Computing time investigations for variational multirate integration

Consider a mechanical system that contains slow and fast dynamics. Let it be possible, to split the potential energy into a slow and a fast potential and the configuration vector into slow and fast variables. For such systems, multirate schemes simulate the different parts using different time steps with the goal to save computing time. For the proposed multirate scheme, a time grid consisting of micro and macro nodes is used and the integrator is derived from a discrete variational principle. Variational integrators conserve properties like symplecticity and momentum maps and have good energy behavior. To solve the resulting system of coupled nonlinear equations, a Newton-Raphson iteration with an analytical Jacobian is used. It is demonstrated that the multirate approach leads to less computing time compared to singlerate simulation by means of three example systems, the Fermi-Pasta-Ulam problem, a triple spherical pendulum and a simple atomistic model, where the latter two are subject to constraints. Computing times are compared for different numbers of micro and macro nodes for dynamic simulations during a certain time interval. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)