Identifying combinations of tetrahedra into hexahedra: A vertex based strategy. (December 2018)

• Record Type: Journal Article
• Authors: Pellerin, Jeanne; Johnen, Amaury; Verhetsel, Kilian; Remacle, Jean-François
• Is Part Of: Computer aided design. Volume 105(2018)
• Page Start: 1
• Page End: 10
• Publication Date: 2018-12
• Subjects: Finite element -- Hex-dominant mesh -- Indirect meshing -- Triangulation -- Prism -- Pyramid; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2018.05.004
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra that may be combined to form hexahedra, prisms and pyramids. 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, prisms, or pyramids. All identified cells are valid for engineering analysis. First, all combinations of eight/six/five vertices whose connectivity in T matches the connectivity of a hexahedron/prism/pyramid are computed. The subset of tetrahedra of T triangulating each potential cell is then determined. Quality checks allow to early discard poor quality cells and to dramatically improve the efficiency of the method. Each potential hexahedron/prism/pyramid is computed only once. Around 3 millions potential hexahedra are computed in 10 s on a laptop. We finally demonstrate that the set of potential hexes built by our algorithm is significantly larger than those built using predefined patterns of subdivision of a hexahedron in tetrahedral elements. Highlights: We introduce an algorithm to combine tetrahedra into hexahedra. The algorithm identifies all valid hexahedra in an existing tetrahedral mesh. Hybrid meshes of hexahedra, prisms, and tetrahedra are efficiently generated. We demonstrate our hybrid meshing method on 12 complex models.