR from DIUE of the Generalitat de Catalunya and the European Social Fund (Grant FI-DGR).

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Authors and Affiliations

  1. Laboratori de Càlcul Numèric (LaCàN), Universitat Politècnica de Catalunya, 08034 , Barcelona, Spain

    Abel Gargallo-Peiró & Josep Sarrate

  2. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA , 02139, USA

    Xevi Roca & Jaime Peraire

Authors
  1. Abel Gargallo-Peiró
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  2. Xevi Roca
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  3. Jaime Peraire
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  4. Josep Sarrate
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Corresponding author

Correspondence to Abel Gargallo-Peiró.

Additional information

A preliminary short version of this work appeared in the Proceedings of the 2013 International Meshing Roundtable [13].

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Gargallo-Peiró, A., Roca, X., Peraire, J. et al. Distortion and quality measures for validating and generating high-order tetrahedral meshes. Engineering with Computers 31, 423–437 (2015). https://doi.org/10.1007/s00366-014-0370-1

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