Revisiting Geometric Integrators in Mechanics

Aziz Hamdouni (1) , Vladimir Salnikov (1)

1 LaSIE - Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356

We address the question of effcient construction of geometric integrators - numerical methods preserving some internal geometric structure of the system of equations. Such methods are of particular importance for modelling and simulation of mechanical systems, where these structures permit to control the conservation of physically relevant quantities. We focus our attention on the so called generalized geometry, for which we present an approach to design higher order Runge-Kutta style numerical methods.

Mots clés: geometric integrators; constraint mechanics; Dirac structures; Runge-Kutta methods; geometric integrators; geometric integrators; geometric integrators

Domaines: Géométrie différentielle [math.DG]; Analyse numérique [cs.NA]; Modélisation et simulation

Aziz Hamdouni, Vladimir Salnikov. Revisiting Geometric Integrators in Mechanics. pp.65-68, 2021. ⟨hal-03445340⟩