Efficient implementation of the overlap operator on multi-GPUs

Alexandru, Andrei; Lujan, Michael; Pelissier, Craig; Gamari, Ben; Lee, Frank

doi:10.48550/arxiv.1106.4964

Cited by 6 publications

(6 citation statements)

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“…Compared to the earlier implementation of the overlap operator [21], the current implementation further improves the performance of data exchange on different nodes of the cluster and uses the polynomial approximation for the overlap operator instead of the rational approximation, and has achieved better scaling and further speed up of the calculation by a factor of two on average [22].…”

Section: Numerical Detailsmentioning

confidence: 99%

Stochastic method with low mode substitution for nucleon isovector matrix elements

et al. 2016

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We introduce a stochastic method with low-mode substitution to evaluate the connected threepoint functions. The isovector matrix elements of the nucleon for the axial-vector coupling g 3 A , scalar couplings g 3 S and the quark momentum fraction x u−d are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a 24 3 ×64 lattice at mπ = 330 MeV with lattice spacing a = 0.114 fm.

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Section: Numerical Detailsmentioning

confidence: 99%

Stochastic method with low mode substitution for nucleon isovector matrix elements

et al. 2016

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“…Since then LQCD has been at the forefront of the adoption of GPUs in HPC. Notable publications include multi-GPU parallelization [21,22,23], the use of additive-Schwarz preconditioning to improve strong scaling [24], implementation of multi-grid solvers [25], software-managed cacheblocking strategies [26], and JIT-compilation to enable the offload of the entire underlying data-parallel framework of the Chroma [27] application without any high-level source changes [28].…”

Section: Previous Workmentioning

confidence: 99%

Pushing memory bandwidth limitations through efficient implementations of Block-Krylov space solvers on GPUs

Clark

Strelchenko

Vaquero

et al. 2018

Computer Physics Communications

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The cost of the iterative solution of a sparse matrix-vector system against multiple vectors is a common challenge within scientific computing. A tremendous number of algorithmic advances, such as eigenvector deflation and domain-specific multi-grid algorithms, have been ubiquitously beneficial in reducing this cost. However, they do not address the intrinsic memory-bandwidth constraints of the matrix-vector operation dominating iterative solvers. Batching this operation for multiple vectors and exploiting cache and register blocking can yield a super-linear speed up. Block-Krylov solvers can naturally take advantage of such batched matrix-vector operations, further reducing the iterations to solution by sharing the Krylov space between solves. Practical implementations typically suffer from the quadratic scaling in the number of vector-vector operations. We present an implementation of the block Conjugate Gradient algorithm on NVIDIA GPUs which reduces the memory-bandwidth complexity of vector-vector operations from quadratic to linear. As a representative case, we consider the domain of lattice quantum chromodynamics and present results for one of the fermion discretizations. Using the QUDA library as a framework, we demonstrate a 5× speedup compared to highly-optimized independent Krylov solves on NVIDIA's SaturnV cluster.

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“…The low-energy constant ∆ mix , which measures the mismatch of the mixed valence and sea pion masses between the domain-wall fermion and the overlap fermion, is shown to be very small [13]. Since overlap fermion accommodates the multi-mass algorithm and the eigenvectors are the same for different quark masses, we use 1000 pairs of eigenvectors plus the zero modes for deflation in calculating quark propagators for several masses on 45 configurations (see Ref [14] for details). The bare mass parameters are chosen as am (val) q = 0.00170, 0.00240, 0.00300, 0.00455, 0.00600 and 0.02030, which give the pion mass ranging from 114 to 371 MeV.…”

Section: ρ Meson Massmentioning

confidence: 99%

Anatomy of the ρ resonance from lattice QCD at the physical point

et al. 2018

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We propose a strategy to access the qq component of the ρ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the qq component is derived at different valence quark masses, and shows a linear dependence on m 2 π . The slope is determined to be c1 = 0.505(3) GeV −1 , from which the valence πρ sigma term is extracted to be σ (val) πρ = 9.82(6) MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the qq component is interpolated to be mρ = 775.9 ± 6.0 ± 1.8 MeV, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the qq component to be f ρ − = 208.5 ± 5.5 ± 0.9 MeV, which can be compared with the experimental value f exp ρ ≈ 221 MeV through the relation f exp ρ = Zρf ρ ± with Zρ ≈ 1.13 being the on-shell wavefunction renormalization of ρ owing to the ρ − π interaction. We emphasize that mρ and fρ of the qq component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in effective field theory studies where ρ acts as a fundamental degree of freedom.

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Efficient implementation of the overlap operator on multi-GPUs

Cited by 6 publications

References 0 publications

Stochastic method with low mode substitution for nucleon isovector matrix elements

Stochastic method with low mode substitution for nucleon isovector matrix elements

Pushing memory bandwidth limitations through efficient implementations of Block-Krylov space solvers on GPUs

Anatomy of the ρ resonance from lattice QCD at the physical point

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