Automatic Generation of Triangular Mesh Utilizing the Bucket Method for Finite Element Method

In this paper we describe an algorithm for generating a triangular mesh within an arbitrary planar domain. When the finite element method is applied to numerical simulation, the discretization of the domain becomes on essential part of the procedure. There are many reports on automatic mesh generation methods, such as coordinate transformation, blending function, the Quadtree method, the Delaunay method, and the advancing front method. The main characteristic of the proposed algorithm is that the position of the nodes is generated in the original polygonal region as much as possible in the form of an equilateral triangle and the triangulation of the inner nodes is carried out by the bucket method of computational geometry prior to the global construction of the triangular mesh model. Then the triangulation of the remaining region is carried out utilizing the advancing front method. The processing scheme is developed and applied to several examples. The numerical results are demonstrated and the effectiveness is discussed.