Hex-dominant Meshing Approach based on Frame Field Smoothness

We propose here an indirect approach for building hex-dominant meshes, using the recombination of tetrahedra to create hexahedra. The efficiency of this recombination depends on the location of the initial points. A two-dimensional frame field is obtained on the boundaries by solving an elliptic PDE. We first propose a procedure to extend the two dimensional field inside the volume and to obtain a smooth three-dimensional frame field, used to insert new points. Then, we propose a point insertion algorithm based on a frame field smoothness estimator: new points are preferentially inserted in smooth frame field regions. The meshes obtained clearly exhibit a larger ratio of hexahedra, compared to more straightforward approaches.