Automatic boundary sizing for 2D and 3D meshes

The numerical solution of problems in science and engineering via the finite element method requires, as a first step, the discretization of a domain into a set of simply shaped elements. Determining the size of these elements along the domain, including the boundary, to form well-shaped elements is a difficult task. We present in this paper a simple technique, called smart sizing, which automatically computes high quality initial element sizing on curves for triangular, quadrilateral and tetrahedral elements. Curve divisions are computed based on curve and surface curvatures as well as feature proximity. In the three dimensional case, refinement of facets is performed as needed to create reasonably sized surface elements. Computing a boundary mesh appropriately is a key step to successfully determine the size and distribution of new elements towards the interior of the domain, especially for the advancing front and constrained Delaunay meshing techniques. The approach presented here is geometry based and does not attempt to account for the physics of the problem.