No CrossRef data available.
Article contents
Adapted Nested Force-Gradient Integrators: The Schwinger Model Case
Part of:
Numerical problems in dynamical systems
Numerical analysis: Ordinary differential equations
Qualitative theory
Published online by Cambridge University Press: 08 March 2017
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
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.
Keywords
Information
- Type
- Research Article
- Information
- Copyright
- Copyright © Global-Science Press 2017
References
[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.Google Scholar
[2]
Borici, E., Joó, C., Frommer, A., Numerical methods in QCD, Springer, Berlin, 2002.Google Scholar
[3]
Clark, M.A., Joó, B., Kennedy, A.D., Silva, P.J., Better HMC integrators for dynamical simulations, PoS 323(2010).Google Scholar
[4]
Christian, N., Jansen, K., Nagai, K., Pollakowski, B., Scaling test of fermion actions in the Schwinger model, Nuclear Physics B
739 (2006), pp. 60–84.Google Scholar
[5]
Duane, S., Kennedy, A.D., Pendleton, B.J., Roweth, D., Hybrid Monte Carlo, Phys. Lett. B195 (1987), pp. 216–222.Google Scholar
[6]
Hairer, E., Lubich, C., Wanner, G., Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer, Berlin, 2002.Google Scholar
[7]
Kennedy, A.D., Clark, M.A., Speeding up HMC with better integrators, PoS 038(2007).Google Scholar
[8]
Kennedy, A. D., Clark, M. A., Silva, P. J., Force Gradient Integrators, PoS 021(2009).Google Scholar
[9]
Kennedy, A.D., Silva, P.J., Clark, M.A., Shadow Hamiltonians, Poisson Brackets and Gauge Theories, Phys. Rev. D
87 (2013), 034511.Google Scholar
[10]
Lüscher, M., Schäfer, S., Lattice QCD with open boundary conditions and twisted-mass reweighting, Comput. Phys. Commun.
184(2013), pp 519–528.Google Scholar
[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. 272–314.Google Scholar
[12]
Schwinger, J.S., Gauge Invariance and Mass. 2, Phys. Rev.
128 (1962), pp. 2425–2429.Google Scholar
[13]
Sexton, J.C., Weingarten, D.H., Hamiltonian evolution for the hybrid Monte Carlo algorithm, Nucl. Phys. B380 (1992), pp. 665–678.Google Scholar
[14]
Shcherbakov, D., Ehrhardt, M., Multistep Methods for Lattice QCD Simulations, PoS (Lattice 2011), pp. 327–333.Google Scholar
[15]
Shcherbakov, D., Ehrhardt, M., Günther, M., Peardon, M., Force-gradient nested multirate methods for Hamiltonian systems, Comput. Phys. Commun.
187(2015), pp 91–97.Google Scholar
[16]
Silva, P.J., Kennedy, A.D., Clark, M.A., Tuning HMC using Poisson brackets, PoS 041(2008).Google Scholar
[17]
Yin, H., Mawhinney, R. D., Improving DWF Simulations: the Force Gradient Integrator and the Möbius Accelerated DWF Solver, PoS (Lattice 2011) 051.Google Scholar
You have
Access
- 6
- Cited by