An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics

TL;DR

This paper introduces a new explicit time-integration scheme for Hamiltonian systems that conserves pseudo-energy and momentum, offering second-order accuracy and an asynchronous variant suitable for complex simulations.

Contribution

The paper presents a novel explicit pseudo-energy conserving scheme with a two-step formulation and an asynchronous version for Hamiltonian dynamics, improving energy conservation and flexibility.

Findings

Scheme is formally second-order accurate.

Pseudo-energy conservation holds under exact force integration.

Validated on benchmarks and wave propagation problems.

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.