Full Automatic Grid Generation Using the Symmetric Axial Transformation
K. Yahia (Bosch, Stuttgart)
A full automatic method for grid generation for FEM in polygonal areas is described. The symmetric axis transformation divides the whole area in sub-domains, that depend strongly on the problem geometry. The procedure of Lee[Lee92] has been used. The algorithms have been largely adopted and improved.
In the discretisation a new path has been chosen, that uses the property of Delauny triangulation in advance by dividing the sub-domain in strips. The discretisation of a strip has the complexity O(N), where N is the number of the vertices of the grid. The Delauny criterion does not have to be confirmed.
Compared to the classic triangulation with the complexity O(N2), the whole discretisation is a lot faster. Besides that, a new algorithm for smoothing will be presented, that moves vertices along the edges, to relax the grid.
[Lee92] Lee R. Nachman: Automatic Mesh Generation Using the Symmetric Axis Transformation of Polygonal Domains. Proceeding of the IEEE. VOL. 80, NO. 9, Sep. 1992