Multigrid accelerated simulations for Twisted Mass fermions

TL;DR

This paper demonstrates that multigrid preconditioning, specifically the DD-αAMG solver, significantly accelerates twisted mass fermion simulations at physical pion mass, reducing computational time by over four times.

Contribution

It introduces a hybrid simulation approach combining multiple solvers with multigrid acceleration for twisted mass fermions at physical quark masses.

Findings

Multigrid preconditioning speeds up simulations by more than four times.

The DD-αAMG solver maintains stability during large-scale simulations.

Hybrid solver strategy effectively reduces critical slowing down.

Abstract

Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion mass are being performed to generate $N_f = 2$ and $N_f = 2 + 1 + 1$ gauge ensembles using twisted mass fermions. The adaptive aggregation-based domain decomposition multigrid solver, referred to as DD-$\alpha$AMG method, is employed for these simulations. Our simulation strategy consists of an hybrid approach of different solvers, involving the Conjugate Gradient (CG), multi-mass-shift CG and DD-$\alpha$AMG solvers. We present an analysis of the multigrid performance during the simulations discussing the stability of the method. This significant speeds up the Hybrid Monte Carlo simulation by more than a factor $4$ at physical pion mass compared to the usage of the CG solver.