Terminal-Edge Algorithms: an Integrated Approach for Mesh Generation

  • Maria-Cecilia Rivara
  • Nancy Hitschfeld-Kahler


In the adaptive finite element context, several algorithms for the refinement and/or derefinement of quality unstructured triangulations, based on the bisection of triangles by its longest edge, have been discussed and used in the last 20 years (see [1]–[5]). In two dimensions, they guarantee the construction of refined, nested and irregular triangulations of analogous quality as the input triangulation.


Delaunay Triangulation Longe Edge Refinement Algorithm Polygonal Region Adaptive Refinement 
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  1. 1.
    M.C. Rivara, Algorithms for refining triangular grids suitable for adaptive and multigrid techniques, Internat. J. Numer. Methods Engrg. 20 (1984), 745–756.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    M.C. Rivara, Selective refinement/derefinement algorithms for sequences of nested triangulations. Internat. J. Numer. Methods Engrg. 28 (1989), 2889–2906.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    M.C. Rivara and C. Levin, A 3d refinement algorithm for adaptive and multigrid techniques, Comm. Appl. Numer. Methods 8 (1992), 281–290.CrossRefMATHGoogle Scholar
  4. 4.
    S.N. Muthukrishnan, P.S. Shiakolos, R.V. Nambiar, and K.L. Lawrence, Simple algorithm for adaptive refinement of three-dimensional finite element tetrahedral meshes, AIAA J. 33 (1995), 928–932.CrossRefMATHGoogle Scholar
  5. 5.
    N. Nambiar, R. Valera, K.L. Lawrence, R.B. Morgan, and D. Amil, An algorithm for adaptive refinement of triangular finite element meshes, Internat. J. Numer. Methods Engrg. 36 (1993), 499–509.CrossRefMATHGoogle Scholar
  6. 6.
    M.C. Rivara and M. Venere, Cost analysis of the longest-side (triangle bisection) refinement algorithms for triangulations, Engineering with Computers 12 (1996), 224–234.CrossRefGoogle Scholar
  7. 7.
    M.C. Rivara, New longest-edge algorithms for the refinement and/ or improvement of unstructured triangulations, Internat. J. Numer. Methods Engrg. 40 (1997), 3313–3324.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    J. Ruppert, A Delaunay refinement algorithm for quality 2-dimensional mesh generation, J. Algorithms 18 (1995), 548–585.MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    N. Hitschfeld and M.C. Rivara, Automatic construction of non-obtuse boundary and/or interface Delaunay triangulations for control volume methods, Internat. J. Numer. Methods Engrg. 55 (2002), 803–816.CrossRefMATHGoogle Scholar
  10. 10.
    N. Hitschfeld, L. Villablanca, J. Krause, and M.C. Rivara, Improving the quality of meshes for the simulation of semiconductor devices using Lepp-based algorithms, Internat. J. Numer. Methods Engrg. 58 (2003), 333–347.CrossRefMATHGoogle Scholar
  11. 11.
    M.C. Rivara, N. Hitschfeld, and R.B. Simpson, Terminal edges Delaunay (small angle based) algorithm for the quality triangulation problem, Computer-Aided Design 33 (2001), 263–277.CrossRefGoogle Scholar
  12. 12.
    M.C. Rivara and M. Palma, New LEPP algorithms for quality polygon and volume triangulation: implementation issues and practical behavior, in Trends in Unstructured Mesh Generation, S.A. Cannan (ed.), Saigal, AMD 220 (1997), 1–8.Google Scholar

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© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Maria-Cecilia Rivara
  • Nancy Hitschfeld-Kahler

There are no affiliations available

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