The removal of critical slowing down

TL;DR

This paper introduces an adaptive multigrid solver for the non-Hermitian Wilson-Dirac system in 4D, effectively reducing critical slowing down by preserving near null spaces through adaptive coarse grid projections.

Contribution

It develops a novel adaptive multigrid algorithm specifically designed for non-Hermitian systems, improving convergence near the chiral limit.

Findings

Weak dependence on gauge coupling

Extremely mild critical slowing down

Effective preservation of near null space

Abstract

We present promising initial results of our adaptive multigrid solver developed for application directly to the non-Hermitian Wilson-Dirac system in 4 dimensions, as opposed to the solver developed in [1] for the corresponding normal equations. The key behind the success of this algorithm is the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix. We demonstrate that the resulting algorithm has weak dependence on the gauge coupling and exhibits extremely mild critical slowing down in the chiral limit.