Filling space with tetrahedra

Abstract

In the context of 3D finite element meshes various options for filling an indefinite space (such as would be approached within a fine mesh) with tetrahedra are considered. This problem is not trivial as it is in 2-D since, unlike equilateral triangles, regular tetrahedra cannot be fitted together to fill space. Various groupings, or assemblies, which can be repeated indefinitely to fill 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 different shaped tetrahedra. A number of conditioning measures are used to confirm this. Finally, actual meshes which fit boundaries are briefly considered. Copyright © 1999 John Wiley & Sons, Ltd.