MANY MASSES ON ONE STROKE: ECONOMIC COMPUTATION OF QUARK PROPAGATORS

Andreas Frommer, Bertold Nöckel, Stephan Güsken, Thomas Lippert and Klaus Schilling
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Andreas Frommer: Mathematics Department, University of Wuppertal, 42097 Wuppertal, Germany
Bertold Nöckel: Mathematics Department, University of Wuppertal, 42097 Wuppertal, Germany
Stephan Güsken: Physics Department, University of Wuppertal, 42097 Wuppertal, Germany
Thomas Lippert: Physics Department, University of Wuppertal, 42097 Wuppertal, Germany
Klaus Schilling: HLRZ c/o KFA DESY, D-52425 Jülich, Germany

International Journal of Modern Physics C (IJMPC), 1995, vol. 06, issue 05, 627-638

Abstract: The computational effort in the calculation of Wilson fermion quark propagators in Lattice Quantum Chromodynamics can be considerably reduced by exploiting the Wilson fermion matrix structure in inversion algorithms based on the non-symmetric Lanczos process. We consider two such methods: QMR (quasi minimal residual) and BCG (biconjugate gradients).Based on the decompositionM/κ =1/κ−Dof the Wilson mass matrix, using QMR, one can carry out inversions on a whole trajectory of masses simultaneously, merely at the computational expense of a single propagator computation. In other words, one has to compute the propagator corresponding to the lightest mass only, while all the heavier masses are given for free, at the price of extra storage.Moreover, the symmetryγ5M = M†γ5can be used to cut the computational effort in QMR and BCG by a factor of two. We show that both methods then become — in the critical regime of small quark masses — competitive to BiCGStab and significantly better than the standard MR method, with optimal relaxation factor, and CG as applied to the normal equations.

Keywords: Lattice QCD; Relaxation Algorithm; Parallel Computer (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1142/S0129183195000538

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