A new method for coarsening tetrahedral meshes

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, we present a new node-removal operator created by revising a topological transformation called small polyhedron reconnection. 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. In addition, 2 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. Our strategy consists of constructing a coarse node set using the sphere-packing method and removing the nodes in a reversed kd-tree sequence. The excellent performance of the new method is demonstrated by applying it to examples of adaptive meshing and multigrid hierarchy creation and comparing the results with those of the edge collapsing method.