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Local Bisection for Conformal Refinement of Unstructured 4D Simplicial Meshes

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27th International Meshing Roundtable (IMR 2018)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 127))

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Abstract

We present a conformal bisection procedure for local refinement of 4D unstructured simplicial meshes with bounded minimum shape quality. Specifically, we propose a recursive refine to conformity procedure in two stages, based on marking bisection edges on different priority levels and defining specific refinement templates. Two successive applications of the first stage ensure that any 4D unstructured mesh can be conformingly refined. In the second stage, the successive refinements lead to a cycle in the number of generated similarity classes and thus, we can ensure a bound over the minimum shape quality. In the examples, we check that after successive refinement the mesh quality does not degenerate. Moreover, we refine a 4D unstructured mesh and a space-time mesh (3D + 1D) representation of a moving object.

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Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 715546. This work has also received funding from the Generalitat de Catalunya under grant number 2017 SGR 1731. The work of X. Roca has been partially supported by the Spanish Ministerio de Economía y Competitividad under the personal grant agreement RYC-2015-01633.

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Authors and Affiliations

  1. Computer Applications in Science and Engineering, Barcelona Supercomputing Center, Barcelona, Spain

    Guillem Belda-Ferrín, Abel Gargallo-Peiró & Xevi Roca

Authors
  1. Guillem Belda-Ferrín
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  2. Abel Gargallo-Peiró
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  3. Xevi Roca
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Corresponding author

Correspondence to Abel Gargallo-Peiró .

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Editors and Affiliations

  1. Barcelona Supercomputing Center, Mataró, Barcelona, Spain

    Xevi Roca

  2. Inria, Palaiseau, France

    Adrien Loseille

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Belda-Ferrín, G., Gargallo-Peiró, A., Roca, X. (2019). Local Bisection for Conformal Refinement of Unstructured 4D Simplicial Meshes. In: Roca, X., Loseille, A. (eds) 27th International Meshing Roundtable. IMR 2018. Lecture Notes in Computational Science and Engineering, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-030-13992-6_13

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