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

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

Applied Mathematics and Computation, 2024, vol. 472, issue C

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.

Keywords: Tetrahedra; Longest Edge Bisection; Meshes; Similarity classes (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324001036

DOI: 10.1016/j.amc.2024.128631

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