Automatic Sizing Functions for 3D Unstructured Mesh Generation

We present a novel algorithm to automatically create high-quality sizing functions for unstructured volume mesh generation. Firstly, appropriate techniques are proposed to create a tetrahedral background mesh, in which an initial sizing function is defined by considering geometrical factors and user-specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function. This function corresponds to a mesh satisfying necessary gradient constraint conditions and containing reduced number of elements. Finally, the smoothed sizing function is used by an advancing front surface mesher and a Delaunay tetrahedralization based volume mesher. With the aid of a walk-through algorithm, efficient sizing-value query schemes are developed. Various meshing experiments are presented to demonstrate that the proposed approach enables an accurate and fully automatic unstructured mesh generation pipeline.