Abstract

Analytic solutions for most PDEs are known only for some simple domains, such as a circle, square, or sphere. In order to obtain solutions for more realistic domains, numerical approximations such as the finite element method (FEM) and finite volume methods (FVM) are used. Mesh generation is a key step prior to these numerical methods. It is itself an active research topic with background in mathematics, computer science, and engineering. Apart from numerical solution of PDEs, its applications are numerous and have practical uses in fields such as archaeology, cinematography and robotics.

In this talk, we will begin with triangle mesh generation and adaptation in the plane. This problem has been well studied. Efficient algorithms are developed. We will then move to tetrahedral mesh generation in 3d, which is still challenged by many theoretical and practical issues. In this talk, we will highlight some recent development in this field.