ASPECTS OF 2-D DELAUNAY MESH GENERATION

SUMMARY This paper aims to outline the dierent phases necessary to implement a Delaunay-type automatic mesh generator. First, it summarizes this method and then describes a variant which is numerically robust by mentioning at the same time the problems to solve and the dierent solutions possible. The Delaunay insertion process by itself, the boundary integrity problem, the way to create the eld points as well as the optimization procedures are discussed. The two-dimensional situation is described fully and possible extensions to the three-dimensional case are briey indicated. ? 1997 by John Wiley & Sons, Ltd. There exist a large number of papers dealing with 2-D-mesh generation using the Delaunay method (see Reference 1). Nevertheless, we propose a new scheme with ambition to optimize, if possible, the dierent steps used in the practical application of the algorithm. We have tried to develop for each step an optimal solution. The method has been implemented and results show the performance of the algorithm. So we can construct a well-shaped mesh constituted by a million of triangles in a few minutes on a HP 735 workstation. The 2-D case is fully detailed for clarity but most of the results can be extended without diculty in three dimensions. The problem to be solved is to construct a consistent mesh of a domain essentially from its boundary data segments. The resulting mesh will be the support of a nite element computation which can indicate if it is adapted or must be adapted by any method (it is not the goal of this paper). Nevertheless, it is important to begin with a well-shaped mesh knowing that this request can only be based on geometric considerations, since the sole known information is of geometric nature. Thus, the shape and the size of the elements must be consistent with these data.