The development of algorithms for the automatic creation of finite element meshes composed entirely of hexahedra (all-hex) is an active area of research. All-hex meshes are desirable for their characteristic of high accuracy with a low node count. Sweeping is one of the most widely used algorithms for generating all-hex meshes. A limitation of sweeping, however, is that it can currently be applied only to prismatic or extruded geometry types. This thesis develops a method to combine sweeping with another algorithm known as "Grafting". Grafting adjusts the mesh on one volume to conform to a second volume. In this manner it is useful for meshing multi-axis geometry in that a single axis can be meshed with sweeping and then secondary axes can be grafted on. By creating an algorithm for automatically performing these processes, the base set of geometry that can be automatically meshed with these methods is greatly increased. This new algorithm is called Graft-Sweeping. With the combination of sweeping and Grafting, geometry that contains multiple source surfaces, multiple target surfaces, and multiple sweep axes can be meshed. The results of this algorithm on several example geometries are given showing the strengths and weaknesses of this technique. From the results it can be seen that the Graft-Sweep algorithm can produce a finite element mesh in about half the time of manual Grafting and sweeping operations with similar mesh quality. When compared to sweeping alone, Graft-Sweeping is several times faster but the quality is usually reduced. A second area of research for this thesis is to determine when Grafting can be used to enhance the meshing process. It is shown that the best results are obtained when Grafting is used on structured meshes and the mesh size is considerably smaller than the size of the feature that is being grafted.



College and Department

Ira A. Fulton College of Engineering and Technology; Mechanical Engineering



Date Submitted


Document Type





finite element, mesh generation, hexahedral, grafting, sweeping