Using finite element codes as a numerical platform to run molecular dynamics simulations

A mathematically rigorous methodology for embedding the governing equations of molecular dynamics in the formalism of the finite element method is presented. Only one generalized finite element type is needed to cover all different types of existing interatomic potentials. The finite element type is simply specified by two parameters characterizing the type of the interatomic potential to be considered. Built on this formulation a partitioned Runge–Kutta method—summarizing a wide range of explicit and implicit, single- and multi-stage, lower and higher order time integration schemes—is embedded in a unified manner. The required finite element residual vector and the related Jacobian matrix are stated explicitly. The related FE-mesh coincides with the neighborhood lists used in standard molecular dynamics enabling the use of common tools. The range, versatility and performance of the proposed finite element formulation have been demonstrated by means of several numerical examples.