An Optimisation-Based Approach to Mesh Smoothing: Reformulation and Extensions

The Laplacian approach, when applied to mesh smoothing leads in many cases to convergence problems. It also leads to shrinking of the Mesh. In this work, the, authors reformulate the mesh smoothing problem as an optimisation one. This approach gives the means of controlling the steps to assure monotonic convergence. Furthermore, a new optimisation function is proposed that reduces the shrinking effect of the method. Examples are given to illustrate the properties of the proposed approches.