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Towards new paradigms for time integrators in computational dynamics

The purpose of this special issue is to survey some recent advances in time integrators for both finite dimensional mechanical systems as well as continuum mechanics. These advances include the general development of discrete mechanics, application to dissipative systems, collisions, space-time integration algorithms, Heterogeneous and/or Asynchronous Time Integrators.
Indeed, it is now well established that discrete energy conservation/dissipation plays a key-role for the unconditional stability of time integration schemes in nonlinear dynamics.
For instance, the significant progresses on symplectic, multi symplectic, variational time integrators or port Hamiltonian combined with Discrete Exterior Calculus both for multi-body dynamics, non-linear smooth and non-smooth dynamics require to propose a useful guide to the literature as well as future directions and open problems in the subject.
It adresses dynamic stability of deterministic/stochastic, Hamiltonian/non-Hamiltonian and holonomic/non-holonomic, self-excitation, auto-parametric systems under deterministic/random excitations, wave propagation, solitons and waves in stochastic continuum, and waves in dispersive, heterogeneous and multi-layered medium. It is devoted also on recent advances and properties of modern and novel time and space-time discretization schemes.

Edited by: Anthony Gravouil


  1. A new formulation of geometrically exact planar Euler-Bernoulli beam in multi-body dynamics is proposed. For many applications, the use of the Euler-Bernoulli model is sufficient and has the advantage of being...

    Authors: Carlo Sansour, Tien Long Nguyen, Mohammed Hjiaj and Sophy Chhang
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2020 7:33
  2. Considering a large class of muscle contraction models accounting for actin–myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermody...

    Authors: François Kimmig, Dominique Chapelle and Philippe Moireau
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2019 6:6
  3. This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponential...

    Authors: Dina Razafindralandy, Vladimir Salnikov, Aziz Hamdouni and Ahmad Deeb
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2019 6:5
  4. This research work presents some comparisons and analyses of the time discontinuous space–time Galerkin method and the space discontinuous Galerkin method applied to elastic wave propagation in anisotropic and...

    Authors: Bing Tie
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2019 6:3
  5. This article introduces benchmark cases for time integrators devoted to non-smooth impact dynamics. It focuses on numerical properties of explicit integrators. Each case tests one necessary numerical property ...

    Authors: Jean Di Stasio, David Dureisseix, Anthony Gravouil, Gabriel Georges and Thomas Homolle
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2019 6:2
  6. The aim of the present paper is to study theoretically and numerically the Verlet scheme for the explicit time-integration of elastodynamic problems with a contact condition approximated by Nitsche’s method. T...

    Authors: Franz Chouly and Yves Renard
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2018 5:31
  7. The principal aim of this work is to provide an adapted numerical scheme for the approximation of elastic wave propagation in incompressible solids. We rely on high-order conforming finite element with mass lu...

    Authors: Federica Caforio and Sébastien Imperiale
    Citation: Advanced Modeling and Simulation in Engineering Sciences 2018 5:30