Automatic merging of hexahedral meshes

Abstract

A generic algorithm is proposed to merge structured and unstructured hexahedral meshes automatically into one single valid finite element mesh of hexahedral, tetrahedral and pyramid elements. In view of the success of merging arbitrary tetrahedral meshes in addressing the industrial need for rapid modification, update and manipulation of meshed objects, the merging algorithm is extended to hexahedral meshes by first dividing each hexahedral element into five or six tetrahedral elements. Non-intersected hexahedral elements can be easily recovered from the merged tetrahedral mesh as the constituent tetrahedra as a subdivision of the original hexahedral elements are intact and present in the mesh. Like the merging of tetrahedral meshes, the procedure is robust and efficient as all operations such as loops of intersection, incorporation of intersection segments, partition of boundary surfaces and identification of regions of intersection are deterministic and topological. The mesh merging algorithm provides a means to combine, modify and insert new features to existing hexahedral and tetrahedral meshes. It is also a powerful tool to create new meshes from existing hexahedral and tetrahedral meshes through the Boolean operations. High-quality regular hexahedral elements of the original mesh generated by mapping or extrusion will be preserved, which is important for finite element analysis as hexahedral elements are sensitive to shape distortions. Examples with details for each step of the mesh merging process are presented to elucidate the main ideas of the algorithm.