A Global Optimization Approach to Quadrilateral Meshing

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.155, October 1997

MESHING
RESEARCH
CORNER

Sandia National Laboratories and University of New Mexico, Albuquerque

Abstract
A novel method is presented for automatically generating quadrilateral meshes on arbitrary two-dimensional domains. The method is based on global minimization of a potential function that governs the mesh characteristics. The potential is comprised of several terms that 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 finds alternative connectivities. Unused edges, representing holes in the mesh, are moved to either coalesce, or to a boundary. We will describe the components of the potential, the minimization procedure, and the connectivity refinement algorithm. The method shows promise for extension to automatic three- dimensional hexahedral meshing.

Download Full Paper (Postscript Format)