PARALLELIZATION OF AN 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 wit h i fixed-point iterations for solving the resulting nonlinear system of equations, is presented. The algorithm is used for numerical soluti on of molecular dynamics equations on the distributed memory computers in the ring topology. It is designed for the two-stage fourth-order G LRK method for i = 4 and applied to a system of N particles interactin g through the Lennard-Jones potential. The theoretical time complexity estimation is performed, and time results are also measured on differ ent computers for comparison. The proposed parallel algorithm is scala ble with the number of processors p, and its time requirement is pract ically proportional to siN 2/2p if N/p is large enough.