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A 2D Topology-Adaptive Mesh Deformation Framework for Mesh Warping

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New Challenges in Grid Generation and Adaptivity for Scientific Computing

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 5))

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Abstract

We propose a framework for performing anisotropic mesh deformations. Our goal is to produce high quality meshes with no inverted elements on domains which undergo large deformations. To the greatest extent possible, the meshes should have similar element shape; however, topological changes are performed as necessary in order to improve mesh quality. Our framework is based upon the previous work of two of the authors and their collaborators (Kim et al., Int. J. Numer. Methods Eng. 94(1):20–42, 2013; Kim et al., Computer and Mathematics with Applications, Submitted, November 2014) and consists of four steps. The first step is to perform anisotropic finite element-based mesh warping to estimate the interior vertex positions based upon an appropriate choice of the PDE coefficients. The second step is to perform multiobjective mesh optimization in order to eliminate inverted elements and improve element shape. Edge swaps are then performed to further improve the mesh quality. A final mesh smoothing pass is then performed. Our numerical results show that our framework can be used to generate high quality meshes with no inverted elements for very large deformations. In particular, the addition of topological changes to our hybrid mesh deformation algorithm (Kim et al., Computer and Mathematics with Applications, Submitted, November 2014) proved to be an extremely efficient way of improving the mesh quality.

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Acknowledgements

The work of the third author is supported in part by NSF grant CAREER Award ACI-1330054 (formerly OCI-1054459). The authors wish to thank the anonymous referee for his/her careful reading of the paper and for the helpful suggestions which strengthened it.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Incheon National University, Incheon, South Korea

    Jibum Kim

  2. CD-adapco, Austin, TX, 78750, USA

    David McLaurin

  3. University of Kansas, Lawrence, KS, 66045, USA

    Suzanne M. Shontz

Authors
  1. Jibum Kim
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  2. David McLaurin
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  3. Suzanne M. Shontz
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Corresponding author

Correspondence to Suzanne M. Shontz .

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Editors and Affiliations

  1. MOX Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Simona Perotto

  2. MOX Dipartimento di Matematica, Politecnico di Milano, Milano, Milano, Italy

    Luca Formaggia

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Kim, J., McLaurin, D., Shontz, S.M. (2015). A 2D Topology-Adaptive Mesh Deformation Framework for Mesh Warping. In: Perotto, S., Formaggia, L. (eds) New Challenges in Grid Generation and Adaptivity for Scientific Computing. SEMA SIMAI Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06053-8_13

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