| Abstract: |
| A fixed time step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive time step variational integrators that conserve the energy in addition to being symplectic and momentum-preserving. Their utility, however, is still an open question due to the numerical difficulties associated with solving the governing discrete equations. In this work, we study the numerical performance of energy-preserving, adaptive time step variational integrators. First, we consider a particle in a double well potential and study the energy behavior as well as the solvability of adaptive time step for different trajectories. We also investigate the effect of initial time step on the conservation properties. Second, we derive the adaptive algorithm for a damped harmonic oscillator and study the energy performance and adaptive time step behavior. Finally, we study the relationship between different adaptive time step variational integrators and compare their numerical performance for Kepler`s problem. |
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