Chapter 6: Advancing-Front Technique for Mesh Generation
The advancing-front technique for mesh generation has been investigated for more than 35 years since the pioneering work of [A.George-1971], who studied a two-dimensional case. The classical advancing-front method, in its current form, was first described by [Lo-1985] and [Peraire et al. 1987]. Numerous improvements in this technique have been proposed over the years, first by [L hner, Parikh-1988], [Golgolab-1989] and more recently by [Mavriplis-1992] and [Shostko, L hner-1995]. This approach is now a very powerful and mature technique for generating high-quality unstructured meshes composed of simplices (triangles or tetrahedra) for domains of arbitrary shape. Variants of this technique have even been proposed to generate quadrilaterals or hexahedra in two and three dimensions (cf. [Blacker, Stephenson-1991], [Blacker, Meyers-1993]).
Classical advancing-front approaches start from a discretization of the domain boundaries as a set of edges in two dimensions or a set of triangular faces in three dimensions. The name of this class of methods refers to a strategy that consists of creating the mesh sequentially, element by element, creating new points and connecting them with previously created elements, thus marching into as yet unmeshed space and sweeping a front across the domain. The process stops when the front is empty, i.e., when the domain is entirely meshed. The front is the region(s) separating the part (or parts) of the domain already meshed from those that are still unmeshed. Hence, depending of the strategy, the front can have multiple connected components (Figure 6.1) or not (Figure 6.2).
Figure 6.1: Various...