Lattice QCD and the Schwarz alternating procedure

Lüscher, Martin

doi:10.1088/1126-6708/2003/05/052

Cited by 92 publications

(148 citation statements)

References 32 publications

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“…Fit results are summarized in Table 10. Systematic errors due to the choice of the fit ranges are estimated from the (maximum) change in the fit parameters by shifting [t min , t max ] to [4,6] or varying r min and r max in ranges r min ∈ [2,3] and…”

Section: Static Quark Potentialmentioning

confidence: 99%

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Two-flavor QCD simulation with exact chiral symmetry

et al. 2008

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We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably large and fine lattices by a careful choice of the lattice action and algorithmic improvements. Our production runs are carried out on a 16 3 × 32 lattice at a single lattice spacing around 0.12 fm. We explore the sea quark mass region down to m s /6, where m s is the physical strange quark mass, for a good control of the chiral extrapolation in future calculations of physical observables. We describe in detail our setup and algorithmic properties of the production simulations and present results for the static quark potential to fix the lattice scale and the locality of the overlap operator.

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Section: Static Quark Potentialmentioning

confidence: 99%

“…In particular, recent algorithmic improvements [1][2][3][4][5][6][7][8] as well as development of computer technology enable us to approach the chiral regime of QCD [9][10][11][12][13][14][15][16][17] and to include all three light flavors of quarks dynamically [9,10,[14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Two-flavor QCD simulation with exact chiral symmetry

et al. 2008

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“…Domain decomposition was introduced in lattice QCD in [3] and in [10] the resulting factorisation of the fermion determinant was used to separate short distance and long distance physics in the HMC algorithm.…”

Section: Domain Decompositionmentioning

confidence: 99%

“…The advantage of our approach, based on recursive domain decomposition, is that it allows for a decoupling of updates within the domains and thus parallel domain-wise acceptance steps in the filter (section 3). In [3] a serial hierarchical filter of increasing block size was proposed, but never tested.…”

Section: Introductionmentioning

confidence: 99%

Fermions as global correction in lattice QCD

Leder¹,

Finkenrath²,

Knechtli³

2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

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The fermion determinant is a highly non-local object and its logarithm is an extensive quantity. For these reasons it is widely believed that the determinant cannot be treated in acceptance steps of gauge link configurations that differ in a large fraction of the links. However, for exact factorisations of the determinant that separate the ultraviolet from the infra-red modes of the Dirac operator it is known that the latter show less variation under changes of the gauge field compared to the former. Using a factorisation based on recursive domain decomposition allows for a hierarchical algorithm that starts with pure gauge updates of the links within the domains and ends after a number of filters with a global acceptance step. We find that the global acceptance rate is high on moderate lattice sizes. Whether this type of algorithm can help in curing the problem of critical slowing down is presently under study.

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“…First one is the QR decomposition, which is known to improve the numerical accuracy in block CG [2,7] and also useful for block BiCGSTAB algorithm [8]. Second one is Schwarz alternating procedure (SAP) preconditioner proposed by Lüscher [9], which is applied to the domain-decomposed lattice. We can minimize communication overhead with the SAP preconditioner.…”

Section: Introductionmentioning

confidence: 99%

Modified block BiCGSTAB for lattice QCD

Nakamura¹,

Ishikawa²,

Kuramashi³

et al. 2012

Computer Physics Communications

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We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on a 32 3 × 64 lattice at almost physical quark masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.

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Lattice QCD and the Schwarz alternating procedure

Cited by 92 publications

References 32 publications

Two-flavor QCD simulation with exact chiral symmetry

Two-flavor QCD simulation with exact chiral symmetry

Fermions as global correction in lattice QCD

Modified block BiCGSTAB for lattice QCD

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