A New Approach to Automatic Generation of All Graded Triangular and Quadrilateral Finite Element Mesh Over Polygonal Domains (International Journal of Engineering and Computer Science, 2018)
This paper presents a new automesh generation method for a convex and cracked convex polygonal domains. We first decompose the  polygon into simple sub regions in the shape of triangles. These simple regions are then triangulated to generate a   mesh of graded  3-node triangular elements. We propose then an automatic 6-node triangluar  conversion scheme by inserting midside nodes to these triangles. Each isolated 6-node triangle is split into four triangles according to the usual scheme,that is,by joining the midside nodes  by straight lines. To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given convex  or cracked convex polygonal  domain   into all triangles, thus propagating  a uniform or graded  refinement. The quadrangulation of   graded 3-node linear triangles is done by inserting three midside nodes and a centroidal node.Then each graded triangle is split into three quadrilaterals by joining the centroid to the  midside nodes. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples are presented to illustrate the simplicity and efficiency of the new mesh generation method for standard and arbitrary shaped polygonal domains. We have appended MATLAB programs which incorporate the mesh generation scheme developed in this paper. These programs provide valuable  output on the nodal coordinates ,element connectivity  and graphic display of the all triangular and quadrangular  meshes  for application to finite element analysis.