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Measuring geometrical quality of different 3D linear element types


In this article, we analyze how to measure quality on meshes composed of different types of 3D linear element. In particular, we focus on meshes composed of tetrahedra, pyramids, prisms and hexahedra. We propose a metric based on the scaled Jacobian that can be applied to all four element types and it is normalized in the range [− 1,1]. We validated empirically its effectiveness to properly detect invalid and bad-quality elements using several test cases where our metric is contrasted with already existing ones. We also coded a simple mesh repair algorithm where the reallocation of the nodes was driven from different quality metrics. The results allow to compare the robustness of each metric and its effectiveness on improving overall mesh quality. Finally, it is known that Jacobian-based metrics fail to detect stretched and flat prisms and hexahedra, so we also propose a normalization of the aspect–ratio in those cases.

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This work has been partially supported by the Franco–Chilean ECOS–Sud Conicyt C16E05 project and by Chilean Fondecyt–1181506 and 1211484 projects.

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Correspondence to Claudio Lobos.

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Lobos, C., Arenas, C., Daines, E. et al. Measuring geometrical quality of different 3D linear element types. Numer Algor (2021).

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  • Quality metric
  • Different element types
  • Finite element method
  • Scaled Jacobian

Mathematics Subject Classification (2010)

  • 65D18
  • 65D20
  • 74P20