  In this paper, we present a family of multivariate grid transfer operators
appropriate for anisotropic multigrid methods. Our grid transfer operators are
derived from a new family of anisotropic interpolatory subdivision schemes. We
study the minimality, polynomial reproduction and convergence properties of
these interpolatory schemes and link their properties to the convergence and
optimality of the corresponding multigrid methods. We compare the performance
of our interpolarory grid transfer operators with the ones derived from a
family of corresponding approximating subdivision schemes.
