Shcherbakov, Dmitry; Ehrhardt, Matthias; Finkenrath, Jacob; Günther, Michael; Knechtli, Francesco; Peardon, Michael Adapted nested force-gradient integrators: the Schwinger model case. (English) Zbl 1388.65182 Commun. Comput. Phys. 21, No. 4, 1141-1153 (2017). Summary: 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. MSC: 65P10 Numerical methods for Hamiltonian systems including symplectic integrators 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations PDFBibTeX XMLCite \textit{D. Shcherbakov} et al., Commun. Comput. Phys. 21, No. 4, 1141--1153 (2017; Zbl 1388.65182) Full Text: DOI arXiv