Abstract
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.
Highlights
For numerical simulations with complex geometries, mesh generation typically represents a large portion of the overall computational time
We present an alternative solution based on the proposed shell transformation routine (i.e., Algorithm 3)
We introduce the set of smoothing, point insertion and point suppression schemes incorporated in our mesh improver
Summary
For numerical simulations with complex geometries, mesh generation typically represents a large portion of the overall computational time. Recursive shell transformations could be performed on a much larger element set than that of edge removal, thereby leading the way towards a better local optimum solution Another focus of this study is about the efficient implementation of the new local reconnection technique, because local reconnections need to be employed for a large number of times during the entire mesh improvement workflow. To ensure the applicability of this newly developed mesh improver for large-scale problems, an essential requirement we will take into account is the cost-effectiveness of the mesh improver, i.e., the ability to balance the conflict requirements of resulting in a high-quality mesh and saving computing time of mesh improvement Following this concept, a set of existing smoothing, point insertion and point suppression schemes are selected.
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