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Session I.5 - Geometric Integration and Computational Mechanics

Wednesday, June 14, 14:00 ~ 14:30

Explicit Energy-Preserving Momentum-Scaling Schemes for Hamiltonian Systems

Andy Wan

University of Northern British Columbia, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We introduce a novel class of explicit energy-preserving momentum-scaling (EPMS) schemes for Hamiltonian systems of the form $H(\boldsymbol q,\boldsymbol p)=\frac{1}{2}{\boldsymbol p}^T M^{-1}(\boldsymbol q)\boldsymbol p+U(\boldsymbol q)$. EPMS schemes consist of two main steps: first, utilize an explicit scheme satisfying a non-degenerate condition; second, follow by scaling of momentum variables to achieve exact energy preservation. We show that EPMS schemes are consistent. Moreover, we give a sufficient condition for explicit Runge-Kutta methods to satisfy the non-degenerate condition, showing that a wide class of explicit Runge-Kutta methods can be turned into EPMS schemes. Numerical experiments showcasing computational efficiency of EPMS schemes versus implicit energy-preserving schemes are presented.

Joint work with Molei Tao (Georgia Institute of Technology).

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