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