Long Time Integration of Molecular Dynamics at Constant Temperature with the Symplectic Euler Method

Abstract: Simulations of particle systems at constant temperature may be used to estimate several of the system’s physical properties, and some require integration over very long time to be accurate. To achieve sufficient accuracy in finite time the choice of numerical scheme is important and we suggest to use the symplectic Euler method combined with a step in an Ornstein-Uhlenbeck process. This scheme is computationally very cheap and is often used in applications of molecular dynamics. This thesis strives to motivate the usage of the scheme due to the lack of theoretical results and comparisons to alternative methods. We conduct three numerical experiments to evaluate the scheme. The design of each experiment aims to expose weaknesses or strengths of the method. For both model problems and more realistic experiments are the results positive in favor of the method; the symplectic Euler method combined with an Ornstein- Uhlenbeck step does perform well over long times.