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arXiv · 2108.05420

Performance Assessment of Energy-preserving, Adaptive Time-step Variational Integrators

Harsh Sharma·Jeff Borggaard·Mayuresh Patil·Craig Woolsey
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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.

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Harsh Sharma, Jeff Borggaard, Mayuresh Patil, Craig Woolsey. 2021-08-11. Performance Assessment of Energy-preserving, Adaptive Time-step Variational Integrators. https://doi.org/10.1016/j.cnsns.2022.106646

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