Towards Anisotropic Quality Tetrahedral Mesh Generation.

Many physical problems exhibit anisotropic features, i.e., their solutions change more significantly in one direction than others.Examples include in particular convection-dominated problems whose solutions have, e.g., layers, shocks, or corner singularities.When numerical methods are used to approximate these problems, it is of great importance that the used meshes represent suchfeatures to achieve high accuracy at a low computational cost.

Tetrahedral meshes are very popular for discretizing three-dimensional domains. They can be easily adapted to arbitrary geometries,they can be refined locally, and they can be generated automatically. However, the generation of anisotropic quality tetrahedral meshesis a complex problem and it is an active research topic.

This talk addresses the state of the art in high quality tetrahedral mesh generation, presenting in particular a relative robust and efficient methodology implemented in the program { tt TetGen} for generating isotropicmeshes, and it discusses important open questions which arise in generalizationsto the anisotropic case.

Contact: simona.perotto@polimi.it dassifraa@gmail.com