8 - Automatic mesh generation

Abstract

The process of creating a finite element mesh is often termed as mesh generation. Mesh generation has always been a time-consuming and error-prone process. This is true in the practical science and engineering computations, where meshes have to be generated for three-dimensional geometries of various levels of complexity. The attempt to create a fully automatic mesh generator, which is a particular mesh generation algorithm that is capable of generating valid finite element meshes over arbitrary domains and needs only the information of the specified geometric boundary of the domain and the required distribution of the element size, started in the early 1970s. Since then, many methodologies have been proposed and different algorithms have been devised in the development of automatic mesh generators. This chapter focuses on the automatic mesh generation methods based on the advancing front method and the Delaunay triangulation method. These are the basis of many existing mesh generation programs and the basis of current research. This chapter discusses the algorithmic procedures of the advancing front method in two dimensions and the Delaunay triangulation method in three dimensions. It also discusses curve and surface mesh generations.