In a famous talk, Pr. Thomas Hughes estimated to be of the order of a million analyses a day performed in engineering design offices throughout the world. Engineering designs are encapsulated in Computer Aided Design (CAD) systems. Up to manufacturing tolerances, CAD systems exactly represent the geometry of designs. The analysis process begins with CAD geometry but the predominate method of analysis, finite elements, requires a mesh which is an alternative (discrete) representation of a geometry.
Even though efficient 2D mesh generation techniques were already available in the early 1970’s, the first automatic unstructured mesh generation system for general 3D domains was proposed in the early 1990’s with Paul-Louis George’s seminal work on 3D constrained Delaunay triangulation. It is interesting to note that today’s most widely used 3D mesh generation algorithm is still the one developed at that time. Three-dimensional mesh generation is a problem that is extraordinary complicated. Only half a dozen research teams in the world have the technology to build tetrahedral meshes for general domains in an automatic manner. Pr. Jean-Francois Remacle belongs to this short list with Gmsh, the only open source complete mesh generator available today.
In his talk, Pr. Hughes stated: "Mesh generation accounts for more than 80% of overall analysis time and is the major bottleneck". Every simulation engineer is aware that finite elements come with the very high price of mesh generation. Reducing the hassle of mesh generation in finite element analysis has been a major domain of research in the last 20 years. Yet, most of this effort has been devoted to design some alternative simulation methods that would not require a mesh or that would significantly simplify meshing issues. Up to now, none of those methods can be considered as a true alternative to the usual mesh based analysis.
In HEXTREME, the point of view is different. We believe that time has come for pushing innovation in mesh generation. HEXTREME aims at creating two breakthroughs in the art of mesh generation that will be directly beneficial to the finite element community at large: all the developments will be carried out in the open software platform Gmsh (
http://gmsh.info(s’ouvre dans une nouvelle fenêtre)) which is actively developed.
1) Hexahedral meshing
Hexahedral meshes in 3D and quadrilateral meshes in 2D are considered to be superior to triangular meshes in the finite element community. There exist nowadays no method for generating hex meshes. The first objective of HEXTREME is to create this breakthrough. and propose a fully automatic and reliable way of generating conforming hexahedral meshes.
2) Real time meshing
In the last decades, the size of the meshes that are used in industry has grown considerably due to the availability of massively parallel computers. It is not uncommon now to generate meshes that
have over 100 million of tetrahedra. In a user point of view, generating a finite element mesh of a complex domain usually involves the generation of some intermediary meshes that are progressively enhanced in order to fulfill some adequate design requirements. Today’s best 3D meshing algorithms are able to generate about five million tetrahedra per minute on one single core. Each iteration in the meshing process takes long minutes and users spend most of their time waiting for the mesh generator to provide outputs. Practitioners consider mesh generation procedures to be too slow: we will fasten the process by at least one order of magnitude.
