Identifying combinations of tetrahedra into hexahedra: a vertex based strategy

Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set 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 seconds 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.Comment: Preprint submitted to CAD (26th IMR special issue

Hexahedral-dominant meshing

This article introduces a method that generates a hexahedral-dominant mesh from an input tetrahedral mesh.It follows a three-steps pipeline similar to the one proposed by Carrier-Baudoin et al.:(1) generate a frame field; (2) generate a pointset P that is mostly organized on a regulargrid locally aligned with the frame field; and (3) generate thehexahedral-dominant mesh by recombining the tetrahedra obtained from the constrained Delaunay triangulation of P.For step (1), we use a state of the art algorithm to generate a smooth frame field. For step (2), weintroduce an extension of Periodic Global Parameterization to the volumetric case. As compared withother global parameterization methods (such as CubeCover), our method relaxes some global constraintsand avoids creating degenerate elements, at the expense of introducing some singularities that aremeshed using non-hexahedral elements. For step (3), we build on the formalism introduced byMeshkat and Talmor, fill-in a gap in their proof and provide a complete enumeration of all thepossible recombinations, as well as an algorithm that efficiently detects all the matches in a tetrahedral mesh.The method is evaluated and compared with the state of the art on adatabase of examples with various mesh complexities, varying fromacademic examples to real industrial cases. Compared with the methodof Carrier-Baudoin et al., the method results in better scoresfor classical quality criteria of hexahedral-dominant meshes(hexahedral proportion, scaled Jacobian, etc.). The methodalso shows better robustness than CubeCover and its derivativeswhen applied to complicated industrial models