We develop an efficient multiple timestep (MTS) force splitting scheme for biological applications in the AMBER program in the context of the Particle-Mesh Ewald (PME) algorithm. Our method applies a symmetric Trotter factorization of the Liouville operator based on the Position Verlet scheme to Newtonian and Langevin dynamics.
Following a brief review of the MTS and PME algorithms, we discuss performance speedup and the force balancing involved to maximize accuracy, maintain long-time stability, and accelerate computational times. Compared to prior MTS efforts in the context of the AMBER program, advances are reported by optimizing PME parameters for MTS applications and by using the Position verlet, rather than Velocity Verlet scheme, for the inner loop. Moreover, ideas from the Langevin/MTS algorithm LN developed recently are applied to Newtonian formulations here. The algorithm's performance is optimized and tested on water, solvated DNA, and solvated protein systems. We find CPU speedup ratios of over 3 for Newtonian formulations when compared to a 1 fs timestep single-step Verlet algorithm using outer timesteps of 6 fs in a three-class splitting scheme; accurate conservation of energies is demonstrated. With modest Langevin forces, we obtain stable outer timesteps up to 12 fs and corresponding speedup ratios approaching 5.
We end by suggesting that modified Ewald formulations, using tailored alternatives to the Gaussian screening
functions for the Coulombic terms, may allow larger timesteps and thus further speedups for both Newtonian and Langevin protocols; such developments will be reported
separately.
