Tetrahedral mesh improvement by shell transformation

Existing flips for tetrahedral meshes simply make a selection from a few possible configurations within a single shell (i.e., a polyhedron that can be filled up with a mesh composed of a set of elements that meet each other at one edge), and their effectiveness is usually confined. A new topological operation for tetrahedral meshes named shell transformation is proposed. Its recursive callings execute a sequence of shell transformations on neighboring shells, acting like composite edge removal transformations. Such topological transformations are able to perform on a much larger element set than that of a single flip, thereby leading the way towards a better local optimum solution. Hence, a new mesh improvement algorithm is developed by combining this recursive scheme with other schemes, including smoothing, point insertion, and point suppression. Numerical experiments reveal that the proposed algorithm can well balance some stringent and yet sometimes even conflict requirements of mesh improvement, i.e., resulting in high-quality meshes and reducing computing time at the same time. Therefore, it can be used for mesh quality improvement tasks involving millions of elements, in which it is essential not only to generate high-quality meshes, but also to reduce total computational time for mesh improvement.