Filling space with tetrahedra. (English) Zbl 0941.65012
This paper is a contribution to the increasing use of tetrahedra in the finite element methods for three-dimensional problems. The author considers various options for filling a space with tetrahedra. Three important criteria have been suggested for assessing the quality of different assemblies: the conditioning efficiency, the (lack of) variation in volume, and the ergonomics of mesh orientation. The relevant comparisons are between the so-called cub5, oct4, cub6 and par6 patterns as well as the icosahedral assembly of D. A. Field [Implementing Watson’s algorithm in three-dimensions. Proc. 2nd Annual ACM Symposium on Computational Geometry, 246-259 (1986)]. The main conlusion is that the space-filling assembly involving just one shape of tetrahedron – the isotet – is the best conditioned. This answers the question posed by Field.
Reviewer: Mária Lukáčová (Brno)
MSC:
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
References:
| [1] | Weatherill, International Journal for Numerical Methods in Engineering 37 pp 2005– (1994) |
| [2] | Weatherill, AIAA Journal 33 pp 1196– (1995) |
| [3] | Canales dam?a 3D collapse settlement study. Internal Report No. CR/902/95, Department of Civil Engineering, University of Wales Swansea., 1995. |
| [4] | Bowyer, Computer Journal 24 pp 162– (1981) |
| [5] | Cavendish, International Journal for Numerical Methods in Engineering 21 pp 329– (1985) |
| [6] | Field, International Journal for Numerical Methods in Engineering 31 pp 413– (1991) |
| [7] | Lohner, International Journal for Numerical Methods in Fluids 8 pp 1135– (1988) · Zbl 0661.65017 |
| [8] | Peraire, International Journal for Numerical Methods in Engineering 26 pp 2135– (1988) |
| [9] | Watson, Computer Journal 24 pp 167– (1981) |
| [10] | Weatherill, S?dhan? 16 pp 1– (1991) |
| [11] | Senechal, Mathematics Magazine 54 pp 227– (1981) |
| [12] | Sommerville, Proceedings of the Edinburgh Mathematical Society 41 pp 49– (1923) |
| [13] | Implementing Watson’s algorithm in three dimensions. Proceedings of the 2nd Annual ACM Symposium on Computational Geometry 1986:246-259. |
| [14] | Liu, Mathematics of Computation 63 pp 141– (1994) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
