The successive node snapping scheme: A method to obtain conforming meshes for an evolving curve in 2D and 3D

摘要

We introduce a novel method called the successive node snapping (SNS) scheme to construct conforming meshes for an evolving curve in 2D and 3D, with a given simplicial background mesh. In the procedure, only a small fraction of nodes of the background mesh are moved and the nodal connectivities remain unaltered. The core of the method is to snap chosen nodes to the evolving curve and to simultaneously relax nodes within the vicinity of the curve. Following the curve, we adjust each portion of the curve's neighborhood successively to obtain a mesh conforming to the entire curve. The curve and the background mesh are under very mild geometric requirements: The curve can be open or closed, and the background mesh can have obtuse-angled triangles or tetrahedra as well as acute-angled ones. With no a priori conformity requirements, the same background mesh can be utilized for a series of snapshots of the evolving curve, permitting tractable variable remapping. Since all the operations on the mesh are local, the method is especially suitable for evolving curve problems where the curve only updates a small portion each time, for example, crack propagation in 2D and dislocation dynamics in 3D.