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International Meshing Roundtable

IMR 2018: 27th International Meshing Roundtable pp 249–267Cite as

A Construction of Anisotropic Meshes Based on Quasi-Conformal Mapping

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

Abstract

In this paper we discuss an algorithm to generate anisotropic mesh based on metric tensors. We transform this problem to finding a quasi conformal mapping f defined on an isotropic mesh, such that the image of f is an anisotropic triangulation. According to the metric tensors, the Beltrami coefficients of f can be calculated, then we use discrete Yamabe flow to construct f. The topology of the original triangulation will be updated if necessary, while the number of vertices won’t be changed during the process. We also use our method to compute the intersection of functions, and experiments show that the interpolation functions on anisotropic meshes have less errors than the interpolation functions on isotropic mesh.

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Notes

  1. 1.

    Available in FreeFEM++ (http://www.freefem.org).

  2. 2.

    http://www.wias-berlin.de/people/si/detri2.html.

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Author information

Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, China

    Yuxue Ren

  2. Beijing Advanced Innovation Center for Imaging Technology, Capital Normal University, Beijing, China

    Yuxue Ren & Na Lei

  3. DUT-RU ISE, Dalian University of Technology, Dalian, China

    Na Lei

  4. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Hang Si

  5. Department of Computer Science, Stony Brook University, Stony Brook, NY, USA

    Xianfeng David Gu

Authors
  1. Yuxue Ren
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  2. Na Lei
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  3. Hang Si
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  4. Xianfeng David Gu
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Corresponding author

Correspondence to Na Lei .

Editor information

Editors and Affiliations

  1. Barcelona Supercomputing Center, Mataró, Barcelona, Spain

    Xevi Roca

  2. Inria, Palaiseau, France

    Adrien Loseille

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Ren, Y., Lei, N., Si, H., Gu, X.D. (2019). A Construction of Anisotropic Meshes Based on Quasi-Conformal Mapping. 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_14

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