Skip to main content

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)...

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.

Corresponding author
*Corresponding author. Email addresses: (D. Shcherbakov), (M. Ehrhardt), (J. Finkenrath), (M. Günther), (F. Knechtli), (M. Peardon)
Hide All
[1] Bazavov A. et al., Chiral transition and U(1) A symmetry restoration from lattice QCD using domain wall fermions, Phys. Rev. D 86 (201), 094503.
[2] Borici E., Joó C., Frommer A., Numerical methods in QCD, Springer, Berlin, 2002.
[3] Clark M.A., Joó B., Kennedy A.D., Silva P.J., Better HMC integrators for dynamical simulations, PoS 323(2010).
[4] Christian N., Jansen K., Nagai K., Pollakowski B., Scaling test of fermion actions in the Schwinger model, Nuclear Physics B 739 (2006), pp. 6084.
[5] Duane S., Kennedy A.D., Pendleton B.J., Roweth D., Hybrid Monte Carlo, Phys. Lett. B195 (1987), pp. 216222.
[6] Hairer E., Lubich C., Wanner G., Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, Berlin, 2002.
[7] Kennedy A.D., Clark M.A., Speeding up HMC with better integrators, PoS 038(2007).
[8] Kennedy A. D., Clark M. A., Silva P. J., Force Gradient Integrators, PoS 021(2009).
[9] Kennedy A.D., Silva P.J., Clark M.A., Shadow Hamiltonians, Poisson Brackets and Gauge Theories, Phys. Rev. D 87 (2013), 034511.
[10] Lüscher M., Schäfer S., Lattice QCD with open boundary conditions and twisted-mass reweighting, Comput. Phys. Commun. 184(2013), pp 519528.
[11] Omelyan I.P., Mryglod I.M., Folk R., Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics, Comput. Phys. Commun. 151 (2003), pp. 272314.
[12] Schwinger J.S., Gauge Invariance and Mass. 2, Phys. Rev. 128 (1962), pp. 24252429.
[13] Sexton J.C., Weingarten D.H., Hamiltonian evolution for the hybrid Monte Carlo algorithm, Nucl. Phys. B380 (1992), pp. 665678.
[14] Shcherbakov D., Ehrhardt M., Multistep Methods for Lattice QCD Simulations, PoS (Lattice 2011), pp. 327333.
[15] Shcherbakov D., Ehrhardt M., Günther M., Peardon M., Force-gradient nested multirate methods for Hamiltonian systems, Comput. Phys. Commun. 187(2015), pp 9197.
[16] Silva P.J., Kennedy A.D., Clark M.A., Tuning HMC using Poisson brackets, PoS 041(2008).
[17] Yin H., Mawhinney R. D., Improving DWF Simulations: the Force Gradient Integrator and the Möbius Accelerated DWF Solver, PoS (Lattice 2011) 051.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 15 *
Loading metrics...

Abstract views

Total abstract views: 87 *
Loading metrics...

* Views captured on Cambridge Core between 8th March 2017 - 20th November 2017. This data will be updated every 24 hours.