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Defining a Stretching and Alignment Aware Quality Measure for Linear and Curved 2D 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 define a regularized shape distortion (quality) measure for curved high-order 2D elements on a Riemannian plane. To this end, we measure the deviation of a given 2D element, straight-sided or curved, from the stretching and alignment determined by a target metric. The defined distortion (quality) is suitable to check the validity and the quality of straight-sided and curved elements on Riemannian planes determined by constant and point-wise varying metrics. The examples illustrate that the distortion can be minimized to curve (deform) the elements of a given high-order (linear) mesh and try to match with curved (linear) elements the point-wise alignment and stretching of an analytic target metric tensor.

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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. Barcelona Supercomputing Center, Barcelona, Spain

    Guillermo Aparicio-Estrems, Abel Gargallo-Peiró & Xevi Roca

Authors
  1. Guillermo Aparicio-Estrems
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  2. Abel Gargallo-Peiró
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  3. Xevi Roca
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Correspondence to Xevi Roca .

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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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Aparicio-Estrems, G., Gargallo-Peiró, A., Roca, X. (2019). Defining a Stretching and Alignment Aware Quality Measure for Linear and Curved 2D 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_3

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