Abstract : The simulation of a physical phenomenon by the finite element method or other numerical analysis methods requires a spatial decomposition, or mesh, of the studied domain. In order that the simulation process converges rapidly and reaches the desired accuracy, the size and shape quality of the mesh plays a crucial role.
This report constitutes a survey of my contributions concerning the automatic generation of meshes respecting as well as possible these quality criteria. These different research works have been carried out in the Gamma group at INRIA.
In this document, the following themes are successively addressed:
- the discretization of curves in the plane or in the 3D space,
- the meshing of planar domains with fix or variable contours,
- the meshing of parametric or discrete warped surfaces.
During these discretization and meshing operations, the size and shape of the elements are controlled by a metric field reflecting geometric and/or physical constraints. The presented methods have all been validated on many academic or industrial examples, notably in solid and fluid mechanics.