Implicit Runge-Kutta method for molecular dynamics integration

A parallelized algorithm of an implicit Runge-Kutta integration scheme, the s-stage Gauss-Legendre Runge-Kutta (GLRK) method of order 2s with i xed-point iterations for solving the resulting nonlinear system of equations is presented. The algorithm is used for numerical solution of molecular dynamics equation on the distributed memory computers in the ring topology. It is designed for the two-stage 4 th order GLRK method for i = 4 and applied to a system of N particles interacting through the Lennard-Jones potential. The theoretical time complexity estimation is performed and time results were also measured on diierent computers for comparison. The proposed parallel algorithm is scalable with the number of processors p, and its time requirement is practically proportional to siN 2 =2p if N=p is large enough. 1