notes on energy drift in time integrators

Final Project Idea

Energy drift - usually damping - is substantial for numerical integration schemes that are not symplectic, such as the Runge-Kutta family.

Symplectic integrators usually used in molecular dynamics, such as the Verlet integrator family, exhibit increases in energy over very long time scales, though the error remains roughly constant. These integrators do not in fact reproduce the Hamiltonian mechanics of the system; instead, they reproduce a closely related “shadow” Hamiltonian whose value they conserve many orders of magnitude more closely.

Paper Presentation - FEPR

This week we have paper presentations and I talk about this paper to the class, Fast Energy Projection for Real-time Simulation of Deformable Objects by Dinev, Liu et. al. Reference links are at the bottom.

The link to the slides is http://bit.ly/yuifepr

References

• FEPR: Fast Energy Projection for Real-time Simulation of Deformable Objects
• Superior video by Liu explaining the method they used
• Erin Catto’s slides with the mass-spring phase portrait
• Position-based Dynamics
• Projective Dynamics
• Fast Projection (Goldenthal et al)
• Selector Matrices

Final Project Presentation