Session A5 - Geometric Integration and Computational Mechanics
July 10, 17:30 ~ 18:00
Higher order variational integrators and their relation to Runge-Kutta methods for unconstrained and constrained systems
University of Oxford, United Kingdom - email@example.com
In this talk higher order variational integrators are developed and their relation to Runge-Kutta methods is investigated. While it is well known that particular higher order variational integrators are equivalent to symplectic partitioned Runge- Kutta methods, this is not true for more generally constructed variational integrators. Based on existing results, modified schemes of Runge-Kutta integrators are derived and shown to be equivalent to a new class of higher order variational integrators which distinguishes in the dimension of the function space for approximating the solution curves compared to classical Galerkin variational integrators. Conditions are derived under which both variational integrators are identical and demonstrated numerically by simple mechanical examples. The results are extended to systems with holonomic constraints.
Joint work with Sigrid Leyendecker (University of Erlangen-Nuremberg, Germany), Theresa Wenger (University of Erlangen-Nuremberg, Germany).