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 Nf = 2 and Nf = 2 + 1 + 1 gauge ensembles using twisted mass fermions. The adaptive aggregation-based domain decomposition multigrid solver, referred to as DD-αAMG 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-αAMG 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.
Highlights
Simulations at the physical value of the pion mass have been intensively pursued by a number of lattice QCD collaborations
Our simulation strategy consists of an hybrid approach of different solvers, involving the Conjugate Gradient (CG), multi-mass-shift CG and DD-αAMG solvers
We focus on simulations with twisted mass (TM) fermions
Summary
Simulations at the physical value of the pion mass have been intensively pursued by a number of lattice QCD collaborations. We focus on simulations with twisted mass (TM) fermions This discretization scheme has the advantage that all observables are automatically O(a) improved when tuned at maximal twist [5]. The presence of a finite TM term bounds the spectrum of DD† from below by a positive quantity μ2, where D is the Wilson Dirac operator and μ is the TM parameter This avoids exceptional configurations and, at the same time, gives an upper bound to the condition number, satisfying the convergence of numerical methods. We will show results for two simulations at maximal twist and at the physical value of the pion mass, which have been generated in the last two years using twisted mass fermions We discuss our strategy for the calculation of the force terms and the generation of the multigrid subspace during the integration of the molecular dynamics (MD) and demonstrate that this yields stable simulations with an improved performance
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