Section: Application Domains

Keywords : Unstructured meshes, finite element method, finite volume method.

Scientific computing

Meshes are the basic tools for scientific computing using finite element methods. Unstructured meshes are used to discretize domains bounded by complex shapes while allowing local refinements. Geometrica contributes to 2D, 3D as well as surface mesh generation. Most of our methods are based upon Delaunay triangulations, Voronoi diagrams and their variants. Affine diagrams are used in the context of volume element methods, while non-affine diagrams are used to generate anisotropic meshes. We investigate in parallel both greedy and variational mesh generation techniques. The greedy algorithms consist of inserting vertices in an initial coarse mesh using the Delaunay refinement paradigm, while the variational algorithms consists of minimizing an energy related to the shape and to the size of the elements. Our goal is to show the complementarity of these two paradigms. Quadrangle surface meshes are also of interest for reverse engineering and geometry processing applications. Our approach consists of sampling a set of curves on the surface so as to control the final edge alignment, the mesh sizing and the regularity of the quadrangulation.