Cluster-Computing und Computational Science mit der Wuppertaler Alpha-Linux-Cluster-Engine ALiCE

Arndt, Holger; Arnold, Guido; Eicker, N.; Fliegner, Denny; Frommer, Andreas; Hentschke, Renato; Isaila, Florin; Kabrede, Hendrik; Krech, M.; Lippert, Thomas; Neff, H.; Orth, Boris; Schilling, Klaus; Schroers, Wolfram; Tichy, Walter F.

doi:10.1515/piko.2002.21

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2002

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“…In this section we report on the performance of some of the discussed methods for realistic configurations in QCD. All the experiments are carried out on the cluster computer AliCE installed at Wuppertal University [44].…”

Section: Numerical Experimentsmentioning

confidence: 99%

Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds

Eshof

Frommer

Lippert

et al. 2002

Computer Physics Communications

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143

181

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The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix-vector product that involves the sign function of the hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.

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Section: Numerical Experimentsmentioning

confidence: 99%