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Adapted Nested Force-Gradient Integrators: The Schwinger Model Case

Part of: Numerical analysis: Ordinary differential equations Qualitative theory Numerical problems in dynamical systems

Published online by Cambridge University Press:  08 March 2017

Dmitry Shcherbakov ,
Matthias Ehrhardt ,
Jacob Finkenrath ,
Michael Günther ,
Francesco Knechtli  and
Michael Peardon
Dmitry Shcherbakov*
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
Matthias Ehrhardt*
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
Jacob Finkenrath*
Affiliation:
CaSToRC, CyI, 20 Constantinou Kavafi Street, 2121 Nicosia, Cyprus
Michael Günther*
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
Francesco Knechtli*
Affiliation:
Theoretische Physik, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany
Michael Peardon*
Affiliation:
School of Mathematics, Trinity CollegeDublin 2, Ireland
*
*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)
*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)
*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)
*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)
*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)
*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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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.

Keywords

Numerical geometric integrationdecomposition methodsenergy conservationforce-gradientnested algorithmsmulti-rate schemesoperator splittingSchwinger model

MSC classification

Secondary: 65P10: Hamiltonian systems including symplectic integrators 65L06: Multistep, Runge-Kutta and extrapolation methods 34C40: Equations and systems on manifolds
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1141 - 1153
Copyright
Copyright © Global-Science Press 2017 

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References

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