A scalable preconditioner for a DPG method

TL;DR

This paper develops a scalable algebraic preconditioner for the primal DPG method by leveraging existing AMG techniques, enabling efficient solutions for large-scale DPG problems.

Contribution

It introduces the first massively scalable algebraic preconditioner specifically designed for DPG methods using AMG algorithms.

Findings

Preconditioner achieves scalability for large DPG systems.

Utilizes existing AMG software for efficient implementation.

Demonstrates effectiveness on interface unknowns in DPG formulations.

Abstract

We show how a scalable preconditioner for the primal discontinuous Petrov-Galerkin (DPG) method can be developed using existing algebraic multigrid (AMG) preconditioning techniques. The stability of the DPG method gives a norm equivalence which allows us to exploit existing AMG algorithms and software. We show how these algebraic preconditioners can be applied directly to a Schur complement system of interface unknowns arising from the DPG method. To the best of our knowledge, this is the first massively scalable algebraic preconditioner for DPG problems.