Recently, International Journal For Numerical Methods In Engineering, the top journal on computational mechanics, published an article of Prof. Liu’s group entitled “A new method for coarsening tetrahedral meshes”.
Mesh coarsening is necessary to simplify geometric representations, which is urgently needed in computer graphics and numerical simulation.
To coarsen a mesh, we usually remove a set of selected nodes one by one. Currently, the basic operation used to remove a node is edge collapsing, which does not perform well when applied to handling narrow regions in a tetrahedron mesh and could produce low-quality elements or even fail to give valid results.
To overcome the drawbacks of edge collapsing, Liu’s group presents a new node-removal operator created by revising a topological transformation called small polyhedron reconnection (SPR). This new operator can guarantee success if the cavity that forms after a node is removed is meshable, and it produces higher-quality results and keeps the nodes unmoved, which is preferred for applications such as multigrid hierarchies.
a b c
Figure 1. Coarsening to double the mesh sizes of a tube-intersection joint: (a) initial mesh, (b) result of edge collapsing, and (c) result of the new method.
Figure 1 demonstrates the coarsening results by edge collapsing and the new method respectively.
In addition, two other aspects of mesh coarsening that determine whether a node should be removed and the sequence in which to remove the selected nodes are also studied by Liu’s group. Their strategy consists of constructing a coarse node set using the sphere-packing method and removing the nodes in a reversed kd-tree sequence. These two techniques, as well as point-in-polyhedron test via determining triangles which is also used in the new coarsening method, were proposed by Prof. Liu in his earlier papers.
The second and third authors are Dr. Feifei Shang, who graduated from the group last summer and is now a researcher at Institute of Industry Technology, Guangzhou & Chinese Academy of Sciences, and Ms. Ting Song, who graduated from the group three years ago and is now a Ph.D. student at Duke University.