Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
For researchers in computational geometry and simulation, this work offers an incremental improvement by integrating existing techniques into a unified framework.
This paper combines moving mesh smoothing, lazy flipping, and RBF surface reconstruction to improve tetrahedral mesh quality, achieving results comparable or better than previous methods.
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.