All-Hexahedral Mesh Generation By Iterative Method

Hexahedral finite element meshes have offered some mathematical benefit over tetrahedral finite element meshes in terms of reduced error and smaller element counts. However, generating hexahedral meshes can be difficult to perform and automate, and the process often takes several orders of magnitude longer time than current methods for generating tetrahedral meshes. In this paper a method based on iterative subdivision fitting is presented. Firstly, an initial control hexahedral mesh solid is constructed based on the skeleton of an input model if the input model has obvious skeleton information. Otherwise we generate the control hexahedra mesh by voxelization algorithm. Then we extracted the surface quad mesh of the control mesh and fitted it to the input model by iterative subdivision fitting algorithm. In each round of iteration, the movement of the surface mesh is diffused to the inner vertices by a limit length level smooth method. It ensures that the generated hexahedral mesh has no negative scaled Jacobian value. After the iteration stops, an all-hex mesh is generated by subdividing the control mesh with a modified multi-linear cell-averaging (MLCA) volume subdivision rule. Since the hexahedral mesh has no negative Jacobian value, its mesh quality can be further improved by optimization method.