Kilian Verhetsel
PhD student
Ir. at UCL in 2017

Main project: All-hexahedral meshing
Funding: ERC
Supervisor(s): Jean-François Remacle

While there exist algorithms to generate hex-dominant meshes, which contain a majority of hexahedra as well as a mixture of tetrahedra, prisms, and pyramids, automatically generating hexahedral meshes with elements of a reasonable quality is not currently possible. Subdividing the elements of a hex-dominant mesh could allow hexahedral meshes to be generated automatically, but the best known subdivision of a pyramid requires too many elements to be practical (see figure).

My work focuses on finding all-hexahedral meshes of small models such as this pyramid by first finding a topological solution using combinatorial search techniques. A geometric mesh will then be produced by finding coordinates for each vertex in the mesh.

IMMC main research direction(s):
Computational science

mesh generation

Research group(s): MEMA


Recent publications

See complete list of publications

Journal Articles

1. Verhetsel, Kilian; Pellerin, Jeanne; Remacle, Jean-François. Finding hexahedrizations for small quadrangulations of the sphere. In: ACM Transactions on Graphics, Vol. 38, no.4, p. 53(1-13) (2019). doi:10.1145/3306346.3323017.

2. Pellerin, Jeanne; Verhetsel, Kilian; Remacle, Jean-François. There are 174 subdivisions of the hexahedron into tetrahedra. In: ACM Transactions on Graphics, Vol. 37, no. 6 (2018) (2018). doi:10.1145/3272127.3275037.

Conference Papers

1. Verhetsel, Kilian; Pellerin, Jeanne; Remacle, Jean-François. A 44-element mesh of Schneiders' pyramid: Bounding the difficulty of hex-meshing problems. 2018 xxx.

2. Verhetsel, Kilian; Pellerin, Jeanne; Johnen, Amaury; Remacle, Jean-François. Solving the Maximum Weight Independent Set Problem: Application to Indirect Hexahedral Mesh Generation. 2017 xxx.