This paper presents the implementation results of an integrated sequential algorithm, which the second author developed mathematically in a pseudo code format previously to improve computational efficiency of computer simulation of the dynamical behaviors of multibody molecular structures in polymers and biopolymers. This new algorithm is a seamless integration between multibody molecular algorithm (MMA: a multibody-dynamics-based procedure for motion simulation of molecular structure) and fast multipole method (FMM). The fast multipole method is used to calculate interatomic forces from potentials, and the multibody molecular algorithm is used to generate equations of motion associated with molecular structures. The algorithm improves computational efficiency when comparing with its counterpart procedures.

A study case of an opened-chain molecular structure was used to demonstrate the algorithm works and to study improvement of computing efficiency of the algorithm. The algorithm is coded in MATLAB and run on both laptop and workstations computers with various numbers of molecules along the chain. FMM started with scaling all atoms into a box with coordinate ranges to ensure numerical stability of subsequent operations. The flow of calculations in FMM was carried out along the chain structure with five computational passes. MMA began with numbering subsets, forming bond graph, and developing three computing passes along the chain structure. Flows of both calculations and data in FMM and MMA were lined up recursively along the chain structure to obtain an O(N)1 computational efficiency. Simulation results were compared with results produced by MMA and traditional methods of FMM for interatomic force calculation procedure.

Implementation presented in this paper first proves that the integration between FMM and MMA works and the integrated algorithm improves computing efficiency associated with both calculation of interatomic forces from potentials and formation/solution of equations of motion. Implementation results also indicates that the integrated algorithm works more efficiently for a large-sized molecular chain than a small-sized molecular chain. Further work is needed to optimize the related FMM codes.

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