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Finite number of similarity classes in Longest Edge Bisection of nearly equilateral tetrahedra

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  • Trujillo-Pino, Agustín
  • Suárez, Jose Pablo
  • Padrón, Miguel A.

Abstract

In 1983 Adler [1] pointed out that if a tetrahedron is nearly equilateral (edge lengths within 5% of each other) and the first and second longest edges are opposite, then the iterative Longest Edge Bisection (LEB) method produces ≤37 similarity classes. The importance of nearly equilateral tetrahedra is that they generate a finite number of similarity classes during the iterative LEB, a desirable property in Finite Element computations.

Suggested Citation

  • Trujillo-Pino, Agustín & Suárez, Jose Pablo & Padrón, Miguel A., 2024. "Finite number of similarity classes in Longest Edge Bisection of nearly equilateral tetrahedra," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    • Handle: RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324001036
    DOI: 10.1016/j.amc.2024.128631
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    References listed on IDEAS

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    1. Jose P. Suárez & Agustín Trujillo & Tania Moreno, 2021. "Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
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