Dmitry Shcherbakov

Dmitry Shcherbakov, Matthias Ehrhardt, Jacob Finkenrath et al.

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.

Dmitry Shcherbakov, Matthias Ehrhardt

It is well-known that molecular dynamics integrators, which are used for lattice quantum chromodynamics (QCD), suffer from instabilities and possess a rather low order of the accuracy. Hence, it is highly desirable to construct a new class of geometric integrators, that overcomes these instability problems and increases the order of accuracy without increasing remarkably the computational costs. In this paper we consider for this purpose multistep methods and give an overview of known results to systematize important knowledge for such methods being the right choice for lattice QCD simulations. At the end we try to answer the question: can multistep method be used as molecular dynamic integrators and what might be the advantage of it.