Molecular dynamics threedimensional simulations of the dispersed system dynamics at the molecular levelVictor Malyshev, Elena Moiseeva, Dmitriy Marin, Nail Gumerov, Constantin Mikhaylenko
Molecular dynamics (MD) is a computer simulation of the dynamics of the singlephase and multiphase systems. It is based on the idea that all the particles follow the trajectories derived from the equations of motion. Molecular dynamics simulations are used for modeling the processes at micro and nanoscale when the classical continuum models could not be applied because of the extremely small amount of the molecules in the system. Molecular dynamics simulations require considerable computational resources, dramatically increasing with the growth of the system size. In the direct mathematical formulation, the computations of all the forces acting on the particles require the solving of the system of linear algebraic equations, the amount of which is defined by the number of atoms. It is known, that the algorithmic complexity of the direct method is of the order of magnitude O(N^{2}).
The use of the modern highperformance computational algorithms allow to reduce the complexity. Thus, the computation of the forces, defined by the LennardJones potential, has the complexity O(NlogN) when using the special data structures. The calculations of the farfield forces, defined by the Coulomb potential, can be accelerated using the Fast Multipole method (FMM). FMM allows one to decrease the complexity to O(N). The latter is particularly important for the simulations of the water molecules, because the 3/4 of all the intermolecular interactions are determined by the Coulomb potential.
Further decrease of the computational time is achieved by the use of modern hardware, such as highperformance computing GPU (Graphics Processing Unit, GPU). Currently, the calculations of one time step for a system of 1000000 water molecules take 30 seconds on a personal computer equipped with two Intel Xeon processors and computer graphics card NVidia Tesla 2050. For a characteristic time step of 10 femtoseconds, the computational performance of 1 picoseconds per hour can be achieved for the simulations of a system of one million water molecules.
