Adaptive Multigrid Algorithm for Lattice QCD

TL;DR

This paper introduces an adaptive multigrid solver tailored for the Dirac operator in lattice QCD, effectively reducing critical slowing down and maintaining performance across varying gauge couplings.

Contribution

It develops a novel adaptive projection method for multigrid algorithms that preserves near null spaces, improving efficiency in lattice QCD simulations.

Findings

Weak dependence on gauge coupling

Minimal critical slowing down in the chiral limit

Effective for 2D U(1) Schwinger model

Abstract

We present a new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields. The key behind the success of the algorithm is an adaptive projection onto the coarse grids that preserves the near null space. The resulting algorithm has weak dependence on the gauge coupling and exhibits very little critical slowing down in the chiral limit. Results are presented for the Wilson Dirac operator of the 2d U(1) Schwinger model.