Variational Grid Generation Using Exponentials of Area

Proceedings, 10th International Meshing Roundtable, Sandia National Laboratories, pp.111-119, October 7-10 2001

MESHING
RESEARCH
CORNER

10th International Meshing Roundtable
Newport Beach, California, U.S.A.
October 7-10, 2001

Pablo Barrera Sanchez
Facultad de Ciencias, U.N.A.M.
Circuito Exterior, Ciudad Universitaria
Mexico, D.F., 04510.
Email: pablo@athena.fciencias.unam.mx

Guilmer F. Gonzalez F.
Facultad de Ciencias, U.N.A.M.
Email: gfgf@athena.fciencias.unam.mx

Francisco J. Dominguez Mota
Escuela de Ciencias Fisico-Matematicas, U.M.S.N.H.
Morelia, Mexico, 58000.
Email: dmota@zeus.umich.mx

Abstract
Some variational methods for grid generation have been successfully developed in the works of Tinoco and Barrera ([8],[9],[10]) by the use of generalizations of Winslow's smoothness functional ([2]) in terms of the so called k-functionals, on which a parameter plays an important role in the construction of a sequence of grids which tends to an existing convex one for a given planar region. However, a parameter of this kind is global for a given configura- tion, and so it doesn't follow in a straightforward way which one is the continuous analog functional from where the discrete k-functional should be coming. This remains as an important issue when we consider the dynamical behavior of these set of expressions.

In this work, in order to construct a convex grid in a given region, we present another discrete functional written in terms of the area of the triangles conforming the cells, which achieves its minimal value when the total area of the region is averaged in the cells, by only asking elementary geometrical requirements.

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