Filling space with tetrahedra

In the context of 3D finite element meshes various options for filling an i ndefinite space (such as would be approached within a fine mesh) with tetra hedra are considered. This problem is not trivial as it is in 2-D since, un like equilateral triangles, regular tetrahedra cannot be fitted together to fill space. Various groupings, or assemblies, which can be repeated indefi nitely to fill space are considered. By altering the shape of the tetrahedr a in one of these to minimize a suitable function a unique shape of tetrahe dron is obtained which optimizes the conditioning. The mesh thus produced i s shown to be better conditioned than alternatives based on assemblies of d ifferent shaped tetrahedra. A number of conditioning measures are used to c onfirm this. Finally, actual meshes which fit boundaries are briefly consid ered. Copyright (C) 1999 John Wiley & Sons, Ltd.