THE GRAFT TOOL: AN ALL-HEXAHEDRAL TRANSITION ALGORITHM FOR CREATING A MULTI-DIRECTIONAL SWEPT VOLUME MESH * Steven R. Jankovich 1 , Steven E. Benzley 2 , Jason F. Shepherd 3 , Scott A. Mitchell 1 Brigham Young University, Provo, UT, U.S.A. jankovic@et.byu.edu 2 Brigham Young University, Provo, UT, U.S.A. seb@byu.edu 3 Sandia National Laboratories, Albuquerque, NM, U.S.A. jfsheph@sandia.gov ABSTRACT Sweeping algorithms have become very mature and can create a semi-structured mesh on a large set of solids. However, these algorithms require that all linking surfaces be mappable or submappable. This restriction excludes solids with imprints or protrusions on the linking surfaces. The grafting algorithm allows these solids to be swept. It then locally modifies the position and connectivity of the nodes on the linking surfaces to align with the graft surfaces. Once a high-quality surface mesh is formed on the graft surface, it is swept along the branch creating a 2¾-D mesh. Keywords: mesh generation, hexahedral meshing, refinement, sweeping, 2½-D * This work was partly funded by Sandia National Laboratories, operated for the U.S. DOE under contract No. DE-AL04- 94AL8500. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. DOE. Scott Mitchell, samitch@sandia.gov, was supported by the Mathematical, Information and Computational Sciences Division of the U.S. Department of Energy, Office of Energy Research and works at Sandia National Laboratories. 1. INTRODUCTION Three-dimensional finite element analysis (FEA) is an important design tool for physicists and engineers. Before the analysis can begin, a mesh needs to be generated on the model. During the last several decades, much research has been devoted to mesh generation. Tetrahedral mesh generators are well developed and many have been implemented in software packages. Only recently has the research focus shifted to hexahedral meshes. For most applications, hexahedral elements are preferred over tetrahedral elements for meshing 3-D solids [1,2]. Unfortunately, a high quality mesh of hexahedral elements is more difficult to generate. Minimally, the mesh needs to be conformal between adjoining solids and have high quality elements at the bounding surfaces. Because of the constraints on hexahedral elements, automatic generation of high quality hexahedral meshes on arbitrary 3-D solids has proven elusive [3]. Over the last several years much work has been put into sweeping algorithms. These algorithms can mesh a wide range of 2½-D (prismatic) solids. The sweeping algorithms generally take a 2-D unstructured quadrilateral mesh from the source surface and project it through the volume to the target surface. Sweeping algorithms have matured to handle non- planar, non-parallel source and target surfaces and variable cross-sectional area [4] as well as multiple source and target surfaces [5,6]. To maintain the structured mesh in the sweep direction, sweeping algorithms require the linking surfaces (those that connect the source to the target) to be mappable or submappable. This constraint limits the number of solids that