Comparison of time discretization schemes to simulate the motion of an inextensible beam

Abstract

We compare three different time discretization schemes in combination with an augmented Lagrangian method to simulate the motion of an inextensible beam. The resulting saddle-point problem is solved with an Uzawa-Douglas-Rachford algorithm. The three schemes are tested on a benchmark with an analytical solution and on a more challenging application. We found that in order to obtain optimal convergence behavior in time, the stopping tolerance for the Uzawa-type algorithm should be balanced against the time step size.