Aspects of adaptive mesh generation based on domain decomposition and Delaunay triangulation

The finite element method requires the generation of a mesh, based on an appropriate density distribution, so that the numerical analysis using it provides as optimal a result as possible with a reasonably low computational cost. The generation of inner points in a spatial domain of analysis may be accomplished via two types of quadtree decomposition for two-dimensional cases. The density formulations are quoted and analyses of their performance are given. Delaunay triangulation has been utilized within the mesh generator to connect the interior points. The robustness of this technique has been investigated. For real engineering applications, boundary recovery algorithms have been adopted in order to ensure the integrity of the boundary. A series of benchmark tests have been carried out on this work. Mesh quality improvement and the conversion from triangles to quadrilaterals has also been discussed. © 1995.