# Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems

## Abstract

The present work deals with the numerical long-time integration of damped Hamiltonian systems. The method that we analyze combines a specific Strang splitting, that separates linear dissipative effects from conservative ones, with an energy-preserving averaged vector field (AVF) integrator for the Hamiltonian subproblem. This construction faithfully reproduces the energy-dissipation structure of the continuous model, its equilibrium points and its natural Lyapunov function. As a consequence of these structural similarities, both the convergence to equilibrium and, more interestingly, the energy decay rate of the continuous dynamical system are recovered at a discrete level. The possibility of replacing the implicit AVF integrator by an explicit Störmer-Verlet one is also discussed, while numerical experiments illustrate and support the theoretical findings.

## Authors

A. Viorel
Babeş-Bolyai University, Romania

C.D. Alecsa
Romanian Institute of Science and Technology and
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

T.O. Pinţa
Institute for Numerical and Applied Mathematics, University of Göttingen, Germany

## Keywords

Structure-preserving integrator, dissipative system, optimization, Łojasiewicz inequality.

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##### Cite this paper as:

A. Viorel, C.D. Alecsa, T.O. Pinţa, Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems, Discrete and Continuous Dynamical Systems, 2021, 41(7), pp. 3319-3341. doi: 10.3934/dcds.2020407

##### Journal

Discrete and Continous Dynamical Systems

1078-0947

1553-5231