The complexity of parallel symplectic molecular dynamics algorithms

Parallelized algorithms for molecular dynamics integration, the explicit Leap-Frog-Verlet (LFV), the implicit Gauss-Legendre Runge-Kutta (GLRK), and the new Split Integration Symplectic Method (SISM) are described and compared. All three methods are evaluated on a system of N linear molecules of the form H-(-C=C-)(r)-H with the number of atoms in the chain equal to n = 2r + 2. The parallel algorithms, memory requirements, and the complexity of computations are estimated for all three methods. Run-time results of the implemented simulations are given for different high-performance computers.