An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics
Abstract
We propose a new explicit pseudo-energy and momentum conserving scheme for the time integration of Hamiltonian systems. The scheme, which is formally second-order accurate, is based on two key ideas: the integration during the time-steps of forces between free-flight particles and the use of momentum jumps at the discrete time nodes leading to a two-step formulation for the acceleration. The pseudo-energy conservation is established under exact force integration, whereas it is valid to second-order accuracy in the presence of quadrature errors. Moreover, we devise an asynchronous version of the scheme that can be used in the framework of slow-fast time-stepping strategies. The scheme is validated against classical benchmarks and on nonlinear or inhomogeneous wave propagation problems.
Keywords
Cite
@article{arxiv.2008.06000,
title = {An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics},
author = {Frédéric Marazzato and Alexandre Ern and Christian Mariotti and Laurent Monasse},
journal= {arXiv preprint arXiv:2008.06000},
year = {2020}
}