Anisotropic, interpolatory subdivision and multigrid
It provides a novel method for anisotropic multigrid, which is important for solving PDEs on anisotropic grids.
The paper introduces a new family of anisotropic interpolatory subdivision schemes for grid transfer in multigrid methods, demonstrating improved convergence and optimality over approximating schemes.
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.