Adaptive tetrahedral mesh generation of 3D heterogeneous objects

Abstract

In this paper, a step-wise tetrahedral mesh generation method is introduced to solve the adaptive meshing problems of 3D heterogeneous objects, in which both the material heterogeneity and the geometric complexity have to be taken into account. In light of that, the proposed meshing strategy embraces three steps: initial mesh generation, material-oriented refinement, and geometry-oriented refinement. In the material-oriented refinement, a global refinement algorithm based on optimal Delaunay triangulation (ODT) is designed to control the mesh adaptation in terms of the material distribution. Compared to the refinement strategies based on local modifications, the global refinement algorithm takes full advantages of the material heterogeneity information and distributes the material composition variation over elements as equally as possible. As a result, the number of elements is reduced to a great extent regarding a given material threshold. Implementations show that the proposed approach guarantees desirable mesh adaptation as well as high mesh quality.