Though computational molecular dynamics is an effective tool for nano-scale phenomenon analysis, computational costs associated with its computer simulation are extremely high. There are two major computational steps associated with computer simulation of dynamics of molecular structures. They are calculation of interatomic forces and formation and solution of the equations of motion. Currently, these two computational steps are treated separately in most commonly-used methods. For example, Fast Multipole Method (FMM) and Cell Multipole Method (CMM) have been used for calculation of interatomic forces, and Cartesian Coordinate Method (CCM) and Internal Coordinate Molecular Dynamics Method (ICMD) have been created for the formation and solution of equations of motion of an atomistic molecular system.

In this paper, a new procedure is presented through a proper integration between multibody molecular algorithms (MMA) and fast multipole methods to improve computational efficiency for computer simulation of the dynamical behaviors of multibody molecular structures in polymers and biopolymers. For the computational costs associated with interatomic forces, a fast multipole method is used to calculate the interatomic forces due to the potentials. For the computational costs associated with formation and solution of equations of motion, a multibody molecular algorithm developed by the author in his previous work will be utilized to integrate with fast multipole methods. The algorithm significantly improves computational efficiency when comparing with its counterpart procedures.

The fast multipole method begins by scaling all atoms into a box with coordinate ranges to ensure numerical stability of subsequent operations. The parent box is then divided into half in the direction of each Cartesian axis and each child box is then subdivided to form a computational family tree. The flow of calculations is carried out along the tree structure with five passes. The fast multipole method has been improved and modified to achieve better effectiveness and higher efficiency since it was created.

The multibody molecular algorithm starts with numbering subsets, forming bond graph, and developing three computing passes along the tree structure of an atomistic molecular system. Computing data flows in the fast multipole method and the multibody molecular algorithm will properly line up with the parent-child recursive relationship along the configuration of the tree structure due to linear recursive natures of both fast multipole method and multibody molecular algorithm. Then the time spent on the recursive simulation passes in the fast multipole method for computing forces may overlap with the time spent on the three recursive computational passes in the multibody molecular algorithm for forming and solving equations of motion.

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