Identifying combinations of tetrahedra into hexahedra: a vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra that may be combined to form hexahedra. In this paper we introduce an algorithm that performs this identification and builds the set H of all possible combinations of tetrahedral elements of an input mesh T into hexahedra. All identified hexahedral elements are valid for engineering analysis. The new method first computes all combinations of eight vertices whose connectivity in T matches the connectivity of a hexahedron. The subset of tetrahedra of T triangulating each potential hexahedron is then determined. Quality checks allow to early discard poor quality hexahedra and to dramatically improve the efficiency of the method. Each potential hexahedron is computed only once. Around 3 millions potential hexahedra are computed in 10 seconds on a laptop. We finally demonstrate that the set of potential hexes H built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements.