Adaptive aggregation-based domain decomposition multigrid for twisted mass fermions

Alexandrou, C.; Bacchio, Simone; Finkenrath, Jacob; Frommer, Andreas; Kahl, Karsten; Rottmann, Matthias

doi:10.1103/physrevd.94.114509

Cited by 67 publications

(70 citation statements)

References 32 publications

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“…Thus, a tuning of the precision of the solver has to be carried out. To invert the Dirac operator, we use the adaptive multigrid solver with twisted mass fermion support [96] and require the residual to be r HP =10 −10 for HP inversions. After testing different values of the residual for LP inversions, we find that the stopping criterion…”

Section: Lattice Techniquesmentioning

confidence: 99%

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

et al. 2019

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We present a detailed study of the helicity-dependent and helicity-independent collinear parton distribution functions (PDFs) of the nucleon, using the quasi-PDF approach. The lattice QCD computation is performed employing twisted mass fermions with a physical value of the light quark mass. We give a systematic and in-depth account of the salient features entering in the evaluation of quasi-PDFs and their relation to the light-cone PDFs. In particular, we give details for the computation of the matrix elements, including the study of the various sources of systematic uncertainties, such as excited states contamination. In addition, we discuss the non-perturbative renormalization scheme used here and its systematics, effects of truncating the Fourier transform and different matching prescriptions. Finally, we show improved results for the PDFs and discuss future directions, challenges and prospects for evaluating precisely PDFs from lattice QCD with fully quantified uncertainties. arXiv:1902.00587v1 [hep-lat] 1 Feb 2019of the theoretical and numerical developments, see Ref.[33].On more general grounds, it is very important to realize that quasi-PDFs and light-cone PDFs have been shown to share the same infrared physics [34,35], which is the fundamental observation that allows one to relate both quantities using perturbation theory, provided that the hadron is moving with a large, although necessarily finite, momentum in a chosen spatial direction. It has also been proven that quasi-PDFs can be extracted from lattice QCD in Euclidean spacetime [35] and that they do not suffer from power-divergent mixings with lower-dimensional operators [36][37][38]. A factorization formula makes it possible to extract the PDFs from the quasi-PDFs, an operation called matching [19,20,29,31,34,[39][40][41][42][43]. In general, this procedure is based on a newly developed large-momentum effective theory (LaMET) [44], and it is renormalizable to all orders in perturbation theory [45][46][47][48]. Other approaches for a direct computation of the x-dependence of PDFs include the hadronic tensor [49][50][51], fictitious heavy quark [52], auxiliary light quark [53], good lattice cross sections [54,55] (closely related to the auxiliary light quark method), "OPE without OPE" [56] and pseudo-PDFs [57][58][59][60], where the latter can be seen as a generalization of PDFs off the light-cone. These alternative approaches have been explored in lattice QCD, and recent results can be found in Refs. [38,56,[61][62][63][64][65][66][67]. The new formulation and its successful implementation within lattice QCD has also led to a wider interest on phenomenological studies using models and toy theories of QCD [57,58,[68][69][70][71][72][73][74][75]. A detailed overview of the current status of lattice QCD calculation of PDFs and other partonic distributions can be found in the recent reviews of Refs. [33,76].The remainder of the paper is organized as follows: In Sec. II, we provide the general theoretical aspects, lattice QCD action and parameters. We di...

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Section: Lattice Techniquesmentioning

confidence: 99%

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

et al. 2019

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“…Thus, the identification of the ground-state is presently possible only in the case ofss andcc vector mesons. To improve the statistics we took a significative advantage by using the DD − αAMG solver [45], which has allowed us to increase by a factor of 5 the number of stochastic sources in the case of the strange quark. In this way we find that the quality of the plateaux, shown in figure 5, is acceptable in the strange sector and nice in the charm one.…”

Section: Ground-state Identificationmentioning

confidence: 99%

Strange and charm HVP contributions to the muon (g − 2) including QED corrections with twisted-mass fermions

Giusti

Lubicz

Martinelli

et al. 2017

J. High Energ. Phys.

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We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with N f = 2 + 1 + 1 dynamical quarks at three values of the lattice spacing (a 0.062, 0.082, 0.089 fm) with pion masses in the range M π 210-450 MeV. The strange and charm quark masses are tuned at their physical values. Neglecting disconnected diagrams and after the extrapolations to the physical pion mass and to the continuum limit we obtain: a s µ (α 2 em ) = (53.1 ± 2.5) · 10 −10 , a s µ (α 3 em ) = (−0.018 ± 0.011) · 10 −10 and a c µ (α 2 em ) = (14.75 ± 0.56) · 10 −10 , a c µ (α 3 em ) = (−0.030 ± 0.013) · 10 −10 for the strange and charm contributions, respectively.

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“…We use a three-level DD-αAMG method optimized for TM fermions [3]. No instabilities in the iterations count are seen along the whole simulations.…”

Section: Discussionmentioning

confidence: 99%

“…The DD-αAMG approach has been adapted in Ref. [3] to the Wilson TM operator D(±µ) = D ± iµΓ 5 . Due to the Γ 5 -compatibility, the coarse operator reads similarly to the fine operator, i.e.…”

Section: Dd-αamg Methodsmentioning

confidence: 99%

“…Here we discuss in detail the HMC simulations with a focus on the usage of multigrid methods and in particular the performance of the DD-αAMG solver adapted for TM fermions [3]. 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.…”

Section: Introductionmentioning

confidence: 99%

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Multigrid accelerated simulations for Twisted Mass fermions

2018

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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-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.

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Adaptive aggregation-based domain decomposition multigrid for twisted mass fermions

Cited by 67 publications

References 32 publications

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

Strange and charm HVP contributions to the muon (g − 2) including QED corrections with twisted-mass fermions

Multigrid accelerated simulations for Twisted Mass fermions

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