A new automatic finite element mesh generation scheme of all quadrilaterals over an analytical curved surface by using parabolic arcs

Abstract

This paper presents a new mesh generation method for a  simply connected curved  domain of a planar region which has  curved boundary described by one or more analytical equations. We first decompose this curved domain  into simple sub regions in the shape of curved triangles. These simple regions are then triangulated to generate a fine mesh of   linear triangles in the interior and curved triangles near to the boundary of curved domain. We then propose,  an automatic triangular to quadrilateral conversion scheme. Each isolated triangle is split into three quadrilaterals according to the usual scheme, adding three vertices in the middle of the edges which are either a straight segment or a curved arc and a vertex at the barrycentre(a point located at the average of three vertices) of the element. We have  approximated the curved arcs by  equivalent parabolic arcs.To preserve the mesh conformity a similar procedure is also applied to every triangle of the domain to fully discretize the given curved  domain   into all quadrilaterals, thus propagating  uniform  refinement. This simple method generates a high quality mesh whose elements confirm well to the requested shape by refining the problem domain. Examples on a circular disk, on a cracked circular disk and on a lunar model are presented to illustrate the simplicity and efficiency of the new mesh generation method. We have appended the  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 quadrilateral mesh for application to finite element analysis.