Work

Hessian-free force-gradient integrators

Year: 2024

Type: article

Abstract: We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations.

Source: Computer Physics Communications

DOI: 10.1016/j.cpc.2024.109478

Authors: Kevin Schäfers, Jacob Finkenrath, Michael Günther, Francesco Knechtli

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,410

Funders: Bergische Universität Wuppertal, Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung

Awards: G1604632246, FOR 5269: Zukünftige Methoden für Studien von eingeschlossenen Gluonen in QCD