Fun sheet matching: towards automatic block decomposition for hexahedral meshes

Abstract

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay's algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3-and 4-valent vertices.

A PDE Based Approach to Multidomain Partitioning and Quadrilateral Meshing

“…Several numerical and algorithmic solutions have been proposed over the last decades to generate quadrilateral meshes abiding by those properties. Those methods can be categorized as either structured [2,3] or unstructured [4,5,6,7,8,9], depending on the importance they give to the underlying mesh structure. On the one hand, structured methods are unable to mesh most geometries and to deal with boundary discretization constraints along interface lines.…”

Hex-Mesh Generation and Processing: a Survey

“…Generating a hexahedral block structure can also be seen as coarsening an existing hexahedral mesh. In , authors extend the preliminary work of [Kowalski et al 2012] where a hexahedral mesh, obtained from converting a tetrahedral mesh by splitting each tetrahedron into four hexahedra, is coarsened by removing all nonfunda-mental sheets. They extend the greedy approach proposed in [Kowalski et al 2012] by providing much more quality control and sheet selection procedures.…”

Evocube: A Genetic Labelling Framework for Polycube‐Maps

“…Unfortunately, naive global insertion can also locally decrease mesh quality. Kowalski et al [KLSO12] define three types of fundamental layers that can be added locally to better capture boundary curves and surfaces solving an integer linear program. Similarly, Cherchi et al [CAS * 19] define selective padding which is able to add hex layers with a quality improvement guarantee.…”