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Hexahedral mesh generation in real time

Total Cost €


EC-Contrib. €






Project "HEXTREME" data sheet

The following table provides information about the project.


Organization address
postcode: 1348

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Belgium [BE]
 Project website
 Total cost 2˙244˙237 €
 EC max contribution 2˙244˙237 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-10-01   to  2021-09-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Over one million finite element analyses are preformed in engineering offices every day and finite elements come with the price of mesh generation. This proposal aims at creating two breakthroughs in the art of mesh generation that will be directly beneficial to the finite element community at large. The first challenge of HEXTREME is to take advantage of the massively multi-threaded nature of modern computers and to parallelize all the aspects of the mesh generation process at a fine grain level. Reducing the meshing time by more than one order of magnitude is an ambitious objective: if minutes can become seconds, then success in this research would definitively radically change the way in which engineers deal with mesh generation. This project then proposes an innovative approach to overcoming the major difficulty associated with mesh generation: it aims at providing a fast and reliable solution to the problem of conforming hexahedral mesh generation. Quadrilateral meshes in 2D and hexahedral meshes in 3D are usually considered to be superior to triangular/tetrahedral meshes. Even though direct tetrahedral meshing techniques have reached a level of robustness that allow us to treat general 3D domains, there may never exist a direct algorithm for building unstructured hex-meshes in general 3D domains. In HEXTREME, an indirect approach is envisaged that relies on recent developments in various domains of applied mathematics and computer science such as graph theory, combinatorial optimization or computational geometry. The methodology that is proposed for hex meshing is finally extended to the difficult problem of boundary layer meshing. Mesh generation is one important step of the engineering analysis process. Yet, a mesh is a tool and not an aim. A specific task of the project is dedicated to the interaction with research partners that are committed to beta-test the results of HEXTREME. All the results of HEXTREME will be provided as an open source in Gmsh.


year authors and title journal last update
List of publications.
2017 Georgiadis, Christos; Beaufort, Pierre-Alexandre; Lambrechts, Jonathan; Remacle, Jean-François
High quality mesh generation using cross and asterisk fields: Application on coastal domains
published pages: , ISSN: , DOI:
3 2020-01-14
2018 Célestin Marot, Jeanne Pellerin, Jean‐François Remacle
One machine, one minute, three billion tetrahedra
published pages: , ISSN: 0029-5981, DOI: 10.1002/nme.5987
International Journal for Numerical Methods in Engineering 2020-01-14
2019 Kilian Verhetsel, Jeanne Pellerin, Jean-François Remacle
Finding hexahedrizations for small quadrangulations of the sphere
published pages: 1-13, ISSN: 0730-0301, DOI: 10.1145/3306346.3323017
ACM Transactions on Graphics 38/4 2020-01-14
2018 Verhetsel, Kilian; Pellerin, Jeanne; Remacle, Jean-françois
A 44-element mesh of Schneiders\' pyramid: bounding the difficulty of hex-meshing problems
published pages: , ISSN: , DOI:
2 2020-01-14
2019 C. Marot, K. Verheltsel, JF Remacle
Reviving the Search for Optimal Tetrahedralizations
published pages: , ISSN: , DOI:
Proceedings of the 28th meshing roundtable 2019-09-04
2018 Pellerin, Jeanne; Remacle, Jean-Francois
Enumerating combinatorial triangulations of the hexahedron
published pages: , ISSN: , DOI:
SIGGRAPH ASIA 1 2019-06-13
2018 C. Marot, J. Pellerin and J-F Remacle
One machine, one minute, three billion tetrahedra
published pages: , ISSN: 1097-0207, DOI:
IJNME 2019-06-13
2018 Johnen, Amaury; Weill, Jean-Christophe; Remacle, Jean-François
Robust and efficient validation of the linear hexahedral element
published pages: , ISSN: 0010-4485, DOI:
CAD 2 2019-06-13
2018 Pellerin, Jeanne; Johnen, Amaury; Verhetsel, Kilian; Remacle, Jean-Francois
Identifying combinations of tetrahedra into hexahedra: a vertex based strategy
published pages: , ISSN: 0010-4485, DOI:
CAD 2 2019-06-13
2018 Alexandre Chemin, François Henrotte, Jean-François Remacle, Jean Van Schaftingen
Representing three-dimensional cross fields using 4th order tensors
published pages: , ISSN: , DOI:
2018 A. Johnen, C. Geuzaine, T. Toulorge, J.-F. Remacle
Efficient computation of the minimum of shape quality measures on curvilinear finite elements
published pages: 24-33, ISSN: 0010-4485, DOI: 10.1016/j.cad.2018.03.001
Computer-Aided Design 103 2019-06-03
2019 Jeanne Pellerin, Kilian Verhetsel, Jean-FranÇois Remacle
There are 174 subdivisions of the hexahedron into tetrahedra
published pages: 1-9, ISSN: 0730-0301, DOI: 10.1145/3272127.3275037
ACM Transactions on Graphics 37/6 2019-06-03
2018 Jean-François Remacle, Jonathan Lambrechts
Fast and robust mesh generation on the sphere—Application to coastal domains
published pages: 14-23, ISSN: 0010-4485, DOI: 10.1016/j.cad.2018.03.002
Computer-Aided Design 103 2019-06-03
2018 Kilian Verhetsel, Jeanne Pellerin, Jean-françois Remacle
A 44-element mesh of Schneiders\' pyramid: bounding the difficulty of hex-meshing problems
published pages: , ISSN: , DOI:
Proceedings of the 2019-06-03

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