Nonsimplicial unstructured mesh generation

New automatic methods and algorithms are presented for the generation of unstructured meshes comprised primarily of non-simplicial (non-triangular or non-tetphedral) elements. Within this context, four specific areas are addressed: (1) Element Sizing: Natural Neighbor Interpolation is proposed as a new method for providing sizing information to a surface mesh generator. Several applications of sizing control are provided. (2) Quadrilateral Mesh Generation: A new method, known as Q-Morph, for quadrilateral mesh generation on arbitrary surfaces is presented. The algorithm begins with a triangular mesh, over which systematic transformations are performed on the triangles working from the boundary towards the interior. A boundary-aligned all-quadrilateral mesh with few irregular internal nodes is produced. (3) Hexahedral-Dominant Mesh Generation: H-Morph, the three-dimensional extension of the Q-Morph algorithm is proposed as a method for generating a boundary conforming, hex-dominant mesh for arbitrary volumes. Beginning with a boundary constrained tetrahedral mesh, tetrahedra are methodically transformed and replaced with hexahedral elements. Regions that cannot be filled with hexahedra are left with tetrahedra. (4) Pyramid Element Formation: Pyramid shaped elements are proposed as a convenient mechanism for interfacing tetrahedral elements with hexahedra. Several methods are proposed for their construction and their performance is evaluated.