2D Finite Element Mesh Generation over Planar Domain by Optimized Bisection Refinement

A triangular mesh generator is presented to create two-dimensional finite element meshes by mesh refinement approach. With the initial mesh constructed by triangulation of the boundary polygon, interior nodes are inserted incrementally by edge bisection in accordance with the pre-specified element size, and triangular elements are formed in an optimized way. Unlike the traditional mesh refinement approaches, shape optimization is performed along with edge bisection rather than performed in the post-processing phase. The presented optimized bisection method inserts a new node at the mid-point of the longest edge in the current mesh, and triangles incident to the inserted node are shaped optimized according to the Delaunay criterion. As a post-processing procedure, smoothing operator is employed too, to improve the overall quality of the FE mesh. Examples of mesh generation over arbitrary planar domains and the corresponding characteristics are given to show the effectiveness and robustness of the meshing algorithm.