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Journal Articles Computer Methods in Applied Mechanics and Engineering Year : 2019

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.
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Dates and versions

hal-01661608 , version 1 (12-12-2017)
hal-01661608 , version 2 (15-12-2017)
hal-01661608 , version 3 (08-11-2018)
hal-01661608 , version 4 (09-01-2019)
hal-01661608 , version 5 (09-01-2019)

Identifiers

Cite

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⟩
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