(Semi) regular tetrahedral tilings

Abstract

Triangulation 2D and 3D methods represent an important part of numerical modeling process (e.g. FEM). In many applications it is suitable to use triangulations with a regular structure. Moreover, decomposition with a limited number of different types of tetrahedra enables to reduce the storage and computational demands in the whole modeling process. The submitted contribution presents an overview of possible 3D decompositions using one tetrahedron (regular tilings). These decompositions are confronted with decompositions using six different types of tetrahedra (orthogonal structured tilings). Considering the shape expressivity of particular methods, the paper presents a structure of possible decompositions and comparison of storage demands of the used decompositions.