A Global Minimization-Based, Automatic Quadrilateral Meshing Algorithm

A novel method is presented for automatically generating quadrilateral meshes on arbitrary two-dimensional domains. Global minimization of a potential function governs mesh formation and characteristics. Comprised of several terms, the potential function distributes the elements throughout the domain and aligns the edges of the elements to form valid connectivities. If there are any remaining unlinked element edges, the local connectivity is examined and a \hole elimination" algorithm is applied that successively nds alternative connectivities. Unlinked edges, representing holes in the mesh, are moved to either coalesce, or to a boundary. The components of the potential, the minimization procedure, and the connectivity reenement algorithm are presented. The method shows promise for extension to automatic three-dimensional hexahedral meshing. Initial conditions required to ensure mesh closure include an even number of elements on the boundary and a closed boundary. The desired mesh characteristics are programmed into the algorithm. A Poisson's solution scheme is utilized to generate a better initial placement, density, size and orientation of elements, leading to faster and more robust mesh closure. A number of example geometries have been meshed.