2016, Dassi, Franco, Kamenski, Lennard, Si, Hang

We combine the new moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the new lazy flip technique, a reversible edge removal algorithm for local mesh quality improvement. These strategies already provide good mesh improvement on themselves, but their combination achieves astonishing results not reported so far. Provided numerical comparison with some publicly available mesh improving software show that we can obtain final tetrahedral meshes with dihedral angles between 40° and 123°.

2017, Dassi, Franco, Kamenski, Lennard, Farrell, Patricio, Si, Hang

Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we combine the moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the lazy flip technique, a reversible edge removal algorithm to modify the mesh connectivity. Moreover, we utilize radial basis function (RBF) surface reconstruction to improve tetrahedral meshes with curved boundary surfaces. Numerical tests show that the combination of these techniques into a mesh improvement framework achieves results which are comparable and even better than the previously reported ones.