Filling space with tetrahedra

In the context of 3D Þnite element meshes various options for Þlling an indeÞnite space (such as would be approached within a Þne mesh) with tetrahedra are considered. This problem is not trivial as it is in 2-D since, unlike equilateral triangles, regular tetrahedra cannot be Þtted together to Þll space. Various groupings, or assemblies, which can be repeated indeÞnitely to Þll space are considered. By altering the shape of the tetrahedra in one of these to minimize a suitable function a unique shape of tetrahedron is obtained which optimizes the conditioning. The mesh thus produced is shown to be better conditioned than alternatives based on assemblies of di¤erent shaped tetrahedra. A number of conditioning measures are used to conÞrm this. Finally, actual meshes which Þt boundaries are brießy considered. Copyright