Prof. J. Shewchuk (University of California at Berkeley, USA)
Thursday, November 15, 2018 - 14:00
Weierstraß-Institut
Mohrenstr. 39, 10117 Berlin, Erhard-Schmidt-Hörsaal, Erdgeschoss
Seminar Numerische Mathematik
Most algorithms for guaranteed-quality tetrahedral mesh generation create Delaunay meshes. Delaunay triangulations have many good properties, but the requirement that all tetrahedra be Delaunay often forces mesh generators to overrefine where boundary polygons meet at small angles---that is, they produce too many tetrahedra, making them too small. Relaxing the Delaunay property makes it possible both to reduce overrefinement and to obtain higher-quality tetrahedra.
We describe a provably good algorithm that generates high-quality meshes that are *constrained* Delaunay triangulations, rather than purely Delaunay. This change has two big advantages: it allows us to generate higher-quality tetrahedra than purely Delaunay algorithms do, and it allows us to cope much more successfully with domains that have small angles. Both theory and an implementation show that our algorithm does not overrefine near small domain angles.
submitted by lawrenz (marion.lawrenz@wias-berlin.de, 030 20372566)