Increasing the Number and Volume of Hexahedral and Prism Elements in a Hex-Dominant Mesh by Topological Transformations

This paper describes a new method for increasing the number and the volume of hexahedral and prism elements in a hexdominant mesh by topological transformations. The method takes as input a hex-dominant mesh consisting of hexahedrons, prisms, pyramids and tetrahedrons and modifies the mesh to increase the number and the volume of hexahedrons and prisms while maintaining the relaxed conformity criteria, which allows a connection from two tetrahedrons to a quadrilateral face of a hexahedron or a prism. If a hex-dominant mesh satisfies the relaxed conformity criteria, it can be used in the finite element analysis by applying an error reduction scheme on non-conforming faces [1-3], inserting pyramids on non-conforming faces [4], or converting the mesh to an all-hex mesh by a template method [5, 6]. With more hexahedrons and prisms in a hex-dominant mesh, a more accurate finite element solution can be obtained in a shorter time. Hence the proposed method increases the practical value of a hex-dominant mesh. Several experiments showed the number of hexahedrons increased by about 10% to 20%, yielding hex-dominant meshes with 70% to 90% hexahedron volume ratio.