1. Home
  2. Pied de page
  3. GAMMA3

Automated Mesh Generation and Advanced Methodology

The GAMMA3 project team (common to UTT and INRIA) studies and develops automatic mesh generation algorithms, tools for geometric modeling, as well as advanced adaptive methodologies for numerical simulation.

The GAMMA3 project team was created in 2010. The project's themes include a set of activities, including the automatic generation of meshes, in order to build the supports used by finite element or finite volume methods. Computer methodologies and methods (aspects very close to machine architectures) are also studied, in particular for large meshes, geometric modeling and adaptive computation schemas in engineering sciences in the fields of structural mechanics ( shaping processes, innovative materials), fluid mechanics (Navier-Stokes flows with turbulence and boundary layers), electromagnetism (structured or granular light-material interaction), energetics (combustion process and metrology) and safety (propagation of radioactivity, identification process).

The evolution of the demand in terms of automatic generation of meshes implies an evolution of the classical methods towards methods allowing to build controlled meshes. The meshes must therefore be either isotropic, control over desired sizes, or anisotropic, the control covering both directions and sizes according to these directions. The development of ruled mesh algorithms serves as a natural support for the design of adaptive mesh loops which, via a posterior error estimator, allow to control the quality of the solutions.
These preoccupations lead us to consider not only the problem of the mesh of the computation domains in themselves, but also that of the mesh or the remeshing of their borders constituted of curves and surfaces. Moreover, the size, in terms of the number of nodes, of the meshes necessary for certain simulations, leads to work on the parallelization of the processes of computations. This problematic also leads to an interest in the multi-core aspect at the level of the mesh algorithms themselves.

The project-team relies on the skills and expertise acquired over several years around the theoretical framework put in place and the technologies developed (Delaunay triangulation and meshing, metrics, anisotropy, interpolation error estimator, interpolation of fields, mesh adaptation and adaptive computations).
Our research is based on several theories studied in the team (some in collaboration) to clarify how we see the meshes and justify this way of seeing them.

As such, let's mention :
  • the Delaunay core and its variants,
  • the notion of "unit length" and the underlying but fundamental notion of metrics,
  • the mesh unit,
  • an abstract definition of the notion of "quality" related to the definition of adequate metrics,
  • the development of a method of geometric modeling of specific surfaces (nanostructures, molecules, ...).
In addition, the validation of the results is the primary concern of the team. It is conducted in several ways :
  • blindly using a database,
  • full-scale on cases provided by manufacturers and / or obtained via various contracts (regional, national, linked to competitiveness clusters, ...) or
  • by the manufacturers themselves, through various studies conducted through master's, thesis or post-doc courses.