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Title: Finite number of similarity classes in Longest Edge Bisection of nearly equilateral tetrahedra
Authors: Trujillo Pino, Agustín Rafael 
Suárez Rivero, José Pablo 
Padrón Medina, Miguel Ángel 
UNESCO Clasification: 1204 Geometría
Keywords: Longest Edge Bisection
Similarity classes
Issue Date: 2024
Journal: Applied Mathematics and Computation 
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. We prove the conjecture given by Adler and improve the bound of 5% to 22.47%. A new algorithm is introduced for the computation of similarity classes in the iterative Longest Edge Bisection (SCLEB) of tetrahedra using a compact and efficient edge-based data structure.
ISSN: 0096-3003
DOI: 10.1016/j.amc.2024.128631
Source: Applied Mathematics and Computation [ISSN 0096-3003], v. 472, 128631, (Julio 2024)
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