Tetrahedral mesh improvement using swapping and smoothing

Abstract

Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult 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 different 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 effective in eliminating very small and very large angles. High-quality meshes are obtained in a computationally efficient 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 offer several recommendations for the improvement of tetrahedral meshes. © 1997 John Wiley & Sons, Ltd.