Quality guaranteed all-hex mesh generation by a constrained volume iterative fitting algorithm

• An iterative algorithm is developed to fill a triangular mesh with an all-hex mesh.
• The Jacobian values of the all-hex mesh are guaranteed to be positive.
• The convergence of the iterative algorithm is proved.

The hexahedral mesh (hex mesh) is usually preferred to the tetrahedral mesh (tet mesh) in finite element methods for numerical simulation. In finite element analysis, a valid hex mesh requires that the scaled Jacobian value at each mesh vertex is larger than 00. However, the hex mesh produced by lots of prevailing hex mesh generation methods cannot be guaranteed to be a valid hex mesh. In this paper, we develop a constrained volume iterative fitting (CVIF) algorithm to fill a given triangular mesh model with an all-hex volume mesh. Starting from an initial all-hex mesh model, which is generated by voxelizing the given triangular mesh model, CVIF algorithm fits the boundary mesh of the initial all-hex mesh to the given triangular mesh model by iteratively adjusting the boundary mesh vertices. In each iteration, the movements of the boundary mesh vertices are diffused to the inner all-hex mesh vertices. After the iteration stops, an all-hex volume mesh that fills the given triangular mesh model can be generated. In the CVIF algorithm, the movement of each all-hex mesh vertex is constrained to ensure that the scaled Jacobian value at each mesh vertex is larger than 00, etc. Therefore, the all-hex mesh generated by the CVIF algorithm is guaranteed to be a valid all-hex mesh.