Double mapping of isoparametric mesh generation

Although coordinate-transformation techniques, such as conventional curvilinear isoparametric mesh generating method, normally produce well conditioned meshes, they are commonly the most restrictive mesh generators. This is due mainly to the fact that the number of nodes on the opposite sides of the superelement should be equal [H. Kardestuncer, Finite Element Handbook. McGraw-Hill, New York (1987)]. In this paper, the isoparametric method is improved for two- and three-dimensional problems, such that the opposite sides can have different number of nodes. The extended isoparametric method gives much more flexibility in choosing the number of nodes and looks promising for applying different methods of adaptive mesh generation [M. H. Kadiver and A. Korminezhad, Automatic mesh generation by triangulation, double, isoparametric mapping and bisection mapping, Proc. 10th IASTED Int Conf. Applied Informatic, Innsbruck, Austria (1992)]. A similar method also can be applied in a blending-function mesh generator.