Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/54355
Title: Non-equivalent partitions of d-triangles with Steiner points
Authors: Plaza, Ángel 
Suárez, José P. 
Padrón, Miguel A. 
UNESCO Clasification: 120601 Construcción de algoritmos
Keywords: Steiner points
Triangulation
Bisection
Issue Date: 2004
Journal: Applied Numerical Mathematics 
Abstract: In this paper we present lower and upper bounds for the number of equivalence classes of d-triangles with additional or Steiner points. We also study the number of possible partitions that may appear by bisecting a tetrahedron with Steiner points at the midpoints of its edges. This problem arises, for example, when refining a 3D triangulation by bisecting the tetrahedra. To begin with, we look at the analogous 2D case, and then the 1-irregular tetrahedra (tetrahedra with at most one Steiner point on each edge) are classified into equivalence classes, and each element of the class is subdivided into several non-equivalent bisection-based partitions which are also studied. Finally, as an example of the application of refinement and coarsening of 3D bisection-based algorithms, a simulation evolution problem is shown.
URI: http://hdl.handle.net/10553/54355
ISSN: 0168-9274
DOI: 10.1016/j.apnum.2003.12.017
Source: Applied Numerical Mathematics [ISSN 0168-9274], v. 49 (3-4), p. 415-430
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