Combining Laplacian and optimization-based mesh smoothing techniques

摘要

Local mesh smoothing algorithms have been shown to be effective in repairing distorted elements in automatically generated meshes. The simplest such algorithm is Laplacian smoothing, which moves grid points to the geometric center of incident vertices. Unfortunately, this method operates heuristically and can create invalid meshes or elements of worse quality than those contained in the original mesh. In contrast, optimization-based methods are designed to maximize some measure of mesh quality and are very effective at eliminating extremal angles in the mesh. These improvements come at a higher computational cost, however. In this article the author proposes three smoothing techniques that combine a smart variant of Laplacian smoothing with an optimization-based approach. Several numerical experiments are performed that compare the mesh quality and computational cost for each of the methods in two and three dimensions. The author finds that the combined approaches are very cost effective and yield high-quality meshes.