Converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for FEM accuracy and efficiency

Abstract

This paper presents a computational method for converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for improved solution accuracy and computational efficiency of finite element analysis. The proposed method inserts layers of prism elements and deletes tetrahedral elements in sweepable sub-domains, in which cross-sections remain topologically identical and geometrically similar along a certain sweeping path. The total number of finite elements is reduced because roughly three tetrahedral elements are converted to one prism element. The solution accuracy of the finite element analysis improves since a prism element yields a more accurate solution than a tetrahedral element. Only previously known method for creating such a prism-tetrahedral mesh was to manually decompose a target volume into sweepable and non-sweepable sub-volumes and mesh each sub-volume separately. The proposed method starts from a cross-section of a tetrahedral mesh and replaces the tetrahedral elements with layers of prism elements until prescribed quality criteria can no longer be satisfied. The method applies a sequence of edge-collapse, local-transformation, and smoothing operations to remove or displace nodes located within the volume to be replaced with a layer of prism elements. Series of computational fluid dynamics simulations and structural analyses have been conducted, and the results verified a better performance of prismtetrahedral hybrid mesh in finite element simulations.