Quality mesh generation

Abstract

Many physical phenomena in science and engineering can be modeled by partial differential equations (PDEs) and solved by means of the Finite Element Method (FEM). Such a method uses as computational spatial support a mesh of the domain where the equations are formulated. Mesh quality is a key-point for the accuracy of numerical simulation. In this paper, we are concerned with the generation of quality (or regular) meshes. This question is a particular occurrence of a more general mesh generation issue which aims to complete meshes conforming to a pre-specified size map (such meshes being referred to as `unit' meshes). We propose a method that makes this mesh construction possible. It is based on a Delaunay advancing-front combined method: the field points are defined using an advancing-front method and are connected using a generalized Delaunay type method. Some optimization methods are also discussed.