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P2 Mesh Optimization Operators

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27th International Meshing Roundtable (IMR 2018)

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Abstract

Curved mesh generation starting from a P 1 mesh relies on mesh deformation and mesh optimization techniques. Mesh optimization techniques consist in locally modifying the mesh in order to improve it with respect to a given quality criterion. This work presents the generalization of two mesh quality-based optimization operators to P 2 meshes. The generalized operators consist in mesh smoothing and generalized swapping. With the use of these operators, P 2 mesh generation starting from a P 1 mesh is more robust and P 2 connectivity-change moving mesh methods for large displacements are now possible.

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References

  1. F. Alauzet, A changing-topology moving mesh technique for large displacements. Eng. Comput. 30(2), 175–200 (2014)

    Article  Google Scholar 

  2. F. Alauzet, A. Loseille, D. Marcum, On a robust boundary layer mesh generation process, in 55th AIAA Aerospace Sciences Meeting, AIAA Paper 2017-0585, Grapevine, TX, USA, 2017

    Google Scholar 

  3. H. Borouchaki, P.L. George, Meshing, Geometric Modeling and Numerical Simulation 1: Form Functions, Triangulations and Geometric Modeling (Wiley, Hoboken, 2017)

    Book  Google Scholar 

  4. P.G. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland, Amsterdam, 1978)

    MATH  Google Scholar 

  5. M. Fortunato, P.-O. Persson, High-order unstructured curved mesh generation using the Winslow equations. J. Comput. Phys. 307, 1–14 (2016)

    Article  MathSciNet  Google Scholar 

  6. P.J. Frey, P.L. George, Mesh Generation: Application to Finite Elements (Wiley, New York, 2008)

    Book  Google Scholar 

  7. P.L. George, H. Borouchaki, Construction of tetrahedral meshes of degree two. Int. J. Numer. Methods Eng. 90(9), 1156–1118 (2012)

    Article  MathSciNet  Google Scholar 

  8. P.L. George, H. Borouchaki, F. Alauzet, P. Laug, A. Loseille, L. Maréchal, Meshing, Geometric Modeling and Numerical Simulation 2: Metrics, Meshing and Mesh Adaptation (Wiley, 2019)

    Google Scholar 

  9. R. Hartmann, T. Leicht, Generation of unstructured curvilinear grids and high-order discontinuous Galerkin discretization applied to a 3D high-lift configuration. Int. J. Numer. Methods Fluids 82(6), 316–333 (2016)

    Article  MathSciNet  Google Scholar 

  10. J.S. Hesthaven, T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis and Applications. (Springer, New York, 2008)

    Book  Google Scholar 

  11. A. Johnen, J.-F. Remacle, C. Geuzaine, Geometrical validity of curvilinear finite elements. J. Comput. Phys. 233, 359–372 (2013)

    Article  MathSciNet  Google Scholar 

  12. S.L. Karman, J.T. Erwin, R.S. Glasby, D. Stefanski, High-order mesh curving using WCN mesh optimization, in 46th AIAA Fluid Dynamics Conference, AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics, 2016

    Google Scholar 

  13. D.C. Liu, J. Nocedal, On the limited memory BFGS method for large scale optimization. Math. Program. 45(1), 503–528 (1989)

    Article  MathSciNet  Google Scholar 

  14. D. Moxey, D. Ekelschot, Ü. Keskin, S.J. Sherwin, J. Peirò, High-order curvilinear meshing using a thermo-elastic analogy. Comput. Aided Des. 72, 130–139 (2016)

    Article  Google Scholar 

  15. E. Ruiz-Gironès, X. Roca, J. Sarrate, High-order mesh curving by distortion minimization with boundary nodes free to slide on a 3D CAD representation. Comput. Aided Des. 72, 52–64 (2016); 23rd International Meshing Roundtable Special Issue: Advances in Mesh Generation

    Article  Google Scholar 

  16. T. Toulorge, C. Geuzaine, J.-F. Remacle, J. Lambrechts, Robust untangling of curvilinear meshes. J. Comput. Phys. 254, 8–26 (2013)

    Article  MathSciNet  Google Scholar 

  17. T. Toulorge, J. Lambrechts, J.-F. Remacle, Optimizing the geometrical accuracy of curvilinear meshes. J. Comput. Phys. 310, 361–380 (2016)

    Article  MathSciNet  Google Scholar 

  18. M. Turner, J. Peirò, D. Moxey, A variational framework for high-order mesh generation. Procedia Eng. 163(Supplement C), 340–352 (2016); 25th International Meshing Roundtable

    Article  Google Scholar 

  19. J. Vanharen, G. Puigt, X. Vasseur, J.-F. Boussuge, P. Sagaut, Revisiting the spectral analysis for high-order spectral discontinuous methods. J. Comput. Phys. 337, 379–402 (2017)

    Article  MathSciNet  Google Scholar 

  20. A. Vlachos, P. Jörg, C. Boyd, J.L. Mitchell, Curved PN triangles, in Proceedings of the 2001 Symposium on Interactive 3D Graphics, I3D ’01 (ACM, New York, 2001), pp. 159–166

    Book  Google Scholar 

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Acknowledgements

This work was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.

The authors also would like to thank the reviewers for their fruitful remarks.

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Correspondence to Rémi Feuillet .

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Feuillet, R., Loseille, A., Alauzet, F. (2019). P2 Mesh Optimization Operators. 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_1

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