A Delaunay Mesh Generation Approach without the Use of Convex Hulls

Modeling, generation, and adaptation of unstructured meshes based on e.g. simplicies is of utmost importance for scientific computing, especially in the area of Technology Computer Aided Design (TCAD). Not only does the quality of the results depend on the quality of the mesh, a solution is even impossible, if a mesh cannot be successfully generated. The simulation of microelectronic devices such as transistors is an area of TCAD, which mostly makes use of finite volume schemes for discretization, due to its inherently flux preserving nature, which also implies the fundamental requirement of a Delaunay conform mesh. So far most of the Delaunay mesh generation algorithms utilize convex hulls. A drawback of these approaches is the fact, that a convex hull is initially constructed and meshed. The final mesh is contained in this convex hull and has to be obtained by recreating the given boundary of the modeled structure. This issue may also result in overhead, due to the construction of convex hull parts, which can be of substantial size and also have to be meshed just to be removed at the end of the mesh generation. This uneccessarily complicates and slows down the whole Delaunay mesh generation process. Another issue results from a computer’s finite numerical accuracy becoming especially apparent when performing geometrical tests. Problems with geometrical prediactes can even yield topological inconsistencies. While topological issues do not suffer from numerical instability by themselves, they can result in failure of the whole meshing algorithm. Our approach focuses on theoretical results as well as practical techniques to overcome the complex treatment of Delaunay conform mesh generation. The area of TCAD is chosen for application, because the successful generation of a mesh is of fundamental importance here. The introduced approach is based on a surface treatment algorithm in order to satisfy the constrained Delaunay property for the hull first. A subsequent advancing front algorithm is specially adapted to comply with the consistent Delaunay property and to circumvent colliding fronts.