Performance Assessment of Energy-preserving, Adaptive Time-step Variational Integrators
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 discrete governing equations. In this work, we investigate the numerical performance of energy-preserving, adaptive time-step variational integrators. First, we compare the time adaptation and energy performance of the energy-preserving adaptive algorithm with the adaptive variational integrator for Kepler's two-body problem. Second, we apply tools from Lagrangian backward error analysis to investigate numerical stability of the energy-preserving adaptive algorithm. Finally, we consider a simple mechanical system example to illustrate the backward stability of this energy-preserving, adaptive time-step variational integrator.
Keywords
Cite
@article{arxiv.2108.05420,
title = {Performance Assessment of Energy-preserving, Adaptive Time-step Variational Integrators},
author = {Harsh Sharma and Jeff Borggaard and Mayuresh Patil and Craig Woolsey},
journal= {arXiv preprint arXiv:2108.05420},
year = {2022}
}