Tetrahedral mesh improvement using swapping and smoothing

Automatic mesh generation and adaptive re nement methods for complex three-dimensional domains have proven to be very successful tools for the e cient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more di cult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face- and edge-swapping techniques, which change local connectivity, and optimization-based mesh smoothing methods, which adjust mesh point location. We consider several criteria for each of these two methods and compare the quality of several meshes obtained by using di erent combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly e ective in eliminating very small and very large angles. High-quality meshes are obtained in a computationally e cient manner by using optimization-based smoothing to improve only the worst elements and a smart variant of Laplacian smoothing on the remaining elements. Based on our experiments, we o er several recommendations for the improvement of tetrahedral meshes.