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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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Submitted on : Wednesday, January 9, 2019 - 12:38:16 PM
Last modification on : Thursday, January 7, 2021 - 7:50:03 PM

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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, Elsevier, 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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