Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator

Frommer, Andreas; Kahl, Karsten; Krieg, Stefan; Leder, Björn; Rottmann, Matthias

doi:10.48550/arxiv.1303.1377

Cited by 15 publications

(31 citation statements)

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“…We used a modified version of the Chroma [104] software package, along with the LibHadronAnalysis library and, depending on the target machine, either the multigrid DD-αAMG solver [105] implementation of refs. [106,107] or the domain decomposition solver of openQCD [55] (https://luscher.web.cern.ch/luscher/openQCD/).…”

Section: Discussionmentioning

confidence: 99%

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

Bali

Braun

Bürger

et al. 2019

J. High Energ. Phys.

103

108

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We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors: a π 2 = 0.101 +24 −24 for the pion; a K 1 = 0.0533 +34 −35 and a K 2 = 0.090 +19 −20 for the kaon. The calculation is carried out on 35 different CLS ensembles with N f = 2 + 1 flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to a = 0.039 fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane.

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Section: Discussionmentioning

confidence: 99%

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

Bali

Braun

Bürger

et al. 2019

J. High Energ. Phys.

103

108

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“…Preconditioning improves convergence of linear systems by transforming the input as M −1 P (1) x = M −1 b, where the preconditioner M must be inexpensive to invert and M −1 should be "close" to P (1) −1 , so that M −1 P (1) resembles a matrix close to unity. Identifying an effective preconditioner plays an important role in numerical convergence of iterative methods [8][9][10][11][12] . For lattice QCD applications 13 , the low-lying spectrum of the Dirac operator slows iterative convergence and preconditioning has been used to project out these low-lying modes.…”

Section: Polynomial Systems Of Equationsmentioning

confidence: 99%

Quantum annealing for systems of polynomial equations

Chang

Gambhir

Humble

et al. 2019

Sci Rep

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Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of 10 −8 .

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“…These N f = 2 + 1 simulations employ the nonperturbatively order a improved Wilson (clover) quark action and the tree-level Symanzik improved gauge action. We used a modified version of the Chroma software system [39,40], the LibHadronAnalysis library and efficient inverters [41][42][43]. To enhance the ground state overlap the source interpolators are Wuppertal-smeared [44], employing spatially APE-smeared [45] transporters.…”

Section: Details and Strategy Of The Lattice Simulationmentioning

confidence: 99%

Light-cone distribution amplitudes of the baryon octet

Bali

Braun

Göckeler

et al. 2016

J. High Energ. Phys.

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We present results of the first ab initio lattice QCD calculation of the normalization constants and first moments of the leading twist distribution amplitudes of the full baryon octet, corresponding to the small transverse distance limit of the associated S-wave light-cone wave functions. The P -wave (higher twist) normalization constants are evaluated as well. The calculation is done using N f = 2 + 1 flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to 222 MeV. Significant SU(3) flavor symmetry violation effects in the shape of the distribution amplitudes are observed.

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Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator

Cited by 15 publications

References 0 publications

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

Quantum annealing for systems of polynomial equations

Light-cone distribution amplitudes of the baryon octet

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