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

Frédéric Marazzato (1, 2, 3) , Alexandre Ern (2, 1) , Christian Mariotti (3) , Laurent Monasse (4)

1 SERENA - Simulation for the Environment: Reliable and Efficient Numerical Algorithms
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 LDG - Laboratoire de Détection et de Géophysique (CEA)
4 COFFEE - COmplex Flows For Energy and Environment

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.

Mots clés: Energy–momentum conservation; Ordinary Differential Equations; Wave equations; Explicit time-integration; Nonlinear Hamiltonian dynamics

Domaines: Analyse numérique [math.NA]

Frédéric Marazzato, Alexandre Ern, Christian Mariotti, Laurent Monasse. An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics. Computer Methods in Applied Mechanics and Engineering, 2019, Computer Methods in Applied Mechanics and Engineering, 347, pp.906-927. ⟨10.1016/j.cma.2019.01.013⟩. ⟨hal-01661608v5⟩