Hessian-free force-gradient integrators
arxiv(2024)
摘要
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.
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