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Published in:
2016 | Supplement | Chapter
Efficient Numerical Simulation of the Wilson Flow in Lattice QCD
Authors : Michèle Wandelt, Michael Günther
Published in: Progress in Industrial Mathematics at ECMI 2014
Publisher: Springer International Publishing
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Abstract
Lattice Quantum Chrome Dynamics (Lattice QCD) is a gauge theory formulated on a highly dimensional grid or lattice of points in space and time. It aims at determining observables such as the mass of elementary particles as accurate as possible, with computational costs as low as possible at the same time. Thus high performance computing tools are inevitable, as well as the construction of HPSC hardware tailored to the needs of Lattice QCD. In the Hybrid Monte Carlo (HMC) approach (Duane et al., Phys. Lett. B, 195:216, 1987 http://dx.doi.org/10.1016/0370-2693(87)91197-X), Monte Carlo simulations involving a molecular dynamics step in its core are performed, which yield physical values provided with their statistical errors.
In this talk we concentrate on the Wilson Flow, a system of differential equations defined on the Lie group SU(3). The Wilson Flow can be used, e.g., to determine the physical lattice spacing which influences the result of the HMC simulations. We focus on tailored Runge-Kutta Lie group integration methods with step size prediction. The numerical results confirm that our strategy is able to reduce the statistical errors of the simulation.