Graded mesh generation and transformation

A simple and fast method to generate graded quadrilateral mesh has been developed. This method guarantees the generation of quadrilateral mesh once the triangular base mesh has been generated. The gradation of triangular mesh is self controlled for the internal nodes in the generation process, the boundary nodes gradiation is controlled by assigning nodal spacing. To achieve large gradation around an internal point, the post-local refinement is implemented by splitting the longest edge of the triangles inside the refining area. In order to ensure the quality of the triangular mesh, the triangles are generated as equal-sided as possible, then applied with swapping and the weighted central smoothing. To generate a quadrilateral mesh, the triangular base mesh is transformed into a quadrilateral mesh by combining two suitable triangles into four quadrilaterals, and then the triangles that are left over are split into three quadrilaterals. In comparison with the existing mesh generation methods, this method involves no background mesh interpolation, no recursive region sub-divisions and no sorting during the generation process. Therefore, the mesh generating time, as well as the combining, swapping and smoothing time, are greatly reduced. This method, therefore, is suitable for a repeated mesh generation process such as occurs in the metal forming FEM analysis. The method and data structures are described in detail, and some test examples are given together with their running time