Extrapolated gradientlike algorithms for molecular dynamics and celestial mechanics simulations.
A class of symplectic algorithms is introduced to integrate the equations of motion in many-body systems. The algorithms are derived on the basis of an advanced gradientlike decomposition approach. Its main advantage over the standard gradient scheme is the avoidance of time-consuming evaluations of force gradients by force extrapolation without any loss of precision. As a result, the efficiency of the integration improves significantly. The algorithms obtained are analyzed and optimized using an error-function theory. The best among them are tested in actual molecular dynamics and celestial mechanics simulations for comparison with well-known nongradient and gradient algorithms such as the Störmer-Verlet, Runge-Kutta, Cowell-Numerov, Forest-Ruth, Suzuki-Chin, and others. It is demonstrated that for moderate and high accuracy, the extrapolated algorithms should be considered as the most efficient for the integration of motion in molecular dynamics simulations.
Omelyan
I P
IP
Institute for Condensed Matter Physics, 1 Svientsitskii Street, UA-79011 Lviv, Ukraine.