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Adapted Nested Force-Gradient Integrators: The Schwinger Model Case

  • Dmitry Shcherbakov (a1), Matthias Ehrhardt (a1), Jacob Finkenrath (a2), Michael Günther (a1), Francesco Knechtli (a3) and Michael Peardon (a4)...
Abstract
Abstract

We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a well known benchmark problem. We derive the analytical basis of nested force-gradient type methods and demonstrate the advantage of the proposed approach, namely reduced computational costs compared with other numerical integration schemes in HMC.

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*Corresponding author. Email addresses: shcherbakov@math.uni-wuppertal.de (D. Shcherbakov), ehrhardt@math.uni-wuppertal.de (M. Ehrhardt), j.finkenrath@cyi.ac.cy (J. Finkenrath), guenther@math.uni-wuppertal.de (M. Günther), knechtli@physik.uni-wuppertal.de (F. Knechtli), mjp@maths.tcd.ie (M. Peardon)
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[2] E. Borici , C. Joó , A. Frommer , Numerical methods in QCD, Springer, Berlin, 2002.

[6] E. Hairer , C. Lubich , G. Wanner , Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, Berlin, 2002.

[10] M. Lüscher , S. Schäfer , Lattice QCD with open boundary conditions and twisted-mass reweighting, Comput. Phys. Commun. 184(2013), pp 519528.

[15] D. Shcherbakov , M. Ehrhardt , M. Günther , M. Peardon , Force-gradient nested multirate methods for Hamiltonian systems, Comput. Phys. Commun. 187(2015), pp 9197.

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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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