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arXiv · 2008.06000

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

Frédéric Marazzato·Alexandre Ern·Christian Mariotti·Laurent Monasse
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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.

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Frédéric Marazzato, Alexandre Ern, Christian Mariotti, Laurent Monasse. 2020-08-13. An explicit pseudo-energy conserving time-integration scheme for Hamiltonian dynamics. https://doi.org/10.1016/j.cma.2019.01.013

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