Anisotropic, interpolatory subdivision and multigrid

TL;DR

This paper introduces a new family of anisotropic interpolatory subdivision schemes for multigrid methods, analyzing their properties and demonstrating their effectiveness in improving grid transfer operations.

Contribution

The paper develops novel anisotropic interpolatory subdivision schemes and links their properties to multigrid convergence, offering improved grid transfer operators for anisotropic problems.

Findings

The proposed schemes have favorable polynomial reproduction properties.

They enhance multigrid convergence and efficiency.

Performance comparisons show advantages over existing methods.

Abstract

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.