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Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method

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Abstract

The adaptive variable p- and hp-version finite element method can achieve exponential convergence rate when a near optimal finite element mesh is provided. For general 3D domains, near optimal p-version meshes require large curved elements over the smooth portions of the domain, geometrically graded curved elements to the singular edges and vertices, and a controlled layer of curved prismatic elements in the thin sections. This paper presents a procedure that accepts a CAD solid model as input and creates a curved mesh with the desired characteristics. One key component of the procedure is the automatic identification of thin sections of the model through a set of discrete medial surface points computed from an Octree-based tracing algorithm and the generation of prismatic elements in the thin directions in those sections. The second key component is the identification of geometric singular edges and the generation of geometrically graded meshes in the appropriate directions from the edges. Curved local mesh modification operations are applied to ensure the mesh can be curved to the geometry to the required level of geometric approximation.

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References

  1. Luo XJ, Shephard MS, Remacle JF, O’Bara RM, Beall MW, Szabo BA, Actis R (2002) p-version mesh generation issues. In: Proceedings of the 11th international meshing roundtable, Ithaca, September, pp 343–354

  2. Dey S, Shephard MS, Flaherty JE (1997) Geometry-based issues associated with p-version finite element computations. Comput Methods Appl Mech Engrg 150:39–55

    Article  MATH  MathSciNet  Google Scholar 

  3. Dorr MR (1984) The approximation of solutions of the elliptic boundary-value problems via the p-version of the finite element method. SIAM J Numer Anal 21(6):58–76

    Article  MathSciNet  Google Scholar 

  4. Babuska I, Suri M (1994) The p and h-p versions of the finite element method, basic principles and properties. SIAM Rev 36(4):578–632

    Article  MATH  MathSciNet  Google Scholar 

  5. Reddy JN (1999) Theory and analysis of elastic plates. Taylor & Francies, Philadelphia

    Google Scholar 

  6. Donaghy RJ, Armstrong CG, Price MA (2000) Dimensional reduction of surface models for analysis. Eng Comput 16:24–35

    Article  Google Scholar 

  7. Actis RL, Engelstad SP, Szabo BA (2002) Computational requirements in design and design certification. In: Collection of technical papers—43rd AIAA/ASME/ASCE/AHS/ASC structures. Structural dynamics and materials conference, Denver, April, pp 1379–1389

  8. Szabo BA, Sahrmann GJ (1988) Hierarchic plate and shell models based on p-extension. Int J Numer Meth Eng 26:1855–1881

    Article  MATH  Google Scholar 

  9. Shephard MS, George MK (1992) Reliability of automatic 3D mesh generation. Comput Methods Appl Mech Eng 101:443–462

    Article  MATH  Google Scholar 

  10. Luo XJ, Shephard MS, Obara RM, Nastasia R, Beall MW (2004) Automatic p-version mesh generation for curved domains. Eng Comput 20:265–285

    Article  Google Scholar 

  11. Beall MW, Shephard MS (1997) A general topology-based mesh data structure. Int J Numer Meth Eng 40(9):1573–1596

    Article  MathSciNet  Google Scholar 

  12. Lieutier A (2004) Any open bounded subset of r n has the same homotopy type as its medial axis. Comput Aided Des 36:1029–1046

    Article  Google Scholar 

  13. Patrikalakis NM, Gursoy HN (1990) Shape interrogation by medial axis transform. In: ASME advances in design automation, 16th design automation conference, vol 23, Chicago, pp 77–88

  14. Etzion M, Rappoport A (2002) Computing Voronoi skeletons of a 3-D polyhedron by space subdivision. Comput Geom 21:87–120

    Article  MATH  MathSciNet  Google Scholar 

  15. Li XR, Shephard MS, Beall MW (2003) Accounting for curved domains in mesh adaptation. Int J Numer Meth Eng 150:247–276

    Article  Google Scholar 

  16. Garimella R, Shephard MS (2000) Boundary layer mesh generation for viscous flow simulations in complex geometric domain. Int J Numer Meth Eng 49(1–2):193–218

    Article  MATH  Google Scholar 

  17. Szabo BA (1986) Mesh design for the p-version of the finite element method. Comput Methods Appl Mech Eng 55:181–197

    Article  MATH  Google Scholar 

  18. Luo XJ (2005) An automatic adaptive directional variable p-version method in 3-D curved domains, Ph.D thesis. Rensselaer Polytechnic Institute

  19. Dey S, O’Bara RM, Shephard MS (2001) Curvilinear mesh generation in 3D. Comput Aided Des 33:199–209

    Article  Google Scholar 

  20. Sherwin SJ, Peiro J (2002) Mesh generation in curvilinear domains using high order elements. Int J Numer Meth Eng 53:207–223

    Article  MATH  Google Scholar 

  21. Farin G (1992) Curved and surfaces for computer aided geometric design. Academic Press, New York

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Acknowledgments

This work was supported by the National Science Foundation through SBIR grant number DMI-0132742.

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Authors and Affiliations

  1. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Xiao-Juan Luo, Mark S. Shephard & Lu-Zhong Yin

  2. Kitware Inc., Clifton Park, NY, 12065, USA

    Robert M. O’Bara

  3. Simmetrix Inc., Clifton Park, NY, 12065, USA

    Rocco Nastasi & Mark W. Beall

Authors
  1. Xiao-Juan Luo
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  2. Mark S. Shephard
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  3. Lu-Zhong Yin
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  4. Robert M. O’Bara
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  5. Rocco Nastasi
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  6. Mark W. Beall
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Corresponding author

Correspondence to Mark S. Shephard.

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Luo, XJ., Shephard, M.S., Yin, LZ. et al. Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method. Engineering with Computers 26, 215–229 (2010). https://doi.org/10.1007/s00366-009-0163-0

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  • DOI: https://doi.org/10.1007/s00366-009-0163-0

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