Simplicial grid refinement: On Freudenthal’s algorithm and the optimal number of congruence classes. (English) Zbl 0949.65128

Bey, Jürgen

Numer. Math. 85, No. 1, 1-29 (2000).

This paper concerns the simplex refinement algorithm of H. Freudenthal [Ann. of Math., II. Ser. 43, 580-582 (1942; Zbl 0060.40701)]. The algorithm subdivides any given \((n)\)-simplex into \(2^n\) subsimplices in such a way that recursive application results in a hierarchy of consistent triangulations. The investigations concentrate in particular on the number of congruence classes generated by recursive refinements.

Reviewer: Laura-Iulia Aniţa (Iaşi)

MSC:

65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65D18	Numerical aspects of computer graphics, image analysis, and computational geometry

Keywords:

simplicial grid; simplex refinement algorithm; triangulations

Citations:

Zbl 0060.40701