Anisotropic bivariate subdivision with applications to multigrid

In this paper, motivated by applications to multigrid, we present families of anisotropic, bivariate, interpolating and approximating subdivision schemes. We study the minimality and polynomial generation/reproduction properties of both families and Hölder regularity of their prominent representatives. From the symbols of the proposed subdivision schemes, we define bivariate grid transfer operators for anisotropic multigrid methods. We link the generation/reproduction properties of subdivision to the convergence and optimality of the corresponding multigrid methods. We illustrate the performance of our subdivision based grid transfer operators on examples of anisotropic Laplacian and biharmonic problems.