2D FE Quad Mesh Smoothing via Angle-Based Optimization

  • Hongtao Xu
  • Timothy S. Newman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3514)


A new mesh smoothing algorithm that can improve quadrilateral mesh quality is presented. Poor quality meshes can produce inaccurate finite element analysis; their improvement is important. The algorithm improves mesh quality by adjusting the position of the mesh’s internal nodes based on optimization of a torsion spring system using a Gauss-Newton-based approach. The approach obtains a reasonably optimal location of each internal node by optimizing the spring system’s objective function. The improvement offered by applying the algorithm to real meshes is also exhibited and objectively evaluated using suitable metrics.


Internal Node Mesh Quality Bisectional Line Quadrilateral Mesh Smoothing Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Freitag, L.: On Combining Laplacian and Optimization-Based Mesh Smoothing Techniques. In: Proc., 6th Int’l Mesh. Roundtable, London, AMD-vol. 220, pp. 375–390 (1997)Google Scholar
  2. 2.
    Zhou, T., Shimada, K.: An Angle-Based Approach to Two-Dimensional Mesh Smoothing. In: Proc., 9th Int’l Mesh, Roundtable, New Orleans, pp. 373–384 (2000)Google Scholar
  3. 3.
    Canann, S., Stephenson, M., Blacker, T.: Optismoothing: An optimization-driven approach to mesh smoothing. Finite Elements in Analysis and Design 13, 185–190 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Li, T., Wong, S., Hon, Y., Armstrong, C., McKeag, R.: Smoothing by optimisation for a quadrilateral mesh with invalid element. Finite Elements in Analysis and Design 34, 37–60 (2000)CrossRefGoogle Scholar
  5. 5.
    Amenta, N., Bern, M., Eppstein, D.: Optimal point placement for mesh smoothing. In: Proc., 8th ACM-SIAM Symp. on Disc. Alg., New Orleans, pp. 528–537 (1997)Google Scholar
  6. 6.
    Canann, S., Tristano, J., Staten, M.: An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular, Quadrilateral, and Quad-Dominant Meshes. In: Proc., 7th Int’l Mesh, Roundtable, Dearborn, Mich., pp. 479–494 (1998)Google Scholar
  7. 7.
    Freitag, J., Jones, M., Plassmann, P.: A Parallel Algorithm for Mesh Smoothing. SIAM J. on Scientific Computing 20, 2023–2040 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Hansbo, P.: Generalized Laplacian Smoothing of Unstructured Grids. Communications in Numerical Methods in Engineering 11, 455–464 (1995)zbMATHCrossRefGoogle Scholar
  9. 9.
    Field, D.: Laplacian Smoothing and Delaunay Triangulations. Comm. in Applied Numerical Methods 4, 709–712 (1988)zbMATHCrossRefGoogle Scholar
  10. 10.
    Xu, H.: An Optimization Approach for 2D Finite Element Mesh Smoothing, M. S. Thesis, Dept. of Comp. Sci., Univ. of Ala. in Huntsville, Huntsville (2003)Google Scholar
  11. 11.
    Nocedal, J., Wright, S.: Numerical Optimization. Springer, New York (1999)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hongtao Xu
    • 1
  • Timothy S. Newman
    • 1
  1. 1.Department of Computer ScienceUniversity of Alabama in HuntsvilleHuntsville

Personalised recommendations