Adjacency for grid generation and grid adaptation in Delaunay triangulation

One of the characteristics of Delaunay method for mesh generation is its local remeshing ability. The main part of the process is to identify remeshing block out of the whole domain and to execute remeshing on the block. Adjacency, adjacent element array, is introduced with an accompanying algorithm to make the process so simple and versatile that it will be used in generating the initial mesh, in applying mesh adaptation, in mesh revision for moving boundary problems, and in transforming 3-node base mesh to 6-node mesh. These features are demonstrated in the example problems of heat conduction with point sink, crack propagation, and simple upsetting of a circular cylinder. Proposition is made to take utility array 'adjacency' as basic element data.