Generate Good Triangular Meshes, Conforming to Control Spacing Requirements

To conduct numerical simulations by finite element methods, we often need to generate a high quality mesh, yet with a smaller number of elements. Moreover, the size of each of the elements in the mesh should be approximately equal to a given size requirement. Li et al. recently proposed a new method, named biting, which combines the strengths of advancing front and sphere packing. It generates high quality meshes with a theoretical guarantee. In this paper, we show that biting squares instead of circles not only generates high quality meshes but also has the following advantages. It is easier to generate high quality elements near the boundary with theoretical guarantee; it is very efficient time-wise; in addition, it is easier to implement. Furthermore, it provides simple and straightforward boundary protections in three dimensions. keyword: Unstructured mesh generation, advancing front, biting, sphere packing, spacing function.