A new scheme for the generation of a graded quadrilateral mesh

Abstract

A new scheme for the generation of a quadrilateral element mesh is presented. The algorithm makes use of the fact that a triangular element mesh bounded by an even number of line segments can always be converted into quadrilaterals. By using the advancing front technique for schematically merging of triangular elements, high-quality well-graded quadrilateral meshes can be formed without any tedious treatment for isolated triangles. Unlike many other methods, no cut-lines or manual division of the problem domain into simpler subregions is required before conversion. As the number and the position of the boundary nodes are not altered during the mesh generation process, different material regions sharing common boundary lines can be treated individually. Since a background triangular mesh is all that is needed, the process can be applied to any arbitrary 2D domain with or without internal openings. In fact, the method has an equal area of application as a general triangulator. This also implies that the proposed scheme can be used to generate strongly graded quadrilateral meshes of the same gradation effect as the background triangular meshes for adaptive finite element analysis. © 1994.